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Reservoir EngineeringPermeability

Average Permeability for Linear Flow in Layered Beds

kavg=k1A1+k2A2+k3A3A1+A2+A3k_{avg} = \frac{k_1 A_1 + k_2 A_2 + k_3 A_3}{A_1 + A_2 + A_3}
Open analysis
Reservoir EngineeringPermeability

Average Permeability for Linear Flow - Series Beds

kavg=L1+L2+L3L1k1+L2k2+L3k3k_{avg} = \frac{L_1 + L_2 + L_3}{\frac{L_1}{k_1} + \frac{L_2}{k_2} + \frac{L_3}{k_3}}
Open analysis
Reservoir EngineeringPermeability

Average Permeability for Parallel-Layered Systems

kavg=k1h1+k2h2+k3h3h1+h2+h3k_{avg} = \frac{k_1 h_1 + k_2 h_2 + k_3 h_3}{h_1 + h_2 + h_3}
Open analysis
Reservoir EngineeringPermeability

Average Permeability in Radial Systems

kavg=ka⋅ke⋅ln⁡(rerw)ka⋅ln⁡(rera)+ke⋅ln⁡(rarw)k_{avg} = \frac{k_a \cdot k_e \cdot \ln\left(\frac{r_e}{r_w}\right)}{k_a \cdot \ln\left(\frac{r_e}{r_a}\right) + k_e \cdot \ln\left(\frac{r_a}{r_w}\right)}
Open analysis
Reservoir EngineeringPermeability

Klinkenberg Apparent Gas Permeability

kg=kl(1+bp)k_g = k_l\left(1+\frac{b}{p}\right)
Open analysis
Reservoir EngineeringPermeability

Jones-Owens Klinkenberg Slip Factor

b=12.639k∞−0.33b = 12.639 k_{\infty}^{-0.33}
Open analysis
Reservoir EngineeringPermeability

Gas Permeability from Core Plug Pressure-Squared Flow

k=2μQavgPavgLA(P12−P22)k = \frac{2\mu Q_{avg}P_{avg}L}{A(P_1^2-P_2^2)}
Open analysis
Reservoir EngineeringPermeability

Kozeny Permeability from Porosity and Specific Surface Area

k=ϕkzSp2k=\frac{\phi}{k_zS_p^2}
Open analysis
Reservoir EngineeringPermeability

Kozeny-Carman Permeability from Grain Diameter

k=Bϕ3d2τk=\frac{B\phi^3d^2}{\tau}
Open analysis
Reservoir EngineeringPermeability

Modified Kozeny-Carman Permeability with Percolation Porosity

k=B(ϕ−ϕc)3(1+ϕc−ϕ)2d2k=B\frac{(\phi-\phi_c)^3}{(1+\phi_c-\phi)^2}d^2
Open analysis
Reservoir EngineeringPermeability

Geometric Mean Permeability from Log Average

kg=exp⁡(ln⁡k1+ln⁡k2+ln⁡k33)k_g=\exp\left(\frac{\ln k_1+\ln k_2+\ln k_3}{3}\right)
Open analysis
Reservoir EngineeringPermeability

Binary Power-Average Effective Permeability

keff=[psskssm+(1−pss)kshm]1/mk_{eff}=\left[p_{ss}k_{ss}^m+(1-p_{ss})k_{sh}^m\right]^{1/m}
Open analysis
Reservoir EngineeringPermeability

Lognormal Effective Permeability from Geometric Mean

keff=kgexp⁡[(12−1d)σln⁡k2]k_{eff}=k_g\exp\left[\left(\frac{1}{2}-\frac{1}{d}\right)\sigma_{\ln k}^2\right]
Open analysis
Reservoir EngineeringThermal Gradients

Average Temperature of a Gas Column

T=Tt+Tb2T = \frac{T_t + T_b}{2}
Open analysis
Reservoir EngineeringThermal Gradients

Formation Temperature for a Given Gradient

Tf=Ts+gG⋅(D100)T_f = T_s + g_G \cdot \left( \frac{D}{100} \right)
Open analysis
Reservoir EngineeringThermal Gradients

Geothermal Gradient from Temperature Log Interval

G=Tdeep−Tshallowzdeep−zshallow 1000G = \frac{T_{deep}-T_{shallow}}{z_{deep}-z_{shallow}}\,1000
Open analysis
Reservoir EngineeringThermal Gradients

Conductive Heat Flow from Geothermal Gradient

q=kΔTΔzq = k\frac{\Delta T}{\Delta z}
Open analysis
Reservoir EngineeringThermal Gradients

Horner Time Ratio for Bottom-Hole Temperature Correction

H=tc+ΔtΔtH = \frac{t_c+\Delta t}{\Delta t}
Open analysis
Reservoir EngineeringThermal Gradients

Horner Formation Temperature from Bottom-Hole Temperature

T=Ti−Clog⁡10(tc+ΔtΔt)T = T_i - C\log_{10}\left(\frac{t_c+\Delta t}{\Delta t}\right)
Open analysis
Reservoir EngineeringThermal Gradients

Waples-Ramly Single-Point Bottom-Hole Temperature Correction

Tc=T0+fs(Tmes−T0)T_c = T_0 + f_s(T_{mes}-T_0)
Open analysis
Reservoir EngineeringThermal Gradients

Volumetric Heat Capacity of a Reservoir

Mr=(1−ϕ)Ms+ϕSoMo+ϕSwMw+ϕSg[fgMg+(1−fg)(LvρsΔT+ρsCw)]M_r=(1-\phi)M_s+\phi S_oM_o+\phi S_wM_w+\phi S_g\left[f_gM_g+(1-f_g)\left(\frac{L_v\rho_s}{\Delta T}+\rho_sC_w\right)\right]
Open analysis
Reservoir EngineeringThermal Gradients

Reservoir Heat Required for Temperature Increase

Q=43560VrMr(Tf−Ti)Q=43560V_rM_r(T_f-T_i)
Open analysis
Reservoir EngineeringThermal Gradients

Thermal Conductivity from Heat Flow

k=QLAΔTk=\frac{QL}{A\Delta T}
Open analysis
Reservoir EngineeringThermal Gradients

Thermal Diffusivity

α=kρCp\alpha=\frac{k}{\rho C_p}
Open analysis
Reservoir EngineeringPermeability and Flow

Calculation of Fractional Flow Curve

fw=11+μw⋅krokrw⋅μof_w = \frac{1}{1 + \frac{\mu_w \cdot k_{ro}}{k_{rw} \cdot \mu_o}}
Open analysis
Reservoir EngineeringPermeability and Flow

Crossflow Index

CI=Npcf−NpncfNpu−NpncfCI = \frac{N_{pcf} - N_{pncf}}{N_{pu} - N_{pncf}}
Open analysis
Reservoir EngineeringPermeability and Flow

Normalized Saturation

Son=1−Sw−Sor1−Swi−SorS_{on}=\frac{1-S_w-S_{or}}{1-S_{wi}-S_{or}}
Open analysis
Reservoir EngineeringPermeability and Flow

Relative Permeability from Effective Permeability

kr=keffkk_r = \frac{k_{eff}}{k}
Open analysis
Reservoir EngineeringPermeability and Flow

Normalized Water Saturation for Relative Permeability

Sw∗=Sw−Swi1−Swi−SorS_w^* = \frac{S_w-S_{wi}}{1-S_{wi}-S_{or}}
Open analysis
Reservoir EngineeringPermeability and Flow

Corey Water Relative Permeability

krw=krwo(Sw∗)nwk_{rw} = k_{rw}^o(S_w^*)^{n_w}
Open analysis
Reservoir EngineeringPermeability and Flow

Corey Oil Relative Permeability

kro=kroo(1−Sw∗)nok_{ro} = k_{ro}^o(1-S_w^*)^{n_o}
Open analysis
Reservoir EngineeringPermeability and Flow

Buckley-Leverett Saturation Front Velocity

vS=utϕdfwdSwv_S = \frac{u_t}{\phi}\frac{df_w}{dS_w}
Open analysis
Reservoir EngineeringPermeability and Flow

Buckley-Leverett Breakthrough Pore Volumes

tD,bt=(dfwdSw)shock−1t_{D,bt} = \left(\frac{df_w}{dS_w}\right)_{shock}^{-1}
Open analysis
Reservoir EngineeringPermeability and Flow

Torcaso-Wyllie Relative Permeability Ratio Prediction

kog=krg(1−S)2(1−S2)S4k_{og}=k_{rg}\frac{(1-S)^2(1-S^2)}{S^4}
Open analysis
Reservoir EngineeringPermeability and Flow

Pseudosteady-State Radial Liquid Flow Rate

Q=0.00708kh(Pi−Pwf)Bμ[ln⁡(re/rw)−0.75]Q=\frac{0.00708 k h (P_i-P_{wf})}{B \mu [\ln(r_e/r_w)-0.75]}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Capillary Number

Nc=μw⋅V⋅0.304886400⋅σowN_c = \frac{\mu_w \cdot V \cdot 0.3048}{86400 \cdot \sigma_{ow}}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Capillary Pressure

Pc=2⋅σ⋅cos⁡(θ)rP_c = \frac{2 \cdot \sigma \cdot \cos(\theta)}{r}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Characteristic Time for Linear Diffusion in Reservoirs

τ=Cu(Φ⋅βf+βr)⋅μ⋅l2k\tau = C_u \frac{(\Phi \cdot \beta_f + \beta_r) \cdot \mu \cdot l^2}{k}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Compressibility Drive in Gas Reservoirs

CI=G⋅EfBg⋅GpCI = \frac{G \cdot E_f}{B_g \cdot G_p}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Cumulative Effective Compressibility – Fetkovich

ce=Swi⋅cw+M⋅(cf+cw)+cf1−Swic_e = \frac{S_{wi} \cdot c_w + M \cdot (c_f + c_w) + c_f}{1 - S_{wi}}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Cumulative Oil Production – Undersaturated Oil Reservoirs

Np=N⋅ce⋅(BoiBo)⋅ΔPNp = N \cdot c_e \cdot \left( \frac{B_{oi}}{B_o} \right) \cdot \Delta P
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Effective Compressibility in Undersaturated Oil Reservoirs – Hawkins

ce=Soi⋅co+Swi⋅cw+cf1−Swic_e = \frac{S_{oi} \cdot c_o + S_{wi} \cdot c_w + c_f}{1 - S_{wi}}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Fraction of the Total Solution Gas Retained in the Reservoir as Free Gas

αg=1−(Np⋅RpN⋅Rsi−(N−Np)⋅Rs)\alpha_g = 1 - \left( \frac{N_p \cdot R_p}{N \cdot R_{si} - (N - N_p) \cdot R_s} \right)
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Free Gas in Place

Gf=7758⋅A⋅h⋅ϕ⋅(1−Swi)⋅EgiG_f = 7758 \cdot A \cdot h \cdot \phi \cdot (1 - S_{wi}) \cdot E_{gi}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

API Gravity

API=141.5SGo−131.5API = \frac{141.5}{SG_o} - 131.5
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Oil Saturation Below Bubble Point During Depletion

So=(1−Swi)(1−NpN)BoBoiS_o=(1-S_{wi})\left(1-\frac{N_p}{N}\right)\frac{B_o}{B_{oi}}
Open analysis
Reservoir EngineeringPVT and Rock-Fluid Properties

Total Compressibility from Phase Saturations

ct=cgSg+coSo+cwSw+cfc_t=c_gS_g+c_oS_o+c_wS_w+c_f
Open analysis
Reservoir EngineeringPressure Transient Analysis

Cole Plot

F=G⋅Eg+WeF = G \cdot E_g + W_e
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Pressure – Kamal and Brigham

Pd=k⋅h⋅ΔP141.2⋅Q⋅μ⋅BP_d = \frac{k \cdot h \cdot \Delta P}{141.2 \cdot Q \cdot \mu \cdot B}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Radius of Radial Flow – Constant-Rate Production

rd=rrwr_d = \frac{r}{r_w}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Time for Interference Testing in Homogeneous Reservoirs – Earlougher

tD=0.0002637⋅k⋅tϕ⋅μ⋅ct⋅rw2t_D = \frac{0.0002637 \cdot k \cdot t}{\phi \cdot \mu \cdot c_t \cdot r_w^2}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Vertical Well Critical Rate Correlations – Hoyland, Papatzacos, and Skjaeveland

QoD=651.4⋅μo⋅Bo⋅(qoh2⋅(ρw−ρo)⋅kh)Q_{oD} = 651.4 \cdot \mu_o \cdot B_o \cdot \left( \frac{q_o}{h^2 \cdot (\rho_w - \rho_o) \cdot k_h} \right)
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Wellbore Storage Coefficient of Radial Flow – Constant-Rate Production

Cd=0.8936⋅Cϕ⋅ct⋅h⋅rw2C_d = \frac{0.8936 \cdot C}{\phi \cdot c_t \cdot h \cdot r_w^2}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Estimation of Average Reservoir Pressure – MDH Method

Pr=pws+m⋅(pDMDH1.1513)P_r = p_{ws} + m \cdot \left( \frac{p_{DMDH}}{1.1513} \right)
Open analysis
Reservoir EngineeringPressure Transient Analysis

Shut-In Time for Pressure Build-Up Test - Dietz Method

ts=ϕμctA0.0002637CAkt_s = \frac{\phi\mu c_tA}{0.0002637C_Ak}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Time to End of Infinite-Acting Period in Circular Reservoir

teia=380ϕμctAkt_{eia}=\frac{380\phi\mu c_tA}{k}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Pressure - Radial Flow Constant-Pressure Production

Pd=Pi−PPi−PwfP_d=\frac{P_i-P}{P_i-P_{wf}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Buildup Pressure for Liquid Flow

PDs=kh(Pi−Pws)0.4568vscqBμP_{Ds}=\frac{kh(P_i-P_{ws})}{0.4568v_{sc}qB\mu}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Pressure - Radial Flow Constant-Rate Production

Pd=kh(Pi−P)141.2qBμP_d = \frac{k h (P_i-P)}{141.2 q B \mu}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Horner Time Ratio for Pressure Buildup Test

H=tp+ΔtΔtH=\frac{t_p+\Delta t}{\Delta t}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Horner Semilog Buildup Pressure Extrapolation

pws=p∗−mlog⁡10(H)p_{ws}=p^*-m\log_{10}(H)
Open analysis
Reservoir EngineeringPressure Transient Analysis

Permeability from Pressure Transient Semilog Slope

k=162.6qBμmhk=\frac{162.6qB\mu}{mh}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Skin Factor from Pressure Transient Semilog Analysis

s=1.151[Δp1hrm−log⁡10(kϕμctrw2)+3.23]s=1.151\left[\frac{\Delta p_{1hr}}{m}-\log_{10}\left(\frac{k}{\phi\mu c_tr_w^2}\right)+3.23\right]
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Length for Linear Flow General Case

xD=xAx_D=\frac{x}{\sqrt{A}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Length for Fracture Linear Flow

xD=xLfx_D=\frac{x}{L_f}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Pressure for Linear Flow Constant Rate General Case

pD=kA(pi−p)141.2qBμp_D=\frac{k\sqrt{A}(p_i-p)}{141.2qB\mu}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Time for Linear Flow Constant Rate General Case

tDA=0.0002637ktϕμctAt_{DA}=\frac{0.0002637kt}{\phi\mu c_tA}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Time for Fracture Linear Flow

tLfD=0.0002637ktϕμctLf2t_{LfD}=\frac{0.0002637kt}{\phi\mu c_tL_f^2}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Radius of Investigation

ri=0.0359ktϕμctr_i=0.0359\sqrt{\frac{kt}{\phi\mu c_t}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Radius of Investigation from Flow Time

ri=kt948ϕμctr_i=\sqrt{\frac{kt}{948\phi\mu c_t}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Radius of Investigation from Shut-In Time

ri=kΔt948ϕμctr_i=\sqrt{\frac{k\Delta t}{948\phi\mu c_t}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Production Time

tDA=tDrw2At_{DA}=t_D\frac{r_w^2}{A}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Shut-In Time for MDH Method

ΔtDA=0.0002637kΔtϕμctA\Delta t_{DA}=\frac{0.0002637k\Delta t}{\phi\mu c_tA}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Pseudosteady-State Slope in Pressure Buildup Test

mpss=0.23396QBctAhϕm_{pss}=\frac{0.23396QB}{c_tAh\phi}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Time to Pseudosteady State in Circular Reservoir

tpss=1200ϕμctre2kt_{pss}=\frac{1200\phi\mu c_tr_e^2}{k}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Rate for Radial Flow Constant-Pressure Production

qD=qBμ0.00708kh(pi−pwf)q_D=\frac{qB\mu}{0.00708kh(p_i-p_{wf})}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Cumulative Production for Radial Flow Constant-Pressure Production

QpD=BQp1.119ϕcthrw2(pi−pwf)Q_{pD}=\frac{BQ_p}{1.119\phi c_thr_w^2(p_i-p_{wf})}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Time for Radial Flow Constant-Rate Production

tD=0.0002637ktϕμctrw2t_D=\frac{0.0002637kt}{\phi\mu c_tr_w^2}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Carter Dimensionless Drawdown Correlating Parameter

λ=μgicgiμgavgcgavg\lambda=\frac{\mu_{gi}c_{gi}}{\mu_{gavg}c_{gavg}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

True Wellbore Storage Coefficient for Pressure Buildup Test

C=25.65AwbρwbC=25.65\frac{A_{wb}}{\rho_{wb}}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Pseudosteady-State Dimensionless Pressure Drop for Fractured Vertical Well

PD=2πtDA+0.5ln⁡(xexf)2+0.5ln⁡(2.2458Cf)+1.385P_D=2\pi t_{DA}+0.5\ln\left(\frac{x_e}{x_f}\right)^2+0.5\ln\left(\frac{2.2458}{C_f}\right)+1.385
Open analysis
Reservoir EngineeringPressure Transient Analysis

Pseudosteady-State Dimensionless Pressure Drop for Horizontal Well

PD=2πtDA+0.5ln⁡(A4(L/2)2)+0.5ln⁡(2.2458CAh)+1.385P_D=2\pi t_{DA}+0.5\ln\left(\frac{A}{4(L/2)^2}\right)+0.5\ln\left(\frac{2.2458}{C_{Ah}}\right)+1.385
Open analysis
Reservoir EngineeringPressure Transient Analysis

Minimum Shut-In Time to Pseudosteady State for Hydraulically Fractured Tight Gas Reservoirs

tpss=474ϕμgctxf2kt_{pss}=\frac{474 \phi \mu_g c_t x_f^2}{k}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Horner Pressure Buildup Equation

Pws=Pi−162.6QoBoμokhlog⁡10(tp+ΔtΔt)P_{ws}=P_i-\frac{162.6 Q_o B_o \mu_o}{k h}\log_{10}\left(\frac{t_p+\Delta t}{\Delta t}\right)
Open analysis
Reservoir EngineeringPressure Transient Analysis

Wellbore Storage Coefficient from Fluid Volume Change

C=ΔVmΔPC=\frac{\Delta V_m}{\Delta P}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Fracture Conductivity During Bilinear Flow

FC=[44.1QμBmbfh(ϕμctk)0.25]2F_C=\left[\frac{44.1 Q \mu B}{m_{bf} h (\phi \mu c_t k)^{0.25}}\right]^2
Open analysis
Reservoir EngineeringPressure Transient Analysis

Drawdown Semilog Slope for Bottomhole Flowing Pressure

m=162.6QoμoBokhm=\frac{162.6Q_o\mu_oB_o}{kh}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Infinite-Acting Pseudoradial Bottomhole Flowing Pressure

Pwf=pi−162.6QoμoBokh[log⁡10t+log⁡10(kϕμoctrw2)−3.23+0.87S]P_{wf}=p_i-\frac{162.6Q_o\mu_oB_o}{kh}\left[\log_{10}t+\log_{10}\left(\frac{k}{\phi\mu_oc_tr_w^2}\right)-3.23+0.87S\right]
Open analysis
Reservoir EngineeringPressure Transient Analysis

Line-Source Pressure Beyond the Wellbore

P=Pi+70.6qBμkhln⁡(1.688ϕμctr2kt)P=P_i+\frac{70.6qB\mu}{kh}\ln\left(\frac{1.688\phi\mu c_tr^2}{kt}\right)
Open analysis
Reservoir EngineeringPressure Transient Analysis

Skin During Infinite-Acting Pseudoradial Flow

S=1.151[pi−p1hrm−log⁡10(kϕμtotalctrw2)+3.23]S=1.151\left[\frac{p_i-p_{1hr}}{m}-\log_{10}\left(\frac{k}{\phi\mu_{total}c_tr_w^2}\right)+3.23\right]
Open analysis
Reservoir EngineeringPressure Transient Analysis

Pseudosteady-State Flowing Pressure for Non-Circular Reservoir

Pwf=pi−162.6QBμkhlog⁡10(2.2458ACArw2)−0.23396QBtAhϕctP_{wf}=p_i-\frac{162.6QB\mu}{kh}\log_{10}\left(\frac{2.2458A}{C_Ar_w^2}\right)-\frac{0.23396QBt}{Ah\phi c_t}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Time to Semi-Steady State for Gas Well Drainage Area

tpss=15.8ϕμgictiAkt_{pss}=\frac{15.8\phi\mu_{gi}c_{ti}A}{k}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Buildup Pressure from Semilog Slope

PDs=Pi−Pws0.87mP_{Ds}=\frac{P_i-P_{ws}}{0.87m}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Storage Constant for Gas Buildup Tests

CD=27C′ZTMϕhctrw2C_D=\frac{27C'ZT}{M\phi hc_tr_w^2}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Storage Constant for Liquid Buildup Tests

CD=CBVsc2πϕhctrw2C_D=\frac{CBV_{sc}}{2\pi\phi hc_tr_w^2}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Flow Period Duration for Hydraulically Fractured Wells

t=ϕμctLf2tLfD0.0002637kt=\frac{\phi\mu c_tL_f^2t_{LfD}}{0.0002637k}
Open analysis
Reservoir EngineeringPressure Transient Analysis

Dimensionless Buildup Time

tD=0.3604kDtϕμctrw2t_D=\frac{0.3604k_Dt}{\phi\mu c_tr_w^2}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Communication Factor in a Compartment in Tight Gas Reservoirs

C=0.111924⋅k⋅AT⋅LC = 0.111924 \cdot \frac{k \cdot A}{T \cdot L}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Correction Factor – Hammerlindl

CDI=G⋅Ef,wGp⋅BgCDI = \frac{G \cdot E_{f,w}}{G_p \cdot B_g}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Fractional Gas Recovery Below the Critical Desorption Pressure in Coal Bed Methane Reservoirs

RF=1−[(VmGc⋅b⋅P1+b⋅P)a]RF = 1 - \left[ \left( \frac{V_m}{G_c} \cdot \frac{b \cdot P}{1 + b \cdot P} \right)^a \right]
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Volume of Gas Adsorbed in Coalbed Methane Reservoirs

V=Vmbp1+bpV = \frac{V_m b p}{1 + bp}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Gas Adsorbed in Coalbed Methane Reservoirs

Ga=1359.7AhρbVG_a = 1359.7 A h \rho_b V
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Coalbed Methane Formation Compressibility

ct=WpWi(Pi−Pd)c_t = \frac{W_p}{W_i(P_i-P_d)}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Dimensionless Time for Semi-Steady-State Coalbed Methane Flow

tDA=0.0002637kgtϕμgictiAt_{DA} = \frac{0.0002637 k_g t}{\phi \mu_{gi} c_{ti} A}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Gas Solubility in Coalbed Methane Reservoirs

Rs=(0.17525ρBϕmSom)VR_s = \left(\frac{0.17525\rho_B}{\phi_m S_{om}}\right)V
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Remaining Gas in Place in Coalbed Methane Reservoirs

GR=7758AhϕEg[BwWp7758Ahϕ+(1−Swi)−(Pi−P)(cf+cwSwi)1−(Pi−P)cf]G_R = 7758Ah\phi E_g \left[ \frac{\frac{B_wW_p}{7758Ah\phi} + (1-S_{wi}) - (P_i-P)(c_f+c_wS_{wi})}{1-(P_i-P)c_f} \right]
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Langmuir Adsorbed Gas Content

Gc=VLPPL+PG_c = \frac{V_L P}{P_L + P}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Langmuir Desorbable Gas Content Between Pressures

Gdes=VL(PiPL+Pi−PfPL+Pf)G_{des} = V_L\left(\frac{P_i}{P_L + P_i} - \frac{P_f}{P_L + P_f}\right)
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Coal Mass from Area Thickness and Bulk Density

Mc=1359.7AhρbM_c = 1359.7 A h \rho_b
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Adsorbed Gas in Place from Langmuir Isotherm

Ga=1359.7AhρbVLPPL+PG_a = 1359.7 A h \rho_b \frac{V_LP}{P_L+P}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Adsorbed Gas Recovery Factor from Langmuir Pressures

RFads=1−Pab/(PL+Pab)Pi/(PL+Pi)RF_{ads} = 1 - \frac{P_{ab}/(P_L+P_{ab})}{P_i/(P_L+P_i)}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Payne Intercompartmental Gas Flow in Tight Gas Reservoirs

Q12=(0.111924kATL)[m(P1)−m(P2)]Q_{12}=\left(\frac{0.111924 k A}{T L}\right)\left[m(P_1)-m(P_2)\right]
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Transmissibility of a Tight Gas Compartment

γ=kAzμg\gamma=\frac{k A}{z \mu_g}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Transmissibility Between Tight Gas Compartments

γ=γaγb(L1+L2)γaL2+L1γb\gamma=\frac{\gamma_a \gamma_b (L_1+L_2)}{\gamma_a L_2+L_1 \gamma_b}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Tight Gas Pore Volume from Squared-Pressure Decline

PV=28.27Tμg,avgzavgμgicti(Pi2−Pwf2)qiDiPV=\frac{28.27T\mu_{g,avg}z_{avg}}{\mu_{gi}c_{ti}(P_i^2-P_{wf}^2)}\frac{q_i}{D_i}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Tight-Gas Compartment Underground Withdrawal

F=GEg+WeF=GE_g+W_e
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Somerton Formation Permeability in Coalbed Methane Reservoirs

k=ko[exp⁡(−0.003Δσko0.1)+0.0002(Δσ)1/3ko1/3]k=k_o\left[\exp\left(\frac{-0.003\Delta\sigma}{k_o^{0.1}}\right)+0.0002(\Delta\sigma)^{1/3}k_o^{1/3}\right]
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Hagoort and Hoogstra Tight Gas Compartment Flow

Q=Γ(P12−P22)2P1μg,avgBg,avgQ=\frac{\Gamma(P_1^2-P_2^2)}{2P_1\mu_{g,avg}B_{g,avg}}
Open analysis
Reservoir EngineeringUnconventional Reservoirs

Apparent Sorption Compressibility

cs=0.17525BgVLρBbLϕ(1+bLp)2c_s=\frac{0.17525B_gV_L\rho_Bb_L}{\phi(1+b_Lp)^2}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Cumulative Gas Production – Tarner’s Method

Gp=N⋅[(Rsi−Rs)−Boi−BoBg]−Np⋅(BoBg−Rs)Gp = N \cdot \left[ (Rsi - Rs) - \frac{Boi - Bo}{Bg} \right] - Np \cdot \left( \frac{Bo}{Bg} - Rs \right)
Open analysis
Reservoir EngineeringMaterial Balance and Production

Oil Reservoir Underground Withdrawal

F=Np[Bo+(Rp−Rs)Bg]+WpBwF = N_p\left[B_o + (R_p-R_s)B_g\right] + W_pB_w
Open analysis
Reservoir EngineeringMaterial Balance and Production

Oil and Dissolved Gas Expansion Term

Eo=(Bo−Boi)+(Rsi−Rs)BgE_o = (B_o-B_{oi}) + (R_{si}-R_s)B_g
Open analysis
Reservoir EngineeringMaterial Balance and Production

Connate Water and Rock Expansion Term

Efw=BticwSwi+cf1−SwiΔpE_{fw} = B_{ti}\frac{c_wS_{wi}+c_f}{1-S_{wi}}\Delta p
Open analysis
Reservoir EngineeringMaterial Balance and Production

Total Oil Reservoir Expansion Term

Et=Eo+mEg+EfwE_t = E_o + mE_g + E_{fw}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Original Oil in Place from General Oil Material Balance

N=F−WeEo+mEg+EfwN = \frac{F-W_e}{E_o+mE_g+E_{fw}}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Oil Material Balance Drive Index Closure

DIsum=DDI+GDI+WDI+CDIDI_{sum} = DDI + GDI + WDI + CDI
Open analysis
Reservoir EngineeringMaterial Balance and Production

Hydrocarbon Pore Volume Occupied by Evolved Solution Gas

Vg,ev=(NRsi−NpRp−(N−Np)Rs)BgV_{g,ev}=\left(NR_{si}-N_pR_p-(N-N_p)R_s\right)B_g
Open analysis
Reservoir EngineeringMaterial Balance and Production

Hydrocarbon Pore Volume Occupied by Gas Cap

Vgc=mNBoiBgBgiV_{gc}=\frac{mNB_{oi}B_g}{B_{gi}}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Hydrocarbon Pore Volume Occupied by Remaining Oil

Vro=(N−Np)BoV_{ro}=(N-N_p)B_o
Open analysis
Reservoir EngineeringMaterial Balance and Production

Gas Cap Shrinkage from Gas Cap Production

Gs=GpcBg−mNBoi(BgBgi−1)G_s=G_{pc}B_g-mNB_{oi}\left(\frac{B_g}{B_{gi}}-1\right)
Open analysis
Reservoir EngineeringMaterial Balance and Production

Gas Produced by Gas Expansion

Gp=43560Ahϕ(1−Swi)(1Bgi−1Bg)G_p=43560Ah\phi(1-S_{wi})\left(\frac{1}{B_{gi}}-\frac{1}{B_g}\right)
Open analysis
Reservoir EngineeringMaterial Balance and Production

Hammerlindl Method for Gas in Place

G=GappRG=\frac{G_{app}}{R}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Pore Volume Occupied by Injected Gas and Water

Vt=WINJBw+GINJBGINJV_t=W_{INJ}B_w+G_{INJ}B_{GINJ}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Oil in Place for Undersaturated Oil Reservoirs without Fluid Injection

N=NpBoBo−Boi+Boi(Swicw+cf1−Swi)ΔPN=\frac{N_pB_o}{B_o-B_{oi}+B_{oi}\left(\frac{S_{wi}c_w+c_f}{1-S_{wi}}\right)\Delta P}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Oil in Place in Saturated Oil Reservoirs

N=NpBo+(Gp−NpRs)BgBo−Boi+(Rsi−Rs)BgN=\frac{N_pB_o+(G_p-N_pR_s)B_g}{B_o-B_{oi}+(R_{si}-R_s)B_g}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Oil Bubble Radius for Circular Drainage Area

rob=[5.615Npπϕh((1−Swi)/Boi−So/Bo)]0.5r_{ob}=\left[\frac{5.615N_p}{\pi\phi h\left((1-S_{wi})/B_{oi}-S_o/B_o\right)}\right]^{0.5}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Produced Gas-Oil Ratio

Rp=GpNpR_p=\frac{G_p}{N_p}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Gas Cap Ratio

m=GBgiNBoim=\frac{GB_{gi}}{NB_{oi}}
Open analysis
Reservoir EngineeringMaterial Balance and Production

Cumulative Oil Production in Undersaturated Oil Reservoirs

Np=Nce(BoBoi)ΔPN_p=Nc_e\left(\frac{B_o}{B_{oi}}\right)\Delta P
Open analysis
Reservoir EngineeringWell Performance

Deliverability Equation for Shallow Gas Reservoirs

C=k⋅h1422⋅T⋅μg⋅z⋅(ln⁡(rerw)−0.5)C = \frac{k \cdot h}{1422 \cdot T \cdot \mu_g \cdot z \cdot \left(\ln\left(\frac{r_e}{r_w}\right) - 0.5\right)}
Open analysis
Reservoir EngineeringWell Performance

Effective Wellbore Radius of a Well in Presence of Uniform Flux Fractures

rw=Xfer_w = \frac{X_f}{e}
Open analysis
Reservoir EngineeringWell Performance

Critical Rate for Horizontal Wells in Edge-Water Drive Reservoirs

qo=(4.888×10−4)⋅Δρ⋅h⋅kh⋅kv⋅L⋅qcμoq_o = (4.888 \times 10^{-4}) \cdot \Delta\rho \cdot h \cdot \sqrt{k_h \cdot k_v} \cdot L \cdot \frac{q_c}{\mu_o}
Open analysis
Reservoir EngineeringWell Performance

Effective Wellbore Radius of a Horizontal Well – Method 1 (Anisotropic Reservoirs)

rwd=reh⋅L2a⋅(1+1−(L2a)2)⋅(βh2rw)βhLr_{wd} = \frac{r_{eh} \cdot \frac{L}{2}}{a \cdot \left(1 + \sqrt{1 - \left(\frac{L}{2a}\right)^2}\right) \cdot \left(\frac{\beta h}{2r_w}\right)^{\frac{\beta h}{L}}}
Open analysis
Reservoir EngineeringWell Performance

Effective Wellbore Radius of a Horizontal Well – van der Vlis et al. Method

rwe=L4⋅(0.454⋅sin⁡(360⋅rwh))hLr_{we} = \frac{L}{4} \cdot \left( 0.454 \cdot \sin\left(360 \cdot \frac{r_w}{h} \right) \right)^{\frac{h}{L}}
Open analysis
Reservoir EngineeringWell Performance

Joshi Horizontal Well Productivity Index

Jh=0.00708khhμoBo[ln⁡Rh+βhLln⁡(βh2rw)+s]J_h=\frac{0.00708k_hh}{\mu_oB_o\left[\ln R_h+\frac{\beta h}{L}\ln\left(\frac{\beta h}{2r_w}\right)+s\right]}
Open analysis
Reservoir EngineeringWell Performance

Joshi Horizontal Well Drainage Ellipse Area

Aac=πrehrev43560A_{ac}=\frac{\pi r_{eh}r_{ev}}{43560}
Open analysis
Reservoir EngineeringWell Performance

Prats High-Conductivity Fracture Effective Wellbore Radius

rwe=Xf2r_{we}=\frac{X_f}{2}
Open analysis
Reservoir EngineeringWell Performance

Dimensionless Fracture Conductivity

FCD=kfwfkXfF_{CD}=\frac{k_fw_f}{kX_f}
Open analysis
Reservoir EngineeringWell Performance

Craft and Hawkins Vertical Well Critical Coning Rate

qo=0.007078koh(pws−pwf)μoBoln⁡(re/rw)PRq_o=\frac{0.007078k_oh(p_{ws}-p_{wf})}{\mu_oB_o\ln(r_e/r_w)}PR
Open analysis
Reservoir EngineeringWell Performance

Meyer Gardner Pirson Vertical Well Critical Coning Rate

qo=0.001535ρw−ρoln⁡(re/rw)koμoBo(h2−hp2)q_o=0.001535\frac{\rho_w-\rho_o}{\ln(r_e/r_w)}\frac{k_o}{\mu_oB_o}(h^2-h_p^2)
Open analysis
Reservoir EngineeringWell Performance

Joshi Horizontal Well Critical Rate for Gas Coning

qo=1.535×10−3(ρo−ρg)kh[h2−(h−lv)2]Boμoln⁡(re/rw)q_o=1.535\times10^{-3}\frac{(\rho_o-\rho_g)k_h[h^2-(h-l_v)^2]}{B_o\mu_o\ln(r_e/r_w)}
Open analysis
Reservoir EngineeringWell Performance

Horizontal Well Breakthrough Dimensionless Time

tdbt=kv(ρo−ρg)tbt364.72hϕμot_{dbt}=\frac{k_v(\rho_o-\rho_g)t_{bt}}{364.72h\phi\mu_o}
Open analysis
Reservoir EngineeringWell Performance

Horizontal Well Breakthrough Dimensionless Flow Rate

qd=325.86μoqoBokvkhh(ρo−ρg)q_d=\frac{325.86\mu_oq_oB_o}{\sqrt{k_vk_h}h(\rho_o-\rho_g)}
Open analysis
Reservoir EngineeringWell Performance

Hoyland Papatzacos Skjaeveland Isotropic Vertical Well Critical Rate

Qoc=(ρw−ρo)koBoμo10822[1−(hph)2]1.325h2.238(ln⁡re)−1.99Q_{oc}=\frac{(\rho_w-\rho_o)k_o}{B_o\mu_o10822}\left[1-\left(\frac{h_p}{h}\right)^2\right]^{1.325}h^{2.238}(\ln r_e)^{-1.99}
Open analysis
Reservoir EngineeringWell Performance

Meyer Gardner Pirson Vertical Gas-Coning Critical Rate

qo=0.001535ρo−ρgln⁡(re/rw)koμoBo[h2−(h−hp)2]q_o=0.001535\frac{\rho_o-\rho_g}{\ln(r_e/r_w)}\frac{k_o}{\mu_oB_o}\left[h^2-(h-h_p)^2\right]
Open analysis
Reservoir EngineeringWell Performance

Bournazel Jeanson Vertical Well Water Breakthrough Dimensionless Time

td=(ρw−ρo)gkvtBTfmμoϕeht_d=\frac{(\rho_w-\rho_o)gk_vt_{BT}f_m}{\mu_o\phi_eh}
Open analysis
Reservoir EngineeringWell Performance

Sobocinski Cornelius Vertical Well Cone Height Ratio

Z=0.00307(ρw−ρo)khhhtμoqoBoZ=\frac{0.00307(\rho_w-\rho_o)k_hhh_t}{\mu_oq_oB_o}
Open analysis
Reservoir EngineeringWell Performance

Sobocinski Cornelius Vertical Well Breakthrough Dimensionless Time

tD=0.00137(ρw−ρo)kh(1+Mα)tμoϕh(kh/kv)t_D=\frac{0.00137(\rho_w-\rho_o)k_h(1+M^\alpha)t}{\mu_o\phi h(k_h/k_v)}
Open analysis
Reservoir EngineeringWell Performance

Finite-Conductivity Fracture Effective Wellbore Radius

rwe=0.2807kfbfkr_{we}=\frac{0.2807k_fb_f}{k}
Open analysis
Reservoir EngineeringWell Performance

Joshi Isotropic Horizontal Well Effective Radius

rwd=rehL/2a(1+1−(L2a)2)(h2rw)h/Lr_{wd}=r_{eh}\frac{L/2}{a\left(1+\sqrt{1-\left(\frac{L}{2a}\right)^2}\right)\left(\frac{h}{2r_w}\right)^{h/L}}
Open analysis
Reservoir EngineeringWell Performance

Pseudo-Steady State Horizontal Well Productivity Method 3

Jh=khh70.6μo(F+h0.5Lkhkvsx)J_h=\frac{k_hh}{70.6\mu_o\left(F+\frac{h}{0.5L}\sqrt{\frac{k_h}{k_v}}s_x\right)}
Open analysis
Reservoir EngineeringWell Performance

Gas Flow Rate into the Wellbore

Q=0.007kΔPLuln⁡(Re/Rw)1440Q=\frac{0.007k\Delta PL}{u\ln(R_e/R_w)1440}
Open analysis
Reservoir EngineeringWell Performance

Laminar Gas Flow Rate from Real-Gas Pseudopressure

Qg=kh(φr−φwf)1422T[0.5ln⁡(4A/(1.781CArw2))+S]Q_g=\frac{kh(\varphi_r-\varphi_{wf})}{1422T[0.5\ln(4A/(1.781C_Ar_w^2))+S]}
Open analysis
Reservoir EngineeringWell Performance

High-Pressure Region Gas Flow Rate

Qg=7.08×10−6kh(Pr−Pwf)μgavgBgavg[ln⁡(re/rw)−0.75+S]Q_g=\frac{7.08\times10^{-6}kh(P_r-P_{wf})}{\mu_{gavg}B_{gavg}[\ln(r_e/r_w)-0.75+S]}
Open analysis
Reservoir EngineeringWell Performance

Low-Pressure Non-Circular Gas Flow Rate

Qg=kh(Pr2−Pwf2)1422μgavgTZavg[0.5ln⁡(4A/(1.781CArw2))+S]Q_g=\frac{kh(P_r^2-P_{wf}^2)}{1422\mu_{gavg}TZ_{avg}[0.5\ln(4A/(1.781C_Ar_w^2))+S]}
Open analysis
Reservoir EngineeringWell Performance

Giger-Karcher Horizontal Well Critical Rate

qc=khh2gΔρBμL[1−16(hL)2]q_c=\frac{k_hh^2g\Delta\rho}{B\mu L}\left[1-\frac{1}{6}\left(\frac{h}{L}\right)^2\right]
Open analysis
Reservoir EngineeringWell Performance

Efros Horizontal Well Critical Rate

qo=4.888×10−4khh2(ρw−ρo)LBoμoGEq_o=4.888\times10^{-4}\frac{k_hh^2(\rho_w-\rho_o)L}{B_o\mu_oG_E}
Open analysis
Reservoir EngineeringWell Performance

Generalized Reservoir Gas Flow Deliverability

W=C(pˉ2−pwf2)nW=C(\bar p^2-p_{wf}^2)^n
Open analysis
Reservoir EngineeringReservoir Volumetrics

Original Oil in Place - Volumetric Method

N=7758Ahϕ(1−Swi)BoiN = \frac{7758 A h \phi (1 - S_{wi})}{B_{oi}}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Original Gas in Place - Volumetric Method

G=43560Ahϕ(1−Swi)BgiG = \frac{43560 A h \phi (1 - S_{wi})}{B_{gi}}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Reservoir Pore Volume - Volumetric Method

PV=7758AhϕPV = 7758 A h \phi
Open analysis
Reservoir EngineeringReservoir Volumetrics

Hydrocarbon Pore Volume - Volumetric Method

HCPV=7758Ahϕ(1−Swi)HCPV = 7758 A h \phi(1 - S_{wi})
Open analysis
Reservoir EngineeringReservoir Volumetrics

Gross Rock Volume from Area and Gross Thickness

Vgrv=43560AhgV_{grv}=43560Ah_g
Open analysis
Reservoir EngineeringReservoir Volumetrics

Net Reservoir Rock Volume from Net-to-Gross

Vnrv=43560AhgNTGV_{nrv}=43560Ah_gNTG
Open analysis
Reservoir EngineeringReservoir Volumetrics

Stock Tank Oil Initially In Place with Net-to-Gross

N=7758AhgNTGϕ(1−Swi)BoiN=\frac{7758Ah_gNTG\phi(1-S_{wi})}{B_{oi}}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Original Gas In Place with Net-to-Gross

G=43560AhgNTGϕ(1−Swi)BgiG=\frac{43560Ah_gNTG\phi(1-S_{wi})}{B_{gi}}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Original Water In Place with Net-to-Gross

W=7758AhgNTGϕSwiBwiW=\frac{7758Ah_gNTG\phi S_{wi}}{B_{wi}}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Net Pay Thickness from Gross Thickness and Net-to-Gross

h=hgNTGh=h_gNTG
Open analysis
Reservoir EngineeringReservoir Volumetrics

Reservoir Oil Volume from Stock Tank Oil and Oil FVF

Voi=NBoiV_{oi}=NB_{oi}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Reservoir Gas Volume from Gas In Place and Gas FVF

Vgi=GBgiV_{gi}=GB_{gi}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Original Condensate In Place from Gas In Place and Liquid Content

Nc=GYc106N_c=\frac{GY_c}{10^6}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Original Condensate In Place with Net-to-Gross

Nc=43560AhgNTGϕ(1−Swi)Yc106BgiN_c=\frac{43560Ah_gNTG\phi(1-S_{wi})Y_c}{10^6B_{gi}}
Open analysis
Reservoir EngineeringReservoir Volumetrics

Gross Rock Volume in Acre-Feet from Area and Thickness

Vgrv,af=AhgV_{grv,af}=Ah_g
Open analysis
Reservoir EngineeringReservoir Volumetrics

Gross Rock Volume in Reservoir Barrels

Vgrv,bbl=7758AhgV_{grv,bbl}=7758Ah_g
Open analysis
Reservoir EngineeringReservoir Volumetrics

Net Rock Volume in Reservoir Barrels from Net-to-Gross

Vnrv,bbl=7758AhgNTGV_{nrv,bbl}=7758Ah_gNTG
Open analysis
Reservoir EngineeringReservoir Volumetrics

Pore Volume from Net Rock Volume and Porosity

PV=Vnrv,bblϕPV=V_{nrv,bbl}\phi
Open analysis
Reservoir EngineeringReservoir Volumetrics

Hydrocarbon Pore Volume from Pore Volume and Water Saturation

HCPV=PV(1−Swi)HCPV=PV(1-S_{wi})
Open analysis
Reservoir EngineeringPVT Properties

Gas Formation Volume Factor

Bg=0.02827zTPB_g = 0.02827 \frac{zT}{P}
Open analysis
Reservoir EngineeringPVT Properties

Gas Expansion Factor from Formation Volume Factor

Eg=35.37PzTE_g = 35.37 \frac{P}{zT}
Open analysis
Reservoir EngineeringPVT Properties

Two-Phase Formation Volume Factor

Bt=Bo+Bg(Rsoi−Rso)B_t = B_o + B_g(R_{soi} - R_{so})
Open analysis
Reservoir EngineeringPVT Properties

Instantaneous Gas-Oil Ratio

GOR=Rs+krgμoBokroμgBgGOR = R_s + \frac{k_{rg}\mu_o B_o}{k_{ro}\mu_g B_g}
Open analysis
Reservoir EngineeringPVT Properties

Water Two-Phase Formation Volume Factor

Btw=Bw+Bg(Rs−Ri)B_{tw}=B_w+B_g(R_s-R_i)
Open analysis
Reservoir EngineeringMaterial Balance

Gas Expansion Term in Gas Reservoirs

Eg=Bg−BgiE_g = B_g - B_{gi}
Open analysis
Reservoir EngineeringMaterial Balance

Initial Gas Cap

G=mNBoiBgiG = \frac{m N B_{oi}}{B_{gi}}
Open analysis
Reservoir EngineeringMaterial Balance

Gas Material Balance Equation

Pz=Pizi−(PscTTscV)Gp\frac{P}{z} = \frac{P_i}{z_i} - \left(\frac{P_{sc}T}{T_{sc}V}\right)G_p
Open analysis
Reservoir EngineeringMaterial Balance

Underground Fluid Withdrawal - Havlena and Odeh

F=GpBg+WpBwF = G_p B_g + W_p B_w
Open analysis
Reservoir EngineeringMaterial Balance

Cumulative Gas Production from Gas Expansion

Gp=G(1−BgiBg)G_p = G\left(1-\frac{B_{gi}}{B_g}\right)
Open analysis
Reservoir EngineeringMaterial Balance

Initial Gas In Place for Water-Drive Gas Reservoir

G=GpBg−(We−WpBw)Bg−BgiG=\frac{G_pB_g-(W_e-W_pB_w)}{B_g-B_{gi}}
Open analysis
Reservoir EngineeringMaterial Balance

Gas Drive Index in Gas Reservoirs

GDI=GGp(1−BgiBg)GDI=\frac{G}{G_p}\left(1-\frac{B_{gi}}{B_g}\right)
Open analysis
Reservoir EngineeringMaterial Balance

Water-Drive Index for Gas Reservoirs

WDI=We−WpBwGpBgWDI=\frac{W_e-W_pB_w}{G_pB_g}
Open analysis
Reservoir EngineeringMaterial Balance

Water Influx from Pot Aquifer Model

We=ctWi(Pi−P)W_e=c_tW_i(P_i-P)
Open analysis
Reservoir EngineeringMaterial Balance

Trapped Gas Volume in Water-Invaded Zones

TG=We−WpBw1−Swi−SgrwSgrwTG=\frac{W_e-W_pB_w}{1-S_{wi}-S_{grw}}S_{grw}
Open analysis
Reservoir EngineeringMaterial Balance

Water Influx Constant for van Everdingen-Hurst Aquifer

B=1.119ϕctre2hfB=1.119\phi c_tr_e^2hf
Open analysis
Reservoir EngineeringMaterial Balance

Original Gas in Place from p/z Material Balance

G=Gp1−Pz/(Pi/zi)G=\frac{G_p}{1-P_z/(P_i/z_i)}
Open analysis
Reservoir EngineeringMaterial Balance

Gas Recovery Factor from p/z Material Balance

RFg=1−PzPi/ziRF_g=1-\frac{P_z}{P_i/z_i}
Open analysis
Reservoir EngineeringMaterial Balance

Havlena-Odeh Cumulative Water Influx from Fluid Withdrawal

We=F−GEGW_e=F-GE_G
Open analysis
Reservoir EngineeringMaterial Balance

Modified Cole Plot for Water-Drive Gas Reservoirs

FEt=G+WeEt\frac{F}{E_t}=G+\frac{W_e}{E_t}
Open analysis
Reservoir EngineeringMaterial Balance

Schilthuis Cumulative Water Influx

We=Js(Pi−Pˉ)ΔtW_e=J_s(P_i-\bar{P})\Delta t
Open analysis
Reservoir EngineeringMaterial Balance

van Everdingen-Hurst Single-Step Water Influx

We=BΔpWeDW_e=B\Delta p W_{eD}
Open analysis
Reservoir EngineeringMaterial Balance

Rock Expansion Term in Abnormally Pressured Gas Reservoirs

ER=cf+cwSwi1−SwiE_R=\frac{c_f+c_wS_{wi}}{1-S_{wi}}
Open analysis
Reservoir EngineeringMaterial Balance

Gas Saturation in Water-Drive Gas Reservoirs

Sg=(G−Gp)Bg−We−WpBw1−Swi−SgrwSgrwGBgi1−Swi−We−WpBw1−Swi−SgrwS_g=\frac{(G-G_p)B_g-\frac{W_e-W_pB_w}{1-S_{wi}-S_{grw}}S_{grw}}{\frac{GB_{gi}}{1-S_{wi}}-\frac{W_e-W_pB_w}{1-S_{wi}-S_{grw}}}
Open analysis
Reservoir EngineeringMaterial Balance

Gas Expansion Factor from Cumulative Gas Production

Eg=Egi−Gp43560Ahϕ(1−Swi)E_g=E_{gi}-\frac{G_p}{43560Ah\phi(1-S_{wi})}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Darcy's Law for Linear Single-Phase Flow

q=0.001127kAΔPμLq = \frac{0.001127 k A \Delta P}{\mu L}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Steady-State Radial Liquid Flow Rate

qo=0.00708kh(pe−pwf)μoBo[ln⁡(re/rw)+s]q_o=\frac{0.00708kh(p_e-p_{wf})}{\mu_oB_o[\ln(r_e/r_w)+s]}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Steady-State Radial Liquid Productivity Index

J=0.00708khμoBo[ln⁡(re/rw)+s]J=\frac{0.00708kh}{\mu_oB_o[\ln(r_e/r_w)+s]}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Pseudosteady-State Radial Oil Flow Rate

qo=kh(pR−pwf)141.2μoBo[ln⁡(re/rw)−0.75+s]q_o=\frac{kh(p_R-p_{wf})}{141.2\mu_oB_o[\ln(r_e/r_w)-0.75+s]}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Pseudosteady-State Radial Productivity Index

J=kh141.2μoBo[ln⁡(re/rw)−0.75+s]J=\frac{kh}{141.2\mu_oB_o[\ln(r_e/r_w)-0.75+s]}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Radial Pressure Distribution in Single-Phase Liquid Flow

p(r)=pwf+141.2qoμoBokhln⁡(rrw)p(r)=p_{wf}+\frac{141.2q_o\mu_oB_o}{kh}\ln\left(\frac{r}{r_w}\right)
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Drainage Radius from Area

re=43560Aπr_e=\sqrt{\frac{43560A}{\pi}}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Low-Pressure Gas Radial Flow Rate

qg=0.703kh(pR2−pwf2)Tμgz[ln⁡(re/rw)−0.75+s]q_g=\frac{0.703kh(p_R^2-p_{wf}^2)}{T\mu_gz[\ln(r_e/r_w)-0.75+s]}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Superficial Velocity from Flow Rate and Area

us=qAu_s=\frac{q}{A}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Interstitial Velocity from Flow Rate Area and Porosity

vp=qϕAv_p=\frac{q}{\phi A}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Single Phase Mobility from Permeability and Viscosity

λ=kμ\lambda=\frac{k}{\mu}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Linear Darcy Flow Conductance

CL=0.001127kAμLC_L=\frac{0.001127kA}{\mu L}
Open analysis
Reservoir EngineeringFluid Flow in Porous Media

Hydraulic Diffusivity Coefficient in Field Units

η=0.0002637kϕμct\eta=\frac{0.0002637k}{\phi\mu c_t}
Open analysis
Production EngineeringInflow Performance

Productivity Index and Straight-Line IPR

J=qoPr−PwfJ = \frac{q_o}{P_r - P_{wf}}
Open analysis
Production EngineeringInflow Performance

Vogel Inflow Performance Relationship

qo=qmax[1−0.2(PwfPr)−0.8(PwfPr)2]q_o = q_{max}\left[1 - 0.2\left(\frac{P_{wf}}{P_r}\right) - 0.8\left(\frac{P_{wf}}{P_r}\right)^2\right]
Open analysis
Production EngineeringInflow Performance

Rawlins-Schellhardt Gas Deliverability Rate

qg=CRS(Pr2−Pwf2)nRSq_g=C_{RS}\left(P_r^2-P_{wf}^2\right)^{n_{RS}}
Open analysis
Production EngineeringInflow Performance

Gas Deliverability Pressure-Squared Drawdown

Δp2=Pr2−Pwf2\Delta p^2=P_r^2-P_{wf}^2
Open analysis
Production EngineeringInflow Performance

Rawlins-Schellhardt Absolute Open Flow Potential

qAOF=CRS(Pr2−Patm2)nRSq_{AOF}=C_{RS}\left(P_r^2-P_{atm}^2\right)^{n_{RS}}
Open analysis
Production EngineeringInflow Performance

Rawlins-Schellhardt Deliverability Coefficient from Test Point

CRS=qg(Δp2)nRSC_{RS}=\frac{q_g}{\left(\Delta p^2\right)^{n_{RS}}}
Open analysis
Production EngineeringInflow Performance

Rawlins-Schellhardt Deliverability Exponent from Two Test Points

nRS=ln⁡(qg2/qg1)ln⁡(Δp22/Δp12)n_{RS}=\frac{\ln(q_{g2}/q_{g1})}{\ln(\Delta p_2^2/\Delta p_1^2)}
Open analysis
Production EngineeringInflow Performance

Straight-Line IPR Rate from Test Point

qo=qtestPr−Pwf,test(Pr−Pwf)q_o=\frac{q_{test}}{P_r-P_{wf,test}}(P_r-P_{wf})
Open analysis
Production EngineeringInflow Performance

Vogel IPR Rate from One Test Point

qo=qmax[1−0.2PwfPr−0.8(PwfPr)2]q_o=q_{max}\left[1-0.2\frac{P_{wf}}{P_r}-0.8\left(\frac{P_{wf}}{P_r}\right)^2\right]
Open analysis
Production EngineeringInflow Performance

Fetkovich Oil Deliverability Rate

qo=Cf(Pr2−Pwf2)nfq_o=C_f(P_r^2-P_{wf}^2)^{n_f}
Open analysis
Production EngineeringInflow Performance

Jones-Blount-Glaze Gas Deliverability Rate

qg=−a+a2+4b(Pr2−Pwf2)2bq_g=\frac{-a+\sqrt{a^2+4b(P_r^2-P_{wf}^2)}}{2b}
Open analysis
Production EngineeringInflow Performance

Composite IPR Productivity Index

Ji=q(Pr−Pb)+Pb1.8[1−0.2(PwfPr)−0.8(PwfPr)2]J_i=\frac{q}{(P_r-P_b)+\frac{P_b}{1.8}\left[1-0.2\left(\frac{P_{wf}}{P_r}\right)-0.8\left(\frac{P_{wf}}{P_r}\right)^2\right]}
Open analysis
Production EngineeringInflow Performance

Horizontal Well Fetkovich IPR Rate

qo=qomax[1−(PwfPr)2]nq_o=q_{omax}\left[1-\left(\frac{P_{wf}}{P_r}\right)^2\right]^n
Open analysis
Production EngineeringInflow Performance

Productivity Index for a Gas Well

Jg=kh1422T[0.5ln⁡(4A1.781CArw2)+S]J_g=\frac{kh}{1422T\left[0.5\ln\left(\frac{4A}{1.781C_Ar_w^2}\right)+S\right]}
Open analysis
Production EngineeringInflow Performance

Damaged to Undamaged Productivity Ratio - Acidizing

JsJo=Fkln⁡(re/rw)ln⁡(rs/rw)+Fkln⁡(re/rs)\frac{J_s}{J_o}=\frac{F_k\ln(r_e/r_w)}{\ln(r_s/r_w)+F_k\ln(r_e/r_s)}
Open analysis
Production EngineeringInflow Performance

Flow Coefficient During Drawdown

E=Pi−pwf−ΔpskinPi−pwfE=\frac{P_i-p_{wf}-\Delta p_{skin}}{P_i-p_{wf}}
Open analysis
Production EngineeringInflow Performance

PI Test Skin Factor and Average Permeability

s=(kkj−1)[ln⁡(rerw)−0.75]s=\left(\frac{k}{k_j}-1\right)\left[\ln\left(\frac{r_e}{r_w}\right)-0.75\right]
Open analysis
Drilling EngineeringWell Control

Hydrostatic Pressure from Mud Weight

HP=0.052MW⋅TVDHP = 0.052 MW \cdot TVD
Open analysis
Drilling EngineeringWell Control

Surface Pressure During Drill Stem Test

P=0.052h(EMW−SG⋅8.33)P = 0.052h(EMW - SG\cdot8.33)
Open analysis
Drilling EngineeringWell Control

Specific Gravity to Fluid Weight

FW=8.33SGFW=8.33SG
Open analysis
Drilling EngineeringWell Control

Kick Analysis - Influx Density

I=MW−SICP−SIDPPhi⋅0.052I = MW - \frac{SICP - SIDPP}{h_i\cdot0.052}
Open analysis
Drilling EngineeringWell Control

Kick Analysis - Formation Pressure With Well Shut-In

Pfp=SIDPP+MW⋅0.052⋅hP_{fp} = SIDPP + MW\cdot0.052\cdot h
Open analysis
Drilling EngineeringWell Control

Kick Analysis - Shut-In Drill Pipe Pressure

SIDPP=Pfp−MW⋅0.052⋅hSIDPP = P_{fp} - MW\cdot0.052\cdot h
Open analysis
Drilling EngineeringWell Control

Maximum Allowable Mud Weight From Leak-Off Pressure

MWmax=MW+Pl0.052TVDMW_{max} = MW + \frac{P_l}{0.052TVD}
Open analysis
Drilling EngineeringWell Control

Kick Analysis - Maximum Pit Gain From Gas Kick

MPG=4PVCKWMMPG = 4\sqrt{\frac{PVC}{KWM}}
Open analysis
Drilling EngineeringWell Control

Kick Analysis - Height of Influx

hi=PGACh_i = \frac{PG}{AC}
Open analysis
Drilling EngineeringWell Control

Breakover Point Between Stripping and Snubbing

Lds=Ldc+LbpL_{ds}=L_{dc}+L_{bp}
Open analysis
Drilling EngineeringWell Control

Height Gain from Stripping Into Influx

H=LstrippedCdp+DdpCaH=L_{stripped}\frac{C_{dp}+D_{dp}}{C_a}
Open analysis
Drilling EngineeringWell Control

Casing Pressure Increase from Stripping Into Influx

P=H(G−Gi)P=H(G-G_i)
Open analysis
Drilling EngineeringWell Control

Maximum Allowable Surface Pressure Governed by Casing Burst

MASP=PbcS−(Wu−Wo)0.052HMASP = P_{bc}S - (W_u - W_o)0.052H
Open analysis
Drilling EngineeringWell Control

Minimum Surface Pressure Before Stripping

Pmin=WcLstandDc2(0.7854)P_{min}=\frac{W_cL_{stand}}{D_c^2(0.7854)}
Open analysis
Drilling EngineeringWell Control

Constant Bottomhole Pressure Bleed Volume for Rising Gas

Vbleed=ΔPstepCaGV_{bleed}=\frac{\Delta P_{step}C_a}{G}
Open analysis
Drilling EngineeringWell Control

Kill Weight Mud Determination - Moore Equation

KWM=SIDPP0.052TVD+OMWKWM=\frac{SIDPP}{0.052TVD}+OMW
Open analysis
Drilling EngineeringWell Control

Hydrostatic Pressure in Annulus Due to Slug

P=VaVs(Ws−Wm)0.052P=V_aV_s(W_s-W_m)0.052
Open analysis
Drilling EngineeringWell Control

Additional Mud Returned by Slug

Vadd=(WsWm−1)VsV_{add}=\left(\frac{W_s}{W_m}-1\right)V_s
Open analysis
Drilling EngineeringWell Control

Total Mud Returned by Slug

Vreturn=WsWmVsV_{return}=\frac{W_s}{W_m}V_s
Open analysis
Drilling EngineeringWell Control

Level Drop After Pumping a Slug

Ldrop=(Ws/Wm−1)VsCdpL_{drop}=\frac{(W_s/W_m-1)V_s}{C_{dp}}
Open analysis
Drilling EngineeringWell Control

Rectangular Tank Volume

Vtank=LWH5.615V_{tank}=\frac{LWH}{5.615}
Open analysis
Drilling EngineeringWell Control

Rectangular Tank Capacity per Foot

Crect,ft=LW(0.178)C_{rect,ft}=LW(0.178)
Open analysis
Drilling EngineeringWell Control

Rectangular Tank Capacity per Inch

Crect,in=LW(0.0148)C_{rect,in}=LW(0.0148)
Open analysis
Drilling EngineeringWell Control

Vertical Cylindrical Tank Volume

Vcyl=Ccyl,ftHV_{cyl}=C_{cyl,ft}H
Open analysis
Drilling EngineeringWell Control

Vertical Cylindrical Tank Capacity per Foot

Ccyl,ft=D27.148C_{cyl,ft}=\frac{D^2}{7.148}
Open analysis
Drilling EngineeringWell Control

Hydraulic Force from Pressure and Diameter

F=PD2(0.7854)F=PD^2(0.7854)
Open analysis
Drilling EngineeringWell Control

Equivalent Mud Weight from Surface Pressure

EMW=Psurf0.052TVD+MWEMW=\frac{P_{surf}}{0.052TVD}+MW
Open analysis
Drilling EngineeringWell Control

New Pump Pressure with Mud Weight Change

Pnew=PcurrentMWnewMWoldP_{new}=P_{current}\frac{MW_{new}}{MW_{old}}
Open analysis
Drilling EngineeringWell Control

New MAASP After Kill Mud Weight

MAASPkill=(MWmax−KMW)0.052TVDshoeMAASP_{kill}=(MW_{max}-KMW)0.052TVD_{shoe}
Open analysis
Drilling EngineeringWell Control

Formation Integrity Test Pressure

PFIT=(FIT−MW)0.052TVDP_{FIT}=(FIT-MW)0.052TVD
Open analysis
Drilling EngineeringWell Control

Hydrostatic Pressure Decrease Due to Gas-Cut Mud

Ploss=MGCVP_{loss}=\frac{MG}{C}V
Open analysis
Drilling EngineeringWell Control

Maximum Surface Pressure From Gas Kick in Water-Based Mud

MSP=0.2PVKWMCMSP=0.2\sqrt{\frac{PVKWM}{C}}
Open analysis
Drilling EngineeringWell Control

Initial Circulating Pressure

ICP=SCRP+SIDPPICP=SCRP+SIDPP
Open analysis
Drilling EngineeringWell Control

Final Circulating Pressure

FCP=SCRPKWMOMWFCP=SCRP\frac{KWM}{OMW}
Open analysis
Drilling EngineeringWell Control

Maximum Allowable Annular Surface Pressure from Shoe EMW

MAASP=(MWmax−MW)0.052TVDshoeMAASP=(MW_{max}-MW)0.052TVD_{shoe}
Open analysis
Drilling EngineeringWell Control

Kick Tolerance Bottomhole Gas Volume

KT=min⁡(Vinitial,Vbottom,shoe)KT=\min(V_{initial},V_{bottom,shoe})
Open analysis
Drilling EngineeringWell Control

Accumulator Nitrogen Gas Volume from Boyle Law

VN2=PpreVbottlePsystemV_{N2}=\frac{P_{pre}V_{bottle}}{P_{system}}
Open analysis
Drilling EngineeringWell Control

Stored Hydraulic Fluid Volume in Accumulator Bottle

Vfluid=Vbottle−PpreVbottlePsystemV_{fluid}=V_{bottle}-\frac{P_{pre}V_{bottle}}{P_{system}}
Open analysis
Drilling EngineeringWell Control

Usable Fluid Volume per Surface Accumulator Bottle

Vusable=Vfluid,operating−Vfluid,minV_{usable}=V_{fluid,operating}-V_{fluid,min}
Open analysis
Drilling EngineeringWell Control

Total Usable Fluid Volume from Accumulator Bank

Vtotal=NbottlesVusable,bottleV_{total}=N_{bottles}V_{usable,bottle}
Open analysis
Drilling EngineeringWell Control

Accumulator Bottles Required for BOP Function Volume

Nbottles=⌈VrequiredVusable,bottle⌉N_{bottles}=\left\lceil\frac{V_{required}}{V_{usable,bottle}}\right\rceil
Open analysis
Drilling EngineeringWell Control

Mud Pressure Gradient from Mud Weight

MWG=0.052MWMWG=0.052MW
Open analysis
Drilling EngineeringWell Control

Actual Gas Migration Rate from Casing Pressure Increase

RGM=(Pcsg2−Pcsg1)/Δt0.052MWRGM=\frac{(P_{csg2}-P_{csg1})/\Delta t}{0.052MW}
Open analysis
Drilling EngineeringWell Control

Casing Pressure Increase Rate from Gas Migration

Pinc=RGM MWGP_{inc}=RGM\,MWG
Open analysis
Drilling EngineeringWell Control

Shut-In Pressure Increase from Gas Migration Time

ΔP=RGM MWG Δt\Delta P=RGM\,MWG\,\Delta t
Open analysis
Drilling EngineeringWell Control

Time to MAASP During Gas Migration

tlimit=MAASP−SICPcurrentRGM MWGt_{limit}=\frac{MAASP-SICP_{current}}{RGM\,MWG}
Open analysis
Drilling EngineeringWell Control

Volumetric Mud Bleed from Allowed Pressure Rise

Vbleed=ΔPallowFp/bblV_{bleed}=\frac{\Delta P_{allow}}{F_{p/bbl}}
Open analysis
Drilling EngineeringWell Control

Trip Margin from Yield Point and Annular Clearance

TM=YP11.7(Dh−Dp)TM=\frac{YP}{11.7(D_h-D_p)}
Open analysis
Drilling EngineeringWell Control

Riser Hydrostatic Loss on Disconnect

ΔPriser=0.052MW(WD+AG)−0.052SW WD\Delta P_{riser}=0.052MW(WD+AG)-0.052SW\,WD
Open analysis
Drilling EngineeringWell Control

Riser Margin from Hydrostatic Loss

RM=ΔPriser0.052(TVD−WD−AG)RM=\frac{\Delta P_{riser}}{0.052(TVD-WD-AG)}
Open analysis
Drilling EngineeringWell Control

Casing Pressure After Subsea Start-Up

Pstart=SICP−PclP_{start}=SICP-P_{cl}
Open analysis
Drilling EngineeringWell Control

Surface-to-Bit Strokes for Wait and Weight Schedule

Sbit=CdpTDPOS_{bit}=\frac{C_{dp}TD}{PO}
Open analysis
Drilling EngineeringWell Control

Wait and Weight Pressure Drop per Stroke

ΔPstk=ICP−FCPSbit\Delta P_{stk}=\frac{ICP-FCP}{S_{bit}}
Open analysis
Drilling EngineeringWell Control

Wait and Weight Pressure Drop over Stroke Interval

ΔPinterval=(ICP−FCP)SintervalSbit\Delta P_{interval}=\frac{(ICP-FCP)S_{interval}}{S_{bit}}
Open analysis
Drilling EngineeringWell Control

Wait and Weight Drill Pipe Pressure at Schedule Strokes

Pdp=ICP−(ICP−FCP)SschedSbitP_{dp}=ICP-\frac{(ICP-FCP)S_{sched}}{S_{bit}}
Open analysis
Drilling EngineeringWell Control

Hydrostatic Pressure Drop per Foot Pulling Wet Pipe

ΔPwet/ft=0.052MWCdp+DdpCann\Delta P_{wet/ft}=0.052MW\frac{C_{dp}+D_{dp}}{C_{ann}}
Open analysis
Drilling EngineeringWell Control

Wet Pipe Pulled Before Fill-Up for Pressure Drop

Lwet=ΔP Cann0.052MW(Cdp+Ddp)L_{wet}=\frac{\Delta P\,C_{ann}}{0.052MW(C_{dp}+D_{dp})}
Open analysis
Drilling EngineeringWell Control

Hydrostatic Pressure Drop per Foot Pulling Dry Pipe

ΔPdry/ft=0.052MWDdpCann+Cdp\Delta P_{dry/ft}=\frac{0.052MWD_{dp}}{C_{ann}+C_{dp}}
Open analysis
Drilling EngineeringWell Control

Dry Pipe Pulled Before Fill-Up for Pressure Drop

Ldry=ΔP(Cann+Cdp)0.052MWDdpL_{dry}=\frac{\Delta P(C_{ann}+C_{dp})}{0.052MWD_{dp}}
Open analysis
Drilling EngineeringWell Control

Bullheading Formation Fracture Pressure from Gradient

Pfrac=GfracTVDperfP_{frac}=G_{frac}TVD_{perf}
Open analysis
Drilling EngineeringWell Control

Bullheading Initial Hydrostatic Pressure from Formation Pressure

Ph,init=Pform−SITPP_{h,init}=P_{form}-SITP
Open analysis
Drilling EngineeringWell Control

Bullheading Initial Average Fluid Density

ρinit=Ph,init0.052TVDperf\rho_{init}=\frac{P_{h,init}}{0.052TVD_{perf}}
Open analysis
Drilling EngineeringWell Control

Bullheading Maximum Initial Surface Pressure

Psurf,init,max=Pfrac−Ph,initP_{surf,init,max}=P_{frac}-P_{h,init}
Open analysis
Drilling EngineeringWell Control

Bullheading Maximum Final Surface Pressure

Psurf,final,max=Pfrac−KFW 0.052TVDperfP_{surf,final,max}=P_{frac}-KFW\,0.052TVD_{perf}
Open analysis
Drilling EngineeringWell Control

Workover Kill Fluid Weight from Shut-In Tubing Pressure

KFW=SITP0.052TVDperf+OFWKFW=\frac{SITP}{0.052TVD_{perf}}+OFW
Open analysis
Drilling EngineeringWell Control

Workover Kill Fluid Weight from Bottomhole Pressure

KFW=BHP0.052TVDKFW=\frac{BHP}{0.052TVD}
Open analysis
Drilling EngineeringWell Control

Bullheading Volume to Perforations

Vbh=Vlines+Vsurface→EOT+VEOT→top+Vtop→bottomV_{bh}=V_{lines}+V_{surface\to EOT}+V_{EOT\to top}+V_{top\to bottom}
Open analysis
Drilling EngineeringWell Control

Bullhead Pump Speed to Exceed Gas Migration

SPMbh=(RGM/60)CtbgPOSPM_{bh}=\frac{(RGM/60)C_{tbg}}{PO}
Open analysis
Drilling EngineeringWell Control

Workover Buoyancy Factor from Fluid Weight

BF=65.4−FW65.4BF=\frac{65.4-FW}{65.4}
Open analysis
Drilling EngineeringWell Control

Open-Ended Pipe Buoyed Weight

Wbuoyed,open=WairBFW_{buoyed,open}=W_{air}BF
Open analysis
Drilling EngineeringWell Control

Closed-Ended Pipe Buoyed Weight with No Fluid Inside

Wbuoyed,closed=Wair−OD2FW24.5W_{buoyed,closed}=W_{air}-\frac{OD^2FW}{24.5}
Open analysis
Drilling EngineeringWell Control

Tubular Buoyed Weight with Different Internal and Annular Fluids

Wbuoyed,diff=Wair+ID2FWtbg24.5−OD2FWann24.5W_{buoyed,diff}=W_{air}+\frac{ID^2FW_{tbg}}{24.5}-\frac{OD^2FW_{ann}}{24.5}
Open analysis
Drilling EngineeringWell Control

Brine Fluid Density to Mix for Temperature Correction

ρmix=ρavg+(Tavg−Tsurface)WL\rho_{mix}=\rho_{avg}+(T_{avg}-T_{surface})WL
Open analysis
Drilling EngineeringWell Control

Pore Pressure Gradient - Rehm and McClendon

gp=0.398log⁡10(dcn−dco)+0.86g_p=0.398\log_{10}(d_{cn}-d_{co})+0.86
Open analysis
Drilling EngineeringWell Control

Pore Pressure Gradient - Zamora

gp=gndcndcog_p=g_n\frac{d_{cn}}{d_{co}}
Open analysis
Drilling EngineeringWell Control

Surface Test Pressure Required to Frac the Formation

PST=FGD−0.052ρmDP_{ST}=FGD-0.052\rho_mD
Open analysis
Drilling EngineeringWell Control

Pressure by Each Barrel of Mud in Casing

Pbbl=1029.4⋅0.052MWDh2−Dp2P_{bbl}=1029.4\cdot0.052\frac{MW}{D_h^2-D_p^2}
Open analysis
Drilling EngineeringWell Control

Subsea Choke Line Pressure Loss

CLPL=0.000061MWLQ1.86ID4.86CLPL=\frac{0.000061MWLQ^{1.86}}{ID^{4.86}}
Open analysis
Drilling EngineeringWell Control

Subsea Choke Line Velocity

V=24.5QID2V=24.5\frac{Q}{ID^2}
Open analysis
Drilling EngineeringWell Control

Subsea Choke Line Pressure Loss Adjusted for Mud Weight

CLPL=WnCLPLoWoCLPL=\frac{W_n CLPL_o}{W_o}
Open analysis
Drilling EngineeringWell Control

Subsea Stack Casing Burst Pressure

CBP=YPc−HP+HPswCBP=YP_c-HP+HP_{sw}
Open analysis
Drilling EngineeringWell Control

Subsea Maximum Allowable Mud Weight from Leakoff Test

Wmax=Plo0.052H+WuW_{max}=\frac{P_{lo}}{0.052H}+W_u
Open analysis
Production EngineeringWell Performance

Productivity Ratio

PR=JJswPR = \frac{J}{J_{sw}}
Open analysis
Production EngineeringWell Performance

Additional Pressure Drop in the Skin Zone

ΔPskin=141.2QoBoμoSkh\Delta P_{skin} = \frac{141.2 Q_o B_o \mu_o S}{k h}
Open analysis
Production EngineeringWell Performance

Skin Factor from Damaged Zone Permeability

s=(kks−1)ln⁡(rsrw)s = \left(\frac{k}{k_s} - 1\right)\ln\left(\frac{r_s}{r_w}\right)
Open analysis
Production EngineeringWell Performance

Effective Wellbore Radius from Skin Factor

rwa=rwe−sr_{wa} = r_w e^{-s}
Open analysis
Production EngineeringWell Performance

Flow Efficiency with Skin Pressure Drop

E=p−pwf−141.2qBμskhp−pwfE = \frac{p-p_{wf}-\frac{141.2qB\mu s}{kh}}{p-p_{wf}}
Open analysis
Production EngineeringWell Performance

Recommended Underbalanced Perforation Pressure

pu=103.46055−0.3812log⁡10kp_u = 10^{3.46055 - 0.3812\log_{10}k}
Open analysis
Production EngineeringWell Performance

Tubing Bottomhole Pressure from Wellhead Pressure and Losses

Pwf=Pwh+ΔPh+ΔPf+ΔPaccP_{wf}=P_{wh}+\Delta P_h+\Delta P_f+\Delta P_{acc}
Open analysis
Production EngineeringWell Performance

Darcy-Weisbach Tubing Friction Pressure Drop

ΔPf=fDρLv22gcD⋅144\Delta P_f=\frac{f_D\rho Lv^2}{2g_cD\cdot144}
Open analysis
Production EngineeringWell Performance

Gilbert Critical Choke Liquid Rate

qL=PwhD641.89435GLR0.546q_L=\frac{P_{wh}D_{64}^{1.89}}{435GLR^{0.546}}
Open analysis
Production EngineeringWell Performance

Multiphase Wellhead Pressure Across Choke

Pwh=CRmqLSnP_{wh}=C R^m\frac{q_L}{S^n}
Open analysis
Production EngineeringWell Performance

Single-Phase Liquid Flow Through Choke

q=CdA2gcΔPρq=C_dA\sqrt{\frac{2g_c\Delta P}{\rho}}
Open analysis
Production EngineeringWell Performance

Single-Phase Gas Flow Subsonic

qsc=1248CdAPuk(k−1)γgTu[(PdPu)2/k−(PdPu)(k+1)/k]q_{sc}=1248C_dAP_u\sqrt{\frac{k}{(k-1)\gamma_gT_u}\left[\left(\frac{P_d}{P_u}\right)^{2/k}-\left(\frac{P_d}{P_u}\right)^{(k+1)/k}\right]}
Open analysis
Production EngineeringWell Performance

Choke Outlet Temperature

Tdn=Tuzuzo(PoPu)(k−1)/kT_{dn}=T_u\frac{z_u}{z_o}\left(\frac{P_o}{P_u}\right)^{(k-1)/k}
Open analysis
Production EngineeringWell Performance

Oil-Well Perforation Pressure Drop

Δpp=A(qoN)+B(qoN)2\Delta p_p=A\left(\frac{q_o}{N}\right)+B\left(\frac{q_o}{N}\right)^2
Open analysis
Production EngineeringWell Performance

Turner Critical Gas Rate for Liquid Loading

qgc=3.067PvgcATRzq_{gc}=3.067\frac{Pv_{gc}A}{T_Rz}
Open analysis
Production EngineeringWell Performance

ESP Net Lift from Pump Intake Pressure

Hlift=Dpump−Pintake0.433SGfH_{lift}=D_{pump}-\frac{P_{intake}}{0.433SG_f}
Open analysis
Production EngineeringWell Performance

ESP Wellhead Pressure Head

Hwhp=Pwhp0.433SGfH_{whp}=\frac{P_{whp}}{0.433SG_f}
Open analysis
Production EngineeringWell Performance

ESP Total Dynamic Head from Components

TDH=Hlift+Hfriction+HwhpTDH=H_{lift}+H_{friction}+H_{whp}
Open analysis
Production EngineeringWell Performance

ESP Total Pump Head from Stages

Htotal=NstagesHstageH_{total}=N_{stages}H_{stage}
Open analysis
Production EngineeringWell Performance

ESP Stages Required with Safety Margin

Nstages=⌈TDHHstageSF⌉N_{stages}=\left\lceil\frac{TDH}{H_{stage}}SF\right\rceil
Open analysis
Production EngineeringWell Performance

ESP Brake Horsepower from TDH and Efficiency

BHP=QgpmTDHSGf3960ηpBHP=\frac{Q_{gpm}TDHSG_f}{3960\eta_p}
Open analysis
Production EngineeringWell Performance

ESP Total Brake Horsepower from Stage Curve

BHPtotal=NstagesBHPstageBHP_{total}=N_{stages}BHP_{stage}
Open analysis
Production EngineeringWell Performance

ESP Flow Rate Speed Correction

Q2=Q1N2N1Q_2=Q_1\frac{N_2}{N_1}
Open analysis
Production EngineeringWell Performance

ESP Head Speed Correction

H2=H1(N2N1)2H_2=H_1\left(\frac{N_2}{N_1}\right)^2
Open analysis
Production EngineeringWell Performance

ESP Brake Horsepower Speed Correction

BHP2=BHP1(N2N1)3BHP_2=BHP_1\left(\frac{N_2}{N_1}\right)^3
Open analysis
Production EngineeringWell Performance

ESP BEP Operating Ratio

RBEP=QdesignQBEPR_{BEP}=\frac{Q_{design}}{Q_{BEP}}
Open analysis
Production EngineeringWell Performance

Souders-Brown Maximum Gas Velocity for Separator

VGmax=KSρL−ρGρGV_{Gmax}=K_S\sqrt{\frac{\rho_L-\rho_G}{\rho_G}}
Open analysis
Production EngineeringWell Performance

Separator Minimum Diameter from Gas Capacity

Dmin=4qaπFGVGmaxD_{min}=\sqrt{\frac{4q_a}{\pi F_GV_{Gmax}}}
Open analysis
Production EngineeringWell Performance

Separator Gas Capacity from Diameter

qa,max=VGmaxFGπD24q_{a,max}=V_{Gmax}F_G\frac{\pi D^2}{4}
Open analysis
Production EngineeringWell Performance

Separator Actual Gas Velocity

VG=4qaπFGD2V_G=\frac{4q_a}{\pi F_GD^2}
Open analysis
Production EngineeringWell Performance

Separator Gas Capacity Utilization

UG=VGVGmaxU_G=\frac{V_G}{V_{Gmax}}
Open analysis
Production EngineeringWell Performance

Separator Required Liquid Retention Volume

Vreq=WLtret1440V_{req}=\frac{W_Lt_{ret}}{1440}
Open analysis
Production EngineeringWell Performance

Three-Phase Separator Liquid Retention Volume

Vreq=Woto+Wwtw1440V_{req}=\frac{W_ot_o+W_wt_w}{1440}
Open analysis
Production EngineeringWell Performance

Horizontal Separator Liquid Volume from Geometry

VL=FLπD2L4(5.615)V_L=\frac{F_L\pi D^2L}{4(5.615)}
Open analysis
Production EngineeringWell Performance

Horizontal Separator Length for Liquid Retention

Lreq=4(5.615)VreqπFLD2L_{req}=\frac{4(5.615)V_{req}}{\pi F_LD^2}
Open analysis
Production EngineeringWell Performance

Separator Liquid Retention Utilization

UL=VreqVavailableU_L=\frac{V_{req}}{V_{available}}
Open analysis
Production EngineeringWell Performance

Average Liquid Specific Gravity for Mixed Liquid Stream

SL=qoSo+qwSwqo+qwS_L=\frac{q_oS_o+q_wS_w}{q_o+q_w}
Open analysis
Production EngineeringWell Performance

Gas-Liquid Ratio from Gas and Liquid Rates

R=1000000QgqLR=\frac{1000000Q_g}{q_L}
Open analysis
Production EngineeringWell Performance

API RP 14E Gas-Liquid Mixture Density

ρm=12409SLP+2.7RSgP198.7P+RTZ\rho_m=\frac{12409S_LP+2.7RS_gP}{198.7P+RTZ}
Open analysis
Production EngineeringWell Performance

API RP 14E Erosional Velocity

Ve=CρmV_e=\frac{C}{\sqrt{\rho_m}}
Open analysis
Production EngineeringWell Performance

API RP 14E Minimum Flow Area per 1000 Barrels Liquid

A1000=9.35+RTZ21.25PVeA_{1000}=\frac{9.35+\frac{RTZ}{21.25P}}{V_e}
Open analysis
Production EngineeringWell Performance

API RP 14E Required Pipe Inside Diameter

Dmin=4A1000qL1000πD_{min}=\sqrt{\frac{4A_{1000}q_L}{1000\pi}}
Open analysis
Production EngineeringWell Performance

API RP 14E Total Wellstream Weight Flow Rate

W=3180QgSg+14.6qLSLW=3180Q_gS_g+14.6q_LS_L
Open analysis
Production EngineeringWell Performance

API RP 14E Two-Phase Flowline Pressure Drop

ΔP100=0.000336fW2Di5ρm\Delta P_{100}=\frac{0.000336fW^2}{D_i^5\rho_m}
Open analysis
Production EngineeringWell Performance

Wellstream Volumetric Flow Rate from Weight Flow

qv=W3600ρmq_v=\frac{W}{3600\rho_m}
Open analysis
Production EngineeringWell Performance

API RP 14E Actual Mixture Velocity

Vm=4qvπ(Di/12)2V_m=\frac{4q_v}{\pi(D_i/12)^2}
Open analysis
Production EngineeringWell Performance

API RP 14E Erosional Velocity Utilization

Ue=VmVeU_e=\frac{V_m}{V_e}
Open analysis
Production EngineeringWell Performance

API RP 14E Minimum Velocity Ratio

Rmin=VmVminR_{min}=\frac{V_m}{V_{min}}
Open analysis
Production EngineeringWell Performance

Stokes Law Droplet Settling Velocity

Vt=1000gDp2(ρp−ρc)18μcV_t=\frac{1000gD_p^2(\rho_p-\rho_c)}{18\mu_c}
Open analysis
Production EngineeringWell Performance

Separator Droplet Reynolds Number

Rep=1000DpVtρcμcRe_p=\frac{1000D_pV_t\rho_c}{\mu_c}
Open analysis
Production EngineeringWell Performance

Stokes Region Maximum Droplet Diameter

Dp,max=KCR[μc2gρc(ρp−ρc)]1/3D_{p,max}=K_{CR}\left[\frac{\mu_c^2}{g\rho_c(\rho_p-\rho_c)}\right]^{1/3}
Open analysis
Production EngineeringWell Performance

Intermediate Law Droplet Settling Velocity

Vt=2.94g0.71Dp1.14(ρp−ρc)0.71ρc0.29μc0.43V_t=\frac{2.94g^{0.71}D_p^{1.14}(\rho_p-\rho_c)^{0.71}}{\rho_c^{0.29}\mu_c^{0.43}}
Open analysis
Production EngineeringWell Performance

Newton Law Droplet Settling Velocity

Vt=1.74gDp(ρp−ρc)ρcV_t=1.74\sqrt{\frac{gD_p(\rho_p-\rho_c)}{\rho_c}}
Open analysis
Production EngineeringWell Performance

Horizontal Separator Maximum Vapor Velocity from Droplet Settling

Vh,max=LSETVtHSETV_{h,max}=\frac{L_{SET}V_t}{H_{SET}}
Open analysis
Production EngineeringWell Performance

ASME Separator Pressure Criterion - Internal Radius

P=SEtRi+0.6tP=\frac{SEt}{R_i+0.6t}
Open analysis
Production EngineeringWell Performance

ASME Separator Pressure Criterion - External Radius

P=SEtRo−0.4tP=\frac{SEt}{R_o-0.4t}
Open analysis
Production EngineeringWell Performance

ASME Spherical Separator Shell Thickness

t=PR2SE−0.2Pt=\frac{PR}{2SE-0.2P}
Open analysis
Production EngineeringWell Performance

Required Oil Section Length in Separator

Lo=toqoAoL_o=\frac{t_oq_o}{A_o}
Open analysis
Production EngineeringWell Performance

Required Water Section Length in Separator

Lw=twqwAwL_w=\frac{t_wq_w}{A_w}
Open analysis
Production EngineeringWell Performance

Polished Rod Horsepower - Sucker Rod Pump

PRHP=CSNA33000⋅12LPRHP=\frac{CSNA}{33000\cdot12L}
Open analysis
Production EngineeringWell Performance

Range of Load - Sucker Rod Pump

ROL=PPRL−MPRLROL=PPRL-MPRL
Open analysis
Production EngineeringWell Performance

Average Upstroke Load - Sucker Rod Pump

AUL=CAupper+AlowerLAUL=C\frac{A_{upper}+A_{lower}}{L}
Open analysis
Production EngineeringWell Performance

Average Downstroke Load - Sucker Rod Pump

ADL=CAlowerLADL=C\frac{A_{lower}}{L}
Open analysis
Production EngineeringWell Performance

Minimum Polished Rod Load - Sucker Rod Pump

MPRL=CdMPRL=Cd
Open analysis
Production EngineeringWell Performance

Correct Counterbalance - Sucker Rod Pump

CCB=AUL+ADL2CCB=\frac{AUL+ADL}{2}
Open analysis
Production EngineeringWell Performance

Approximate Ideal Counterbalanced Load

AICB=PPRL+MPRL2AICB=\frac{PPRL+MPRL}{2}
Open analysis
Production EngineeringWell Performance

Peak Polished Rod Load - Sucker Rod Pump

PPRL=CDPPRL=CD
Open analysis
Production EngineeringWell Performance

Progressive Cavity Pump Flow Rate

Qe=7.12DEPsN−QsQ_e=7.12DEP_sN-Q_s
Open analysis
Production EngineeringWell Performance

Progressive Cavity Pump Head Rating

ΔP=(2np−1)Δp\Delta P=(2n_p-1)\Delta p
Open analysis
Production EngineeringWell Performance

Entrance Hole Size from Casing Yield Strength

d=(σyrσy)0.5drd=\left(\frac{\sigma_{yr}}{\sigma_y}\right)^{0.5}d_r
Open analysis
Production EngineeringWell Performance

Perforation Hole Size from Brinell Hardness

d=(2250+4.2xr2250+4.2x)0.5drd=\left(\frac{2250+4.2x_r}{2250+4.2x}\right)^{0.5}d_r
Open analysis
Production EngineeringWell Performance

Perforation Friction Pressure

ΔPpf=22.335Q2ρn2C2Dp4\Delta P_{pf}=22.335\frac{Q^2\rho}{n^2C^2D_p^4}
Open analysis
Production EngineeringWell Performance

Perforation Skin Factor

sp=sH+sv+swb+spds_p=s_H+s_v+s_{wb}+s_{pd}
Open analysis
Production EngineeringWell Performance

Skin Factor Due to Reduced Crushed-Zone Permeability

sc=(kkdp−kkd)12hpNLpln⁡(rdprp)s_c=\left(\frac{k}{k_{dp}}-\frac{k}{k_d}\right)12\frac{h_p}{NL_p}\ln\left(\frac{r_{dp}}{r_p}\right)
Open analysis
Production EngineeringWell Performance

Shape Factor Expressed as Skin Factor for Vertical Wells

sCA=ln⁡[(31.62CA)0.5]s_{CA}=\ln\left[\left(\frac{31.62}{C_A}\right)^{0.5}\right]
Open analysis
Production EngineeringWell Performance

Well Flowing Pressure Line-Source Solution by Including Skin Factor

Pwf=Pi+70.6qμBkh[ln⁡(1688ϕμctr2kt)−2S]P_{wf}=P_i+\frac{70.6q\mu B}{kh}\left[\ln\left(\frac{1688\phi\mu c_tr^2}{kt}\right)-2S\right]
Open analysis
Production EngineeringWell Performance

Density of Brine (Completion and Workover Fluids)

ρs=ρm[1+Cte(Tm−Ts)]\rho_s=\rho_m\left[1+C_{te}(T_m-T_s)\right]
Open analysis
Production EngineeringWell Performance

Suspension Property of Static Fluids (Completion and Workover Fluids)

v=d2(ρp−ρf)gμ(4.5×106)v=\frac{d^2(\rho_p-\rho_f)g}{\mu(4.5\times10^6)}
Open analysis
Production EngineeringWell Performance

Workover Operations Maximum Allowed Tubing Pressure

MATP=FGH−PtMATP=FGH-P_t
Open analysis
Production EngineeringWell Performance

Close-Ended Displacement Volume of Pipe

Vc=0.7854Do2L808.5V_c=\frac{0.7854D_o^2L}{808.5}
Open analysis
Production EngineeringWell Performance

Choke Discharge Coefficient

Cd=dcd+0.3167(dc/d)0.6+0.025(log⁡10NR−4)C_d=\frac{d_c}{d}+\frac{0.3167}{(d_c/d)^{0.6}}+0.025\left(\log_{10}N_R-4\right)
Open analysis
Production EngineeringWell Performance

Gas Mass Velocity in Separator

mg=0.785wd2Fgm_g=0.785wd^2F_g
Open analysis
Production EngineeringWell Performance

Gas-Lift Valve Opening Casing Pressure

P1=Pbt−P2(Ap/Ab)1−(Ap/Ab)P_1=\frac{P_{bt}-P_2\left(A_p/A_b\right)}{1-\left(A_p/A_b\right)}
Open analysis
Production EngineeringWell Performance

Perforation Length in Formation

Lp=Lpc−0.5(dwb−dci)L_p=L_{pc}-0.5\left(d_{wb}-d_{ci}\right)
Open analysis
Production EngineeringWell Performance

Incremental Density in Wellbore Interval - Completion and Workover Fluids

Δρi=BgpΔD−AgTΔD\Delta\rho_i=B g_p\Delta D-A g_T\Delta D
Open analysis
Production EngineeringWell Performance

ASME Separator Wall Thickness from Internal Radius

t=PRiSE−0.6Pt=\frac{PR_i}{SE-0.6P}
Open analysis
Production EngineeringWell Performance

ASME Separator Wall Thickness from External Radius

t=PRoSE+0.4Pt=\frac{PR_o}{SE+0.4P}
Open analysis
Production EngineeringWell Performance

Pipe Volume Capacity

V=0.7854Di2L808.5V=\frac{0.7854D_i^2L}{808.5}
Open analysis
Production EngineeringWell Performance

Water Volume to Dilute Brine in Two-Salt Systems

V8.33=Vdρi−ρdρi−ρ8.33V_{8.33}=V_d\frac{\rho_i-\rho_d}{\rho_i-\rho_{8.33}}
Open analysis
Production EngineeringWell Performance

Single-Salt Brine Density Increase Salt Addition Method II

ms=CsfVf−CsiVim_s=C_{sf}V_f-C_{si}V_i
Open analysis
Production EngineeringWell Performance

CaCl2 and CaBr2 Salt Addition for Two-Salt Brine

m95=V8.33C95Wim_{95}=\frac{V_{8.33}C_{95}}{W_i}
Open analysis
Production EngineeringWell Performance

Wellbore Storage Due to Fluid Level

CFL=144Aa5.615ρC_{FL}=\frac{144A_a}{5.615\rho}
Open analysis
Production EngineeringWell Performance

Progressive Cavity Pump Mechanical Resistant Torque

Tm=144VoΔPepT_m=\frac{144V_o\Delta P}{e_p}
Open analysis
Production EngineeringWell Performance

Pressure Drop Across Perforations in Gas Wells

psf=pwb2+A(qgn)+B(qgn)2p_{sf}=\sqrt{p_{wb}^2+A\left(\frac{q_g}{n}\right)+B\left(\frac{q_g}{n}\right)^2}
Open analysis
Production EngineeringWell Performance

Separator Gas Capacity at Standard Conditions

qs=67824Ksd2Fg1zPPsTsT(ρl−ρgρg)0.5q_s=67824K_sd^2F_g\frac{1}{z}\frac{P}{P_s}\frac{T_s}{T}\left(\frac{\rho_l-\rho_g}{\rho_g}\right)^{0.5}
Open analysis
Production EngineeringWell Performance

Gas Separator Internal Diameter from Mass Flow

d=0.0188(mg/(FgKs))0.5((ρl−ρg)/ρg)0.25d=\frac{0.0188\left(m_g/(F_gK_s)\right)^{0.5}}{\left((\rho_l-\rho_g)/\rho_g\right)^{0.25}}
Open analysis
Production EngineeringWell Performance

Liquid-Liquid Vessel Retention Time

Tr=Aμγb−γtT_r=\frac{A\mu}{\gamma_b-\gamma_t}
Open analysis
Production EngineeringWell Performance

Safety Relief Valve Vapor Flow Capacity

w=BCKoAP(MZT)0.5w=BCK_oAP\left(\frac{M}{ZT}\right)^{0.5}
Open analysis
Production EngineeringWell Performance

Refrigeration Outlet Temperature for Gas Conditioning

To=Ti+Ti[(PoPi)m−1]ET_o=T_i+T_i\left[\left(\frac{P_o}{P_i}\right)^m-1\right]E
Open analysis
Production EngineeringWell Performance

TEG Weight Percent in Glycol Dehydration Unit

wtTEG=100mTEGmTEG+wabs+wleanwt_{TEG}=\frac{100m_{TEG}}{m_{TEG}+w_{abs}+w_{lean}}
Open analysis
Production EngineeringWell Performance

Glycol Dehydration Still Column Diameter

d=9.1qgd=9.1\sqrt{q_g}
Open analysis
Production EngineeringWell Performance

Gas Conditioning Stripping Factor

S=KVLS=\frac{KV}{L}
Open analysis
Production EngineeringWell Performance

Gas Conditioning Relative Humidity

RH=PwPsatRH=\frac{P_w}{P_{sat}}
Open analysis
Production EngineeringWell Performance

Fuel Gas Wobbe Index

W=GHVγgW=\frac{GHV}{\sqrt{\gamma_g}}
Open analysis
Production EngineeringWell Performance

Foamless Separator Length-Diameter Correction Factor

K=(L/D5)0.56K=\left(\frac{L/D}{5}\right)^{0.56}
Open analysis
Production EngineeringWell Performance

Gas Pressure Testing Time for Unsteady Gas Flow

tm=3d2LPt_m=\frac{3d^2L}{P}
Open analysis
Production EngineeringWell Performance

Gas Mass Velocity in an Adsorption Unit

w=162vgγgPTzw=\frac{162v_g\gamma_gP}{Tz}
Open analysis
Production EngineeringWell Performance

Adsorption Unit Bed Length from Mass Transfer Zone

hb=0.45hzxsxs−xh_b=\frac{0.45h_zx_s}{x_s-x}
Open analysis
Production EngineeringWell Performance

Adsorption Unit Mass Transfer Zone Length

hz=375q0.7895vg0.5506RS0.2646h_z=\frac{375q^{0.7895}}{v_g^{0.5506}RS^{0.2646}}
Open analysis
Production EngineeringWell Performance

Packed Column Actual Height

h=HTU NTUh=HTU\,NTU
Open analysis
Production EngineeringWell Performance

Raoult's Law Water Fraction in Glycol Dehydration

xw=PPvywx_w=\frac{P}{P_v}y_w
Open analysis
Production EngineeringWell Performance

Velocity of Fluid in Pipe

vp=Q2.448Di2v_p=\frac{Q}{2.448D_i^2}
Open analysis
Production EngineeringWell Performance

Pseudo-Skin Factor Due to Partial Penetration - Papatzacos Correlation

sp=1−bbln⁡(πhd2)+1bln⁡[bb+2Ap−1Bp−1]s_p=\frac{1-b}{b}\ln\left(\frac{\pi h_d}{2}\right)+\frac{1}{b}\ln\left[\frac{b}{b+2}\sqrt{\frac{A_p-1}{B_p-1}}\right]
Open analysis
Production EngineeringWell Performance

Skin Factor for a Deviated Well

sθ=−(θw41)2.06−(θw56)1.865log⁡10(hd100)s_\theta=-\left(\frac{\theta_w}{41}\right)^{2.06}-\left(\frac{\theta_w}{56}\right)^{1.865}\log_{10}\left(\frac{h_d}{100}\right)
Open analysis
Production EngineeringWell Performance

Total Skin in Partially Depleted Wells for a Buildup Test

S=34.7rewϕμctk[ps−pwm+1Δt]−1S=34.7r_{ew}\sqrt{\frac{\phi\mu c_t}{k}}\left[\frac{p_s-p_w}{m}+\frac{1}{\sqrt{\Delta t}}\right]-1
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Pseudo-Reduced Conditions

Pr=P(PcAPcB)0.5P_r = \frac{P}{(P_{cA}P_{cB})^{0.5}}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Sutton Pseudo-Critical Gas Properties

Tpc=169.2+349.5γg−74.0γg2T_{pc}=169.2+349.5\gamma_g-74.0\gamma_g^2
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Pseudo-Reduced Gas Properties from Critical Properties

Ppr=PPpcP_{pr}=\frac{P}{P_{pc}}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Papay Gas Z-Factor Correlation

z=1−3.53Ppr100.9813Tpr+0.274Ppr2100.8157Tprz=1-\frac{3.53P_{pr}}{10^{0.9813T_{pr}}}+\frac{0.274P_{pr}^2}{10^{0.8157T_{pr}}}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Beggs-Brill Gas Z-Factor Correlation

z=A+(1−A)e−B+CPprDz=A+(1-A)e^{-B}+CP_{pr}^{D}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Generalized Virial Gas Z-Factor Correlation

z=1+(B0+ωB1)PprTprz=1+\frac{(B^0+\omega B^1)P_{pr}}{T_{pr}}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Gas Molecular Weight from Specific Gravity

Mg=28.967γgM_g=28.967\gamma_g
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Real Gas Density

ρg=PMgzRT\rho_g=\frac{P M_g}{zRT}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Real Gas Isothermal Compressibility with Z-Factor Derivative

cg=1P−1z(dzdP)Tc_g=\frac{1}{P}-\frac{1}{z}\left(\frac{dz}{dP}\right)_T
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Real Gas Pseudopressure Derivative

dmdp=2pμgz\frac{dm}{dp}=\frac{2p}{\mu_g z}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Real Gas Pseudopressure Difference for Constant Mu-Z

Δm=p22−p12μgz\Delta m=\frac{p_2^2-p_1^2}{\mu_g z}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Real Gas Pseudopressure Trapezoidal Increment

Δm=12(D1+D2)(p2−p1)\Delta m=\frac{1}{2}(D_1+D_2)(p_2-p_1)
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Lee-Gonzalez-Eakin Gas Viscosity

μg=10−4Kexp⁡(XρgY)\mu_g=10^{-4}K\exp(X\rho_g^Y)
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Standing Dry Gas Pseudo-Critical Properties

Tpc=168+325γg−12.5γg2T_{pc}=168+325\gamma_g-12.5\gamma_g^2
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Standing Wet Gas Pseudo-Critical Properties

Tpc=187+330γg−71.5γg2T_{pc}=187+330\gamma_g-71.5\gamma_g^2
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Kay Mixing Rule Gas Pseudo-Critical Properties

Tpc=∑iyiTciT_{pc}=\sum_i y_iT_{ci}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Wichert-Aziz Sour Gas Pseudo-Critical Correction

Tpc′=Tpc∗−ϵT'_{pc}=T^*_{pc}-\epsilon
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Corrected Sour Gas Pseudo-Reduced Properties

Ppr′=PPpc′P'_{pr}=\frac{P}{P'_{pc}}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Specific Gravity of Gas Hydrate Forming Components

Γh=mh28.96\Gamma_h=\frac{m_h}{28.96}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Gas Hydrate Dissociation Pressure

ph=0.1450377exp⁡([2.50744×10−3(γh+0.46852)3+1.214644×10−2Fm−4.676111×10−4Fm2+0.0720122]T+3.6625×10−4(γh−0.485054)3−5.44376Fm+3.89×10−3Fm2−29.9351)p_h=0.1450377\exp\left(\left[\frac{2.50744\times10^{-3}}{(\gamma_h+0.46852)^3}+1.214644\times10^{-2}F_m-4.676111\times10^{-4}F_m^2+0.0720122\right]T+\frac{3.6625\times10^{-4}}{(\gamma_h-0.485054)^3}-5.44376F_m+3.89\times10^{-3}F_m^2-29.9351\right)
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Water Content of Sour Gas

W=yWhc+yCO2WCO2+yH2SWH2SW=yW_{hc}+y_{CO2}W_{CO2}+y_{H2S}W_{H2S}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Necessary Inhibitor Concentration Required in Liquid Phase to Reduce Hydrate Point

X=100dMdM+2335X=\frac{100dM}{dM+2335}
Open analysis
Phase Behavior and ThermodynamicsGas Properties

Hydrate Formation Temperature from Modified Clapeyron Criterion

Th=3.89Ch0.5T_h=3.89C_h^{0.5}
Open analysis
PetrophysicsRock Properties

Total Porosity from Pore Volumes

ϕ=Vi+VdVb\phi = \frac{V_i + V_d}{V_b}
Open analysis
PetrophysicsRock Properties

Liquid Permeability - Permeameter Lab Measurement

k=μVLAPtk = \frac{\mu V L}{A P t}
Open analysis
PetrophysicsRock Properties

Raymer-Hunt Transform - Porosity Transit Time Relationship

Δt=((1−ϕ)2Δtma+ϕΔtf)−1\Delta t=\left(\frac{(1-\phi)^2}{\Delta t_{ma}}+\frac{\phi}{\Delta t_f}\right)^{-1}
Open analysis
PetrophysicsRock Properties

Error Percentage of Porosity Measurements

Eϕ=ϕm−ϕpsϕm100E_\phi=\frac{\phi_m-\phi_{ps}}{\phi_m}100
Open analysis
PetrophysicsRock Properties

Acoustic Transit Time

Δt=106v\Delta t=\frac{10^6}{v}
Open analysis
PetrophysicsRock Properties

Gamma Ray Log Shale Index

IGR=GR−GRclGRsh−GRclI_{GR}=\frac{GR-GR_{cl}}{GR_{sh}-GR_{cl}}
Open analysis
PetrophysicsRock Properties

Fraction of Total Porosity Occupied by Clays

q=ΦS−ΦDΦSq=\frac{\Phi_S-\Phi_D}{\Phi_S}
Open analysis
PetrophysicsRock Properties

Fresh Water-Filled Porosity - Limestones

Φ=ρls−ρbρls−ρw\Phi=\frac{\rho_{ls}-\rho_b}{\rho_{ls}-\rho_w}
Open analysis
PetrophysicsRock Properties

Density Log Porosity from Bulk Density

Φ=ρma−ρbρma−ρf\Phi=\frac{\rho_{ma}-\rho_b}{\rho_{ma}-\rho_f}
Open analysis
PetrophysicsRock Properties

Gas-Effect Corrected Porosity from Neutron-Density Logs

Φcorr=(ΦD2+ΦN22)0.5\Phi_{corr}=\left(\frac{\Phi_D^2+\Phi_N^2}{2}\right)^{0.5}
Open analysis
PetrophysicsRock Properties

Neutron Porosity in a Shaly Formation

ΦN=ΦT+VshΦNsh\Phi_N=\Phi_T+V_{sh}\Phi_{Nsh}
Open analysis
PetrophysicsRock Properties

Wyllie Time-Average Sonic Porosity - Compacted Formations

Φs=Δt−ΔtmaΔtf−Δtma\Phi_s=\frac{\Delta t-\Delta t_{ma}}{\Delta t_f-\Delta t_{ma}}
Open analysis
PetrophysicsRock Properties

Sonic Compaction Correction Factor from Shale Transit Time

Cp=Δtshc100C_p=\Delta t_{sh}\frac{c}{100}
Open analysis
PetrophysicsRock Properties

Wyllie Time-Average Sonic Porosity - Uncompacted Formations

Φs=(Δt−Δtma)/(Δtf−Δtma)Bcp\Phi_s=\frac{(\Delta t-\Delta t_{ma})/(\Delta t_f-\Delta t_{ma})}{B_{cp}}
Open analysis
PetrophysicsRock Properties

True Sonic Porosity from Compaction Correction

Φt=ΦaCp\Phi_t=\frac{\Phi_a}{C_p}
Open analysis
PetrophysicsRock Properties

Larionov Older-Rock Shale Volume from Gamma Ray Index

Vsh=0.33(22IGR−1)V_{sh}=0.33\left(2^{2I_{GR}}-1\right)
Open analysis
PetrophysicsRock Properties

Larionov Tertiary-Rock Shale Volume from Gamma Ray Index

Vsh=0.083(23.7IGR−1)V_{sh}=0.083\left(2^{3.7I_{GR}}-1\right)
Open analysis
PetrophysicsRock Properties

Stieber Shale Volume from Gamma Ray Index

Vsh=IGR3−2IGRV_{sh}=\frac{I_{GR}}{3-2I_{GR}}
Open analysis
PetrophysicsRock Properties

Clavier Shale Volume from Gamma Ray Index

Vsh=1.7−3.38−(IGR+0.7)2V_{sh}=1.7-\sqrt{3.38-(I_{GR}+0.7)^2}
Open analysis
PetrophysicsRock Properties

Effective Photoelectric Absorption Cross Section Index

Pe=(Z10)3.6P_e=\left(\frac{Z}{10}\right)^{3.6}
Open analysis
PetrophysicsRock Properties

Electron Density Index for Gamma-Gamma Absorption Logging

ρe=2NeNA\rho_e=\frac{2N_e}{N_A}
Open analysis
PetrophysicsRock Properties

Contact Angle from Interfacial Tensions

θ=cos⁡−1(σso−σswσwo)\theta=\cos^{-1}\left(\frac{\sigma_{so}-\sigma_{sw}}{\sigma_{wo}}\right)
Open analysis
PetrophysicsRock Properties

Adhesion Tension from Water-Oil Interfacial Tension

τ=σwocos⁡θ\tau=\sigma_{wo}\cos\theta
Open analysis
PetrophysicsRock Properties

Volumetric Photoelectric Absorption Cross Section

U=PeρeU=P_e\rho_e
Open analysis
PetrophysicsRock Properties

Linear Absorption Attenuation Coefficient

αl=σN\alpha_l=\sigma N
Open analysis
PetrophysicsRock Properties

Mean Free Path Photon Absorption

h=1αlh=\frac{1}{\alpha_l}
Open analysis
PetrophysicsRock Properties

Half Thickness Value

h1/2=0.693αlh_{1/2}=\frac{0.693}{\alpha_l}
Open analysis
PetrophysicsRock Properties

Photoelectric Absorption Cross Sectional Area

αpe=12.1Z3.6Eγ3.15\alpha_{pe}=\frac{12.1Z^{3.6}}{E_\gamma^{3.15}}
Open analysis
PetrophysicsRock Properties

Composite Capture Cross Section of the Formation Schlumberger Thermal Decay Time Tool

Σ=4.55τ\Sigma=\frac{4.55}{\tau}
Open analysis
PetrophysicsRock Properties

Atlas Wireline Neutron Lifetime Log

Σ=3.15τ\Sigma=\frac{3.15}{\tau}
Open analysis
PetrophysicsRock Properties

Epithermal Neutron Diffusion Coefficient

De=ξLe2ΣeD_e=\xi L_e^2\Sigma_e
Open analysis
PetrophysicsRock Properties

Neutron Lethargy Logarithmic Energy Decrement

u=ln⁡(EoE)u=\ln\left(\frac{E_o}{E}\right)
Open analysis
PetrophysicsRock Properties

Rate of Radioactive Decay

N=Noe−CdtN=N_o e^{-C_d t}
Open analysis
PetrophysicsRock Properties

Relation Between Concentration of K Th or U and Recorded Total Gamma Ray Signal

γ=4CTh+8CU+CK\gamma=4C_{Th}+8C_U+C_K
Open analysis
PetrophysicsRock Properties

Amplitude Transmission Coefficient in Seismic Reflection and Refraction

T=2Z1Z2+Z1T=\frac{2Z_1}{Z_2+Z_1}
Open analysis
PetrophysicsRock Properties

Poissons Ratio Seismic Arrival Time Method

ν=Vp2−2Vs22(Vp2−Vs2)\nu=\frac{V_p^2-2V_s^2}{2\left(V_p^2-V_s^2\right)}
Open analysis
PetrophysicsRock Properties

Spacing Between Transmitter and Receiver

(Ls)c=2soff1+Cmf1−Cmf(L_s)_c=2s_{off}\sqrt{\frac{1+C_{mf}}{1-C_{mf}}}
Open analysis
PetrophysicsRock Properties

Integrated Radial Geometric Factor

G(r)=1−e−r/hˉG(r)=1-e^{-r/\bar{h}}
Open analysis
PetrophysicsRock Properties

Pair Production Gamma Ray Interactions

Ee=Ec−EE_e=E_c-E
Open analysis
PetrophysicsRock Properties

Wavelength Equation

λ=Cf\lambda=\frac{C}{f}
Open analysis
PetrophysicsRock Properties

Epithermal Neutron Flux Distribution

ψe=NN4πDee−r/Ler\psi_e=\frac{N_N}{4\pi D_e}\frac{e^{-r/L_e}}{r}
Open analysis
PetrophysicsRock Properties

Apparent Gamma Ray Recorder Intensity

Ja(t)=J1+(J2−J1)(1−e−t/rc)J_a(t)=J_1+(J_2-J_1)(1-e^{-t/r_c})
Open analysis
PetrophysicsRock Properties

Porosity from Neutron Flux Response

ϕ=α−βlog⁡10(N)\phi=\alpha-\beta\log_{10}(N)
Open analysis
PetrophysicsRock Properties

Amott-Harvey Wettability Index

IAH=Iw−IoI_{AH}=I_w-I_o
Open analysis
PetrophysicsRock Properties

USBM Wettability Index

IU=log⁡10(A1A2)I_U=\log_{10}\left(\frac{A_1}{A_2}\right)
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PetrophysicsRock Properties

Reservoir Wettability Characterization Rise-in-Core Method

cos⁡θ12=μ1ρ22−μ2ρ12ρ12ρ22CγL2L1m2t\cos\theta_{12}=\frac{\mu_1\rho_2^2-\mu_2\rho_1^2}{\rho_1^2\rho_2^2C\gamma_{L2L1}}\frac{m^2}{t}
Open analysis
PetrophysicsRock Properties

Pycnometer Volume Correction

Vg=Vk[1+Ω(Tt−Tk)]V_g=V_k\left[1+\Omega(T_t-T_k)\right]
Open analysis
PetrophysicsRock Properties

Apparent Interfacial Tension - de Nouy Ring Method

S=mg2lS=\frac{mg}{2l}
Open analysis
PetrophysicsRock Properties

de Nouy Ring Interfacial Tension Correction Factor

C=0.7250+0.01452Sl2(ρD−ρd)+0.04534−1.679rRC=0.7250+\sqrt{\frac{0.01452S}{l^2(\rho_D-\rho_d)}+0.04534-\frac{1.679r}{R}}
Open analysis
PetrophysicsRock Properties

Corrected Interfacial Tension - de Nouy Ring Method

σ=SC\sigma=SC
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PetrophysicsRock Properties

Air Density for de Nouy Upper Phase Correction

ρair=4.324×10−2PT\rho_{air}=4.324\times10^{-2}\frac{P}{T}
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PetrophysicsRock Properties

Relative Centrifugal Force

RCF=(RPM265)2dRCF=\left(\frac{RPM}{265}\right)^2d
Open analysis
PetrophysicsRock Properties

Shale Index from Gamma Ray Spectrometry - Thorium

Ish,Th=CTh,log−CTh,minCTh,sh−CTh,minI_{sh,Th}=\frac{C_{Th,log}-C_{Th,min}}{C_{Th,sh}-C_{Th,min}}
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PetrophysicsRock Properties

Shale Index from Gamma Ray Spectrometry - Potassium

Ish,K=CK,log−CK,minCK,sh−CK,minI_{sh,K}=\frac{C_{K,log}-C_{K,min}}{C_{K,sh}-C_{K,min}}
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PetrophysicsRock Properties

Shale Index from Gamma Ray Spectrometry - Uranium-Free Gamma

Ish,Uf=GUf,log−GUf,minGUf,sh−GUf,minI_{sh,Uf}=\frac{G_{Uf,log}-G_{Uf,min}}{G_{Uf,sh}-G_{Uf,min}}
Open analysis
PetrophysicsRock Properties

Sonic Porosity Raymer-Hunt-Gardner Method

Φsonic=CRHGΔt−ΔtmaΔt\Phi_{sonic}=C_{RHG}\frac{\Delta t-\Delta t_{ma}}{\Delta t}
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PetrophysicsRock Properties

Sonic First-Arrival Time in a Borehole

tlog=Lsvf+dh−(dt+2lc)vm1−(vmvf)2t_{log}=\frac{L_s}{v_f}+\frac{d_h-(d_t+2l_c)}{v_m}\sqrt{1-\left(\frac{v_m}{v_f}\right)^2}
Open analysis
PetrophysicsRock Properties

Slowness of the Formation

Δt=tlLs−DbΔtm2(Ls2+Db2)−tl2Ls2+Db2\Delta t=\frac{t_lL_s-D_b\sqrt{\Delta t_m^2(L_s^2+D_b^2)-t_l^2}}{L_s^2+D_b^2}
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PetrophysicsRock Properties

NMR Free-Fluid Index from Porosity Partition

FFI=MPHI−BVI\mathrm{FFI}=\mathrm{MPHI}-\mathrm{BVI}
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PetrophysicsRock Properties

Coates NMR Permeability from Free-Fluid Ratio

k=(ϕNMRC)4(FFIBVI)2k=\left(\frac{\phi_{NMR}}{C}\right)^4\left(\frac{\mathrm{FFI}}{\mathrm{BVI}}\right)^2
Open analysis
PetrophysicsRock Properties

SDR NMR Permeability from T2 Geometric Mean

k=aϕNMR4T2gm2k=a\phi_{NMR}^4T_{2gm}^2
Open analysis
PetrophysicsResistivity Logs

Archie Water Saturation from Resistivity Logs

Sw=[(aϕm)(RwRt)]1/nS_w = \left[\left(\frac{a}{\phi^m}\right)\left(\frac{R_w}{R_t}\right)\right]^{1/n}
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PetrophysicsResistivity Logs

Formation Factor - Archie's Equation

F=TϕF = \frac{T}{\phi}
Open analysis
PetrophysicsResistivity Logs

Formation Resistivity and Permeability - Carothers Limestones

k=4×108F3.65k=\frac{4\times10^8}{F^{3.65}}
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PetrophysicsResistivity Logs

Formation Resistivity and Permeability - Carothers Sandstones

k=7×108F4.5k=\frac{7\times10^8}{F^{4.5}}
Open analysis
PetrophysicsResistivity Logs

Resistivity Index - Archie's Law

RI=RtRoRI=\frac{R_t}{R_o}
Open analysis
PetrophysicsResistivity Logs

Humble Formation Factor from Porosity

F=0.62ϕ2.15F=\frac{0.62}{\phi^{2.15}}
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PetrophysicsResistivity Logs

Chevron Formation Factor from Porosity

F=1.13ϕ1.73F=\frac{1.13}{\phi^{1.73}}
Open analysis
PetrophysicsResistivity Logs

Porter-Carothers Formation Factor - California Pliocene Logs

Fg=2.45ϕ1.08F_g=\frac{2.45}{\phi^{1.08}}
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PetrophysicsResistivity Logs

Porter-Carothers Formation Factor - Gulf Coast Miocene Logs

Fc=1.97ϕ1.29F_c=\frac{1.97}{\phi^{1.29}}
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PetrophysicsResistivity Logs

Tortuosity from Resistivity Log Path Lengths

T=La2L2T=\frac{L_a^2}{L^2}
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PetrophysicsResistivity Logs

Phillips Formation Factor - Average Sands

F=1.45ϕ1.54F=\frac{1.45}{\phi^{1.54}}
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PetrophysicsResistivity Logs

Carothers Formation Factor - Shaly Sands

F=1.65ϕ1.33F=\frac{1.65}{\phi^{1.33}}
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PetrophysicsResistivity Logs

Carothers Formation Factor - Calcareous Sands

F=1.45ϕ1.70F=\frac{1.45}{\phi^{1.70}}
Open analysis
PetrophysicsResistivity Logs

Chalky Carbonate Formation Factor from Porosity

Fc=1ϕ2F_c=\frac{1}{\phi^2}
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PetrophysicsResistivity Logs

Compacted Carbonate Formation Factor from Porosity

FcO=1ϕaF_{cO}=\frac{1}{\phi^a}
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PetrophysicsResistivity Logs

Shell Formation Factor - Low-Porosity Carbonates

Fl=1ϕ1.87+0.019/ϕF_l=\frac{1}{\phi^{1.87+0.019/\phi}}
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PetrophysicsResistivity Logs

Sethi Formation Factor - Clean Granular Formations

F=1ϕ2.05−ϕF=\frac{1}{\phi^{2.05-\phi}}
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PetrophysicsResistivity Logs

Simandoux Water Saturation from Shaly Sand Logs

Sw=−VshRsh+(VshRsh)2+4FRw(1−Vsh)Rt2FRw(1−Vsh)S_w=\frac{-\frac{V_{sh}}{R_{sh}}+\sqrt{\left(\frac{V_{sh}}{R_{sh}}\right)^2+\frac{4}{F R_w (1-V_{sh}) R_t}}}{\frac{2}{F R_w (1-V_{sh})}}
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PetrophysicsResistivity Logs

Indonesian Water Saturation from Shaly Sand Logs

Sw=[1/RtVsh1−0.5VshRsh+ϕemaRw]2/nS_w=\left[\frac{\sqrt{1/R_t}}{\frac{V_{sh}^{1-0.5V_{sh}}}{\sqrt{R_{sh}}}+\sqrt{\frac{\phi_e^m}{aR_w}}}\right]^{2/n}
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PetrophysicsResistivity Logs

Arps Formation Water Resistivity Temperature Correction

Rw2=Rw1T1F+6.77T2F+6.77R_{w2}=R_{w1}\frac{T_{1F}+6.77}{T_{2F}+6.77}
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PetrophysicsResistivity Logs

Equivalent Formation Water Resistivity from SP

Rwe=Rmfe10−SSP/K,K=61+0.133TFR_{we}=\frac{R_{mfe}}{10^{-SSP/K}},\quad K=61+0.133T_F
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PetrophysicsResistivity Logs

Mud Filtrate Resistivity from Mud Resistivity

Rmf=KmRm1.07R_{mf}=K_mR_m^{1.07}
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PetrophysicsResistivity Logs

Mud Cake Resistivity from Mud and Filtrate Resistivity

Rmc=0.69Rmf(RmRmf)2.65R_{mc}=0.69R_{mf}\left(\frac{R_m}{R_{mf}}\right)^{2.65}
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PetrophysicsResistivity Logs

Water Saturation from Neutron Capture Cross Section

Sw=(Σlog−Σma)−ϕ(Σh−Σma)ϕ(Σw−Σh)S_w=\frac{(\Sigma_{log}-\Sigma_{ma})-\phi(\Sigma_h-\Sigma_{ma})}{\phi(\Sigma_w-\Sigma_h)}
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PetrophysicsResistivity Logs

Water-Saturated Shaly Sand Resistivity Vsh Model

Ro=1Vsh/Rsh+1/(FRw)R_o=\frac{1}{V_{sh}/R_{sh}+1/(FR_w)}
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PetrophysicsResistivity Logs

Partially Saturated Shaly Sand Resistivity Vsh Model

Rt=1(Vsh/Rsh)Sw+(1/F)Sw2/RwR_t=\frac{1}{(V_{sh}/R_{sh})S_w+(1/F)S_w^2/R_w}
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PetrophysicsResistivity Logs

Archie Flushed-Zone Water Saturation from Shallow Resistivity

Sxo=(aRmfϕmRxo)1/nS_{xo}=\left(\frac{aR_{mf}}{\phi^mR_{xo}}\right)^{1/n}
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PetrophysicsResistivity Logs

Flushed-Zone Water Saturation from Formation Factor

Sxo=(FRmfRxo)1/nS_{xo}=\left(\frac{FR_{mf}}{R_{xo}}\right)^{1/n}
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PetrophysicsResistivity Logs

Movable Hydrocarbon Saturation from Flushed Zone

Shm=Sxo−SwS_{hm}=S_{xo}-S_w
Open analysis
PetrophysicsResistivity Logs

Residual Hydrocarbon Saturation from Flushed Zone

Shr=1−SxoS_{hr}=1-S_{xo}
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PetrophysicsResistivity Logs

Bulk Volume Water from Porosity and Water Saturation

BVW=ϕSwBVW=\phi S_w
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PetrophysicsResistivity Logs

Oil Saturation from IE and CDN Resistivity Logs

So=1−RoRtS_o=1-\sqrt{\frac{R_o}{R_t}}
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PetrophysicsResistivity Logs

Hingle Crossplot True Resistivity

Rt=[ϕ(SwnaRw)1/m]−mR_t=\left[\phi\left(\frac{S_w^n}{aR_w}\right)^{1/m}\right]^{-m}
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PetrophysicsResistivity Logs

Pickett Crossplot Log True Resistivity

log⁡10Rt=−mlog⁡10(ϕ)+log⁡10(Rw)−nlog⁡10(Sw)\log_{10}R_t=-m\log_{10}(\phi)+\log_{10}(R_w)-n\log_{10}(S_w)
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PetrophysicsResistivity Logs

Fertl-Hammack Shaly Sand Water Saturation

Sw=(FRwRt)0.5−VshRw0.4ϕeRshS_w=\left(\frac{FR_w}{R_t}\right)^{0.5}-\frac{V_{sh}R_w}{0.4\phi_eR_{sh}}
Open analysis
PetrophysicsResistivity Logs

Water Salinity Index Ratio

Sw=CaCS_w=\frac{C_a}{C}
Open analysis
PetrophysicsResistivity Logs

Flushed-Zone Apparent Formation Factor from Apparent Saturation

Fxo=FsSxo2F_{xo}=\frac{F_s}{S_{xo}^2}
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PetrophysicsResistivity Logs

Simandoux Total Shale Equation

Sw=0.4Rwϕe2[−VshRsh+(VshRsh)2+5ϕe2RwRt]S_w=\frac{0.4R_w}{\phi_e^2}\left[-\frac{V_{sh}}{R_{sh}}+\sqrt{\left(\frac{V_{sh}}{R_{sh}}\right)^2+\frac{5\phi_e^2}{R_wR_t}}\right]
Open analysis
PetrophysicsResistivity Logs

Water Saturation from IE and CDN Resistivity Logs

Sw=RoRtS_w=\sqrt{\frac{R_o}{R_t}}
Open analysis
Production EngineeringHydraulic Fracturing

Equivalent Skin Factor in Fractured Wells

Sf=0.7−ln⁡(xfrw)S_f = 0.7 - \ln\left(\frac{x_f}{r_w}\right)
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Production EngineeringHydraulic Fracturing

Annulus Pressure Loss Due to Friction - Turbulent Flow

ΔPf=fLρv225.80(d0−di)\Delta P_f = \frac{f L \rho v^2}{25.80(d_0 - d_i)}
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Production EngineeringHydraulic Fracturing

Annulus Pressure Loss Due to Friction During Hydraulic Fracturing - Laminar Flow

ΔPf=μpLv1000(d0−di)2+τyL200(d0−di)\Delta P_f=\frac{\mu_pLv}{1000(d_0-d_i)^2}+\frac{\tau_yL}{200(d_0-d_i)}
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Maximum Treatment Pressure - Hydraulic Fracturing

Psi=Pb−ΔPh+ΔPfP_{si} = P_b - \Delta P_h + \Delta P_f
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Production EngineeringHydraulic Fracturing

Fracture Width - Perkins and Kern Method

Wmax=0.389((1−ν2)QμLE)0.25W_{max}=0.389\left(\frac{(1-\nu^2)Q\mu L}{E}\right)^{0.25}
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Production EngineeringHydraulic Fracturing

Flow Through Fracture in Response to Pressure Gradient

Q=πΔP8μ(L(1−ν2)(Pf−Sc)E)3Q=\frac{\pi\Delta P}{8\mu}\left(\frac{L(1-\nu^2)(P_f-S_c)}{E}\right)^3
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Production EngineeringHydraulic Fracturing

Principal Stress Due to Petro-Static Pressure - Hydraulic Fracturing

σz=γh10\sigma_z=\frac{\gamma h}{10}
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Production EngineeringHydraulic Fracturing

Ideal Fracture Conductivity Created by Acid Reaction

wa=Xit2xLh(1−ϕ)w_a=\frac{Xit}{2x_Lh(1-\phi)}
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Production EngineeringHydraulic Fracturing

Hydraulic Horsepower for Hydraulic Fracturing Operation

Hh=0.0245PinjqtH_h=0.0245P_{inj}q_t
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Production EngineeringHydraulic Fracturing

Pressure Loss Due to Perforations During Hydraulic Fracturing

ΔPp=ρq28090A22\Delta P_p=\frac{\rho q^2}{8090A_2^2}
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Production EngineeringHydraulic Fracturing

Carter Leakoff Volume for Hydraulic Fracturing

VL=AL(2CLt+Sp)V_L=A_L\left(2C_L\sqrt{t}+S_p\right)
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Net Fracture Pressure from Fracture and Closure Pressure

Pnet=Pfrac−SclosureP_{net}=P_{frac}-S_{closure}
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Fracture Conductivity from Proppant Permeability and Width

FC=kfwfF_C=k_fw_f
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Fracture Volume - GDK Method

Vf=0.03561(μQL6H3G)0.25V_f=0.03561\left(\frac{\mu QL^6H^3}{G}\right)^{0.25}
Open analysis
Production EngineeringHydraulic Fracturing

Fracture Volume - Perkins and Kern Method

Vf=0.04H((1−ν2)μQE)0.25L5/4V_f=0.04H\left(\frac{(1-\nu^2)\mu Q}{E}\right)^{0.25}L^{5/4}
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Production EngineeringHydraulic Fracturing

Fracture Width - GDK Method

w=0.272(μQL2GH)0.25w=0.272\left(\frac{\mu QL^2}{GH}\right)^{0.25}
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Production EngineeringHydraulic Fracturing

Proppant Settlement Drag Coefficient in Fracture

CD=4(ρp−ρf)gdpρfvt2C_D=\frac{4(\rho_p-\rho_f)gd_p}{\rho_fv_t^2}
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Production EngineeringHydraulic Fracturing

Sand Weight to Refill Hydraulically Fractured Reservoir Volume

S=V(1−ϕ)ρsandS=V(1-\phi)\rho_{sand}
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Production EngineeringHydraulic Fracturing

Average Fracture Width - Acidizing

wˉ=πww4\bar{w}=\frac{\pi w_w}{4}
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Fracture-Fluid Invasion Velocity - Acidizing

vN=0.0374kϕΔPvμtv_N=0.0374\sqrt{\frac{k\phi\Delta P_v}{\mu t}}
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Production EngineeringHydraulic Fracturing

Fracture Coefficient of Hydraulically Fractured Reservoir

Cf=0.0164mAfC_f=\frac{0.0164m}{A_f}
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Production EngineeringHydraulic Fracturing

Capacity Ratio of Hydraulically Fractured Surface

cf=kfWkhc_f=\frac{k_fW}{kh}
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Average Permeability of Hydraulically Fractured Formation

kavg=kkavgzln⁡(re/rw)kavgzln⁡(re/rf)+kln⁡(rf/rw)k_{avg}=\frac{kk_{avgz}\ln(r_e/r_w)}{k_{avgz}\ln(r_e/r_f)+k\ln(r_f/r_w)}
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Productivity Ratio of Hydraulically Fractured Formation

PRf=(kfWkh)(khkfW+1)ln⁡(re/rw)(kfWkh+1)ln⁡(re/rf)+ln⁡(rf/rw)PR_f=\left(\frac{k_fW}{kh}\right)\frac{\left(\frac{kh}{k_fW}+1\right)\ln(r_e/r_w)}{\left(\frac{k_fW}{kh}+1\right)\ln(r_e/r_f)+\ln(r_f/r_w)}
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Production EngineeringHydraulic Fracturing

Fracture Fluid Coefficient - Reservoir-Controlled Liquids

Cr=cΔPkcfϕμC_r=c\Delta P\sqrt{\frac{kc_f\phi}{\mu}}
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Production EngineeringHydraulic Fracturing

Fracture Fluid Coefficient - Viscosity-Controlled Liquids

Cv=ckΔPϕμfC_v=c\sqrt{\frac{k\Delta P\phi}{\mu_f}}
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Production EngineeringHydraulic Fracturing

Dynamic-Test Fluid Loss per Unit Area - Acidizing

V=Vspt+vNtV=V_{spt}+v_Nt
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Production EngineeringHydraulic Fracturing

Static-Test Fluid Loss per Unit Area - Acidizing

V=Vspt+2CwtV=V_{spt}+2C_w\sqrt{t}
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Production EngineeringHydraulic Fracturing

Filter-Cake Fluid-Loss Velocity - Acidizing

vN=Cwtv_N=\frac{C_w}{\sqrt{t}}
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Production EngineeringHydraulic Fracturing

Peclet Number for Fluid Loss - Acidizing

NPe=wˉvˉN2De∞N_{Pe}=\frac{\bar{w}\bar{v}_N}{2D_e^{\infty}}
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Production EngineeringHydraulic Fracturing

Acid Penetration Distance - Acidizing

xL=wˉLaD2(NReNRe∗)x_L=\frac{\bar{w}L_{aD}}{2}\left(\frac{N_{Re}}{N_{Re}^{*}}\right)
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Reynolds Number for Acid Flow into the Fracture - Acidizing

NRe=ρiμhgN_{Re}=\frac{\rho i}{\mu h_g}
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Production EngineeringHydraulic Fracturing

Fracture Fluid-Loss Reynolds Number - Acidizing

NRe∗=2wˉvˉNρμN_{Re}^{*}=\frac{2\bar{w}\bar{v}_N\rho}{\mu}
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Production EngineeringHydraulic Fracturing

Wormhole Fluid-Loss Reynolds Number - Acidizing

NRe∗=2rcvˉNρμN_{Re}^{*}=\frac{2r_c\bar{v}_N\rho}{\mu}
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Production EngineeringHydraulic Fracturing

Acid Dissolving Power for 15 Percent HCl - Acidizing

X15=ρ15%HClβ15%HClρCaCO3X_{15}=\frac{\rho_{15\%HCl}\beta_{15\%HCl}}{\rho_{CaCO_3}}
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Production EngineeringHydraulic Fracturing

Treatment Fracture Gradient - Hydraulic Fracturing

Gf=Pinj+ΔPh−ΔPf−ΔPpDG_f=\frac{P_{inj}+\Delta P_h-\Delta P_f-\Delta P_p}{D}
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Production EngineeringHydraulic Fracturing

Wellbore Pressure Loss Due to Friction - Turbulent Flow

ΔPwb=fLρv225.80d\Delta P_{wb}=\frac{fL\rho v^2}{25.80d}
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Production EngineeringHydraulic Fracturing

Downhole Operating Pressure - Hydraulic Fracturing

PF=GfDP_F=G_fD
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Injection Pressure for Hydraulic Fracturing

Pinj=PF+ΔPf+ΔPp−ΔPhP_{inj}=P_F+\Delta P_f+\Delta P_p-\Delta P_h
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Wellbore Fracture Width - Acidizing

Ww=L(μqhEL2)0.25W_w=L\left(\frac{\mu q_h}{EL^2}\right)^{0.25}
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Production EngineeringHydraulic Fracturing

Average Specific Weight of Formation - Hydraulic Fracturing

γformation=(1−ϕ)γmin+ϕγliq\gamma_{formation}=(1-\phi)\gamma_{min}+\phi\gamma_{liq}
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Production EngineeringHydraulic Fracturing

Initial Rate Following a Hydraulic Fracturing Operation

Q=Qpre(kf/ke)ln⁡(re/rw)ln⁡(rf/rw)+(kf/ke)ln⁡(re/rf)Q=Q_{pre}\frac{(k_f/k_e)\ln(r_e/r_w)}{\ln(r_f/r_w)+(k_f/k_e)\ln(r_e/r_f)}
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Productivity Ratio from Average Permeability - Hydraulic Fracturing

PR=kavgkPR=\frac{k_{avg}}{k}
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Formation Fluid Compressibility - Acidizing

Kfl=SoKo+SwKw+SgKgK_{fl}=S_oK_o+S_wK_w+S_gK_g
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Production EngineeringHydraulic Fracturing

Mass of Rock Dissolved per Unit Mass of Acid - Acidizing

β=MwmAMwaB\beta=\frac{M_{wm}A}{M_{wa}B}
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Production EngineeringHydraulic Fracturing

Mass Transfer in Acid Solutions by Fick's Law - Acidizing

Ua,y=−DAdcadYU_{a,y}=-D_A\frac{dc_a}{dY}
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Production EngineeringHydraulic Fracturing

Convective Mass Transfer for Laminar Flow (Acidizing)

Ua,y=−DAdcadY+caVNU_{a,y}=-D_A\frac{dc_a}{dY}+c_aV_N
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Production EngineeringHydraulic Fracturing

Turbulent Acidizing Mass Transfer Flux - Effective Diffusivity Form

⟨Ua,y⟩=−DEd⟨ca⟩dY+⟨ca⟩⟨VN⟩\langle U_{a,y}\rangle=-D_E\frac{d\langle c_a\rangle}{dY}+\langle c_a\rangle\langle V_N\rangle
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Production EngineeringHydraulic Fracturing

Turbulent Acidizing Mass Transfer Flux - Coefficient Form

⟨Ua,y⟩=Kg(⟨ca⟩−⟨ca(w)⟩)+⟨ca⟩⟨VN⟩\langle U_{a,y}\rangle=K_g\left(\langle c_a\rangle-\langle c_a(w)\rangle\right)+\langle c_a\rangle\langle V_N\rangle
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Production EngineeringHydraulic Fracturing

Young Modulus from Sonic Travel Time (Acidizing)

E=2.16×108[ρma(1−ϕ)+ρflϕ](1−2ν)(1+ν)(1−ν)ts2E=2.16\times10^8\frac{[\rho_{ma}(1-\phi)+\rho_{fl}\phi](1-2\nu)(1+\nu)}{(1-\nu)t_s^2}
Open analysis
Production EngineeringHydraulic Fracturing

Frictional Pressure Drop - Economides and Nolte

ΔPf=518ρ0.79q1.79μ0.207L1000D4.79\Delta P_f=\frac{518\rho^{0.79}q^{1.79}\mu^{0.207}L}{1000D^{4.79}}
Open analysis
Production EngineeringHydraulic Fracturing

Hydraulic Fracture Efficiency from Saydam Leakoff Function

η=100exD2erfc⁡(xD)+2xD/π−1xD2\eta=100\frac{e^{x_D^2}\operatorname{erfc}(x_D)+2x_D/\sqrt{\pi}-1}{x_D^2}
Open analysis
Production EngineeringHydraulic Fracturing

Fracture Area from Saydam Leakoff Function

Af=qiWf4πCL2(exD2erfc⁡(xD)+2xDπ−1)A_f=\frac{q_iW_f}{4\pi C_L^2}\left(e^{x_D^2}\operatorname{erfc}(x_D)+\frac{2x_D}{\sqrt{\pi}}-1\right)
Open analysis
Production EngineeringInjection Wells

Injectivity Index

Ii=qiPwf−PrI_i = \frac{q_i}{P_{wf} - P_r}
Open analysis
Production EngineeringInjection Wells

Radial Water Injection Rate

qw=0.00708krwkh(Piwf−Pe)μwBw[ln⁡(re/rw)+s]q_w=\frac{0.00708k_{rw}kh(P_{iwf}-P_e)}{\mu_wB_w[\ln(r_e/r_w)+s]}
Open analysis
Production EngineeringInjection Wells

Radial Water Injectivity Index

Iw=0.00708krwkhμwBw[ln⁡(re/rw)+s]I_w=\frac{0.00708k_{rw}kh}{\mu_wB_w[\ln(r_e/r_w)+s]}
Open analysis
Production EngineeringInjection Wells

Water Injection Bottom-Hole Pressure from Radial Flow

Piwf=Pe+qwμwBw[ln⁡(re/rw)+s]0.00708krwkhP_{iwf}=P_e+\frac{q_w\mu_wB_w[\ln(r_e/r_w)+s]}{0.00708k_{rw}kh}
Open analysis
Production EngineeringInjection Wells

Waterflood Mobility Ratio

M=krw/μwkro/μoM=\frac{k_{rw}/\mu_w}{k_{ro}/\mu_o}
Open analysis
Production EngineeringInjection Wells

Voidage Replacement Ratio

VRR=WiBwi+GiBginjNpBo+WpBwp+Bg(GOR−Rs)NpVRR=\frac{W_iB_{wi}+G_iB_{ginj}}{N_pB_o+W_pB_{wp}+B_g(GOR-R_s)N_p}
Open analysis
Production EngineeringInjection Wells

Injected Hydrocarbon Pore Volumes

HCPVinj=WiBwi7758AhϕSoHCPV_{inj}=\frac{W_iB_{wi}}{7758Ah\phi S_o}
Open analysis
Production EngineeringInjection Wells

Hall Plot Pressure-Time Increment

ΔH=(Piwf−Pavg)Δt\Delta H=(P_{iwf}-P_{avg})\Delta t
Open analysis
Production EngineeringInjection Wells

Cumulative Hall Plot Pressure Integral

H=Hprev+ΔHH=H_{prev}+\Delta H
Open analysis
Production EngineeringInjection Wells

Cumulative Water Injected for Hall Plot

Wi=Wprev+qiΔtW_i=W_{prev}+q_i\Delta t
Open analysis
Production EngineeringInjection Wells

Hall Plot Slope from Two Surveillance Points

mH=H2−H1Wi2−Wi1m_H=\frac{H_2-H_1}{W_{i2}-W_{i1}}
Open analysis
Production EngineeringInjection Wells

Hall Injectivity Coefficient from Slope

CH=1mHC_H=\frac{1}{m_H}
Open analysis
Production EngineeringInjection Wells

Hall Injectivity Change Ratio from Slopes

RC=CnewCbase=mbasemnewR_C=\frac{C_{new}}{C_{base}}=\frac{m_{base}}{m_{new}}
Open analysis
Drilling EngineeringDrilling Hydraulics

Hydraulic Horsepower at Bit

HHP=PsQ1714HHP = \frac{P_s Q}{1714}
Open analysis
Drilling EngineeringDrilling Hydraulics

Annular Velocity from Pump Output

AV=24.5QDh2−Dp2AV = \frac{24.5Q}{D_h^2 - D_p^2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Strokes per Minute Required for Target Annular Velocity

SPM=AV ACqoSPM=\frac{AV\,AC}{q_o}
Open analysis
Drilling EngineeringDrilling Hydraulics

Critical Flow Rate for Flow Regime Change

Qc=2.448VcDi2Q_c=2.448V_cD_i^2
Open analysis
Drilling EngineeringDrilling Hydraulics

Nozzle Area from Three Jet Sizes

Na=N12+N22+N321303.8N_a=\frac{N_1^2+N_2^2+N_3^2}{1303.8}
Open analysis
Drilling EngineeringDrilling Hydraulics

Cuttings Slip Velocity

Vs=0.45PVMWDcut(36800Dcut(DenP/MW−1)(PV/(MWDcut))2+1−1)V_s=0.45\frac{PV}{MWD_{cut}}\left(\sqrt{\frac{36800D_{cut}(DenP/MW-1)}{(PV/(MWD_{cut}))^2}+1}-1\right)
Open analysis
Drilling EngineeringDrilling Hydraulics

Cuttings Net Rise Velocity

Vnet=AV−VsV_{net}=AV-V_s
Open analysis
Drilling EngineeringDrilling Hydraulics

Bit Nozzle Jet Velocity

Vn=417.2QN12+N22+N32V_n = \frac{417.2 Q}{N_1^2 + N_2^2 + N_3^2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Equivalent Circulating Density

ECD=MW+ΔPa0.052TVDECD = MW + \frac{\Delta P_a}{0.052TVD}
Open analysis
Drilling EngineeringDrilling Hydraulics

Bit Nozzle Pressure Loss

Pb=156.5Q2MW(N12+N22+N32)2P_b = \frac{156.5Q^2MW}{(N_1^2+N_2^2+N_3^2)^2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Percentage Pressure Loss at Bit

Ppsib=100PbPsP_{psib} = \frac{100P_b}{P_s}
Open analysis
Drilling EngineeringDrilling Hydraulics

Hydraulic Horsepower per Unit Bit Area

HHPba=QPb1.271714B2HHP_{ba} = \frac{QP_b1.27}{1714B^2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Impact Force per Unit Bit Area

IFa=MWVnQ1.271930B2IF_a = \frac{MWV_nQ1.27}{1930B^2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Maximum Drilling Rate for Larger Holes

MDR=67(MWo−MWi)qcDh2MDR = \frac{67(MW_o - MW_i)q_c}{D_h^2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Velocity of Fluid in Annulus

va=Q2.448(Do2−Dp2)v_a = \frac{Q}{2.448(D_o^2-D_p^2)}
Open analysis
Drilling EngineeringDrilling Hydraulics

Drill String Volume

B=ID21029.4PLB = \frac{ID^2}{1029.4}PL
Open analysis
Drilling EngineeringDrilling Hydraulics

Drill Pipe or Drill Collar Capacity

C=ID21029.4C=\frac{ID^2}{1029.4}
Open analysis
Drilling EngineeringDrilling Hydraulics

Annular Capacity - bbl/ft

ACbbl=Dh2−Dp21029.4AC_{bbl}=\frac{D_h^2-D_p^2}{1029.4}
Open analysis
Drilling EngineeringDrilling Hydraulics

Annular Capacity - gal/ft

ACgal=Dh2−Dp224.51AC_{gal}=\frac{D_h^2-D_p^2}{24.51}
Open analysis
Drilling EngineeringDrilling Hydraulics

Tubular and Open-Hole Capacity

Cbbl=Di21029.4C_{bbl}=\frac{D_i^2}{1029.4}
Open analysis
Drilling EngineeringDrilling Hydraulics

Triplex Pump Output per Stroke

PO=0.000243Dl2LsPO=0.000243D_l^2L_s
Open analysis
Drilling EngineeringDrilling Hydraulics

Duplex Pump Output per Stroke

PO=0.000162S(2Dl2−dr2)PO=0.000162S(2D_l^2-d_r^2)
Open analysis
Drilling EngineeringDrilling Hydraulics

Bit Nozzle Impact Force

IF=MWVnQ1930IF=\frac{MWV_nQ}{1930}
Open analysis
Drilling EngineeringDrilling Hydraulics

Triplex Pump Output Rate with Volumetric Efficiency

Qgpm=0.000243Dl2LsEvSPM⋅42Q_{gpm}=0.000243D_l^2L_sE_vSPM\cdot42
Open analysis
Drilling EngineeringDrilling Hydraulics

Duplex Pump Output Rate with Volumetric Efficiency

Qgpm=0.000162S(2Dl2−dr2)EvSPM⋅42Q_{gpm}=0.000162S(2D_l^2-d_r^2)E_vSPM\cdot42
Open analysis
Drilling EngineeringDrilling Hydraulics

New Pump Circulating Pressure - Square Law

Pnew=Pcurrent(NnewNold)2P_{new}=P_{current}\left(\frac{N_{new}}{N_{old}}\right)^2
Open analysis
Drilling EngineeringDrilling Hydraulics

Pump Pressure Exponent from Two Pump Tests

n=ln⁡(P1/P2)ln⁡(Q1/Q2)n=\frac{\ln(P_1/P_2)}{\ln(Q_1/Q_2)}
Open analysis
Drilling EngineeringDrilling Hydraulics

New Pump Circulating Pressure with Friction Exponent

Pnew=Pcurrent(QnewQold)nP_{new}=P_{current}\left(\frac{Q_{new}}{Q_{old}}\right)^n
Open analysis
Drilling EngineeringDrilling Hydraulics

Bit-to-Surface Lag Time from Annular Volume

tlag=VAVPO⋅SPMt_{lag}=\frac{V_{AV}}{PO\cdot SPM}
Open analysis
Drilling EngineeringDrilling Hydraulics

Plastic Viscosity from 600 and 300 RPM Readings

PV=θ600−θ300PV=\theta_{600}-\theta_{300}
Open analysis
Drilling EngineeringDrilling Hydraulics

Yield Point from 600 and 300 RPM Readings

YP=2θ300−θ600YP=2\theta_{300}-\theta_{600}
Open analysis
Drilling EngineeringDrilling Hydraulics

Apparent Viscosity from 600 RPM Reading

AV=θ6002AV=\frac{\theta_{600}}{2}
Open analysis
Drilling EngineeringDrilling Hydraulics

Power Law Flow Behavior Index from Rheometer Readings

n=3.322log⁡10(θ600θ300)n=3.322\log_{10}\left(\frac{\theta_{600}}{\theta_{300}}\right)
Open analysis
Drilling EngineeringDrilling Hydraulics

Power Law Consistency Index from 300 RPM Reading

Keff=5111−nθ300K_{eff}=511^{1-n}\theta_{300}
Open analysis
Drilling EngineeringDrilling Hydraulics

Cuttings Carrying Capacity Index

CCI=MW AV Keff400000CCI=\frac{MW\,AV\,K_{eff}}{400000}
Open analysis
Drilling EngineeringDrilling Hydraulics

Open-Ended Displacement Volume of Pipe

Vo=0.7854(Do2−Di2)L808.5V_o=\frac{0.7854(D_o^2-D_i^2)L}{808.5}
Open analysis
Drilling EngineeringDrilling Hydraulics

Drill Pipe or Drill Collar Displacement and Weight

Disp=OD2−ID21029.4Disp=\frac{OD^2-ID^2}{1029.4}
Open analysis
Drilling EngineeringDrilling Hydraulics

Total Circulation Strokes from Drillstring and Annular Volume

S=VDS+VAVOS=\frac{V_{DS}+V_{AV}}{O}
Open analysis
Drilling EngineeringDrilling Hydraulics

Linear Pipe Capacity

Ci=0.7854Di2808.5C_i=\frac{0.7854D_i^2}{808.5}
Open analysis
Drilling EngineeringDrilling Hydraulics

Linear Annular Capacity of Pipe

Co=0.7854(Dh2−Do2)808.5C_o=\frac{0.7854(D_h^2-D_o^2)}{808.5}
Open analysis
Drilling EngineeringDrilling Hydraulics

Annular Volume Capacity of Pipe

Va=0.7854(Dh2−Do2)L808.5V_a=\frac{0.7854(D_h^2-D_o^2)L}{808.5}
Open analysis
Drilling EngineeringDrilling Hydraulics

Pump Input Power from Fuel Consumption Rate

Pi=QfH2545P_i=\frac{Q_fH}{2545}
Open analysis
Drilling EngineeringDrilling Hydraulics

New Pump Circulating Pressure

Pc=Pp(qnqo)2P_c=P_p\left(\frac{q_n}{q_o}\right)^2
Open analysis
Drilling EngineeringDrilling Hydraulics

Pump Pressure from Bit Drop and Friction Losses

Pp=ΔPbit+PdP_p=\Delta P_{bit}+P_d
Open analysis
Drilling EngineeringDrilling Hydraulics

Overall Diesel-to-Mud-Pump Efficiency

ηo=ηeηlηmηv\eta_o=\eta_e\eta_l\eta_m\eta_v
Open analysis
Drilling EngineeringDrilling Hydraulics

Overall Power System Efficiency

Ei=PQiE_i=\frac{P}{Q_i}
Open analysis
Drilling EngineeringDrilling Hydraulics

Annular Capacity Between Casing and Multiple Strings of Tubing

Ca=Di2−(T12+T22)1029.4C_a=\frac{D_i^2-(T_1^2+T_2^2)}{1029.4}
Open analysis
Drilling EngineeringDrilling Hydraulics

Depth of a Washout - Method 1

Dw=NsPoCpD_w=\frac{N_sP_o}{C_p}
Open analysis
Drilling EngineeringDrilling Hydraulics

Depth of a Washout - Method 2

Dw=NsPoCp+CaD_w=\frac{N_sP_o}{C_p+C_a}
Open analysis
Reservoir EngineeringReserves and Recovery

Oil Recovery Factor from Cumulative Production

RF=NpNRF = \frac{N_p}{N}
Open analysis
Reservoir EngineeringReserves and Recovery

Arps Exponential Decline Rate

q(t)=qie−Ditq(t)=q_i e^{-D_i t}
Open analysis
Reservoir EngineeringReserves and Recovery

Arps Exponential Decline Cumulative Production

Np(t)=qiDi(1−e−Dit)N_p(t)=\frac{q_i}{D_i}\left(1-e^{-D_i t}\right)
Open analysis
Reservoir EngineeringReserves and Recovery

Arps Hyperbolic Decline Rate

q(t)=qi(1+bDit)1/bq(t)=\frac{q_i}{(1+bD_it)^{1/b}}
Open analysis
Reservoir EngineeringReserves and Recovery

Arps Hyperbolic Decline Cumulative Production

Np(t)=qi(1−b)Di[1−(1+bDit)1−1/b]N_p(t)=\frac{q_i}{(1-b)D_i}\left[1-(1+bD_it)^{1-1/b}\right]
Open analysis
Reservoir EngineeringReserves and Recovery

Arps Harmonic Decline Rate

q(t)=qi1+Ditq(t)=\frac{q_i}{1+D_it}
Open analysis
Reservoir EngineeringReserves and Recovery

Arps Harmonic Decline Cumulative Production

Np(t)=qiDiln⁡(1+Dit)N_p(t)=\frac{q_i}{D_i}\ln(1+D_it)
Open analysis
Reservoir EngineeringReserves and Recovery

Exponential Decline Time to Economic Limit

tecon=1Diln⁡(qiqecon)t_{econ}=\frac{1}{D_i}\ln\left(\frac{q_i}{q_{econ}}\right)
Open analysis
Reservoir EngineeringReserves and Recovery

Gas-Condensate Liquid Content from Producing GOR

Yc=106GORpY_c=\frac{10^6}{GOR_p}
Open analysis
Reservoir EngineeringReserves and Recovery

Condensate Production Rate from Gas Rate and Yield

qc=qgYc1000q_c=\frac{q_gY_c}{1000}
Open analysis
Reservoir EngineeringReserves and Recovery

NGL Production Rate from Gas Rate and Yield

qNGL=qgYNGL1000q_{NGL}=\frac{q_gY_{NGL}}{1000}
Open analysis
Reservoir EngineeringReserves and Recovery

Recoverable Condensate from Cumulative Gas and Yield

Nc=GpYcN_c=G_pY_c
Open analysis
Reservoir EngineeringReserves and Recovery

Oil Lost During Gas-Cap Migration

O=7758AhϕSorgBoaO=7758Ah\phi\frac{S_{org}}{B_{oa}}
Open analysis
PetrophysicsElectrical Properties

Electrical Resistivity from Resistance Geometry

R=rALR = r \frac{A}{L}
Open analysis
PetrophysicsElectrical Properties

Electrical Conductivity from Resistivity

σ=1ρe\sigma = \frac{1}{\rho_e}
Open analysis
PetrophysicsElectrical Properties

Formation Factor from Water-Filled Rock Resistivity

F=RoRwF = \frac{R_o}{R_w}
Open analysis
PetrophysicsElectrical Properties

Archie Formation Factor from Porosity

F=1ϕmF = \frac{1}{\phi^m}
Open analysis
PetrophysicsElectrical Properties

Archie Resistivity Index from Water Saturation

RI=Sw−nRI = S_w^{-n}
Open analysis
PetrophysicsElectrical Properties

Archie True Formation Resistivity

Rt=RwϕmSwnR_t = \frac{R_w}{\phi^m S_w^n}
Open analysis
PetrophysicsElectrical Properties

Archie Water Saturation from Formation Factor

Sw=(FRwRt)1/nS_w = \left(\frac{FR_w}{R_t}\right)^{1/n}
Open analysis
PetrophysicsElectrical Properties

Generalized Archie Formation Factor with Lithology Coefficient

F=aϕmF=\frac{a}{\phi^m}
Open analysis
PetrophysicsElectrical Properties

Archie Cementation Exponent from Formation Factor

m=ln⁡(F/a)ln⁡(1/ϕ)m=\frac{\ln(F/a)}{\ln(1/\phi)}
Open analysis
PetrophysicsElectrical Properties

Resistivity Index from True and Water-Filled Resistivity

I=RtRoI=\frac{R_t}{R_o}
Open analysis
PetrophysicsElectrical Properties

Static Spontaneous Potential from Equivalent Resistivities

SSP=−Klog⁡10(RmfeRwe)SSP=-K\log_{10}\left(\frac{R_{mfe}}{R_{we}}\right)
Open analysis
PetrophysicsElectrical Properties

Formation Water Resistivity from Resistivity Ratio Method

Rw=RtRxoRmfR_w=\frac{R_t}{R_{xo}}R_{mf}
Open analysis
PetrophysicsElectrical Properties

Diffuse-Layer Thickness from Salt Concentration

xd=3n−1/2x_d=3n^{-1/2}
Open analysis
PetrophysicsElectrical Properties

Effect of Clay on Conductivity

Co=CwF+CsC_o=\frac{C_w}{F}+C_s
Open analysis
PetrophysicsElectrical Properties

Electric Resistance to Radial Current from a Wellbore

Re=ln⁡(re/rw)2πhσR_e=\frac{\ln(r_e/r_w)}{2\pi h\sigma}
Open analysis
PetrophysicsElectrical Properties

Electrochemical Potential - SP Log

Ec=2tClRTFln⁡(a1a2)E_c=2t_{Cl}\frac{RT}{F}\ln\left(\frac{a_1}{a_2}\right)
Open analysis
PetrophysicsElectrical Properties

Waxman-Smits Clean-Sand Brine-Saturated Rock Conductivity

Co=1F(Ccl+Cw)C_o=\frac{1}{F}\left(C_{cl}+C_w\right)
Open analysis
PetrophysicsElectrical Properties

Dual-Water Brine-Saturated Rock Conductivity

Co=1Fo(Cwf+fdlvQQv(Cwb−Cwf))C_o=\frac{1}{F_o}\left(C_{wf}+f_{dl}v_QQ_v(C_{wb}-C_{wf})\right)
Open analysis
PetrophysicsElectrical Properties

Non-Ideal Shale Membrane Efficiency from Shale Resistivity

meff=0.47+0.3Rshm_{eff}=0.47+0.3R_{sh}
Open analysis
PetrophysicsElectrical Properties

Non-NaCl Static Self Potential from Ion Activities

Essp=−Klog⁡10(aNa+(aCa+aMg)0.5aNam+(aCam+aMgm)0.5)E_{ssp}=-K\log_{10}\left(\frac{a_{Na}+(a_{Ca}+a_{Mg})^{0.5}}{a_{Nam}+(a_{Cam}+a_{Mgm})^{0.5}}\right)
Open analysis
PetrophysicsElectrical Properties

Rock Conductivity for Clean Water-Bearing Rocks

Co=CwFC_o=\frac{C_w}{F}
Open analysis
PetrophysicsElectrical Properties

Total Rock Conductivity from Water Saturation

Ct=CwSwϕEC_t=C_wS_w\phi E
Open analysis
PetrophysicsElectrical Properties

Resistivity Bed Reflection Coefficient

CR=R1−R2R1+R2C_R=\frac{R_1-R_2}{R_1+R_2}
Open analysis
PetrophysicsElectrical Properties

Apparent Resistivity

R=GtΔV12IR=G_t\frac{\Delta V_{12}}{I}
Open analysis
PetrophysicsElectrical Properties

Electrode Array Geometric Coefficient

Gt=4πr1r2r2−r1G_t=4\pi r_1\frac{r_2}{r_2-r_1}
Open analysis
PetrophysicsElectrical Properties

Normal Sonde Geometric Coefficient

GN=4πAMG_N=4\pi AM
Open analysis
PetrophysicsElectrical Properties

Lateral Device Geometric Coefficient

GL=4πAMANMNG_L=4\pi AM\frac{AN}{MN}
Open analysis
PetrophysicsElectrical Properties

Wellbore Electric Voltage Generation

V=Ve,w−ΔVeln⁡(r/rw)ln⁡(re/rw)V=V_{e,w}-\Delta V_e\frac{\ln(r/r_w)}{\ln(r_e/r_w)}
Open analysis
PetrophysicsElectrical Properties

Electrokinetic Potential Across Mud Cake

Ek=xpyE_k=xp^y
Open analysis
PetrophysicsElectrical Properties

Membrane Potential for SP Log

Em=RTFln⁡(a1a2)E_m=\frac{RT}{F}\ln\left(\frac{a_1}{a_2}\right)
Open analysis
PetrophysicsElectrical Properties

Relationship Between SSP and Rw - NaCl Predominant

SSP=−Ksplog⁡10(RmfeqRweq)SSP=-K_{sp}\log_{10}\left(\frac{R_{mfeq}}{R_{weq}}\right)
Open analysis
PetrophysicsElectrical Properties

Static Self Potential from NaCl Activities

Essp=−Klog⁡10(awamf)E_{ssp}=-K\log_{10}\left(\frac{a_w}{a_{mf}}\right)
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Average Compressibility of Oil

Co=−1V(V1−V2p1−p2)C_o = -\frac{1}{V}\left(\frac{V_1 - V_2}{p_1 - p_2}\right)
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Villena-Lanzi Saturated Oil Compressibility

co=exp⁡[−0.664−1.430ln⁡p−0.395ln⁡pb+0.390ln⁡T+0.455ln⁡Rsb+0.262ln⁡API]c_o=\exp[-0.664-1.430\ln p-0.395\ln p_b+0.390\ln T+0.455\ln R_{sb}+0.262\ln API]
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Saturated Oil Compressibility from FVF and Solution GOR Derivatives

co=−1BodBodp+BgBodRsdpc_o=-\frac{1}{B_o}\frac{dB_o}{dp}+\frac{B_g}{B_o}\frac{dR_s}{dp}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Average Gas Solubility

Savg=s1−s2p1−p2S_{avg} = \frac{s_1 - s_2}{p_1 - p_2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Solution Gas-Oil Ratio - Beggs-Standing Correlation Below Bubble Point

Rso=γg(p18⋅10Yg)1.204R_{so} = \gamma_g\left(\frac{p}{18\cdot10^{Y_g}}\right)^{1.204}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Equation of State Pressure

P=RTvm−b−avm2P = \frac{RT}{v_m-b} - \frac{a}{v_m^2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Attraction Parameter from Critical Properties

a=27R2Tc264Pca = \frac{27R^2T_c^2}{64P_c}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Covolume from Critical Properties

b=RTc8Pcb = \frac{RT_c}{8P_c}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Critical Pressure from Parameters

Pc=a27b2P_c = \frac{a}{27b^2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Critical Temperature from Parameters

Tc=8a27RbT_c = \frac{8a}{27Rb}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Critical Molar Volume

vc=3bv_c = 3b
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Solution Gas-Oil Ratio - Standing Correlation

Rs=γg[p18100.0125API100.00091t]1.2048R_s=\gamma_g\left[\frac{p}{18}\frac{10^{0.0125API}}{10^{0.00091t}}\right]^{1.2048}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Standing Oil Formation Volume Factor

Bo=0.9759+0.00012F1.2B_o=0.9759+0.00012F^{1.2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Beggs-Standing Oil Formation Volume Factor Below Bubble Point

Bo=0.972+0.000147F1.175B_o=0.972+0.000147F^{1.175}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Beggs-Standing Oil Formation Volume Factor Above Bubble Point

Bo=Bbexp⁡[co(pb−p)]B_o=B_b\exp\left[c_o(p_b-p)\right]
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Solution Gas-Water Ratio

Rsw=Rswp10−0.0840655ST−0.285854R_{sw}=R_{swp}10^{-0.0840655ST^{-0.285854}}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

McCain Water Formation Volume Factor

Bw=(1+ΔVwT)(1+ΔVwP)B_w=(1+\Delta V_{wT})(1+\Delta V_{wP})
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Solution Gas-Oil Ratio from Pressure

Rs=C1γgpC2exp⁡(C3APIT+460)R_s=C_1\gamma_g p^{C_2}\exp\left(\frac{C_3API}{T+460}\right)
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Bubble Point Pressure from Solution GOR

pb=[RsbC1γgexp⁡(C3API/(T+460))]1/C2p_b=\left[\frac{R_{sb}}{C_1\gamma_g\exp(C_3API/(T+460))}\right]^{1/C_2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Saturated Oil Formation Volume Factor

Bo=1+A1Rs+A2(T−60)APIγgc+A3Rs(T−60)APIγgcB_o=1+A_1R_s+A_2(T-60)\frac{API}{\gamma_{gc}}+A_3R_s(T-60)\frac{API}{\gamma_{gc}}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Undersaturated Oil Compressibility

co=−1433+5Rsb+17.2T−1180γg+12.61API105pc_o=\frac{-1433+5R_{sb}+17.2T-1180\gamma_g+12.61API}{10^5p}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Undersaturated Oil Formation Volume Factor

Bo=Bobexp⁡[co(pb−p)]B_o=B_{ob}\exp[c_o(p_b-p)]
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Al-Marhoun Bubble Point Pressure

pb=0.00538088Rsb0.715082γg−1.87784γo3.1437(T+459.67)1.32657p_b=0.00538088R_{sb}^{0.715082}\gamma_g^{-1.87784}\gamma_o^{3.1437}(T+459.67)^{1.32657}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Al-Marhoun Solution Gas-Oil Ratio from Bubble Point Pressure

Rsb=[pbγg1.877840.00538088γo3.1437(T+459.67)1.32657]1/0.715082R_{sb}=\left[\frac{p_b\gamma_g^{1.87784}}{0.00538088\gamma_o^{3.1437}(T+459.67)^{1.32657}}\right]^{1/0.715082}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Al-Marhoun Saturated Oil Formation Volume Factor

Bob=0.497069+0.000862963(T+459.67)+0.00182594F+0.00000318099F2B_{ob}=0.497069+0.000862963(T+459.67)+0.00182594F+0.00000318099F^2
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Glaso Bubble Point Pressure

pb=101.7669+1.7447log⁡10(pb∗)−0.30218[log⁡10(pb∗)]2p_b=10^{1.7669+1.7447\log_{10}(p_b^*)-0.30218[\log_{10}(p_b^*)]^2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Glaso Saturated Oil Formation Volume Factor

Bo=1+10−6.58511+2.91329log⁡10(Bo∗)−0.27683[log⁡10(Bo∗)]2B_o=1+10^{-6.58511+2.91329\log_{10}(B_o^*)-0.27683[\log_{10}(B_o^*)]^2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Glaso Solution Gas-Oil Ratio from Pressure

Rs=γg(pb∗API0.989T0.172)1/0.816R_s=\gamma_g\left(\frac{p_b^*API^{0.989}}{T^{0.172}}\right)^{1/0.816}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Glaso Solution Gas-Oil Ratio from Saturated Oil FVF

Rs=Bo∗−0.968T(γg/γo)0.526R_s=\frac{B_o^*-0.968T}{(\gamma_g/\gamma_o)^{0.526}}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Glaso Undersaturated Oil Formation Volume Factor

Bo=Bobexp⁡[co(pb−p)]B_o=B_{ob}\exp[c_o(p_b-p)]
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Bubble Point Pressure

pb=112.727[Rsb0.5774γg0.843910x−12.34]p_b=112.727\left[\frac{R_{sb}^{0.5774}}{\gamma_g^{0.8439}}10^x-12.34\right]
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Solution Gas-Oil Ratio from Pressure

Rs=[(p112.727+12.34)γg0.843910x]1.73184R_s=\left[\left(\frac{p}{112.727}+12.34\right)\gamma_g^{0.8439}10^x\right]^{1.73184}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Saturated Oil Formation Volume Factor

Bob=1.0113+7.2046×10−5F3.0936B_{ob}=1.0113+7.2046\times10^{-5}F^{3.0936}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Undersaturated Oil Compressibility

co=1.705×10−7Rsb0.69357γg0.1885API0.3272T0.6729p−0.5906c_o=1.705\times10^{-7}R_{sb}^{0.69357}\gamma_g^{0.1885}API^{0.3272}T^{0.6729}p^{-0.5906}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Undersaturated Oil Formation Volume Factor

Bo=Bobexp⁡[co(pb−p)]B_o=B_{ob}\exp[c_o(p_b-p)]
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Equilibrium Vaporization Ratio

K=yxK=\frac{y}{x}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Equilibrium Vaporization Ratio of Heptane

K=Ka(Kb/Ka)bK=\frac{K_a}{(K_b/K_a)^b}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Latent Heat of Hydrocarbon Mixture

Δhm=TM(7.58+4.57log⁡10T)\Delta h_m=\frac{T}{M}\left(7.58+4.57\log_{10}T\right)
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Jacoby Aromaticity Factor

Ja=γ+15.8M−0.84680.2456−1.77MJ_a=\frac{\gamma+\frac{15.8}{M}-0.8468}{0.2456-\frac{1.77}{M}}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Redlich-Kwong PVT Equation

P=RTV−b−aT0.5V(V+b)P=\frac{RT}{V-b}-\frac{a}{T^{0.5}V(V+b)}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Benedict-Webb-Rubin PVT Equation

P=RTρ+(BRT−A−CT2)ρ2+(bRT−a)ρ3+aαρ6+cρ3T2(1+γρ2)e−γρ2P=RT\rho+\left(BRT-A-\frac{C}{T^2}\right)\rho^2+(bRT-a)\rho^3+a\alpha\rho^6+\frac{c\rho^3}{T^2}(1+\gamma\rho^2)e^{-\gamma\rho^2}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Liquid-Phase Component Mole Fraction

x=zL+VKx=\frac{z}{L+VK}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Peng-Robinson Characterization Factor

kCi=0.0289+0.0001633Mk_{Ci}=0.0289+0.0001633M
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Peng-Robinson PVT Equation

P=RTV−b−aTV(V+b)+b(V−b)P=\frac{RT}{V-b}-\frac{aT}{V(V+b)+b(V-b)}
Open analysis
Phase Behavior and ThermodynamicsPVT Properties

Watson Characterization Factor from Boiling Point and Specific Gravity

Kw=Tb1/3γ60K_w=\frac{T_b^{1/3}}{\gamma_{60}}
Open analysis
Reservoir EngineeringRock Properties

Total Pore Volume Compressibility

cf=1PVi(PVi−PVpPi−P)c_f = \frac{1}{PV_i}\left(\frac{PV_i - PV_p}{P_i - P}\right)
Open analysis
Reservoir EngineeringRock Properties

Exponential Pore Volume from Rock Compressibility

PV=PVrefexp⁡(cr(P−Pref))PV = PV_{ref}\exp(c_r(P-P_{ref}))
Open analysis
Reservoir EngineeringRock Properties

Exponential Porosity from Rock Compressibility

ϕ=ϕrefexp⁡(cr(P−Pref))\phi = \phi_{ref}\exp(c_r(P-P_{ref}))
Open analysis
Reservoir EngineeringRock Properties

Leijnse Porosity from Rock Compressibility

ϕ=1−(1−ϕref)exp⁡[−cr(P−Pref)]\phi = 1-(1-\phi_{ref})\exp[-c_r(P-P_{ref})]
Open analysis
Reservoir EngineeringRock Properties

Quadratic Porosity Multiplier from Rock Compressibility

ϕ=ϕref(1+X+X22)\phi = \phi_{ref}\left(1+X+\frac{X^2}{2}\right)
Open analysis
Reservoir EngineeringRock Properties

Effective Porosity from Connected Pore Volume

ϕe=VconnectedVb\phi_e = \frac{V_{connected}}{V_b}
Open analysis
Reservoir EngineeringRock Properties

Total Porosity from Pore and Bulk Volume

ϕt=VpVb\phi_t=\frac{V_p}{V_b}
Open analysis
Reservoir EngineeringRock Properties

Total Porosity from Bulk and Grain Volume

ϕt=Vb−VgVb\phi_t=\frac{V_b-V_g}{V_b}
Open analysis
Reservoir EngineeringRock Properties

Total Porosity from Pore and Grain Volume

ϕt=VpVp+Vg\phi_t=\frac{V_p}{V_p+V_g}
Open analysis
Reservoir EngineeringRock Properties

Core Pore Volume from Saturated and Dry Weights

Vp=Ws−WdρsV_p=\frac{W_s-W_d}{\rho_s}
Open analysis
Reservoir EngineeringRock Properties

Core Bulk Volume from Saturated and Immersed Weights

Vb=Ws−WiρsV_b=\frac{W_s-W_i}{\rho_s}
Open analysis
Reservoir EngineeringRock Properties

Pore Throat Sorting from Capillary Pressure Quartiles

PTS=(Q3Q1)0.5PTS=\left(\frac{Q_3}{Q_1}\right)^{0.5}
Open analysis
Reservoir EngineeringRock Properties

Leverett J-Function from Capillary Pressure

J=Pcσcos⁡θ(kϕ)0.5J=\frac{P_c}{\sigma\cos\theta}\left(\frac{k}{\phi}\right)^{0.5}
Open analysis
Reservoir EngineeringRock Properties

Maximum Oil Column Height in Cap Rock

H=Pa−Pw+Gohα+Pcρ−GoH=\frac{P_a-P_w+G_oh\alpha+P_c}{\rho-G_o}
Open analysis
Reservoir EngineeringRock Properties

Ineffective Porosity from Disconnected Pore Volume

ϕin=VdisVb\phi_{in}=\frac{V_{dis}}{V_b}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Viscosibility

cv=1μdμdPc_v = \frac{1}{\mu}\frac{d\mu}{dP}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Stock-Tank Oil Density from API Gravity

ρo,st=ρw141.5API+131.5\rho_{o,st}=\rho_w\frac{141.5}{API+131.5}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Live Oil Density from Formation Volume Factor

ρo=ρo,st+0.0136RsγgBo\rho_o=\frac{\rho_{o,st}+0.0136R_s\gamma_g}{B_o}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Standing Live Oil Density Correlation

ρo=62.4γo+0.0136Rsγg0.972+0.000147(Rsγg/γo+1.25t)1.175\rho_o=\frac{62.4\gamma_o+0.0136R_s\gamma_g}{0.972+0.000147\left(R_s\sqrt{\gamma_g/\gamma_o}+1.25t\right)^{1.175}}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Kinematic Viscosity from Dynamic Viscosity and Density

ν=μρ\nu=\frac{\mu}{\rho}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Newtonian Shear Stress from Viscosity

τ=μdudy\tau=\mu\frac{du}{dy}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Standing Dead Oil Viscosity Correlation

μod=(0.32+1.8×107API4.53)(360t+200)a\mu_{od}=\left(0.32+\frac{1.8\times10^7}{API^{4.53}}\right)\left(\frac{360}{t+200}\right)^a
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Beggs-Robinson Dead Oil Viscosity Correlation

μod=10x−1\mu_{od}=10^x-1
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Beggs-Robinson Live Oil Viscosity Correlation

μo=AμodB\mu_o=A\mu_{od}^{B}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Vasquez-Beggs Oil Viscosity Above Bubble Point

μo=μob(ppb)m\mu_o=\mu_{ob}\left(\frac{p}{p_b}\right)^m
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Water Viscosity at Atmospheric Pressure

μw1=ATB\mu_{w1}=AT^B
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Water Viscosity at Reservoir Pressure

μw=μw1(0.9994+4.0295×10−5p+3.1062×10−9p2)\mu_w=\mu_{w1}\left(0.9994+4.0295\times10^{-5}p+3.1062\times10^{-9}p^2\right)
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Osif Water Isothermal Compressibility

cw=17.033P+0.5415Cmg/L−537T+403300c_w=\frac{1}{7.033P+0.5415C_{mg/L}-537T+403300}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Formation Water Density at Standard Conditions

ρwSC=Cmg/L25000+62.428\rho_{wSC}=\frac{C_{mg/L}}{25000}+62.428
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Formation Water Density at Reservoir Conditions

ρwR=ρwSCBw\rho_{wR}=\frac{\rho_{wSC}}{B_w}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Formation Water Specific Gravity from Density

SGw=ρw62.428SG_w=\frac{\rho_w}{62.428}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Formation Water Salinity from Density

Cmg/L=25000(SGw−1)62.428C_{mg/L}=25000(SG_w-1)62.428
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Gas-Water Interfacial Tension at 74 F

σ74=75−1.108P0.349\sigma_{74}=75-1.108P^{0.349}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Gas-Water Interfacial Tension at 280 F

σ280=53−0.1048P0.637\sigma_{280}=53-0.1048P^{0.637}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Gas-Water Interfacial Tension by Temperature

σw=σ74+(T−74)(σ280−σ74)280−74\sigma_w=\sigma_{74}+\frac{(T-74)(\sigma_{280}-\sigma_{74})}{280-74}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Dead-Oil Gas-Oil Interfacial Tension

σod=σ68+(T−68)(σ100−σ68)100−68\sigma_{od}=\sigma_{68}+\frac{(T-68)(\sigma_{100}-\sigma_{68})}{100-68}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Live-Oil Gas-Oil Interfacial Tension

σo=σod(1−0.024P0.45)\sigma_o=\sigma_{od}\left(1-0.024P^{0.45}\right)
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Pure-Water Solution Gas-Water Ratio

Rswp=A+BP+CP2R_{swp}=A+BP+CP^2
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Brine Gas-Solubility Salinity Correction

Fs=10−0.0840655ST−0.285854F_s=10^{-0.0840655ST^{-0.285854}}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Brine Solution Gas-Water Ratio

Rsw=RswpFsR_{sw}=R_{swp}F_s
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Solution Gas-Water Pressure Derivative

(∂Rsw∂P)T=Fs(B+2CP)\left(\frac{\partial R_{sw}}{\partial P}\right)_T=F_s(B+2CP)
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

McCain Saturated Water Compressibility with Gas Liberation

cwsat=cwunder+BgBw(∂Rsw∂P)Tc_{wsat}=c_{wunder}+\frac{B_g}{B_w}\left(\frac{\partial R_{sw}}{\partial P}\right)_T
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Logarithmic Crude Oil Viscosity from API Gravity

log⁡μo=a−0.035API\log\mu_o=a-0.035API
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Egbogah Dead Oil Viscosity Below Bubble Point

μod=10101.8653−0.025086API−0.5644log⁡10T\mu_{od}=10^{10^{1.8653-0.025086API-0.5644\log_{10}T}}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Standard Discharge Time for Saybolt Viscosimeter Measurements

ts=to[1+0.000064(To−Ts)]t_s=t_o\left[1+0.000064(T_o-T_s)\right]
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Kinematic Viscosity for Saybolt Viscosimeter Measurements

v=0.220to−180tov=0.220t_o-\frac{180}{t_o}
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Absolute Viscosity for Saybolt Viscosimeter Measurements

μ=vρ\mu=v\rho
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Absolute Viscosity for Ubbelohde Viscosimeter Measurements

μ=Cut\mu=C_ut
Open analysis
Phase Behavior and ThermodynamicsFluid Properties

Einstein Effective Viscosity for Dilute Suspensions

μeff=μ0(1+2.5ϕ)\mu_{eff}=\mu_0(1+2.5\phi)
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Fracture Storativity

ω=ϕfhfctfϕfhfctf+ϕmhmctm\omega = \frac{\phi_f h_f c_{tf}}{\phi_f h_f c_{tf} + \phi_m h_m c_{tm}}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Matrix Block Shape Factor from Surface Area

α=AVmx\alpha=\frac{A}{V_mx}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Warren-Root Shape Factor from Fracture Sets

α=4n(n+2)Lm2\alpha=\frac{4n(n+2)}{L_m^2}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Warren-Root Interporosity Flow Coefficient

λ=αrw2kmkf\lambda=\alpha r_w^2\frac{k_m}{k_f}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Cubic Matrix Block Interporosity Flow Coefficient

λ=60Lm2rw2kmkf\lambda=\frac{60}{L_m^2}r_w^2\frac{k_m}{k_f}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Spherical Matrix Block Interporosity Flow Coefficient

λ=15rm2rw2kmkf\lambda=\frac{15}{r_m^2}r_w^2\frac{k_m}{k_f}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Slab Matrix Block Interporosity Flow Coefficient

λ=12hs2rw2kmkf\lambda=\frac{12}{h_s^2}r_w^2\frac{k_m}{k_f}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Linear Fracture Intensity from Scanline Count

P10=NfLsP_{10}=\frac{N_f}{L_s}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Average Fracture Spacing from Linear Intensity

Sf=1P10S_f=\frac{1}{P_{10}}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Areal Fracture Intensity from Trace Length

P21=LtAsP_{21}=\frac{L_t}{A_s}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Volumetric Fracture Intensity from Fracture Area

P32=AfVrP_{32}=\frac{A_f}{V_r}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Fracture Porosity from Aperture and Volumetric Intensity

ϕf=bfP32\phi_f=b_fP_{32}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Fracture Permeability from Hydraulic Aperture Cubic Law

kf=bh212k_f=\frac{b_h^2}{12}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Parallel Fracture Set Permeability from Cubic Law

kset=bh312sfk_{set}=\frac{b_h^3}{12s_f}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Single-Fracture Flow Rate from Cubic Law

Q=Wbh3Δp12μLQ=\frac{Wb_h^3\Delta p}{12\mu L}
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Kazemi Rectangular Matrix-Block Shape Factor

α=4(1Lmx2+1Lmy2+1Lmz2)\alpha=4\left(\frac{1}{L_{mx}^2}+\frac{1}{L_{my}^2}+\frac{1}{L_{mz}^2}\right)
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Lim-Aziz Anisotropic Rectangular Matrix-Block Shape Factor

α=π2kmg(kxLmx2+kyLmy2+kzLmz2)\alpha=\frac{\pi^2}{k_{mg}}\left(\frac{k_x}{L_{mx}^2}+\frac{k_y}{L_{my}^2}+\frac{k_z}{L_{mz}^2}\right)
Open analysis
Geomechanics and FracturingNaturally Fractured Reservoirs

Matrix-Block Shape Factor from Dimensionless Constant

α=σDLm2\alpha=\frac{\sigma_D}{L_m^2}
Open analysis
Drilling EngineeringMud and Cementing

Difference in Pressure Gradient Between Cement and Mud

PG=(Wc−Wm)0.052PG = (W_c - W_m)0.052
Open analysis
Drilling EngineeringMud and Cementing

Mud Weight Reduction by Dilution

Vr=VmW1−W2W2−DwV_r = V_m\frac{W_1 - W_2}{W_2 - D_w}
Open analysis
Drilling EngineeringMud and Cementing

Pressure Required to Overcome Mud Gel Strength in Annulus

Pm=yL300(Dh−Dp)P_m = \frac{yL}{300(D_h - D_p)}
Open analysis
Drilling EngineeringMud and Cementing

Pressure Required to Overcome Mud Gel Strength Inside Drill String

Pm=yL300dP_m=\frac{yL}{300d}
Open analysis
Drilling EngineeringMud and Cementing

Increase Mud Density by Barite

B=1470W2−W135−W2B=1470\frac{W_2-W_1}{35-W_2}
Open analysis
Drilling EngineeringMud and Cementing

Increase Mud Density by Calcium Carbonate

B=945W2−W122.5−W2B=945\frac{W_2-W_1}{22.5-W_2}
Open analysis
Drilling EngineeringMud and Cementing

Increase Mud Density by Hematite

B=1680W2−W140−W2B=1680\frac{W_2-W_1}{40-W_2}
Open analysis
Drilling EngineeringMud and Cementing

Increase Volume by Barite

V=100W2−W135−W2V=100\frac{W_2-W_1}{35-W_2}
Open analysis
Drilling EngineeringMud and Cementing

Increase Volume by Calcium Carbonate

V=100W2−W122.5−W2V=100\frac{W_2-W_1}{22.5-W_2}
Open analysis
Drilling EngineeringMud and Cementing

Increase Volume by Hematite

V=100W2−W140−W2V=100\frac{W_2-W_1}{40-W_2}
Open analysis
Drilling EngineeringMud and Cementing

Initial Volume Required with Barite

Vi=Vf35−W235−W1V_i=V_f\frac{35-W_2}{35-W_1}
Open analysis
Drilling EngineeringMud and Cementing

Initial Volume Required with Calcium Carbonate

Vi=Vf22.5−W222.5−W1V_i=V_f\frac{22.5-W_2}{22.5-W_1}
Open analysis
Drilling EngineeringMud and Cementing

Initial Volume Required with Hematite

Vi=Vf40−W240−W1V_i=V_f\frac{40-W_2}{40-W_1}
Open analysis
Drilling EngineeringMud and Cementing

Weight of Additive per Sack of Cement

Wa=PaWcW_a=P_aW_c
Open analysis
Drilling EngineeringMud and Cementing

Total Water Requirement per Sack of Cement

Qw=Qc+QaQ_w=Q_c+Q_a
Open analysis
Drilling EngineeringMud and Cementing

Volume of Slurry per Sack of Cement

Vs=94Sc8.33+WaSa8.33+QwV_s=\frac{94}{S_c8.33}+\frac{W_a}{S_a8.33}+Q_w
Open analysis
Drilling EngineeringMud and Cementing

Slurry Density for Cementing Calculations

σs=94+Wa+8.33QwVs\sigma_s=\frac{94+W_a+8.33Q_w}{V_s}
Open analysis
Drilling EngineeringMud and Cementing

Cement Slurry Yield from Slurry Volume

Y=Vs7.48Y=\frac{V_s}{7.48}
Open analysis
Drilling EngineeringMud and Cementing

Cement Sacks Required from Slurry Volume

N=VcYN=\frac{V_c}{Y}
Open analysis
Drilling EngineeringMud and Cementing

Total Required Mixing Water for Cement Job

Vw=NQwV_w=NQ_w
Open analysis
Drilling EngineeringMud and Cementing

Lead Cement Sacks Required in Annulus

Nf=hcACEY1N_f=\frac{h_cACE}{Y_1}
Open analysis
Drilling EngineeringMud and Cementing

Tail Cement Sacks Required in Annulus

Na=htACEY2N_a=\frac{h_tACE}{Y_2}
Open analysis
Drilling EngineeringMud and Cementing

Tail Cement Sacks Required in Casing

Nc=hfcCY2N_c=\frac{h_{fc}C}{Y_2}
Open analysis
Drilling EngineeringMud and Cementing

Total Tail Cement Sacks Required

Nt=Na+NcN_t=N_a+N_c
Open analysis
Drilling EngineeringMud and Cementing

Spacer Volume Behind Slurry to Balance Cement Plug

Vs=CaEVaCpV_s=\frac{C_a}{E}V_aC_p
Open analysis
Drilling EngineeringMud and Cementing

Cuttings Volume Generated per Foot Drilled

Vc=Dh2(1−ϕ)1029.4V_c=\frac{D_h^2(1-\phi)}{1029.4}
Open analysis
Drilling EngineeringMud and Cementing

Total Solids Generated While Drilling

Wcg=350ChL(1−ϕ)SGcW_{cg}=350C_hL(1-\phi)SG_c
Open analysis
Drilling EngineeringMud and Cementing

Dilution Volume to Maintain Circulating Low-Gravity Solids

Vwm=VmFl−FoFl−FaV_{wm}=V_m\frac{F_l-F_o}{F_l-F_a}
Open analysis
Drilling EngineeringMud and Cementing

Annular Cement Volume for Casing Section

Vcem=CannLcemV_{cem}=C_{ann}L_{cem}
Open analysis
Drilling EngineeringMud and Cementing

Annular Spacer Volume for Casing Job

Vspacer=CannLspacerV_{spacer}=C_{ann}L_{spacer}
Open analysis
Drilling EngineeringMud and Cementing

Casing Displacement Volume to Float Collar

Vdisp=CcsgLfcV_{disp}=C_{csg}L_{fc}
Open analysis
Drilling EngineeringMud and Cementing

Displacement Strokes to Bump Cement Plug

Nstk=VdispPON_{stk}=\frac{V_{disp}}{PO}
Open analysis
Drilling EngineeringMud and Cementing

Spacer Contact Time from Turbulent-Flow Volume

tcontact=Vtf5.616qdispt_{contact}=\frac{V_{tf}}{5.616q_{disp}}
Open analysis
Drilling EngineeringMud and Cementing

Cement Slurry Pressure Gradient from Density

Gcem=0.05195ρcemG_{cem}=0.05195\rho_{cem}
Open analysis
Drilling EngineeringMud and Cementing

Cement Slurry Hydrostatic Pressure at Depth

Ph=GcemDP_h=G_{cem}D
Open analysis
Drilling EngineeringMud and Cementing

Internal Hydrostatic Pressure While Landing Cement Plug

Pint=0.05195(ρcemLshoe+ρdispLdisp)P_{int}=0.05195(\rho_{cem}L_{shoe}+\rho_{disp}L_{disp})
Open analysis
Drilling EngineeringMud and Cementing

Cement Plug Landing Differential Pressure

Pland=Pann−PintP_{land}=P_{ann}-P_{int}
Open analysis
Drilling EngineeringMud and Cementing

Cement Plug Landing Upward Force

Fup=AcsgPlandF_{up}=A_{csg}P_{land}
Open analysis
Drilling EngineeringMud and Cementing

Resulting Force After Casing Cementing Job

Fres=Fdown−FupF_{res}=F_{down}-F_{up}
Open analysis
Drilling EngineeringMud and Cementing

Cement Plug Sacks Required for Planned Length

Nplug=LplugChEYN_{plug}=\frac{L_{plug}C_hE}{Y}
Open analysis
Drilling EngineeringMud and Cementing

Cement Plug Slurry Volume from Sacks

Vslurry=NYV_{slurry}=NY
Open analysis
Drilling EngineeringMud and Cementing

Cement Remaining in Casing Above Cementing Tool

Vcsg=(Dset−Dtool)CcsgV_{csg}=(D_{set}-D_{tool})C_{csg}
Open analysis
Drilling EngineeringMud and Cementing

Cement Height in Annulus from Slurry Volume

hann=Vslurry−VcsgCannEh_{ann}=\frac{V_{slurry}-V_{csg}}{C_{ann}E}
Open analysis
Drilling EngineeringMud and Cementing

Top of Cement Depth from Annular Cement Height

Dtoc=Dset−hannD_{toc}=D_{set}-h_{ann}
Open analysis
Drilling EngineeringMud and Cementing

Balanced Cement Plug Length Before Pipe Withdrawal

Lpre=NYCannE+CpipeL_{pre}=\frac{NY}{C_{ann}E+C_{pipe}}
Open analysis
Drilling EngineeringMud and Cementing

Mud Volume Required to Spot Balanced Cement Plug

Vspot=(Dpipe−Lplug)Cpipe−VspacerV_{spot}=(D_{pipe}-L_{plug})C_{pipe}-V_{spacer}
Open analysis
Drilling EngineeringMud and Cementing

Load to Break Cement Bond

F=0.969ScdHF=0.969S_cdH
Open analysis
Drilling EngineeringMud and Cementing

API Water Loss from Seven-and-a-Half Minute Filtrate

V30=2Va−VspV_{30}=2V_a-V_{sp}
Open analysis
Drilling EngineeringMud and Cementing

Maximum Recommended Solids Fraction in Drilling Fluid

SF=2.917MW−14.17SF=2.917MW-14.17
Open analysis
Drilling EngineeringMud and Cementing

Maximum Recommended Low-Gravity Solids

LGS=200[SF100−0.3125(MW8.33−1)]LGS=200\left[\frac{SF}{100}-0.3125\left(\frac{MW}{8.33}-1\right)\right]
Open analysis
Drilling EngineeringMud and Cementing

Solid Content Ratio of Drilling Mud

fsm=fschmcAVmf_{sm}=\frac{f_{sc}h_{mc}A}{V_m}
Open analysis
Drilling EngineeringMud and Cementing

Filtration Rate for API Fluid Loss Measurement

dVfdt=kAΔPμhmc\frac{dV_f}{dt}=\frac{kA\Delta P}{\mu h_{mc}}
Open analysis
Drilling EngineeringMud and Cementing

Filtration Volume with Spurt Loss

Vf=Vsp+Vf2−Vf1t2−t1tV_f=V_{sp}+\frac{V_{f2}-V_{f1}}{\sqrt{t_2}-\sqrt{t_1}}\sqrt{t}
Open analysis
Drilling EngineeringMud and Cementing

Yield of Clays as Drilling Fluids

Eclay=1MclayE_{clay}=\frac{1}{M_{clay}}
Open analysis
Drilling EngineeringMud and Cementing

Drilling Mud Density - Solid Content Analysis of Drilling Muds

ρm=ρwfw+ρlgflg+ρBfB+ρofo\rho_m=\rho_wf_w+\rho_{lg}f_{lg}+\rho_Bf_B+\rho_of_o
Open analysis
Drilling EngineeringMud and Cementing

Area Below the Casing Shoe

A=0.7854Dc2A=0.7854D_c^2
Open analysis
Drilling EngineeringMud and Cementing

Differential Hydrostatic Pressure Between Cement Annulus and Mud in Casing

Pd=Pa−PcP_d=P_a-P_c
Open analysis
Drilling EngineeringMud and Cementing

Upward Force at the Bottom of the Casing Shoe

Fu=AΔPF_u=A\Delta P
Open analysis
Drilling EngineeringMud and Cementing

Specific Gravity of Cuttings by Mud Balance

SGc=12−0.12WrSG_c=\frac{1}{2-0.12W_r}
Open analysis
Drilling EngineeringMud and Cementing

Solids Analysis for High-Salt Content Muds

SW=(5.88×10−8CCl1.2+1)PvwSW=(5.88\times10^{-8}C_{Cl}^{1.2}+1)P_{vw}
Open analysis
Drilling EngineeringMud and Cementing

Lateral Load Imposed on a Casing Centralizer

FL,+=mWLsin⁡θ+2Tsin⁡δF_{L,+}=mWL\sin\theta+2T\sin\delta
Open analysis
Drilling EngineeringMud and Cementing

Radial Force Related to Axial Load in Cementing Slips

Wr=1−μtan⁡αμ+tan⁡αFW_r=\frac{1-\mu\tan\alpha}{\mu+\tan\alpha}F
Open analysis
Drilling EngineeringMud and Cementing

Volume of Liquid Oil plus Water Required to Prepare a Desired Volume of Mud

SV=35−W235−W1DVSV=\frac{35-W_2}{35-W_1}DV
Open analysis
Drilling EngineeringMud and Cementing

Combined Solubility of Hydrocarbon Gas, CO2, and H2S in a Mud Component

rs,c=fhrsh+fCO2rsCO2+fH2SrsH2Sr_{s,c}=f_hr_{sh}+f_{CO_2}r_{sCO_2}+f_{H_2S}r_{sH_2S}
Open analysis
Drilling EngineeringMud and Cementing

Gas Solubility in a Mud System

rsm=forso+fwrsw+ferser_{sm}=f_or_{so}+f_wr_{sw}+f_er_{se}
Open analysis
Drilling EngineeringMud and Cementing

Mud Weight Increase Required to Balance Pressure

Wm=FA(0.052)LcW_m=\frac{F}{A(0.052)L_c}
Open analysis
Drilling EngineeringMud and Cementing

Lateral Load Imposed on a Casing Centralizer with a Dogleg

FL,+=mWLsin⁡θ+2Tsin⁡δF_{L,+}=mWL\sin\theta+2T\sin\delta
Open analysis
Drilling EngineeringMud and Cementing

Optimal Solids Removal Efficiency

ηrs=1−1−Vs1−Vs+Vc/Vs\eta_{rs}=1-\frac{1-V_s}{1-V_s+V_c/V_s}
Open analysis
Drilling EngineeringMud and Cementing

Solids Control Efficiency

ηsce=VrVdVh\eta_{sce}=V_r\frac{V_d}{V_h}
Open analysis
Drilling EngineeringMud and Cementing

Solids Buildup in Mud System

Vsb=Vh(1−ηs)V_{sb}=V_h(1-\eta_s)
Open analysis
Drilling EngineeringMud and Cementing

Hydrocyclone Solids Removal Evaluation

MS=19530SFhcVTMS=19530SF_{hc}\frac{V}{T}
Open analysis
Drilling EngineeringMud and Cementing

Centrifuge Mud Processing Evaluation

QU=QM(MW−PO)−QW(PO−PW)PU−POQ_U=\frac{Q_M(MW-P_O)-Q_W(P_O-P_W)}{P_U-P_O}
Open analysis
Drilling EngineeringDirectional Drilling

Vertical Curvature for Deviated Wells

VC=(Ib−Ia)100ΔLVC = (I_b - I_a)\frac{100}{\Delta L}
Open analysis
Drilling EngineeringDirectional Drilling

Directional Curvature for a Deviated Well

DC=Δϕ100ΔLDC = \Delta\phi\frac{100}{\Delta L}
Open analysis
Drilling EngineeringDirectional Drilling

Dogleg Angle - Minimum Curvature Method

β=cos⁡−1[cos⁡I1cos⁡I2+sin⁡I1sin⁡I2cos⁡(A2−A1)]\beta=\cos^{-1}[\cos I_1\cos I_2+\sin I_1\sin I_2\cos(A_2-A_1)]
Open analysis
Drilling EngineeringDirectional Drilling

Dogleg Severity - Minimum Curvature Method

DLS=βdeg100ΔMDDLS=\frac{\beta_{deg}100}{\Delta MD}
Open analysis
Drilling EngineeringDirectional Drilling

Minimum Curvature Ratio Factor

RF=2βtan⁡(β2)RF=\frac{2}{\beta}\tan\left(\frac{\beta}{2}\right)
Open analysis
Drilling EngineeringDirectional Drilling

Minimum Curvature Survey Displacements

ΔN=ΔMD2(sin⁡I1cos⁡A1+sin⁡I2cos⁡A2)RF\Delta N=\frac{\Delta MD}{2}(\sin I_1\cos A_1+\sin I_2\cos A_2)RF
Open analysis
Drilling EngineeringDirectional Drilling

Radius of Curvature from Dogleg Severity

Rc=180πDLS100R_c=\frac{180}{\pi DLS}100
Open analysis
Drilling EngineeringDirectional Drilling

Tangential Survey Displacements

ΔN=ΔMDsin⁡I2cos⁡A2\Delta N=\Delta MD\sin I_2\cos A_2
Open analysis
Drilling EngineeringDirectional Drilling

Balanced Tangential Survey Displacements

ΔN=ΔMD2(sin⁡I1cos⁡A1+sin⁡I2cos⁡A2)\Delta N=\frac{\Delta MD}{2}(\sin I_1\cos A_1+\sin I_2\cos A_2)
Open analysis
Drilling EngineeringDirectional Drilling

Average Angle Survey Displacements

ΔN=ΔMDsin⁡(I1+I22)cos⁡(A1+A22)\Delta N=\Delta MD\sin\left(\frac{I_1+I_2}{2}\right)\cos\left(\frac{A_1+A_2}{2}\right)
Open analysis
Drilling EngineeringDirectional Drilling

Closure Distance and Direction

CD=N2+E2CD=\sqrt{N^2+E^2}
Open analysis
Drilling EngineeringDirectional Drilling

Build or Drop Rate from Inclination Change

BUR=(I2−I1)100ΔMDBUR=\frac{(I_2-I_1)100}{\Delta MD}
Open analysis
Drilling EngineeringDirectional Drilling

Projected Turn Rate from Azimuth Change

TR=(A2−A1)sin⁡(I1+I22)100ΔMDTR=\frac{(A_2-A_1)\sin\left(\frac{I_1+I_2}{2}\right)100}{\Delta MD}
Open analysis
Drilling EngineeringDirectional Drilling

Horizontal Wellbore Center-to-Center Separation

Sh=ΔN2+ΔE2S_h=\sqrt{\Delta N^2+\Delta E^2}
Open analysis
Drilling EngineeringDirectional Drilling

Three-Dimensional Wellbore Center-to-Center Separation

S3D=ΔN2+ΔE2+ΔTVD2S_{3D}=\sqrt{\Delta N^2+\Delta E^2+\Delta TVD^2}
Open analysis
Drilling EngineeringDirectional Drilling

EOU Clearance Distance for Wellbore Collision Avoidance

Eclear=CC−(Rref+Roff)E_{clear}=C_C-(R_{ref}+R_{off})
Open analysis
Drilling EngineeringDirectional Drilling

Wellbore Separation Factor from EOU Radii

SF=CCRref+RoffSF=\frac{C_C}{R_{ref}+R_{off}}
Open analysis
Drilling EngineeringDirectional Drilling

Minimum Allowable Separation Distance from Separation Factor

MASD=SFmin(Rref+Roff)MASD=SF_{min}(R_{ref}+R_{off})
Open analysis
Drilling EngineeringDirectional Drilling

Wellbore Separation Ratio to Minimum Allowable Distance

RMASD=CCMASDR_{MASD}=\frac{C_C}{MASD}
Open analysis
Drilling EngineeringDirectional Drilling

Build Section Measured Depth from Build Rate

ΔMD=I2−I1BUR/100\Delta MD=\frac{I_2-I_1}{BUR/100}
Open analysis
Drilling EngineeringDirectional Drilling

Radius-of-Curvature Build Section TVD Gain

ΔTVD=180ΔMD(sin⁡I2−sin⁡I1)π(I2−I1)\Delta TVD=\frac{180\Delta MD(\sin I_2-\sin I_1)}{\pi(I_2-I_1)}
Open analysis
Drilling EngineeringDirectional Drilling

Radius-of-Curvature Build Section Departure

ΔDEP=180ΔMD(cos⁡I1−cos⁡I2)π(I2−I1)\Delta DEP=\frac{180\Delta MD(\cos I_1-\cos I_2)}{\pi(I_2-I_1)}
Open analysis
Drilling EngineeringDirectional Drilling

Kickoff Point from Target TVD and Build Sections

KOP=TVDtarget−ΔTVDbuild1−ΔTVDtangent−ΔTVDbuild2KOP=TVD_{target}-\Delta TVD_{build1}-\Delta TVD_{tangent}-\Delta TVD_{build2}
Open analysis
Drilling EngineeringDirectional Drilling

Horizontal Section Inclination from Bed Dip and Thickness

Ih=90∘−dip−sin⁡−1(hresLh)I_h=90^\circ-dip-\sin^{-1}\left(\frac{h_{res}}{L_h}\right)
Open analysis
Drilling EngineeringDirectional Drilling

Target TVD Increase from Bed Dip and Departure

ΔTVDtarget=DEPtan⁡(dip)\Delta TVD_{target}=DEP\tan(dip)
Open analysis
Drilling EngineeringDirectional Drilling

Required Dogleg Severity from Build and Turn Components

DLSreq=BUR2+TR2DLS_{req}=\sqrt{BUR^2+TR^2}
Open analysis
Drilling EngineeringDirectional Drilling

Toolface Angle from Build and Turn Components

TF=atan2⁡(TR,BUR)TF=\operatorname{atan2}(TR,BUR)
Open analysis
Drilling EngineeringDirectional Drilling

Build Rate Component from Dogleg Severity and Toolface

BUR=DLSreqcos⁡(TF)BUR=DLS_{req}\cos(TF)
Open analysis
Drilling EngineeringDirectional Drilling

Turn Rate Component from Dogleg Severity and Toolface

TR=DLSreqsin⁡(TF)TR=DLS_{req}\sin(TF)
Open analysis
Drilling EngineeringDirectional Drilling

Sliding Percentage from Required and Motor Dogleg Severity

Sslide=DLSreqDLSmotor100S_{slide}=\frac{DLS_{req}}{DLS_{motor}}100
Open analysis
Drilling EngineeringDirectional Drilling

Maximum Slanted Well Length in Reservoir Thickness

L=hcos⁡(απ/180)L=\frac{h}{\cos(\alpha\pi/180)}
Open analysis
Drilling EngineeringDirectional Drilling

Curvature Radius for a Borehole

R=180C3.1415kR=\frac{180C}{3.1415k}
Open analysis
Drilling EngineeringDirectional Drilling

Borehole Torsion by Cylindrical Helical Method

t=kh(1+2kv2k2)sin⁡(aπ180)cos⁡(aπ180)t=k_h\left(1+\frac{2k_v^2}{k^2}\right)\sin\left(\frac{a\pi}{180}\right)\cos\left(\frac{a\pi}{180}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Effective Stress on Individual Grains

σg=S−Pp\sigma_g = S - P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Effect of Pore Pressure on Stress

S=λξoδ+2Gξ−αδPS = \lambda \xi_o \delta + 2G\xi - \alpha\delta P
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Fracture Gradient - Zoback and Healy

Shmin=(1+μf2+μf)−2(Sv−Pp)+PpS_{hmin} = (\sqrt{1 + \mu_f^2} + \mu_f)^{-2}(S_v - P_p) + P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pressure to Grow Fractures - Abe, Mura et al.

Pgrow=Sc1−(Pp/Sc)1−(cf/ci)21−1−(cf/ci)2P_{grow}=S_c\frac{1-(P_p/S_c)\sqrt{1-(c_f/c_i)^2}}{1-\sqrt{1-(c_f/c_i)^2}}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Radial Stress Around a Vertical Wellbore

σrr=0.5(Shmax+Shmin−2Po)(1−R2/r2)+0.5(Shmax−Shmin)(1+3R4/r4−4R2/r2)cos⁡(2θ)+PoR2/r2\sigma_{rr}=0.5(S_{hmax}+S_{hmin}-2P_o)(1-R^2/r^2)+0.5(S_{hmax}-S_{hmin})(1+3R^4/r^4-4R^2/r^2)\cos(2\theta)+P_oR^2/r^2
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Failure Criteria - Mohr-Coulomb Stress Components

τ=0.5(σa−σb)sin⁡(2β)\tau=0.5(\sigma_a-\sigma_b)\sin(2\beta)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Young's Modulus and Poisson Ratio

K=E3(1−2ν)K = \frac{E}{3(1 - 2\nu)}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shear Modulus from Young's Modulus and Poisson Ratio

G=E2(1+ν)G = \frac{E}{2(1 + \nu)}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Minimum Horizontal Stress Fracture Pressure

Shmin=ν1−ν(Sv−Pp)+PpS_{hmin}=\frac{\nu}{1-\nu}(S_v-P_p)+P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Classic Breakdown Pressure for a Vertical Wellbore

Pb=3Shmin−SHmax−Pp+ToP_b=3S_{hmin}-S_{Hmax}-P_p+T_o
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Pore Pressure Gradient from Resistivity Ratio

Gpp=Gob−(Gob−Gnp)(RoRn)1.2G_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{R_o}{R_n}\right)^{1.2}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Pore Pressure Gradient from Sonic Transit Time

Gpp=Gob−(Gob−Gnp)(ΔtnΔto)3G_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{\Delta t_n}{\Delta t_o}\right)^3
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Eaton Pore Pressure Gradient from Corrected D-Exponent

Gpp=Gob−(Gob−Gnp)(dcodcn)1.2G_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{d_{co}}{d_{cn}}\right)^{1.2}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Modified Eaton Pore Pressure Gradient from Specific Energy

Gpp=Gob−(Gob−Gnp)(SPEoSPEn)mG_{pp}=G_{ob}-(G_{ob}-G_{np})\left(\frac{SPE_o}{SPE_n}\right)^m
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Formation Compressibility from Hydrofrac Data

β=1VsdVsdP\beta=\frac{1}{V_s}\frac{dV_s}{dP}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Fracture Pressure - Hubbert and Willis

Shmin=0.3(Sv−Pp)+PpS_{hmin}=0.3(S_v-P_p)+P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Horizontal Effective Stress - Lorenz and Teufel

Shor=ν1−νSv+αP(1−ν1−ν)S_{hor}=\frac{\nu}{1-\nu}S_v+\alpha P\left(1-\frac{\nu}{1-\nu}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Horizontal Maximum Stress - Bredehoeft

Shmax=3Shmin−Pb−PpS_{hmax}=3S_{hmin}-P_b-P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Induced Fracture Dip

Dip=tan⁡−1(hd)\mathrm{Dip}=\tan^{-1}\left(\frac{h}{d}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Isothermal Compressibility of Limestones - Newman Correlation

Ct=97.32×10−6(1+55.8721ϕ)1.42869C_t=\frac{97.32\times10^{-6}}{(1+55.8721\phi)^{1.42869}}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Initial Effective Horizontal Stress

σh=ν1−ν(ρbH144−αPp)\sigma_h=\frac{\nu}{1-\nu}\left(\frac{\rho_bH}{144}-\alpha P_p\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Linearized Mohr Failure Line

τ=So+σnμi\tau=S_o+\sigma_n\mu_i
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Linearized Mohr-Coulomb Criteria

σ1=Co+(μ2+1+μ)2σc\sigma_1=C_o+(\sqrt{\mu^2+1}+\mu)^2\sigma_c
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

M Modulus from Shear and Bulk Modulus

M=K+4G3M=K+\frac{4G}{3}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

M Modulus from Young's Modulus and Poisson Ratio

M=E1−ν(1+ν)(1−2ν)M=E\frac{1-\nu}{(1+\nu)(1-2\nu)}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Pressure and Volume Strain

K=pΔV/VK=\frac{p}{\Delta V/V}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Least Principal Stress - Matthews and Kelly

Shmin=Ki(Sv−Pp)+PpS_{hmin}=K_i(S_v-P_p)+P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Principal Stress in Normal Faulting

σmax=σc(Sv−Pp)Shmin−Pp\sigma_{max}=\frac{\sigma_c(S_v-P_p)}{S_{hmin}-P_p}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Principal Stress in Reverse Faulting

σmax=σc(Shmax−Pp)Sv−Pp\sigma_{max}=\frac{\sigma_c(S_{hmax}-P_p)}{S_v-P_p}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Principal Stress in Strike-Slip Faulting

σmax=σc(Shmax−Pp)Shmin−Pp\sigma_{max}=\frac{\sigma_c(S_{hmax}-P_p)}{S_{hmin}-P_p}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Hoop Stress at the Wellbore Wall

σθ,max=3Shmax−Shmin−2Po−ΔP−Sdt\sigma_{\theta,max}=3S_{hmax}-S_{hmin}-2P_o-\Delta P-S_{dt}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Hoop Stress at the Wellbore Wall

σθ,min=3Shmin−Shmax−2Po−ΔP−Sdt\sigma_{\theta,min}=3S_{hmin}-S_{hmax}-2P_o-\Delta P-S_{dt}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Twisting Stress Around a Vertical Wellbore

τ=12(Shmax−Shmin)(1+2R2r2−3R4r4)sin⁡(2θ)\tau=\frac{1}{2}(S_{hmax}-S_{hmin})\left(1+\frac{2R^2}{r^2}-\frac{3R^4}{r^4}\right)\sin(2\theta)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Hoop Stress at the Wellbore Wall

σθ=Shmax+Shmin−2(Shmax−Shmin)cos⁡(2θ)−2Po−ΔP−Sdt\sigma_\theta=S_{hmax}+S_{hmin}-2(S_{hmax}-S_{hmin})\cos(2\theta)-2P_o-\Delta P-S_{dt}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Tangential Hoop Stress Near a Wellbore

Sgth=12(Shmax+Shmin−2Po)(1+R2r2)−12(Shmax−Shmin)(1+3R4r4)cos⁡(2θ)−PoR2r2−SdtSg_{th}=\frac{1}{2}(S_{hmax}+S_{hmin}-2P_o)\left(1+\frac{R^2}{r^2}\right)-\frac{1}{2}(S_{hmax}-S_{hmin})\left(1+\frac{3R^4}{r^4}\right)\cos(2\theta)-P_o\frac{R^2}{r^2}-S_{dt}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Maximum Horizontal Stress from Wellbore Breakout Width

Shmax=Co+2Pp+P+σt−Shmin(1+2cos⁡θb)1−2cos⁡θb,θb=(π−wb)/2S_{hmax}=\frac{C_o+2P_p+P+\sigma_t-S_{hmin}(1+2\cos\theta_b)}{1-2\cos\theta_b},\quad \theta_b=(\pi-w_b)/2
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Axial Stress at a Vertical Wellbore

σminaxial=3Shmin−Shmax−2Po−P−σt\sigma_{minaxial}=3S_{hmin}-S_{hmax}-2P_o-P-\sigma_t
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Unconfined Compressive Strength of Rock

Co=2So(μ2+1+μ)C_o=2S_o(\sqrt{\mu^2+1}+\mu)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Lame Constant and Shear Modulus

K=λ+2G3K=\lambda+\frac{2G}{3}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shear Wave Velocity from Shear Modulus and Density

Vs=(Gρ)0.5V_s=\left(\frac{G}{\rho}\right)^{0.5}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Mode I Fracture Stress Intensity

KI=(Pf−Sc)πL0.5K_I=(P_f-S_c)\pi L^{0.5}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Path for Induced Normal Faulting

A=1−1(μ2+1+μ)2A=1-\frac{1}{(\sqrt{\mu^2+1}+\mu)^2}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Reservoir Stress Path from Biot Coefficient and Poisson Ratio

A=α(1−2ν)1−νA=\frac{\alpha(1-2\nu)}{1-\nu}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pore Pressure of Shale Flemings

Pp=Sv−1βcln⁡(ϕoϕ)P_p=S_v-\frac{1}{\beta_c}\ln\left(\frac{\phi_o}{\phi}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pore Pressure Increase Due to Fluid Activity Mody and Hale

δP=Em(RTV)ln⁡(ApAm)\delta P=E_m\left(\frac{RT}{V}\right)\ln\left(\frac{A_p}{A_m}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Ratio of Pore Pressure Change to Original Due to Depletion

q=ΔPpShmax−Shminq=\frac{\Delta P_p}{S_{hmax}-S_{hmin}}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shale Compaction

ϕe=ϕe−βsσv\phi_e=\phi e^{-\beta_s\sigma_v}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Perturbation Segall and Fitzgerald

M=α(1−2ν)πH(1−ν)8RM=\alpha\frac{(1-2\nu)\pi H}{(1-\nu)8R}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Velocity of Bulk Compressional Waves

Vb=Eρ1−ν(1+ν)(1−2ν)V_b=\sqrt{\frac{E}{\rho}\frac{1-\nu}{(1+\nu)(1-2\nu)}}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Hoek and Brown Criteria for Principal Stress Failure

σa=σc+Comσc/Co+s\sigma_a=\sigma_c+C_o\sqrt{m\sigma_c/C_o+s}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Pore Pressure of Shale Traugott

Ppsh=z[Svz−(Svz−Phydroz)(RoRn)1.2]P_{psh}=z\left[\frac{S_v}{z}-\left(\frac{S_v}{z}-\frac{P_{hydro}}{z}\right)\left(\frac{R_o}{R_n}\right)^{1.2}\right]
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Components Near Normal Faulting in Reservoir

Sx=Shmax−AdP−AdP2(1−cos⁡2θ)S_x=S_{hmax}-AdP-\frac{AdP}{2}(1-\cos 2\theta)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Rotation of Maximum Principal Stress Near Wellbore

γ=12tan⁡−1(AΔPpsin⁡2θShmax−Shmin+AΔPpcos⁡2θ)\gamma=\frac{1}{2}\tan^{-1}\left(\frac{A\Delta P_p\sin 2\theta}{S_{hmax}-S_{hmin}+A\Delta P_p\cos 2\theta}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Rotation of Maximum Principal Stress Zoback Day Lewis

γ=12tan⁡−1(Aqsin⁡2Δ1+Aqcos⁡2Δ)\gamma=\frac{1}{2}\tan^{-1}\left(\frac{Aq\sin 2\Delta}{1+Aq\cos 2\Delta}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Subsidence Due to Uniform Pore Pressure Reduction in Free Surfaces

uz=−cm(1−ν)DΔPpVπ(r2+D2)1.5u_z=-\frac{c_m(1-\nu)D\Delta P_pV}{\pi(r^2+D^2)^{1.5}}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Tangential Stress Extremes at a Deviated Wellbore

σtmax=12(σzz+σaa+(σzz−σaa)2+4τ2)\sigma_{tmax}=\frac{1}{2}\left(\sigma_{zz}+\sigma_{aa}+\sqrt{(\sigma_{zz}-\sigma_{aa})^2+4\tau^2}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Stress Components in Original Coordinate System in Depletion Drive

Sx=Shmax−APp−AΔPp2(1−cos⁡2Δ)S_x=S_{hmax}-AP_p-\frac{A\Delta P_p}{2}(1-\cos 2\Delta)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Lame Constant and Poisson Ratio

K=λ(1+ν)3νK=\frac{\lambda(1+\nu)}{3\nu}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Bulk Modulus from Shear Modulus and Poisson Ratio

K=2G(1+ν)3(1−2ν)K=\frac{2G(1+\nu)}{3(1-2\nu)}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Compressional and Shear Wave Velocities from Elastic Moduli

Vp=K+4G/3ρV_p=\sqrt{\frac{K+4G/3}{\rho}}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shear Modulus from Force Area and Deformation Angle

G=F/AθG=\frac{F/A}{\theta}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Modified Lade Failure Criterion

η=(I13I3−27)(I1Pa)m\eta=\left(\frac{I_1^3}{I_3}-27\right)\left(\frac{I_1}{P_a}\right)^m
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Weak-Plane Anisotropic Failure Stress

σ=2σc(Sw+μσc)[1−μcot⁡(β)]sin⁡(2β)\sigma=\frac{2\sigma_c(S_w+\mu\sigma_c)}{[1-\mu\cot(\beta)]\sin(2\beta)}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Mud Pressure to Avoid Wellbore Breakout

PWshear=Pp+3σHmax−σhmin−UCS1+qP_{Wshear}=P_p+\frac{3\sigma_{Hmax}-\sigma_{hmin}-UCS}{1+q}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Wellbore Breakout Width from Mud Pressure

wBO=π−arccos⁡(σHmax+σhmin−UCS−(1+q)(PW−Pp)2(σHmax−σhmin))w_{BO}=\pi-\arccos\left(\frac{\sigma_{Hmax}+\sigma_{hmin}-UCS-(1+q)(P_W-P_p)}{2(\sigma_{Hmax}-\sigma_{hmin})}\right)
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Mud Pressure for Target Breakout Width

PWBO=Pp+(σHmax+σhmin)−2(σHmax−σhmin)cos⁡(π−wBO)−UCS1+qP_{WBO}=P_p+\frac{(\sigma_{Hmax}+\sigma_{hmin})-2(\sigma_{Hmax}-\sigma_{hmin})\cos(\pi-w_{BO})-UCS}{1+q}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Thermal Hoop Stress from Wellbore Temperature Change

σΔT=αTE1−νΔT\sigma^{\Delta T}=\frac{\alpha_T E}{1-\nu}\Delta T
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Tensile Breakdown Pressure with Thermal Stress

Pb=Pp−σHmax+3σhmin+Ts+σΔTP_b=P_p-\sigma_{Hmax}+3\sigma_{hmin}+T_s+\sigma^{\Delta T}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Drilling-Induced Tensile Fracture Margin

MT=σθθ+TsM_T=\sigma_{\theta\theta}+T_s
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Matthews-Kelly Fracture Gradient from Stress Ratio

Shmin=(σminσv)(Sv−Pp)+PpS_{hmin}=\left(\frac{\sigma_{min}}{\sigma_v}\right)(S_v-P_p)+P_p
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Radial Stress Near a Wellbore

σrr=12(Shmax+Shmin−2Po)(1−R2r2)+12(Shmax−Shmin)(1−4R2r2+3R4r4)cos⁡(2θ)+PoR2r2\sigma_{rr}=\frac{1}{2}(S_{hmax}+S_{hmin}-2P_o)\left(1-\frac{R^2}{r^2}\right)+\frac{1}{2}(S_{hmax}-S_{hmin})\left(1-4\frac{R^2}{r^2}+3\frac{R^4}{r^4}\right)\cos(2\theta)+P_o\frac{R^2}{r^2}
Open analysis
Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Mody-Hale Osmotic Pore-Pressure Increase from Molar Volume

ΔP=Em(RψLTVw)ln⁡(ApAm)\Delta P=E_m\left(\frac{R_{\psi L}T}{V_w}\right)\ln\left(\frac{A_p}{A_m}\right)
Open analysis
Reservoir EngineeringWaterflooding and EOR

Welge Extension Fractional Flow Relative Permeability Ratio

relpr=μwμo1−foforelpr=\frac{\mu_w}{\mu_o}\frac{1-f_o}{f_o}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Cumulative Oil Displacement from Water Saturation Change

Np=Vp(Sw−Siw)N_p=V_p(S_w-S_{iw})
Open analysis
Reservoir EngineeringWaterflooding and EOR

Waterflood Oil Displacement Ratio from Average Saturation

Qp=Sw−Siw1−fsQ_p=\frac{S_w-S_{iw}}{1-f_s}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Hot-Water Flood Fractional Flow from Mobility Ratio

fw(S,T)=11+M(S,T)−1f_{w(S,T)}=\frac{1}{1+M(S,T)^{-1}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Chromatographic Lag in Polymer Flooding

CL=11+Aρr(1−ϕ)CϕSwCL=\frac{1}{1+\frac{A\rho_r(1-\phi)}{C\phi S_w}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Slug Size in Polymer Floods

S=Aρr(1−ϕ)CϕS=\frac{A\rho_r(1-\phi)}{C\phi}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Areal Extent of Heated Zone in Thermal Recovery

A=QihMrG43560⋅4ΔTαsMs2A=\frac{Q_ihM_rG}{43560\cdot4\Delta T\alpha_sM_s^2}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Water-Drive Recovery Efficiency - Craig Correlation

ER=54.898(ϕ(1−Sw)Boi)0.0422(kμwiμoi)0.0770Sw−0.1903(PiPa)−0.2159E_R=54.898\left(\frac{\phi(1-S_w)}{B_{oi}}\right)^{0.0422}\left(\frac{k\mu_{wi}}{\mu_{oi}}\right)^{0.0770}S_w^{-0.1903}\left(\frac{P_i}{P_a}\right)^{-0.2159}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Latent Heat Fraction in Steam Drive Injection

fhv=[1+Cw(Ti−Ta)fsdhLhc]−1f_{hv}=\left[1+\frac{C_w(T_i-T_a)}{f_{sdh}L_{hc}}\right]^{-1}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steam Drive Heat Injection Rate from Boiler Feed Water

Qi=wi(62.4)(5.615)[Cw(Ti−Ta)+fsdhLhc]Q_i=w_i(62.4)(5.615)[C_w(T_i-T_a)+f_{sdh}L_{hc}]
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steam Zone Reservoir Volume from Injected Heat

Vs=QitEhs38.1⋅43560(Ti−Ta)V_s=\frac{Q_i t E_{hs}}{38.1\cdot43560(T_i-T_a)}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Hot-Water Flood Real Time from Dimensionless Time

t=h2Mr2tD4αsMs2t=\frac{h^2 M_r^2 t_D}{4\alpha_s M_s^2}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Hot-Water Flood Layer Saturation from Temperature

S=0.698−0.1(Tj−117275)S=0.698-0.1\left(\frac{T_j-117}{275}\right)
Open analysis
Reservoir EngineeringWaterflooding and EOR

Myhill-Stegemeier Thermal Dimensionless Time

tD=4(MsMR)2αsht2tt_D=4\left(\frac{M_s}{M_R}\right)^2\frac{\alpha_s}{h_t^2}t
Open analysis
Reservoir EngineeringWaterflooding and EOR

Dykstra-Parsons Coefficient

V=k50−k84.1k50V=\frac{k_{50}-k_{84.1}}{k_{50}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Effective Apparent Transmissivity

Tai=kaihaμaiT_{ai}=\frac{k_{ai}h_a}{\mu_{ai}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Fraction of Injected Heat Remaining in Reservoir

Eh=QQiE_h=\frac{Q}{Q_i}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Oil Solubilization Factor

S=CoCsS=\frac{C_o}{C_s}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Oil Breakthrough Newly Swept Zone

Onsz=PVΔEas(Swbt−Swi)O_{nsz}=PV\Delta E_{as}(S_{wbt}-S_{wi})
Open analysis
Reservoir EngineeringWaterflooding and EOR

Cumulative Heat Injected for Steam Drive - Myhill and Stegemeier

Qi=wi(cwΔT+fsdhLvdh)Q_i=w_i(c_w\Delta T+f_{sdh}L_{vdh})
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steam Drive Cumulative Oil Produced - Prats

Np=7758ϕhnht(Soi−Sor)EcVsN_p=7758\phi\frac{h_n}{h_t}(S_{oi}-S_{or})E_cV_s
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steam-Oil Ratio - Marx and Langenheim

Fso=Ws,eqNpF_{so}=\frac{W_{s,eq}}{N_p}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Heat Released During In-Situ Combustion - Burger and Sahuquet

(dh)a=94−67.9m+31.2x1−0.5m+0.25x(dh)_a=\frac{94-67.9m+31.2x}{1-0.5m+0.25x}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Heat Remaining in Reservoir - Marx and Langenheim

Q=QiMr2h2G4αsMs2Q=\frac{Q_iM_r^2h^2G}{4\alpha_sM_s^2}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Dimensionless Heat Injection Rate - Gringarten and Sauty

QiD=MfMrhti4αsMs2L2Q_{iD}=\frac{M_fM_rh_ti}{4\alpha_sM_s^2L^2}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Reservoir Fuel Burned per Bulk Volume - Nelson and McNiel

mR=1−ϕ1−ϕEmEm_R=\frac{1-\phi}{1-\phi_E}m_E
Open analysis
Reservoir EngineeringWaterflooding and EOR

Dimensionless Time in Wet Combustion - Kuo

tD=4Ms2αstMr2ht2t_D=\frac{4M_s^2\alpha_s t}{M_r^2h_t^2}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Equivalent Atomic H/C Ratio for In-Situ Combustion Fuel

xHC=4(1−mCO)0.27cN2−cO2cCO2+2mCO−4x_{HC}=4(1-m_{CO})\frac{0.27c_{N2}-c_{O2}}{c_{CO2}}+2m_{CO}-4
Open analysis
Reservoir EngineeringWaterflooding and EOR

Minimum Air Flux for Fire-Front Advance - Nelson and McNiel

umin=0.125arEO2u_{min}=\frac{0.125a_r}{E_{O2}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Combustion Front Advancement Rate

vb=EOuaarv_b=E_O\frac{u_a}{a_r}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Dimensionless Air Injection Rate for In-Situ Combustion

iD=iaLhumini_D=\frac{i_a}{Lhu_{min}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Burned Reservoir Volume from Air Requirement

Vrb=0.0230GaEOaRV_{rb}=0.0230\frac{G_aE_O}{a_R}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Water Cut - Stiles

fw=khMwokhMwo+ktht−khf_w=\frac{khM_{wo}}{khM_{wo}+k_th_t-kh}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Average Reservoir Temperature in Cyclic Steam Injection

Ta=Ti+(Ts−Ti)[fVDfHD(1−fpD)−fpD]T_a=T_i+(T_s-T_i)[f_{VD}f_{HD}(1-f_{pD})-f_{pD}]
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steam-Heated Area Growth - Marx and Langenheim

As=QietDEt43560ΔTMrhA_s=\frac{Q_i e^{t_D}E_t}{43560\Delta T M_rh}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Hot-Water Heated-Zone Area Growth Rate

A˙=1.289×10−4qTjfwϕh\dot A=1.289\times10^{-4}\frac{qT_jf_w}{\phi h}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Effective Oil Transmissivity for Thermal Stimulation

Tao=141.2FGRqmaxT_{ao}=141.2\frac{F_G}{R_{qmax}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Equivalent Water Saturation in Burned Zone - Nelson

SwF=0.319xarϕ(4−2m+x)S_{wF}=\frac{0.319xa_r}{\phi(4-2m+x)}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Equivalent Steam Volume Injected - Myhill and Stegemeier

Ws,eq=2.853×10−6Cw(Tsb−Ta)+fsbLvbCw(Ti−To)+fvdhLvdhW_{s,eq}=2.853\times10^{-6}\frac{C_w(T_{sb}-T_a)+f_{sb}L_{vb}}{C_w(T_i-T_o)+f_{vdh}L_{vdh}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Heated-Zone Oil Recovery from Air-Oil Ratio

Ecb=5.615arFϕEO2(Soi−Sof)E_{cb}=\frac{5.615a_r}{F\phi E_{O2}(S_{oi}-S_{of})}
Open analysis
Reservoir EngineeringWaterflooding and EOR

In-Situ Combustion Oil Production - Nelson and McNeil

Np=7758ϕ[Vr(Si−Sf)+0.4(Vp−Vr)Si]N_p=7758\phi\left[V_r(S_i-S_f)+0.4(V_p-V_r)S_i\right]
Open analysis
Reservoir EngineeringWaterflooding and EOR

In-Situ Combustion Water Production - Nelson and McNeil

Wp=7758Vrϕ(Siw−Sfw)W_p=7758V_r\phi(S_{iw}-S_{fw})
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steady-State Five-Spot Steam-Drive Injection Rate

i=(7.082×10−32π)(πk(h/μ)ln⁡(208.71A/rw)−0.964)(Pi−Pb)i=\left(\frac{7.082\times10^{-3}}{2\pi}\right)\left(\frac{\pi k(h/\mu)}{\ln(208.71\sqrt{A}/r_w)-0.964}\right)(P_i-P_b)
Open analysis
Reservoir EngineeringWaterflooding and EOR

Wet In-Situ Combustion Oil Production - Nelson and McNeil

Np=(7758ϕEfirehnht)[Vr(Si−Sf)+Vs(Si−Sr)]N_p=\left(\frac{7758\phi E_{fire}h_n}{h_t}\right)[V_r(S_i-S_f)+V_s(S_i-S_r)]
Open analysis
Reservoir EngineeringWaterflooding and EOR

Ignition Delay Time in In-Situ Combustion

tig=2.04×10−7MrTa2(1+2RTa/Ea)Rexp⁡(Ea/RTa)EaΔhaϕSoρoAcPO2nt_{ig}=\frac{2.04\times10^{-7}M_rT_a^2(1+2RT_a/E_a)R\exp(E_a/RT_a)}{E_a\Delta h_a\phi S_o\rho_oA_cP_{O2}^{n}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Oxygen Reaction Rate per Unit Fuel Mass

moxy=PO2Acexp⁡(EaRTa)m_{oxy}=P_{O2}A_c\exp\left(\frac{E_a}{RT_a}\right)
Open analysis
Reservoir EngineeringWaterflooding and EOR

Dimensionless Steam Heat-Capacity Ratio

Fdh=ρw(CwΔT+fsLv)MrΔTF_{dh}=\frac{\rho_w(C_w\Delta T+f_sL_v)}{M_r\Delta T}
Open analysis
Reservoir EngineeringWaterflooding and EOR

In-Situ Combustion Temperature Increase Rate

dTdt=86400(SoρoϕAcPO2nMr)exp⁡(−EaRTab)\frac{dT}{dt}=86400\left(\frac{S_o\rho_o\phi A_cP_{O2}^{n}}{M_r}\right)\exp\left(-\frac{E_a}{RT_{ab}}\right)
Open analysis
Reservoir EngineeringWaterflooding and EOR

Steam-Zone Growth Increment from Heat Capacity

dzs=(4Msα1/2CwTLvMRse)dtπdz_s=\left(\frac{4M_s\alpha^{1/2}C_wT}{L_vM_{Rse}}\right)\sqrt{\frac{dt}{\pi}}
Open analysis
Reservoir EngineeringWaterflooding and EOR

Oil Volume at Breakthrough - Craig, Geffen, and Morse

Obt=PV Eas,bt(Swbt,av−Swi)O_{bt}=PV\,E_{as,bt}(S_{wbt,av}-S_{wi})
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Maximum Equivalent Derrick Load

Fde=(n+4n)FhF_{de}=\left(\frac{n+4}{n}\right)F_h
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Maximum Length of Drillpipe for a Specific Bottomhole Assembly

Lm=[(Tf)−MOP−Wb]BFWdL_m=\frac{[(Tf)-MOP-W_b]BF}{W_d}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Maximum Weight on Bit

WOB=LdWdBFcos⁡(απ/180)SFWOB=\frac{L_dW_dBF\cos(\alpha\pi/180)}{SF}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Drillstring Buoyancy Factor from Mud Weight

BF=65.5−MW65.5BF=\frac{65.5-MW}{65.5}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Effective Drillstring Weight During Drilling

wo=ws(1−ρoρs)w_o=w_s\left(1-\frac{\rho_o}{\rho_s}\right)
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Round Trip Ton Miles

RTTM=WpD(Lp+D)+2D(2Wb+Wc)5280⋅2000RT_{TM}=\frac{W_pD(L_p+D)+2D(2W_b+W_c)}{5280\cdot2000}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Drilling and Connection Ton Miles

TD=3(T2−T1)T_D=3(T_2-T_1)
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Coring Operation Ton Miles

Tc=2(T4−T3)T_c=2(T_4-T_3)
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Short Trip Ton Miles

TST=T6−T5T_{ST}=T_6-T_5
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Setting Casing Ton Miles

Tc=0.5[WpD(Lcs+D)+DWb]5280⋅2000T_c=\frac{0.5\left[W_pD(L_{cs}+D)+DW_b\right]}{5280\cdot2000}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Stretch Force from Elastic Elongation

F=AE(La−LbLb)F=AE\left(\frac{L_a-L_b}{L_b}\right)
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Crown Block Capacity

Rc=(H1+S)(n+2)nR_c=\frac{(H_1+S)(n+2)}{n}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Efficiency of Block and Tackle System

Ebt=FhvtFfvfE_{bt}=\frac{F_hv_t}{F_fv_f}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Traveling Block Speed from Fast Line Speed

vtb=vfnv_{tb}=\frac{v_f}{n}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Bottomhole Assembly Length for Desired Weight on Bit

L=WbfWdBFL=\frac{W_bf}{W_dBF}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Stuck Pipe Free Point from Pipe Stretch - Method 1

hf=SfpcPFh_f=\frac{Sfpc}{PF}
Open analysis
Drilling EngineeringDrillstring and Rig Mechanics

Stuck Pipe Free Point from Pipe Stretch - Method 2

hf=735294eWdpPdh_f=\frac{735294eW_{dp}}{P_d}
Open analysis
Drilling EngineeringDrilling Operations and Economics

Drill-Rate Model Penetration Rate

R=K(Wdb)aWNaNR=K\left(\frac{W}{d_b}\right)^{a_W}N^{a_N}
Open analysis
Drilling EngineeringDrilling Operations and Economics

Rotary-Speed Drill-Rate Model Penetration Rate

R=K′NaNR=K'N^{a_N}
Open analysis
Drilling EngineeringDrilling Operations and Economics

Bit Run Drilling Cost per Foot

CT=B+CR(t+T)FC_T=\frac{B+C_R(t+T)}{F}
Open analysis
Drilling EngineeringDrilling Operations and Economics

Detailed Drilling Cost per Foot

Cd=Cb+Cto+Cm+(Td+Tt+Tc)(Cr+Cs+Ctr)FTdC_d=\frac{C_b+C_{to}+C_m+(T_d+T_t+T_c)(C_r+C_s+C_{tr})}{FT_d}
Open analysis
Drilling EngineeringDrilling Operations and Economics

D-Exponent from Drilling Parameters

d=log⁡[R/(60N)]log⁡[12Wk/(1000Db)]d=\frac{\log[R/(60N)]}{\log[12W_k/(1000D_b)]}
Open analysis
Drilling EngineeringDrilling Operations and Economics

Rock Removal Rate from Bit Diameter and ROP

qr=db2R11000q_r=\frac{d_b^2R}{11000}
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Drilling EngineeringDrilling Operations and Economics

Gas Portion Entry Rate from Rock Removal

qg=qrϕSgq_g=q_r\phi S_g
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Drilling EngineeringDrilling Operations and Economics

Drilled Gas Entry Rate

qgsc=db2RϕSgp310zTq_{gsc}=\frac{d_b^2R\phi S_gp}{310zT}
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Drilling EngineeringDrilling Operations and Economics

Gas Mud Ratio from Drilled Gas

rm=db2RϕSgp310zTqmr_m=\frac{d_b^2R\phi S_gp}{310zTq_m}
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Drilling EngineeringDrilling Operations and Economics

Rotating Horsepower from Torque and Speed

RHP=TN5252RHP=\frac{TN}{5252}
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Drilling EngineeringDrilling Operations and Economics

Mechanical Specific Energy

MSE=WOBAb+120πNTAbROPMSE=\frac{WOB}{A_b}+\frac{120\pi NT}{A_bROP}
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Drilling EngineeringDrilling Operations and Economics

Hydromechanical Specific Energy

HMSE=WOBAb+120(3.142)NT+1154ηPbQAbROPHMSE=\frac{WOB}{A_b}+\frac{120(3.142)NT+1154\eta P_bQ}{A_bROP}
Open analysis
Drilling EngineeringDrilling Operations and Economics

Control Drilling Maximum Drilling Rate

MDR=67(MWo−MWi)qDh2MDR=67(MW_o-MW_i)\frac{q}{D_h^2}
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