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Reservoir Engineering Calculators

Use 303 reservoir engineering petroleum engineering calculators with formulas, units, default values, and source references.

Reservoir engineering calculators cover volumetrics, Darcy flow, material balance, pressure transient analysis, reserves, recovery, and well performance.

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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}
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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)}
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Reservoir EngineeringPVT and Rock-Fluid Properties

API Gravity

API=141.5SGo−131.5API = \frac{141.5}{SG_o} - 131.5
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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}
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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}
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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)
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Reservoir EngineeringReserves and Recovery

Arps Exponential Decline Rate

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

Arps Harmonic Decline Rate

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

Arps Hyperbolic Decline Rate

q(t)=qi(1+bDit)1/bq(t)=\frac{q_i}{(1+bD_it)^{1/b}}
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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}}
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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}
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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}
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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)}
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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}]
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Reservoir EngineeringThermal Gradients

Average Temperature of a Gas Column

T=Tt+Tb2T = \frac{T_t + T_b}{2}
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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}
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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}
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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}
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Reservoir EngineeringPermeability and Flow

Buckley-Leverett Saturation Front Velocity

vS=utϕdfwdSwv_S = \frac{u_t}{\phi}\frac{df_w}{dS_w}
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Reservoir EngineeringWaterflooding and EOR

Burned Reservoir Volume from Air Requirement

Vrb=0.0230GaEOaRV_{rb}=0.0230\frac{G_aE_O}{a_R}
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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}}
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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}}
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Reservoir EngineeringPVT and Rock-Fluid Properties

Capillary Pressure

Pc=2⋅σ⋅cos⁡(θ)rP_c = \frac{2 \cdot \sigma \cdot \cos(\theta)}{r}
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Reservoir EngineeringPressure Transient Analysis

Carter Dimensionless Drawdown Correlating Parameter

λ=μgicgiμgavgcgavg\lambda=\frac{\mu_{gi}c_{gi}}{\mu_{gavg}c_{gavg}}
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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}
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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}}
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Reservoir EngineeringUnconventional Reservoirs

Coal Mass from Area Thickness and Bulk Density

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

Coalbed Methane Formation Compressibility

ct=WpWi(Pi−Pd)c_t = \frac{W_p}{W_i(P_i-P_d)}
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Reservoir EngineeringPressure Transient Analysis

Cole Plot

F=G⋅Eg+WeF = G \cdot E_g + W_e
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Reservoir EngineeringWaterflooding and EOR

Combustion Front Advancement Rate

vb=EOuaarv_b=E_O\frac{u_a}{a_r}
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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}
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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}
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Reservoir EngineeringReserves and Recovery

Condensate Production Rate from Gas Rate and Yield

qc=qgYc1000q_c=\frac{q_gY_c}{1000}
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Reservoir EngineeringThermal Gradients

Conductive Heat Flow from Geothermal Gradient

q=kΔTΔzq = k\frac{\Delta T}{\Delta z}
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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
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Reservoir EngineeringRock Properties

Core Bulk Volume from Saturated and Immersed Weights

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

Core Pore Volume from Saturated and Dry Weights

Vp=Ws−WdρsV_p=\frac{W_s-W_d}{\rho_s}
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Reservoir EngineeringPermeability and Flow

Corey Oil Relative Permeability

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

Corey Water Relative Permeability

krw=krwo(Sw∗)nwk_{rw} = k_{rw}^o(S_w^*)^{n_w}
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Reservoir EngineeringUnconventional Reservoirs

Correction Factor – Hammerlindl

CDI=G⋅Ef,wGp⋅BgCDI = \frac{G \cdot E_{f,w}}{G_p \cdot B_g}
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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
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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}
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Reservoir EngineeringPermeability and Flow

Crossflow Index

CI=Npcf−NpncfNpu−NpncfCI = \frac{N_{pcf} - N_{pncf}}{N_{pu} - N_{pncf}}
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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}}
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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)
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Reservoir EngineeringMaterial Balance

Cumulative Gas Production from Gas Expansion

Gp=G(1−BgiBg)G_p = G\left(1-\frac{B_{gi}}{B_g}\right)
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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})
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Reservoir EngineeringWaterflooding and EOR

Cumulative Oil Displacement from Water Saturation Change

Np=Vp(Sw−Siw)N_p=V_p(S_w-S_{iw})
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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
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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
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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}
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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)}
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Reservoir EngineeringWaterflooding and EOR

Dimensionless Air Injection Rate for In-Situ Combustion

iD=iaLhumini_D=\frac{i_a}{Lhu_{min}}
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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}
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Reservoir EngineeringPressure Transient Analysis

Dimensionless Buildup Pressure from Semilog Slope

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

Dimensionless Buildup Time

tD=0.3604kDtϕμctrw2t_D=\frac{0.3604k_Dt}{\phi\mu c_tr_w^2}
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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})}
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Reservoir EngineeringWell Performance

Dimensionless Fracture Conductivity

FCD=kfwfkXfF_{CD}=\frac{k_fw_f}{kX_f}
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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}
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Reservoir EngineeringPressure Transient Analysis

Dimensionless Length for Fracture Linear Flow

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

Dimensionless Length for Linear Flow General Case

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

Dimensionless Pressure - Radial Flow Constant-Pressure Production

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

Dimensionless Production Time

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

Dimensionless Radius of Radial Flow – Constant-Rate Production

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

Dimensionless Storage Constant for Gas Buildup Tests

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

Dimensionless Storage Constant for Liquid Buildup Tests

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

Dimensionless Time for Fracture Linear Flow

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

Dimensionless Time for Linear Flow Constant Rate General Case

tDA=0.0002637ktϕμctAt_{DA}=\frac{0.0002637kt}{\phi\mu c_tA}
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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}
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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}
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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}
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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)
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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}
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Reservoir EngineeringFluid Flow in Porous Media

Drainage Radius from Area

re=43560Aπr_e=\sqrt{\frac{43560A}{\pi}}
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Reservoir EngineeringPressure Transient Analysis

Drawdown Semilog Slope for Bottomhole Flowing Pressure

m=162.6QoμoBokhm=\frac{162.6Q_o\mu_oB_o}{kh}
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Reservoir EngineeringWaterflooding and EOR

Dykstra-Parsons Coefficient

V=k50−k84.1k50V=\frac{k_{50}-k_{84.1}}{k_{50}}
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Reservoir EngineeringWaterflooding and EOR

Effective Apparent Transmissivity

Tai=kaihaμaiT_{ai}=\frac{k_{ai}h_a}{\mu_{ai}}
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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}}
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Reservoir EngineeringWaterflooding and EOR

Effective Oil Transmissivity for Thermal Stimulation

Tao=141.2FGRqmaxT_{ao}=141.2\frac{F_G}{R_{qmax}}
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Reservoir EngineeringRock Properties

Effective Porosity from Connected Pore Volume

ϕe=VconnectedVb\phi_e = \frac{V_{connected}}{V_b}
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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}}}
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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}}
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Reservoir EngineeringWell Performance

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

rw=Xfer_w = \frac{X_f}{e}
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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}
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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
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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}}
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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)}
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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)
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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)
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Reservoir EngineeringRock Properties

Exponential Pore Volume from Rock Compressibility

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

Exponential Porosity from Rock Compressibility

ϕ=ϕrefexp⁡(cr(P−Pref))\phi = \phi_{ref}\exp(c_r(P-P_{ref}))
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Reservoir EngineeringWell Performance

Finite-Conductivity Fracture Effective Wellbore Radius

rwe=0.2807kfbfkr_{we}=\frac{0.2807k_fb_f}{k}
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Reservoir EngineeringPressure Transient Analysis

Flow Period Duration for Hydraulically Fractured Wells

t=ϕμctLf2tLfD0.0002637kt=\frac{\phi\mu c_tL_f^2t_{LfD}}{0.0002637k}
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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)
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Reservoir EngineeringWaterflooding and EOR

Fraction of Injected Heat Remaining in Reservoir

Eh=QQiE_h=\frac{Q}{Q_i}
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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)
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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]
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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
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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}
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Reservoir EngineeringUnconventional Reservoirs

Gas Adsorbed in Coalbed Methane Reservoirs

Ga=1359.7AhρbVG_a = 1359.7 A h \rho_b V
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Reservoir EngineeringMaterial Balance and Production

Gas Cap Ratio

m=GBgiNBoim=\frac{GB_{gi}}{NB_{oi}}
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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)
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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)
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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})}
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Reservoir EngineeringPVT Properties

Gas Expansion Factor from Formation Volume Factor

Eg=35.37PzTE_g = 35.37 \frac{P}{zT}
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Reservoir EngineeringMaterial Balance

Gas Expansion Term in Gas Reservoirs

Eg=Bg−BgiE_g = B_g - B_{gi}
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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}
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Reservoir EngineeringPVT Properties

Gas Formation Volume Factor

Bg=0.02827zTPB_g = 0.02827 \frac{zT}{P}
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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
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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)}
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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)
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Reservoir EngineeringMaterial Balance

Gas Recovery Factor from p/z Material Balance

RFg=1−PzPi/ziRF_g=1-\frac{P_z}{P_i/z_i}
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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}}}
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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
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Reservoir EngineeringReserves and Recovery

Gas-Condensate Liquid Content from Producing GOR

Yc=106GORpY_c=\frac{10^6}{GOR_p}
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Reservoir EngineeringWell Performance

Generalized Reservoir Gas Flow Deliverability

W=C(pˉ2−pwf2)nW=C(\bar p^2-p_{wf}^2)^n
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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)
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Reservoir EngineeringThermal Gradients

Geothermal Gradient from Temperature Log Interval

G=Tdeep−Tshallowzdeep−zshallow 1000G = \frac{T_{deep}-T_{shallow}}{z_{deep}-z_{shallow}}\,1000
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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]
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Reservoir EngineeringReservoir Volumetrics

Gross Rock Volume from Area and Gross Thickness

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

Gross Rock Volume in Acre-Feet from Area and Thickness

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

Gross Rock Volume in Reservoir Barrels

Vgrv,bbl=7758AhgV_{grv,bbl}=7758Ah_g
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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}}
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Reservoir EngineeringMaterial Balance and Production

Hammerlindl Method for Gas in Place

G=GappRG=\frac{G_{app}}{R}
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Reservoir EngineeringMaterial Balance

Havlena-Odeh Cumulative Water Influx from Fluid Withdrawal

We=F−GEGW_e=F-GE_G
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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}
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Reservoir EngineeringWaterflooding and EOR

Heat Remaining in Reservoir - Marx and Langenheim

Q=QiMr2h2G4αsMs2Q=\frac{Q_iM_r^2h^2G}{4\alpha_sM_s^2}
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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})}
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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]}
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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)}
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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}
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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)
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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)
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Reservoir EngineeringPressure Transient Analysis

Horner Semilog Buildup Pressure Extrapolation

pws=p∗−mlog⁡10(H)p_{ws}=p^*-m\log_{10}(H)
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Reservoir EngineeringThermal Gradients

Horner Time Ratio for Bottom-Hole Temperature Correction

H=tc+ΔtΔtH = \frac{t_c+\Delta t}{\Delta t}
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Reservoir EngineeringPressure Transient Analysis

Horner Time Ratio for Pressure Buildup Test

H=tp+ΔtΔtH=\frac{t_p+\Delta t}{\Delta t}
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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}}
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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)
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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}
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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}
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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}
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Reservoir EngineeringFluid Flow in Porous Media

Hydraulic Diffusivity Coefficient in Field Units

η=0.0002637kϕμct\eta=\frac{0.0002637k}{\phi\mu c_t}
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Reservoir EngineeringReservoir Volumetrics

Hydrocarbon Pore Volume - Volumetric Method

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

Hydrocarbon Pore Volume from Pore Volume and Water Saturation

HCPV=PV(1−Swi)HCPV=PV(1-S_{wi})
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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
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Reservoir EngineeringMaterial Balance and Production

Hydrocarbon Pore Volume Occupied by Gas Cap

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

Hydrocarbon Pore Volume Occupied by Remaining Oil

Vro=(N−Np)BoV_{ro}=(N-N_p)B_o
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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}}
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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]
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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)
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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})
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Reservoir EngineeringRock Properties

Ineffective Porosity from Disconnected Pore Volume

ϕin=VdisVb\phi_{in}=\frac{V_{dis}}{V_b}
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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]
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Reservoir EngineeringMaterial Balance

Initial Gas Cap

G=mNBoiBgiG = \frac{m N B_{oi}}{B_{gi}}
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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}}
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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}
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Reservoir EngineeringFluid Flow in Porous Media

Interstitial Velocity from Flow Rate Area and Porosity

vp=qϕAv_p=\frac{q}{\phi A}
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Reservoir EngineeringPermeability

Jones-Owens Klinkenberg Slip Factor

b=12.639k∞−0.33b = 12.639 k_{\infty}^{-0.33}
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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)}
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Reservoir EngineeringWell Performance

Joshi Horizontal Well Drainage Ellipse Area

Aac=πrehrev43560A_{ac}=\frac{\pi r_{eh}r_{ev}}{43560}
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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]}
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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}}
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Reservoir EngineeringPermeability

Klinkenberg Apparent Gas Permeability

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

Kozeny Permeability from Porosity and Specific Surface Area

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

Kozeny-Carman Permeability from Grain Diameter

k=Bϕ3d2τk=\frac{B\phi^3d^2}{\tau}
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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]}
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Reservoir EngineeringUnconventional Reservoirs

Langmuir Adsorbed Gas Content

Gc=VLPPL+PG_c = \frac{V_L P}{P_L + P}
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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)
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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}
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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})]
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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}
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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)
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Reservoir EngineeringFluid Flow in Porous Media

Linear Darcy Flow Conductance

CL=0.001127kAμLC_L=\frac{0.001127kA}{\mu L}
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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]
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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]}
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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]}
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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}
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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]
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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)
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Reservoir EngineeringWaterflooding and EOR

Minimum Air Flux for Fire-Front Advance - Nelson and McNiel

umin=0.125arEO2u_{min}=\frac{0.125a_r}{E_{O2}}
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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}
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Reservoir EngineeringMaterial Balance

Modified Cole Plot for Water-Drive Gas Reservoirs

FEt=G+WeEt\frac{F}{E_t}=G+\frac{W_e}{E_t}
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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
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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
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Reservoir EngineeringReservoir Volumetrics

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

h=hgNTGh=h_gNTG
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Reservoir EngineeringReservoir Volumetrics

Net Reservoir Rock Volume from Net-to-Gross

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

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

Vnrv,bbl=7758AhgNTGV_{nrv,bbl}=7758Ah_gNTG
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Reservoir EngineeringReserves and Recovery

NGL Production Rate from Gas Rate and Yield

qNGL=qgYNGL1000q_{NGL}=\frac{q_gY_{NGL}}{1000}
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Reservoir EngineeringPermeability and Flow

Normalized Saturation

Son=1−Sw−Sor1−Swi−SorS_{on}=\frac{1-S_w-S_{or}}{1-S_{wi}-S_{or}}
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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}}
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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
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Reservoir EngineeringWaterflooding and EOR

Oil Breakthrough Newly Swept Zone

Onsz=PVΔEas(Swbt−Swi)O_{nsz}=PV\Delta E_{as}(S_{wbt}-S_{wi})
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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}
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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}
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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}
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Reservoir EngineeringReserves and Recovery

Oil Lost During Gas-Cap Migration

O=7758AhϕSorgBoaO=7758Ah\phi\frac{S_{org}}{B_{oa}}
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Reservoir EngineeringMaterial Balance and Production

Oil Material Balance Drive Index Closure

DIsum=DDI+GDI+WDI+CDIDI_{sum} = DDI + GDI + WDI + CDI
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Reservoir EngineeringReserves and Recovery

Oil Recovery Factor from Cumulative Production

RF=NpNRF = \frac{N_p}{N}
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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
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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}}
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Reservoir EngineeringWaterflooding and EOR

Oil Solubilization Factor

S=CoCsS=\frac{C_o}{C_s}
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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})
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Reservoir EngineeringReservoir Volumetrics

Original Condensate In Place from Gas In Place and Liquid Content

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

Original Gas in Place - Volumetric Method

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

Original Oil in Place - Volumetric Method

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

Original Water In Place with Net-to-Gross

W=7758AhgNTGϕSwiBwiW=\frac{7758Ah_gNTG\phi S_{wi}}{B_{wi}}
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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)
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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]
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Reservoir EngineeringPressure Transient Analysis

Permeability from Pressure Transient Semilog Slope

k=162.6qBμmhk=\frac{162.6qB\mu}{mh}
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Reservoir EngineeringRock Properties

Pore Throat Sorting from Capillary Pressure Quartiles

PTS=(Q3Q1)0.5PTS=\left(\frac{Q_3}{Q_1}\right)^{0.5}
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Reservoir EngineeringReservoir Volumetrics

Pore Volume from Net Rock Volume and Porosity

PV=Vnrv,bblϕPV=V_{nrv,bbl}\phi
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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}
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Reservoir EngineeringWell Performance

Prats High-Conductivity Fracture Effective Wellbore Radius

rwe=Xf2r_{we}=\frac{X_f}{2}
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Reservoir EngineeringMaterial Balance and Production

Produced Gas-Oil Ratio

Rp=GpNpR_p=\frac{G_p}{N_p}
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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)}
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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
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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
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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}
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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]}
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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]}
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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]}
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Reservoir EngineeringPressure Transient Analysis

Pseudosteady-State Slope in Pressure Buildup Test

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

Radius of Investigation

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

Radius of Investigation from Flow Time

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

Radius of Investigation from Shut-In Time

ri=kΔt948ϕμctr_i=\sqrt{\frac{k\Delta t}{948\phi\mu c_t}}
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Reservoir EngineeringReserves and Recovery

Recoverable Condensate from Cumulative Gas and Yield

Nc=GpYcN_c=G_pY_c
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Reservoir EngineeringPermeability and Flow

Relative Permeability from Effective Permeability

kr=keffkk_r = \frac{k_{eff}}{k}
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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]
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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
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Reservoir EngineeringReservoir Volumetrics

Reservoir Gas Volume from Gas In Place and Gas FVF

Vgi=GBgiV_{gi}=GB_{gi}
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Reservoir EngineeringThermal Gradients

Reservoir Heat Required for Temperature Increase

Q=43560VrMr(Tf−Ti)Q=43560V_rM_r(T_f-T_i)
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Reservoir EngineeringReservoir Volumetrics

Reservoir Oil Volume from Stock Tank Oil and Oil FVF

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

Reservoir Pore Volume - Volumetric Method

PV=7758AhϕPV = 7758 A h \phi
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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}}
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Reservoir EngineeringMaterial Balance

Schilthuis Cumulative Water Influx

We=Js(Pi−Pˉ)ΔtW_e=J_s(P_i-\bar{P})\Delta t
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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}
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Reservoir EngineeringFluid Flow in Porous Media

Single Phase Mobility from Permeability and Viscosity

λ=kμ\lambda=\frac{k}{\mu}
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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]
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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]
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Reservoir EngineeringWaterflooding and EOR

Slug Size in Polymer Floods

S=Aρr(1−ϕ)CϕS=\frac{A\rho_r(1-\phi)}{C\phi}
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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)}
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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}
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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]
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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)
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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]}
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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]}
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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
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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}]
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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)}
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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}
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Reservoir EngineeringWaterflooding and EOR

Steam-Oil Ratio - Marx and Langenheim

Fso=Ws,eqNpF_{so}=\frac{W_{s,eq}}{N_p}
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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}}
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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}}
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Reservoir EngineeringFluid Flow in Porous Media

Superficial Velocity from Flow Rate and Area

us=qAu_s=\frac{q}{A}
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Reservoir EngineeringThermal Gradients

Thermal Conductivity from Heat Flow

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

Thermal Diffusivity

α=kρCp\alpha=\frac{k}{\rho C_p}
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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}
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Reservoir EngineeringUnconventional Reservoirs

Tight-Gas Compartment Underground Withdrawal

F=GEg+WeF=GE_g+W_e
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Reservoir EngineeringPressure Transient Analysis

Time to End of Infinite-Acting Period in Circular Reservoir

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

Time to Pseudosteady State in Circular Reservoir

tpss=1200ϕμctre2kt_{pss}=\frac{1200\phi\mu c_tr_e^2}{k}
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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}
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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}
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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
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Reservoir EngineeringMaterial Balance and Production

Total Oil Reservoir Expansion Term

Et=Eo+mEg+EfwE_t = E_o + mE_g + E_{fw}
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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)
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Reservoir EngineeringRock Properties

Total Porosity from Bulk and Grain Volume

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

Total Porosity from Pore and Bulk Volume

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

Total Porosity from Pore and Grain Volume

ϕt=VpVp+Vg\phi_t=\frac{V_p}{V_p+V_g}
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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}
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Reservoir EngineeringUnconventional Reservoirs

Transmissibility of a Tight Gas Compartment

γ=kAzμg\gamma=\frac{k A}{z \mu_g}
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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}
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Reservoir EngineeringPressure Transient Analysis

True Wellbore Storage Coefficient for Pressure Buildup Test

C=25.65AwbρwbC=25.65\frac{A_{wb}}{\rho_{wb}}
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Reservoir EngineeringPVT Properties

Two-Phase Formation Volume Factor

Bt=Bo+Bg(Rsoi−Rso)B_t = B_o + B_g(R_{soi} - R_{so})
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Reservoir EngineeringMaterial Balance

Underground Fluid Withdrawal - Havlena and Odeh

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

van Everdingen-Hurst Single-Step Water Influx

We=BΔpWeDW_e=B\Delta p W_{eD}
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Reservoir EngineeringUnconventional Reservoirs

Volume of Gas Adsorbed in Coalbed Methane Reservoirs

V=Vmbp1+bpV = \frac{V_m b p}{1 + bp}
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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]
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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)
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Reservoir EngineeringWaterflooding and EOR

Water Cut - Stiles

fw=khMwokhMwo+ktht−khf_w=\frac{khM_{wo}}{khM_{wo}+k_th_t-kh}
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Reservoir EngineeringMaterial Balance

Water Influx Constant for van Everdingen-Hurst Aquifer

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

Water Influx from Pot Aquifer Model

We=ctWi(Pi−P)W_e=c_tW_i(P_i-P)
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Reservoir EngineeringPVT Properties

Water Two-Phase Formation Volume Factor

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

Water-Drive Index for Gas Reservoirs

WDI=We−WpBwGpBgWDI=\frac{W_e-W_pB_w}{G_pB_g}
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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}
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Reservoir EngineeringWaterflooding and EOR

Waterflood Oil Displacement Ratio from Average Saturation

Qp=Sw−Siw1−fsQ_p=\frac{S_w-S_{iw}}{1-f_s}
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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}
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Reservoir EngineeringPressure Transient Analysis

Wellbore Storage Coefficient from Fluid Volume Change

C=ΔVmΔPC=\frac{\Delta V_m}{\Delta P}
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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)]
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