Reservoir Engineering Equations

Reservoir EngineeringUnconventional Reservoirs

Adsorbed Gas in Place from Langmuir Isotherm

G_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

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 = \frac{141.5}{SG_o} - 131.5

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Reservoir EngineeringUnconventional Reservoirs

Apparent Sorption Compressibility

c_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=\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

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)=q_i e^{-D_i t}

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Reservoir EngineeringReserves and Recovery

Arps Harmonic Decline Cumulative Production

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)=\frac{q_i}{1+D_it}

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Reservoir EngineeringReserves and Recovery

Arps Hyperbolic Decline Cumulative Production

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)=\frac{q_i}{(1+bD_it)^{1/b}}

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Reservoir EngineeringPermeability

Average Permeability for Linear Flow - Series Beds

k_{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

k_{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

k_{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

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

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 = \frac{T_t + T_b}{2}

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Reservoir EngineeringPermeability

Binary Power-Average Effective Permeability

k_{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

t_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

t_{D,bt} = \left(\frac{df_w}{dS_w}\right)_{shock}^{-1}

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Reservoir EngineeringPermeability and Flow

Buckley-Leverett Saturation Front Velocity

v_S = \frac{u_t}{\phi}\frac{df_w}{dS_w}

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Reservoir EngineeringWaterflooding and EOR

Burned Reservoir Volume from Air Requirement

V_{rb}=0.0230\frac{G_aE_O}{a_R}

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Reservoir EngineeringPermeability and Flow

Calculation of Fractional Flow Curve

f_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

N_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

P_c = \frac{2 \cdot \sigma \cdot \cos(\theta)}{r}

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Reservoir EngineeringPressure Transient Analysis

Carter Dimensionless Drawdown Correlating Parameter

\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

\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=\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

M_c = 1359.7 A h \rho_b

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Reservoir EngineeringUnconventional Reservoirs

Coalbed Methane Formation Compressibility

c_t = \frac{W_p}{W_i(P_i-P_d)}

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Reservoir EngineeringPressure Transient Analysis

Cole Plot

F = G \cdot E_g + W_e

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Reservoir EngineeringWaterflooding and EOR

Combustion Front Advancement Rate

v_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 \cdot \frac{k \cdot A}{T \cdot L}

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Reservoir EngineeringPVT and Rock-Fluid Properties

Compressibility Drive in Gas Reservoirs

CI = \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

q_c=\frac{q_gY_c}{1000}

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Reservoir EngineeringThermal Gradients

Conductive Heat Flow from Geothermal Gradient

q = k\frac{\Delta T}{\Delta z}

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Reservoir EngineeringMaterial Balance and Production

Connate Water and Rock Expansion Term

E_{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

V_b=\frac{W_s-W_i}{\rho_s}

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Reservoir EngineeringRock Properties

Core Pore Volume from Saturated and Dry Weights

V_p=\frac{W_s-W_d}{\rho_s}

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Reservoir EngineeringPermeability and Flow

Corey Oil Relative Permeability

k_{ro} = k_{ro}^o(1-S_w^*)^{n_o}

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Reservoir EngineeringPermeability and Flow

Corey Water Relative Permeability

k_{rw} = k_{rw}^o(S_w^*)^{n_w}

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Reservoir EngineeringUnconventional Reservoirs

Correction Factor – Hammerlindl

CDI = \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

q_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

q_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 = \frac{N_{pcf} - N_{pncf}}{N_{pu} - N_{pncf}}

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Reservoir EngineeringPVT and Rock-Fluid Properties

Cumulative Effective Compressibility – Fetkovich

c_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 \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

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

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

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 \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

N_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 = \frac{0.001127 k A \Delta P}{\mu L}

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Reservoir EngineeringWell Performance

Deliverability Equation for Shallow Gas Reservoirs

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

i_D=\frac{i_a}{Lhu_{min}}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Buildup Pressure for Liquid Flow

P_{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

P_{Ds}=\frac{P_i-P_{ws}}{0.87m}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Buildup Time

t_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

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

F_{CD}=\frac{k_fw_f}{kX_f}

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Reservoir EngineeringWaterflooding and EOR

Dimensionless Heat Injection Rate - Gringarten and Sauty

Q_{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

x_D=\frac{x}{L_f}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Length for Linear Flow General Case

x_D=\frac{x}{\sqrt{A}}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Pressure - Radial Flow Constant-Pressure Production

P_d=\frac{P_i-P}{P_i-P_{wf}}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Pressure - Radial Flow Constant-Rate Production

P_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

P_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

p_D=\frac{k\sqrt{A}(p_i-p)}{141.2qB\mu}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Production Time

t_{DA}=t_D\frac{r_w^2}{A}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Radius of Radial Flow – Constant-Rate Production

r_d = \frac{r}{r_w}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Rate for Radial Flow Constant-Pressure Production

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

\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

F_{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

C_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

C_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

t_{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

t_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

t_{DA}=\frac{0.0002637kt}{\phi\mu c_tA}

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Reservoir EngineeringPressure Transient Analysis

Dimensionless Time for Radial Flow Constant-Rate Production

t_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

t_{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

t_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

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

C_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

r_e=\sqrt{\frac{43560A}{\pi}}

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Reservoir EngineeringPressure Transient Analysis

Drawdown Semilog Slope for Bottomhole Flowing Pressure

m=\frac{162.6Q_o\mu_oB_o}{kh}

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Reservoir EngineeringWaterflooding and EOR

Dykstra-Parsons Coefficient

V=\frac{k_{50}-k_{84.1}}{k_{50}}

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Reservoir EngineeringWaterflooding and EOR

Effective Apparent Transmissivity

T_{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

c_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

T_{ao}=141.2\frac{F_G}{R_{qmax}}

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Reservoir EngineeringRock Properties

Effective Porosity from Connected Pore Volume

\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)

r_{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

r_{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

r_w = \frac{X_f}{e}

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Reservoir EngineeringWell Performance

Efros Horizontal Well Critical Rate

q_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

x_{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

W_{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

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

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

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 = PV_{ref}\exp(c_r(P-P_{ref}))

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Reservoir EngineeringRock Properties

Exponential Porosity from Rock Compressibility

\phi = \phi_{ref}\exp(c_r(P-P_{ref}))

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Reservoir EngineeringWell Performance

Finite-Conductivity Fracture Effective Wellbore Radius

r_{we}=\frac{0.2807k_fb_f}{k}

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Reservoir EngineeringPressure Transient Analysis

Flow Period Duration for Hydraulically Fractured Wells

t=\frac{\phi\mu c_tL_f^2t_{LfD}}{0.0002637k}

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Reservoir EngineeringThermal Gradients

Formation Temperature for a Given Gradient

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

E_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

\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 - \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

F_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

G_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

G_a = 1359.7 A h \rho_b V

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Reservoir EngineeringMaterial Balance and Production

Gas Cap Ratio

m=\frac{GB_{gi}}{NB_{oi}}

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Reservoir EngineeringMaterial Balance and Production

Gas Cap Shrinkage from Gas Cap Production

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=\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

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

E_g = 35.37 \frac{P}{zT}

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Reservoir EngineeringMaterial Balance

Gas Expansion Term in Gas Reservoirs

E_g = B_g - B_{gi}

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Reservoir EngineeringWell Performance

Gas Flow Rate into the Wellbore

Q=\frac{0.007k\Delta PL}{u\ln(R_e/R_w)1440}

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Reservoir EngineeringPVT Properties

Gas Formation Volume Factor

B_g = 0.02827 \frac{zT}{P}

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Reservoir EngineeringMaterial Balance

Gas Material Balance Equation

\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 = \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

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

RF_g=1-\frac{P_z}{P_i/z_i}

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Reservoir EngineeringMaterial Balance

Gas Saturation in Water-Drive Gas Reservoirs

S_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

R_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

Y_c=\frac{10^6}{GOR_p}

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Reservoir EngineeringWell Performance

Generalized Reservoir Gas Flow Deliverability

W=C(\bar p^2-p_{wf}^2)^n

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Reservoir EngineeringPermeability

Geometric Mean Permeability from Log Average

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 = \frac{T_{deep}-T_{shallow}}{z_{deep}-z_{shallow}}\,1000

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Reservoir EngineeringWell Performance

Giger-Karcher Horizontal Well Critical Rate

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

V_{grv}=43560Ah_g

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Reservoir EngineeringReservoir Volumetrics

Gross Rock Volume in Acre-Feet from Area and Thickness

V_{grv,af}=Ah_g

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Reservoir EngineeringReservoir Volumetrics

Gross Rock Volume in Reservoir Barrels

V_{grv,bbl}=7758Ah_g

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Reservoir EngineeringUnconventional Reservoirs

Hagoort and Hoogstra Tight Gas Compartment Flow

Q=\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=\frac{G_{app}}{R}

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Reservoir EngineeringMaterial Balance

Havlena-Odeh Cumulative Water Influx from Fluid Withdrawal

W_e=F-GE_G

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Reservoir EngineeringWaterflooding and EOR

Heat Released During In-Situ Combustion - Burger and Sahuquet

(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=\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

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

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

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

t_{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 = 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

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

p_{ws}=p^*-m\log_{10}(H)

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Reservoir EngineeringThermal Gradients

Horner Time Ratio for Bottom-Hole Temperature Correction

H = \frac{t_c+\Delta t}{\Delta t}

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Reservoir EngineeringPressure Transient Analysis

Horner Time Ratio for Pressure Buildup Test

H=\frac{t_p+\Delta t}{\Delta t}

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Reservoir EngineeringWaterflooding and EOR

Hot-Water Flood Fractional Flow from Mobility Ratio

f_{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\left(\frac{T_j-117}{275}\right)

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Reservoir EngineeringWaterflooding and EOR

Hot-Water Flood Real Time from Dimensionless Time

t=\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

\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

Q_{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

\eta=\frac{0.0002637k}{\phi\mu c_t}

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Reservoir EngineeringReservoir Volumetrics

Hydrocarbon Pore Volume - Volumetric Method

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-S_{wi})

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Reservoir EngineeringMaterial Balance and Production

Hydrocarbon Pore Volume Occupied by Evolved Solution Gas

V_{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

V_{gc}=\frac{mNB_{oi}B_g}{B_{gi}}

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Reservoir EngineeringMaterial Balance and Production

Hydrocarbon Pore Volume Occupied by Remaining Oil

V_{ro}=(N-N_p)B_o

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Reservoir EngineeringWaterflooding and EOR

Ignition Delay Time in In-Situ Combustion

t_{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}}

View formula

Reservoir EngineeringWaterflooding and EOR

In-Situ Combustion Oil Production - Nelson and McNeil

N_p=7758\phi\left[V_r(S_i-S_f)+0.4(V_p-V_r)S_i\right]

View formula

Reservoir EngineeringWaterflooding and EOR

In-Situ Combustion Temperature Increase Rate

\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

W_p=7758V_r\phi(S_{iw}-S_{fw})

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Reservoir EngineeringRock Properties

Ineffective Porosity from Disconnected Pore Volume

\phi_{in}=\frac{V_{dis}}{V_b}

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Reservoir EngineeringPressure Transient Analysis

Infinite-Acting Pseudoradial Bottomhole Flowing Pressure

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 = \frac{m N B_{oi}}{B_{gi}}

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Reservoir EngineeringMaterial Balance

Initial Gas In Place for Water-Drive Gas Reservoir

G=\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 = 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

v_p=\frac{q}{\phi A}

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Reservoir EngineeringPermeability

Jones-Owens Klinkenberg Slip Factor

b = 12.639 k_{\infty}^{-0.33}

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Reservoir EngineeringWell Performance

Joshi Horizontal Well Critical Rate for Gas Coning

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

A_{ac}=\frac{\pi r_{eh}r_{ev}}{43560}

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Reservoir EngineeringWell Performance

Joshi Horizontal Well Productivity Index

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]}

View formula

Reservoir EngineeringWell Performance

Joshi Isotropic Horizontal Well Effective Radius

r_{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

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=\frac{\phi}{k_zS_p^2}

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Reservoir EngineeringPermeability

Kozeny-Carman Permeability from Grain Diameter

k=\frac{B\phi^3d^2}{\tau}

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Reservoir EngineeringWell Performance

Laminar Gas Flow Rate from Real-Gas Pseudopressure

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

G_c = \frac{V_L P}{P_L + P}

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Reservoir EngineeringUnconventional Reservoirs

Langmuir Desorbable Gas Content Between Pressures

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

f_{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

\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=\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=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

C_L=\frac{0.001127kA}{\mu L}

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Reservoir EngineeringPermeability

Lognormal Effective Permeability from Geometric Mean

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

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

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=\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

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

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

u_{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

t_{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

\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\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

t_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=h_gNTG

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Reservoir EngineeringReservoir Volumetrics

Net Reservoir Rock Volume from Net-to-Gross

V_{nrv}=43560Ah_gNTG

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Reservoir EngineeringReservoir Volumetrics

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

V_{nrv,bbl}=7758Ah_gNTG

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Reservoir EngineeringReserves and Recovery

NGL Production Rate from Gas Rate and Yield

q_{NGL}=\frac{q_gY_{NGL}}{1000}

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Reservoir EngineeringPermeability and Flow

Normalized Saturation

S_{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

S_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

E_o = (B_o-B_{oi}) + (R_{si}-R_s)B_g

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Reservoir EngineeringWaterflooding and EOR

Oil Breakthrough Newly Swept Zone

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

r_{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=\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=\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=7758Ah\phi\frac{S_{org}}{B_{oa}}

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Reservoir EngineeringMaterial Balance and Production

Oil Material Balance Drive Index Closure

DI_{sum} = DDI + GDI + WDI + CDI

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Reservoir EngineeringReserves and Recovery

Oil Recovery Factor from Cumulative Production

RF = \frac{N_p}{N}

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Reservoir EngineeringMaterial Balance and Production

Oil Reservoir Underground Withdrawal

F = 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

S_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=\frac{C_o}{C_s}

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Reservoir EngineeringWaterflooding and EOR

Oil Volume at Breakthrough - Craig, Geffen, and Morse

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

N_c=\frac{GY_c}{10^6}

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Reservoir EngineeringReservoir Volumetrics

Original Condensate In Place with Net-to-Gross

N_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 = \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=\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=\frac{43560Ah_gNTG\phi(1-S_{wi})}{B_{gi}}

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Reservoir EngineeringReservoir Volumetrics

Original Oil in Place - Volumetric Method

N = \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 = \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=\frac{7758Ah_gNTG\phi S_{wi}}{B_{wi}}

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Reservoir EngineeringWaterflooding and EOR

Oxygen Reaction Rate per Unit Fuel Mass

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

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=\frac{162.6qB\mu}{mh}

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Reservoir EngineeringRock Properties

Pore Throat Sorting from Capillary Pressure Quartiles

PTS=\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=V_{nrv,bbl}\phi

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Reservoir EngineeringMaterial Balance and Production

Pore Volume Occupied by Injected Gas and Water

V_t=W_{INJ}B_w+G_{INJ}B_{GINJ}

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Reservoir EngineeringWell Performance

Prats High-Conductivity Fracture Effective Wellbore Radius

r_{we}=\frac{X_f}{2}

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Reservoir EngineeringMaterial Balance and Production

Produced Gas-Oil Ratio

R_p=\frac{G_p}{N_p}

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Reservoir EngineeringWell Performance

Pseudo-Steady State Horizontal Well Productivity Method 3

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

P_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

P_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

P_{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}

View formula

Reservoir EngineeringPermeability and Flow

Pseudosteady-State Radial Liquid Flow Rate

Q=\frac{0.00708 k h (P_i-P_{wf})}{B \mu [\ln(r_e/r_w)-0.75]}

View formula

Reservoir EngineeringFluid Flow in Porous Media

Pseudosteady-State Radial Oil Flow Rate

q_o=\frac{kh(p_R-p_{wf})}{141.2\mu_oB_o[\ln(r_e/r_w)-0.75+s]}

View formula

Reservoir EngineeringFluid Flow in Porous Media

Pseudosteady-State Radial Productivity Index

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

m_{pss}=\frac{0.23396QB}{c_tAh\phi}

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Reservoir EngineeringRock Properties

Quadratic Porosity Multiplier from Rock Compressibility

\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)=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

r_i=0.0359\sqrt{\frac{kt}{\phi\mu c_t}}

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Reservoir EngineeringPressure Transient Analysis

Radius of Investigation from Flow Time

r_i=\sqrt{\frac{kt}{948\phi\mu c_t}}

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Reservoir EngineeringPressure Transient Analysis

Radius of Investigation from Shut-In Time

r_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

N_c=G_pY_c

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Reservoir EngineeringPermeability and Flow

Relative Permeability from Effective Permeability

k_r = \frac{k_{eff}}{k}

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Reservoir EngineeringUnconventional Reservoirs

Remaining Gas in Place in Coalbed Methane Reservoirs

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

m_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

V_{gi}=GB_{gi}

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Reservoir EngineeringThermal Gradients

Reservoir Heat Required for Temperature Increase

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

V_{oi}=NB_{oi}

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Reservoir EngineeringReservoir Volumetrics

Reservoir Pore Volume - Volumetric Method

PV = 7758 A h \phi

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Reservoir EngineeringMaterial Balance

Rock Expansion Term in Abnormally Pressured Gas Reservoirs

E_R=\frac{c_f+c_wS_{wi}}{1-S_{wi}}

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Reservoir EngineeringMaterial Balance

Schilthuis Cumulative Water Influx

W_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

t_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

\lambda=\frac{k}{\mu}

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Reservoir EngineeringPressure Transient Analysis

Skin During Infinite-Acting Pseudoradial Flow

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]

View formula

Reservoir EngineeringPressure Transient Analysis

Skin Factor from Pressure Transient Semilog Analysis

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=\frac{A\rho_r(1-\phi)}{C\phi}

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Reservoir EngineeringWell Performance

Sobocinski Cornelius Vertical Well Breakthrough Dimensionless Time

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=\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=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]

View formula

Reservoir EngineeringWaterflooding and EOR

Steady-State Five-Spot Steam-Drive Injection Rate

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)

View formula

Reservoir EngineeringFluid Flow in Porous Media

Steady-State Radial Liquid Flow Rate

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=\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

N_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

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

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

A_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

F_{so}=\frac{W_{s,eq}}{N_p}

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Reservoir EngineeringWaterflooding and EOR

Steam-Zone Growth Increment from Heat Capacity

dz_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=\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

u_s=\frac{q}{A}

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Reservoir EngineeringThermal Gradients

Thermal Conductivity from Heat Flow

k=\frac{QL}{A\Delta T}

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Reservoir EngineeringThermal Gradients

Thermal Diffusivity

\alpha=\frac{k}{\rho C_p}

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Reservoir EngineeringUnconventional Reservoirs

Tight Gas Pore Volume from Squared-Pressure Decline

PV=\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=GE_g+W_e

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Reservoir EngineeringPressure Transient Analysis

Time to End of Infinite-Acting Period in Circular Reservoir

t_{eia}=\frac{380\phi\mu c_tA}{k}

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Reservoir EngineeringPressure Transient Analysis

Time to Pseudosteady State in Circular Reservoir

t_{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

t_{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

k_{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

c_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

E_t = E_o + mE_g + E_{fw}

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Reservoir EngineeringRock Properties

Total Pore Volume Compressibility

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

\phi_t=\frac{V_b-V_g}{V_b}

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Reservoir EngineeringRock Properties

Total Porosity from Pore and Bulk Volume

\phi_t=\frac{V_p}{V_b}

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Reservoir EngineeringRock Properties

Total Porosity from Pore and Grain Volume

\phi_t=\frac{V_p}{V_p+V_g}

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Reservoir EngineeringUnconventional Reservoirs

Transmissibility Between Tight Gas Compartments

\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

\gamma=\frac{k A}{z \mu_g}

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Reservoir EngineeringMaterial Balance

Trapped Gas Volume in Water-Invaded Zones

TG=\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=25.65\frac{A_{wb}}{\rho_{wb}}

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Reservoir EngineeringPVT Properties

Two-Phase Formation Volume Factor

B_t = B_o + B_g(R_{soi} - R_{so})

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Reservoir EngineeringMaterial Balance

Underground Fluid Withdrawal - Havlena and Odeh

F = G_p B_g + W_p B_w

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Reservoir EngineeringMaterial Balance

van Everdingen-Hurst Single-Step Water Influx

W_e=B\Delta p W_{eD}

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Reservoir EngineeringUnconventional Reservoirs

Volume of Gas Adsorbed in Coalbed Methane Reservoirs

V = \frac{V_m b p}{1 + bp}

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Reservoir EngineeringThermal Gradients

Volumetric Heat Capacity of a Reservoir

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

T_c = T_0 + f_s(T_{mes}-T_0)

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Reservoir EngineeringWaterflooding and EOR

Water Cut - Stiles

f_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=1.119\phi c_tr_e^2hf

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Reservoir EngineeringMaterial Balance

Water Influx from Pot Aquifer Model

W_e=c_tW_i(P_i-P)

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Reservoir EngineeringPVT Properties

Water Two-Phase Formation Volume Factor

B_{tw}=B_w+B_g(R_s-R_i)

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Reservoir EngineeringMaterial Balance

Water-Drive Index for Gas Reservoirs

WDI=\frac{W_e-W_pB_w}{G_pB_g}

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Reservoir EngineeringWaterflooding and EOR

Water-Drive Recovery Efficiency - Craig Correlation

E_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

Q_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=\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=\frac{\Delta V_m}{\Delta P}

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Reservoir EngineeringWaterflooding and EOR

Wet In-Situ Combustion Oil Production - Nelson and McNeil

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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