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Pressure Transient Analysis Equations

Browse 50 pressure transient analysis petroleum engineering equations with formulas, inputs, outputs, units, and sources.

Pressure Transient Analysis equations group related upstream petroleum engineering formulas by workflow so engineers can find the right calculation faster.

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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 EngineeringPressure Transient Analysis

Cole Plot

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

Permeability from Pressure Transient Semilog Slope

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

Wellbore Storage Coefficient from Fluid Volume Change

C=ΔVmΔPC=\frac{\Delta V_m}{\Delta P}
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