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Production Engineering Equations

Browse 198 production engineering petroleum engineering equations with variables, units, source references, and calculator links.

Production engineering calculators cover inflow performance, well performance, injection wells, completion fluids, artificial lift, stimulation interfaces, and production-system checks.

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Production EngineeringHydraulic Fracturing

Acid Dissolving Power for 15 Percent HCl - Acidizing

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

Acid Penetration Distance - Acidizing

xL=wˉLaD2(NReNRe∗)x_L=\frac{\bar{w}L_{aD}}{2}\left(\frac{N_{Re}}{N_{Re}^{*}}\right)
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Production EngineeringWell Performance

Additional Pressure Drop in the Skin Zone

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

Adsorption Unit Bed Length from Mass Transfer Zone

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

Adsorption Unit Mass Transfer Zone Length

hz=375q0.7895vg0.5506RS0.2646h_z=\frac{375q^{0.7895}}{v_g^{0.5506}RS^{0.2646}}
View formula
Production EngineeringHydraulic Fracturing

Annulus Pressure Loss Due to Friction - Turbulent Flow

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

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

ΔPf=μpLv1000(d0−di)2+τyL200(d0−di)\Delta P_f=\frac{\mu_pLv}{1000(d_0-d_i)^2}+\frac{\tau_yL}{200(d_0-d_i)}
View formula
Production EngineeringWell Performance

API RP 14E Actual Mixture Velocity

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

API RP 14E Erosional Velocity

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

API RP 14E Erosional Velocity Utilization

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

API RP 14E Gas-Liquid Mixture Density

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

API RP 14E Minimum Flow Area per 1000 Barrels Liquid

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

API RP 14E Minimum Velocity Ratio

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

API RP 14E Required Pipe Inside Diameter

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

API RP 14E Total Wellstream Weight Flow Rate

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

API RP 14E Two-Phase Flowline Pressure Drop

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

Approximate Ideal Counterbalanced Load

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

ASME Separator Pressure Criterion - External Radius

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

ASME Separator Pressure Criterion - Internal Radius

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

ASME Separator Wall Thickness from External Radius

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

ASME Separator Wall Thickness from Internal Radius

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

ASME Spherical Separator Shell Thickness

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

Average Downstroke Load - Sucker Rod Pump

ADL=CAlowerLADL=C\frac{A_{lower}}{L}
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Production EngineeringHydraulic Fracturing

Average Fracture Width - Acidizing

wˉ=πww4\bar{w}=\frac{\pi w_w}{4}
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Production EngineeringWell Performance

Average Liquid Specific Gravity for Mixed Liquid Stream

SL=qoSo+qwSwqo+qwS_L=\frac{q_oS_o+q_wS_w}{q_o+q_w}
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Production EngineeringHydraulic Fracturing

Average Permeability of Hydraulically Fractured Formation

kavg=kkavgzln⁡(re/rw)kavgzln⁡(re/rf)+kln⁡(rf/rw)k_{avg}=\frac{kk_{avgz}\ln(r_e/r_w)}{k_{avgz}\ln(r_e/r_f)+k\ln(r_f/r_w)}
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Production EngineeringHydraulic Fracturing

Average Specific Weight of Formation - Hydraulic Fracturing

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

Average Upstroke Load - Sucker Rod Pump

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

CaCl2 and CaBr2 Salt Addition for Two-Salt Brine

m95=V8.33C95Wim_{95}=\frac{V_{8.33}C_{95}}{W_i}
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Production EngineeringHydraulic Fracturing

Capacity Ratio of Hydraulically Fractured Surface

cf=kfWkhc_f=\frac{k_fW}{kh}
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Production EngineeringHydraulic Fracturing

Carter Leakoff Volume for Hydraulic Fracturing

VL=AL(2CLt+Sp)V_L=A_L\left(2C_L\sqrt{t}+S_p\right)
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Production EngineeringWell Performance

Choke Discharge Coefficient

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

Choke Outlet Temperature

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

Close-Ended Displacement Volume of Pipe

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

Composite IPR Productivity Index

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

Convective Mass Transfer for Laminar Flow (Acidizing)

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

Correct Counterbalance - Sucker Rod Pump

CCB=AUL+ADL2CCB=\frac{AUL+ADL}{2}
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Production EngineeringInjection Wells

Cumulative Hall Plot Pressure Integral

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

Cumulative Water Injected for Hall Plot

Wi=Wprev+qiΔtW_i=W_{prev}+q_i\Delta t
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Production EngineeringInflow Performance

Damaged to Undamaged Productivity Ratio - Acidizing

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

Darcy-Weisbach Tubing Friction Pressure Drop

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

Density of Brine (Completion and Workover Fluids)

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

Downhole Operating Pressure - Hydraulic Fracturing

PF=GfDP_F=G_fD
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Production EngineeringHydraulic Fracturing

Dynamic-Test Fluid Loss per Unit Area - Acidizing

V=Vspt+vNtV=V_{spt}+v_Nt
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Production EngineeringWell Performance

Effective Wellbore Radius from Skin Factor

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

Entrance Hole Size from Casing Yield Strength

d=(σyrσy)0.5drd=\left(\frac{\sigma_{yr}}{\sigma_y}\right)^{0.5}d_r
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Production EngineeringHydraulic Fracturing

Equivalent Skin Factor in Fractured Wells

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

ESP BEP Operating Ratio

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

ESP Brake Horsepower from TDH and Efficiency

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

ESP Brake Horsepower Speed Correction

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

ESP Flow Rate Speed Correction

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

ESP Head Speed Correction

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

ESP Net Lift from Pump Intake Pressure

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

ESP Stages Required with Safety Margin

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

ESP Total Brake Horsepower from Stage Curve

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

ESP Total Dynamic Head from Components

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

ESP Total Pump Head from Stages

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

ESP Wellhead Pressure Head

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

Fetkovich Oil Deliverability Rate

qo=Cf(Pr2−Pwf2)nfq_o=C_f(P_r^2-P_{wf}^2)^{n_f}
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Production EngineeringHydraulic Fracturing

Filter-Cake Fluid-Loss Velocity - Acidizing

vN=Cwtv_N=\frac{C_w}{\sqrt{t}}
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Production EngineeringInflow Performance

Flow Coefficient During Drawdown

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

Flow Efficiency with Skin Pressure Drop

E=p−pwf−141.2qBμskhp−pwfE = \frac{p-p_{wf}-\frac{141.2qB\mu s}{kh}}{p-p_{wf}}
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Production EngineeringHydraulic Fracturing

Flow Through Fracture in Response to Pressure Gradient

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

Foamless Separator Length-Diameter Correction Factor

K=(L/D5)0.56K=\left(\frac{L/D}{5}\right)^{0.56}
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Production EngineeringHydraulic Fracturing

Formation Fluid Compressibility - Acidizing

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

Fracture Area from Saydam Leakoff Function

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

Fracture Coefficient of Hydraulically Fractured Reservoir

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

Fracture Conductivity from Proppant Permeability and Width

FC=kfwfF_C=k_fw_f
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Production EngineeringHydraulic Fracturing

Fracture Fluid Coefficient - Reservoir-Controlled Liquids

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

Fracture Fluid Coefficient - Viscosity-Controlled Liquids

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

Fracture Fluid-Loss Reynolds Number - Acidizing

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

Fracture Volume - GDK Method

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

Fracture Volume - Perkins and Kern Method

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

Fracture Width - GDK Method

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

Fracture Width - Perkins and Kern Method

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

Fracture-Fluid Invasion Velocity - Acidizing

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

Frictional Pressure Drop - Economides and Nolte

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

Fuel Gas Wobbe Index

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

Gas Conditioning Relative Humidity

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

Gas Conditioning Stripping Factor

S=KVLS=\frac{KV}{L}
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Production EngineeringInflow Performance

Gas Deliverability Pressure-Squared Drawdown

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

Gas Mass Velocity in an Adsorption Unit

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

Gas Mass Velocity in Separator

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

Gas Pressure Testing Time for Unsteady Gas Flow

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

Gas Separator Internal Diameter from Mass Flow

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

Gas-Lift Valve Opening Casing Pressure

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

Gas-Liquid Ratio from Gas and Liquid Rates

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

Gilbert Critical Choke Liquid Rate

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

Glycol Dehydration Still Column Diameter

d=9.1qgd=9.1\sqrt{q_g}
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Production EngineeringInjection Wells

Hall Injectivity Change Ratio from Slopes

RC=CnewCbase=mbasemnewR_C=\frac{C_{new}}{C_{base}}=\frac{m_{base}}{m_{new}}
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Production EngineeringInjection Wells

Hall Injectivity Coefficient from Slope

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

Hall Plot Pressure-Time Increment

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

Hall Plot Slope from Two Surveillance Points

mH=H2−H1Wi2−Wi1m_H=\frac{H_2-H_1}{W_{i2}-W_{i1}}
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Production EngineeringWell Performance

Horizontal Separator Length for Liquid Retention

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

Horizontal Separator Liquid Volume from Geometry

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

Horizontal Separator Maximum Vapor Velocity from Droplet Settling

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

Horizontal Well Fetkovich IPR Rate

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

Hydraulic Fracture Efficiency from Saydam Leakoff Function

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

Hydraulic Horsepower for Hydraulic Fracturing Operation

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

Ideal Fracture Conductivity Created by Acid Reaction

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

Incremental Density in Wellbore Interval - Completion and Workover Fluids

Δρi=BgpΔD−AgTΔD\Delta\rho_i=B g_p\Delta D-A g_T\Delta D
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Production EngineeringHydraulic Fracturing

Initial Rate Following a Hydraulic Fracturing Operation

Q=Qpre(kf/ke)ln⁡(re/rw)ln⁡(rf/rw)+(kf/ke)ln⁡(re/rf)Q=Q_{pre}\frac{(k_f/k_e)\ln(r_e/r_w)}{\ln(r_f/r_w)+(k_f/k_e)\ln(r_e/r_f)}
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Production EngineeringInjection Wells

Injected Hydrocarbon Pore Volumes

HCPVinj=WiBwi7758AhϕSoHCPV_{inj}=\frac{W_iB_{wi}}{7758Ah\phi S_o}
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Production EngineeringHydraulic Fracturing

Injection Pressure for Hydraulic Fracturing

Pinj=PF+ΔPf+ΔPp−ΔPhP_{inj}=P_F+\Delta P_f+\Delta P_p-\Delta P_h
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Production EngineeringInjection Wells

Injectivity Index

Ii=qiPwf−PrI_i = \frac{q_i}{P_{wf} - P_r}
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Production EngineeringWell Performance

Intermediate Law Droplet Settling Velocity

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

Jones-Blount-Glaze Gas Deliverability Rate

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

Liquid-Liquid Vessel Retention Time

Tr=Aμγb−γtT_r=\frac{A\mu}{\gamma_b-\gamma_t}
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Production EngineeringHydraulic Fracturing

Mass of Rock Dissolved per Unit Mass of Acid - Acidizing

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

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

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

Maximum Treatment Pressure - Hydraulic Fracturing

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

Minimum Polished Rod Load - Sucker Rod Pump

MPRL=CdMPRL=Cd
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Production EngineeringWell Performance

Multiphase Wellhead Pressure Across Choke

Pwh=CRmqLSnP_{wh}=C R^m\frac{q_L}{S^n}
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Production EngineeringHydraulic Fracturing

Net Fracture Pressure from Fracture and Closure Pressure

Pnet=Pfrac−SclosureP_{net}=P_{frac}-S_{closure}
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Production EngineeringWell Performance

Newton Law Droplet Settling Velocity

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

Oil-Well Perforation Pressure Drop

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

Packed Column Actual Height

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

Peak Polished Rod Load - Sucker Rod Pump

PPRL=CDPPRL=CD
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Production EngineeringHydraulic Fracturing

Peclet Number for Fluid Loss - Acidizing

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

Perforation Friction Pressure

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

Perforation Hole Size from Brinell Hardness

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

Perforation Length in Formation

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

Perforation Skin Factor

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

PI Test Skin Factor and Average Permeability

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

Pipe Volume Capacity

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

Polished Rod Horsepower - Sucker Rod Pump

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

Pressure Drop Across Perforations in Gas Wells

psf=pwb2+A(qgn)+B(qgn)2p_{sf}=\sqrt{p_{wb}^2+A\left(\frac{q_g}{n}\right)+B\left(\frac{q_g}{n}\right)^2}
View formula
Production EngineeringHydraulic Fracturing

Pressure Loss Due to Perforations During Hydraulic Fracturing

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

Principal Stress Due to Petro-Static Pressure - Hydraulic Fracturing

σz=γh10\sigma_z=\frac{\gamma h}{10}
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Production EngineeringInflow Performance

Productivity Index and Straight-Line IPR

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

Productivity Index for a Gas Well

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

Productivity Ratio

PR=JJswPR = \frac{J}{J_{sw}}
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Production EngineeringHydraulic Fracturing

Productivity Ratio from Average Permeability - Hydraulic Fracturing

PR=kavgkPR=\frac{k_{avg}}{k}
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Production EngineeringHydraulic Fracturing

Productivity Ratio of Hydraulically Fractured Formation

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

Progressive Cavity Pump Flow Rate

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

Progressive Cavity Pump Head Rating

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

Progressive Cavity Pump Mechanical Resistant Torque

Tm=144VoΔPepT_m=\frac{144V_o\Delta P}{e_p}
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Production EngineeringHydraulic Fracturing

Proppant Settlement Drag Coefficient in Fracture

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

Pseudo-Skin Factor Due to Partial Penetration - Papatzacos Correlation

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

Radial Water Injection Rate

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

Radial Water Injectivity Index

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

Range of Load - Sucker Rod Pump

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

Raoult's Law Water Fraction in Glycol Dehydration

xw=PPvywx_w=\frac{P}{P_v}y_w
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Production EngineeringInflow Performance

Rawlins-Schellhardt Absolute Open Flow Potential

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

Rawlins-Schellhardt Deliverability Coefficient from Test Point

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

Rawlins-Schellhardt Deliverability Exponent from Two Test Points

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

Rawlins-Schellhardt Gas Deliverability Rate

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

Recommended Underbalanced Perforation Pressure

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

Refrigeration Outlet Temperature for Gas Conditioning

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

Required Oil Section Length in Separator

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

Required Water Section Length in Separator

Lw=twqwAwL_w=\frac{t_wq_w}{A_w}
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Production EngineeringHydraulic Fracturing

Reynolds Number for Acid Flow into the Fracture - Acidizing

NRe=ρiμhgN_{Re}=\frac{\rho i}{\mu h_g}
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Production EngineeringWell Performance

Safety Relief Valve Vapor Flow Capacity

w=BCKoAP(MZT)0.5w=BCK_oAP\left(\frac{M}{ZT}\right)^{0.5}
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Production EngineeringHydraulic Fracturing

Sand Weight to Refill Hydraulically Fractured Reservoir Volume

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

Separator Actual Gas Velocity

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

Separator Droplet Reynolds Number

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

Separator Gas Capacity at Standard Conditions

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

Separator Gas Capacity from Diameter

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

Separator Gas Capacity Utilization

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

Separator Liquid Retention Utilization

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

Separator Minimum Diameter from Gas Capacity

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

Separator Required Liquid Retention Volume

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

Shape Factor Expressed as Skin Factor for Vertical Wells

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

Single-Phase Gas Flow Subsonic

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

Single-Phase Liquid Flow Through Choke

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

Single-Salt Brine Density Increase Salt Addition Method II

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

Skin Factor Due to Reduced Crushed-Zone Permeability

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

Skin Factor for a Deviated Well

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

Skin Factor from Damaged Zone Permeability

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

Souders-Brown Maximum Gas Velocity for Separator

VGmax=KSρL−ρGρGV_{Gmax}=K_S\sqrt{\frac{\rho_L-\rho_G}{\rho_G}}
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Production EngineeringHydraulic Fracturing

Static-Test Fluid Loss per Unit Area - Acidizing

V=Vspt+2CwtV=V_{spt}+2C_w\sqrt{t}
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Production EngineeringWell Performance

Stokes Law Droplet Settling Velocity

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

Stokes Region Maximum Droplet Diameter

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

Straight-Line IPR Rate from Test Point

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

Suspension Property of Static Fluids (Completion and Workover Fluids)

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

TEG Weight Percent in Glycol Dehydration Unit

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

Three-Phase Separator Liquid Retention Volume

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

Total Skin in Partially Depleted Wells for a Buildup Test

S=34.7rewϕμctk[ps−pwm+1Δt]−1S=34.7r_{ew}\sqrt{\frac{\phi\mu c_t}{k}}\left[\frac{p_s-p_w}{m}+\frac{1}{\sqrt{\Delta t}}\right]-1
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Production EngineeringHydraulic Fracturing

Treatment Fracture Gradient - Hydraulic Fracturing

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

Tubing Bottomhole Pressure from Wellhead Pressure and Losses

Pwf=Pwh+ΔPh+ΔPf+ΔPaccP_{wf}=P_{wh}+\Delta P_h+\Delta P_f+\Delta P_{acc}
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Production EngineeringHydraulic Fracturing

Turbulent Acidizing Mass Transfer Flux - Coefficient Form

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

Turbulent Acidizing Mass Transfer Flux - Effective Diffusivity Form

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

Turner Critical Gas Rate for Liquid Loading

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

Velocity of Fluid in Pipe

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

Vogel Inflow Performance Relationship

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

Vogel IPR Rate from One Test Point

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

Voidage Replacement Ratio

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

Water Injection Bottom-Hole Pressure from Radial Flow

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

Water Volume to Dilute Brine in Two-Salt Systems

V8.33=Vdρi−ρdρi−ρ8.33V_{8.33}=V_d\frac{\rho_i-\rho_d}{\rho_i-\rho_{8.33}}
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Production EngineeringInjection Wells

Waterflood Mobility Ratio

M=krw/μwkro/μoM=\frac{k_{rw}/\mu_w}{k_{ro}/\mu_o}
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Production EngineeringWell Performance

Well Flowing Pressure Line-Source Solution by Including Skin Factor

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

Wellbore Fracture Width - Acidizing

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

Wellbore Pressure Loss Due to Friction - Turbulent Flow

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

Wellbore Storage Due to Fluid Level

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

Wellstream Volumetric Flow Rate from Weight Flow

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

Workover Operations Maximum Allowed Tubing Pressure

MATP=FGH−PtMATP=FGH-P_t
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Production EngineeringHydraulic Fracturing

Wormhole Fluid-Loss Reynolds Number - Acidizing

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

Young Modulus from Sonic Travel Time (Acidizing)

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