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Hydraulic Fracturing Equations

Browse 53 hydraulic fracturing petroleum engineering equations with formulas, inputs, outputs, units, and sources.

Hydraulic Fracturing equations group related upstream petroleum engineering formulas by workflow so engineers can find the right calculation faster.

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Production EngineeringHydraulic Fracturing

Acid Dissolving Power for 15 Percent HCl - Acidizing

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

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 EngineeringHydraulic Fracturing

Annulus Pressure Loss Due to Friction - Turbulent Flow

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

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

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

Average Fracture Width - Acidizing

wˉ=πww4\bar{w}=\frac{\pi w_w}{4}
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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 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 EngineeringHydraulic Fracturing

Convective Mass Transfer for Laminar Flow (Acidizing)

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

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 EngineeringHydraulic Fracturing

Equivalent Skin Factor in Fractured Wells

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

Filter-Cake Fluid-Loss Velocity - Acidizing

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

Flow Through Fracture in Response to Pressure Gradient

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

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 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 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 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 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 EngineeringHydraulic Fracturing

Net Fracture Pressure from Fracture and Closure Pressure

Pnet=Pfrac−SclosureP_{net}=P_{frac}-S_{closure}
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Production EngineeringHydraulic Fracturing

Peclet Number for Fluid Loss - Acidizing

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

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 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 EngineeringHydraulic Fracturing

Proppant Settlement Drag Coefficient in Fracture

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

Reynolds Number for Acid Flow into the Fracture - Acidizing

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

Sand Weight to Refill Hydraulically Fractured Reservoir Volume

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

Static-Test Fluid Loss per Unit Area - Acidizing

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

Treatment Fracture Gradient - Hydraulic Fracturing

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

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 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 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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