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Hydraulic Fracturing Calculators

Use 53 hydraulic fracturing petroleum engineering calculators with formulas, inputs, outputs, units, and source references.

Hydraulic Fracturing calculators 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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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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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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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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Average Fracture Width - Acidizing

wˉ=πww4\bar{w}=\frac{\pi w_w}{4}
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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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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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Capacity Ratio of Hydraulically Fractured Surface

cf=kfWkhc_f=\frac{k_fW}{kh}
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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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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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Downhole Operating Pressure - Hydraulic Fracturing

PF=GfDP_F=G_fD
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Dynamic-Test Fluid Loss per Unit Area - Acidizing

V=Vspt+vNtV=V_{spt}+v_Nt
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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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Filter-Cake Fluid-Loss Velocity - Acidizing

vN=Cwtv_N=\frac{C_w}{\sqrt{t}}
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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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Formation Fluid Compressibility - Acidizing

Kfl=SoKo+SwKw+SgKgK_{fl}=S_oK_o+S_wK_w+S_gK_g
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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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Fracture Coefficient of Hydraulically Fractured Reservoir

Cf=0.0164mAfC_f=\frac{0.0164m}{A_f}
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Fracture Conductivity from Proppant Permeability and Width

FC=kfwfF_C=k_fw_f
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Fracture Fluid Coefficient - Reservoir-Controlled Liquids

Cr=cΔPkcfϕμC_r=c\Delta P\sqrt{\frac{kc_f\phi}{\mu}}
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Fracture Fluid Coefficient - Viscosity-Controlled Liquids

Cv=ckΔPϕμfC_v=c\sqrt{\frac{k\Delta P\phi}{\mu_f}}
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Fracture Fluid-Loss Reynolds Number - Acidizing

NRe∗=2wˉvˉNρμN_{Re}^{*}=\frac{2\bar{w}\bar{v}_N\rho}{\mu}
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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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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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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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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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Fracture-Fluid Invasion Velocity - Acidizing

vN=0.0374kϕΔPvμtv_N=0.0374\sqrt{\frac{k\phi\Delta P_v}{\mu t}}
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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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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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Hydraulic Horsepower for Hydraulic Fracturing Operation

Hh=0.0245PinjqtH_h=0.0245P_{inj}q_t
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Ideal Fracture Conductivity Created by Acid Reaction

wa=Xit2xLh(1−ϕ)w_a=\frac{Xit}{2x_Lh(1-\phi)}
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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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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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Mass of Rock Dissolved per Unit Mass of Acid - Acidizing

β=MwmAMwaB\beta=\frac{M_{wm}A}{M_{wa}B}
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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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Maximum Treatment Pressure - Hydraulic Fracturing

Psi=Pb−ΔPh+ΔPfP_{si} = P_b - \Delta P_h + \Delta P_f
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Net Fracture Pressure from Fracture and Closure Pressure

Pnet=Pfrac−SclosureP_{net}=P_{frac}-S_{closure}
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Peclet Number for Fluid Loss - Acidizing

NPe=wˉvˉN2De∞N_{Pe}=\frac{\bar{w}\bar{v}_N}{2D_e^{\infty}}
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Pressure Loss Due to Perforations During Hydraulic Fracturing

ΔPp=ρq28090A22\Delta P_p=\frac{\rho q^2}{8090A_2^2}
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Principal Stress Due to Petro-Static Pressure - Hydraulic Fracturing

σz=γh10\sigma_z=\frac{\gamma h}{10}
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Productivity Ratio from Average Permeability - Hydraulic Fracturing

PR=kavgkPR=\frac{k_{avg}}{k}
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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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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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Reynolds Number for Acid Flow into the Fracture - Acidizing

NRe=ρiμhgN_{Re}=\frac{\rho i}{\mu h_g}
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Sand Weight to Refill Hydraulically Fractured Reservoir Volume

S=V(1−ϕ)ρsandS=V(1-\phi)\rho_{sand}
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Static-Test Fluid Loss per Unit Area - Acidizing

V=Vspt+2CwtV=V_{spt}+2C_w\sqrt{t}
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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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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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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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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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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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Wormhole Fluid-Loss Reynolds Number - Acidizing

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