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Phase Behavior and ThermodynamicsFluid Properties

McCain Brine Gas-Solubility Salinity Correction

Fs=10−0.0840655ST−0.285854F_s=10^{-0.0840655ST^{-0.285854}}
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Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Minimum Hoop Stress at the Wellbore Wall

σθ,min=3Shmin−Shmax−2Po−ΔP−Sdt\sigma_{\theta,min}=3S_{hmin}-S_{hmax}-2P_o-\Delta P-S_{dt}
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Reservoir EngineeringReserves and Recovery

Modified Hyperbolic Decline Rate

q(t)=qi(1+bDith)−1/b×e−Dt(t−th)th=min⁡(t,ts)ts=Di−DtbDiDt\begin{aligned}q(t)&=q_i(1+bD_it_h)^{-1/b}\\&\quad\times e^{-D_t(t-t_h)}\\t_h&=\min(t,t_s)\\t_s&=\frac{D_i-D_t}{bD_iD_t}\end{aligned}
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Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Normal Hoop Stress at the Wellbore Wall

σθ=Shmax+Shmin−2(Shmax−Shmin)cos⁡(2θ)−2Po−ΔP−Sdt\sigma_\theta=S_{hmax}+S_{hmin}-2(S_{hmax}-S_{hmin})\cos(2\theta)-2P_o-\Delta P-S_{dt}
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Phase Behavior and ThermodynamicsGas Properties

Papay Gas Z-Factor Correlation

z=1−3.53Ppr100.9813Tpr+0.274Ppr2100.8157Tprz=1-\frac{3.53P_{pr}}{10^{0.9813T_{pr}}}+\frac{0.274P_{pr}^2}{10^{0.8157T_{pr}}}
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Reservoir EngineeringReserves and Recovery

Power-Law Exponential Decline Rate

q(t)=q^iexp⁡[−D∞t−D^itn]q(t)=\hat q_i\exp[-D_\infty t-\hat D_i t^n]
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Phase Behavior and ThermodynamicsGas Properties

Real Gas Density

ρg=PMgzRT\rho_g=\frac{P M_g}{zRT}
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Phase Behavior and ThermodynamicsGas Properties

Real Gas Isothermal Compressibility with Z-Factor Derivative

cg=1P−1z(dzdP)Tc_g=\frac{1}{P}-\frac{1}{z}\left(\frac{dz}{dP}\right)_T
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Phase Behavior and ThermodynamicsGas Properties

Real Gas Pseudopressure Difference for Constant Mu-Z

Δm=p22−p12μgz\Delta m=\frac{p_2^2-p_1^2}{\mu_g z}
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Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Shale Compaction

ϕe=ϕe−βsσv\phi_e=\phi e^{-\beta_s\sigma_v}
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PetrophysicsRock Properties

Sonic Porosity Raymer-Hunt-Gardner Method

Φsonic=CRHGΔt−ΔtmaΔt\Phi_{sonic}=C_{RHG}\frac{\Delta t-\Delta t_{ma}}{\Delta t}
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Reservoir EngineeringReserves and Recovery

Stretched Exponential Decline Rate

q(t)=q^iexp⁡[−(tτ)n]q(t)=\hat q_i\exp\left[-\left(\frac{t}{\tau}\right)^n\right]
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Drilling EngineeringDrillstring and Rig Mechanics

Stuck Pipe Free Point from Pipe Stretch - Method 1

hf=SfpcPFh_f=\frac{Sfpc}{PF}
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Geomechanics and FracturingIn-Situ Stress and Rock Mechanics

Tangential Stress Extremes at a Deviated Wellbore

σtmax=12(σzz+σaa+(σzz−σaa)2+4τ2)\sigma_{tmax}=\frac{1}{2}\left(\sigma_{zz}+\sigma_{aa}+\sqrt{(\sigma_{zz}-\sigma_{aa})^2+4\tau^2}\right)
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Reservoir EngineeringUnconventional Reservoirs

Tight Gas Pore Volume from Squared-Pressure Decline

PV=28.27Tμg,avgzavgμgicti(Pi2−Pwf2)qiDiPV=\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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PetrophysicsRock Properties

van Genuchten Capillary Pressure

Pc=P0(Se−1/m−1)1−mn=1/(1−m)\begin{aligned}P_c&=P_0(S_e^{-1/m}-1)^{1-m}\\n&=1/(1-m)\end{aligned}
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Phase Behavior and ThermodynamicsFluid Properties

Wood Two-Phase Fluid Bulk Modulus

Kf=(SwKw+1−SwKh)−1K_f=\left(\frac{S_w}{K_w}+\frac{1-S_w}{K_h}\right)^{-1}
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