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Phase Behavior and Thermodynamics Equations

Browse 102 phase behavior and thermodynamics petroleum engineering equations with variables, units, source references, and calculator links.

PVT and phase-behavior calculations estimate oil, gas, and fluid properties used in reservoir, production, and material-balance work.

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Phase Behavior and ThermodynamicsFluid Properties

Absolute Viscosity for Saybolt Viscosimeter Measurements

μ=vρ\mu=v\rho
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Phase Behavior and ThermodynamicsFluid Properties

Absolute Viscosity for Ubbelohde Viscosimeter Measurements

μ=Cut\mu=C_ut
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Phase Behavior and ThermodynamicsPVT Properties

Al-Marhoun Bubble Point Pressure

pb=0.00538088Rsb0.715082γg1.87784γo3.1437(T+459.67)1.32657p_b=0.00538088R_{sb}^{0.715082}\gamma_g^{-1.87784}\gamma_o^{3.1437}(T+459.67)^{1.32657}
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Phase Behavior and ThermodynamicsPVT Properties

Al-Marhoun Saturated Oil Formation Volume Factor

Bob=0.497069+0.000862963(T+459.67)+0.00182594F+0.00000318099F2B_{ob}=0.497069+0.000862963(T+459.67)+0.00182594F+0.00000318099F^2
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Phase Behavior and ThermodynamicsPVT Properties

Al-Marhoun Solution Gas-Oil Ratio from Bubble Point Pressure

Rsb=[pbγg1.877840.00538088γo3.1437(T+459.67)1.32657]1/0.715082R_{sb}=\left[\frac{p_b\gamma_g^{1.87784}}{0.00538088\gamma_o^{3.1437}(T+459.67)^{1.32657}}\right]^{1/0.715082}
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Phase Behavior and ThermodynamicsPVT Properties

Average Compressibility of Oil

Co=1V(V1V2p1p2)C_o = -\frac{1}{V}\left(\frac{V_1 - V_2}{p_1 - p_2}\right)
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Phase Behavior and ThermodynamicsPVT Properties

Average Gas Solubility

Savg=s1s2p1p2S_{avg} = \frac{s_1 - s_2}{p_1 - p_2}
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Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Dead-Oil Gas-Oil Interfacial Tension

σod=σ68+(T68)(σ100σ68)10068\sigma_{od}=\sigma_{68}+\frac{(T-68)(\sigma_{100}-\sigma_{68})}{100-68}
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Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Gas-Water Interfacial Tension at 280 F

σ280=530.1048P0.637\sigma_{280}=53-0.1048P^{0.637}
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Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Gas-Water Interfacial Tension at 74 F

σ74=751.108P0.349\sigma_{74}=75-1.108P^{0.349}
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Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Gas-Water Interfacial Tension by Temperature

σw=σ74+(T74)(σ280σ74)28074\sigma_w=\sigma_{74}+\frac{(T-74)(\sigma_{280}-\sigma_{74})}{280-74}
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Phase Behavior and ThermodynamicsFluid Properties

Baker-Swerdloff Live-Oil Gas-Oil Interfacial Tension

σo=σod(10.024P0.45)\sigma_o=\sigma_{od}\left(1-0.024P^{0.45}\right)
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Phase Behavior and ThermodynamicsGas Properties

Beggs-Brill Gas Z-Factor Correlation

z=A+(1A)eB+CPprDz=A+(1-A)e^{-B}+CP_{pr}^{D}
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Phase Behavior and ThermodynamicsFluid Properties

Beggs-Robinson Dead Oil Viscosity Correlation

μod=10x1\mu_{od}=10^x-1
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Phase Behavior and ThermodynamicsFluid Properties

Beggs-Robinson Live Oil Viscosity Correlation

μo=AμodB\mu_o=A\mu_{od}^{B}
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Phase Behavior and ThermodynamicsPVT Properties

Beggs-Standing Oil Formation Volume Factor Above Bubble Point

Bo=Bbexp[co(pbp)]B_o=B_b\exp\left[c_o(p_b-p)\right]
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Phase Behavior and ThermodynamicsPVT Properties

Beggs-Standing Oil Formation Volume Factor Below Bubble Point

Bo=0.972+0.000147F1.175B_o=0.972+0.000147F^{1.175}
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Phase Behavior and ThermodynamicsPVT Properties

Benedict-Webb-Rubin PVT Equation

P=RTρ+(BRTACT2)ρ2+(bRTa)ρ3+aαρ6+cρ3T2(1+γρ2)eγρ2P=RT\rho+\left(BRT-A-\frac{C}{T^2}\right)\rho^2+(bRT-a)\rho^3+a\alpha\rho^6+\frac{c\rho^3}{T^2}(1+\gamma\rho^2)e^{-\gamma\rho^2}
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Phase Behavior and ThermodynamicsGas Properties

Corrected Sour Gas Pseudo-Reduced Properties

Ppr=PPpcP'_{pr}=\frac{P}{P'_{pc}}
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Phase Behavior and ThermodynamicsFluid Properties

Egbogah Dead Oil Viscosity Below Bubble Point

μod=10101.86530.025086API0.5644log10T\mu_{od}=10^{10^{1.8653-0.025086API-0.5644\log_{10}T}}
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Phase Behavior and ThermodynamicsFluid Properties

Einstein Effective Viscosity for Dilute Suspensions

μeff=μ0(1+2.5ϕ)\mu_{eff}=\mu_0(1+2.5\phi)
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Phase Behavior and ThermodynamicsPVT Properties

Equilibrium Vaporization Ratio

K=yxK=\frac{y}{x}
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Phase Behavior and ThermodynamicsPVT Properties

Equilibrium Vaporization Ratio of Heptane

K=Ka(Kb/Ka)bK=\frac{K_a}{(K_b/K_a)^b}
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Phase Behavior and ThermodynamicsFluid Properties

Formation Water Density at Reservoir Conditions

ρwR=ρwSCBw\rho_{wR}=\frac{\rho_{wSC}}{B_w}
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Phase Behavior and ThermodynamicsFluid Properties

Formation Water Density at Standard Conditions

ρwSC=Cmg/L25000+62.428\rho_{wSC}=\frac{C_{mg/L}}{25000}+62.428
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Phase Behavior and ThermodynamicsFluid Properties

Formation Water Salinity from Density

Cmg/L=25000(SGw1)62.428C_{mg/L}=25000(SG_w-1)62.428
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Phase Behavior and ThermodynamicsFluid Properties

Formation Water Specific Gravity from Density

SGw=ρw62.428SG_w=\frac{\rho_w}{62.428}
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Phase Behavior and ThermodynamicsGas Properties

Gas Hydrate Dissociation Pressure

ph=0.1450377exp([2.50744×103(γh+0.46852)3+1.214644×102Fm4.676111×104Fm2+0.0720122]T+3.6625×104(γh0.485054)35.44376Fm+3.89×103Fm229.9351)p_h=0.1450377\exp\left(\left[\frac{2.50744\times10^{-3}}{(\gamma_h+0.46852)^3}+1.214644\times10^{-2}F_m-4.676111\times10^{-4}F_m^2+0.0720122\right]T+\frac{3.6625\times10^{-4}}{(\gamma_h-0.485054)^3}-5.44376F_m+3.89\times10^{-3}F_m^2-29.9351\right)
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Phase Behavior and ThermodynamicsGas Properties

Gas Molecular Weight from Specific Gravity

Mg=28.967γgM_g=28.967\gamma_g
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Phase Behavior and ThermodynamicsGas Properties

Generalized Virial Gas Z-Factor Correlation

z=1+(B0+ωB1)PprTprz=1+\frac{(B^0+\omega B^1)P_{pr}}{T_{pr}}
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Phase Behavior and ThermodynamicsPVT Properties

Glaso Bubble Point Pressure

pb=101.7669+1.7447log10(pb)0.30218[log10(pb)]2p_b=10^{1.7669+1.7447\log_{10}(p_b^*)-0.30218[\log_{10}(p_b^*)]^2}
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Phase Behavior and ThermodynamicsPVT Properties

Glaso Saturated Oil Formation Volume Factor

Bo=1+106.58511+2.91329log10(Bo)0.27683[log10(Bo)]2B_o=1+10^{-6.58511+2.91329\log_{10}(B_o^*)-0.27683[\log_{10}(B_o^*)]^2}
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Phase Behavior and ThermodynamicsPVT Properties

Glaso Solution Gas-Oil Ratio from Pressure

Rs=γg(pbAPI0.989T0.172)1/0.816R_s=\gamma_g\left(\frac{p_b^*API^{0.989}}{T^{0.172}}\right)^{1/0.816}
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Phase Behavior and ThermodynamicsPVT Properties

Glaso Solution Gas-Oil Ratio from Saturated Oil FVF

Rs=Bo0.968T(γg/γo)0.526R_s=\frac{B_o^*-0.968T}{(\gamma_g/\gamma_o)^{0.526}}
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Phase Behavior and ThermodynamicsPVT Properties

Glaso Undersaturated Oil Formation Volume Factor

Bo=Bobexp[co(pbp)]B_o=B_{ob}\exp[c_o(p_b-p)]
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Phase Behavior and ThermodynamicsGas Properties

Hydrate Formation Temperature from Modified Clapeyron Criterion

Th=3.89Ch0.5T_h=3.89C_h^{0.5}
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Phase Behavior and ThermodynamicsPVT Properties

Jacoby Aromaticity Factor

Ja=γ+15.8M0.84680.24561.77MJ_a=\frac{\gamma+\frac{15.8}{M}-0.8468}{0.2456-\frac{1.77}{M}}
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Phase Behavior and ThermodynamicsGas Properties

Kay Mixing Rule Gas Pseudo-Critical Properties

Tpc=iyiTciT_{pc}=\sum_i y_iT_{ci}
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Phase Behavior and ThermodynamicsFluid Properties

Kinematic Viscosity for Saybolt Viscosimeter Measurements

v=0.220to180tov=0.220t_o-\frac{180}{t_o}
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Phase Behavior and ThermodynamicsFluid Properties

Kinematic Viscosity from Dynamic Viscosity and Density

ν=μρ\nu=\frac{\mu}{\rho}
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Phase Behavior and ThermodynamicsPVT Properties

Latent Heat of Hydrocarbon Mixture

Δhm=TM(7.58+4.57log10T)\Delta h_m=\frac{T}{M}\left(7.58+4.57\log_{10}T\right)
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Phase Behavior and ThermodynamicsGas Properties

Lee-Gonzalez-Eakin Gas Viscosity

μg=104Kexp(XρgY)\mu_g=10^{-4}K\exp(X\rho_g^Y)
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Phase Behavior and ThermodynamicsPVT Properties

Liquid-Phase Component Mole Fraction

x=zL+VKx=\frac{z}{L+VK}
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Phase Behavior and ThermodynamicsFluid Properties

Live Oil Density from Formation Volume Factor

ρo=ρo,st+0.0136RsγgBo\rho_o=\frac{\rho_{o,st}+0.0136R_s\gamma_g}{B_o}
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Phase Behavior and ThermodynamicsFluid Properties

Logarithmic Crude Oil Viscosity from API Gravity

logμo=a0.035API\log\mu_o=a-0.035API
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Phase Behavior and ThermodynamicsFluid Properties

McCain Brine Gas-Solubility Salinity Correction

Fs=100.0840655ST0.285854F_s=10^{-0.0840655ST^{-0.285854}}
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Phase Behavior and ThermodynamicsFluid Properties

McCain Brine Solution Gas-Water Ratio

Rsw=RswpFsR_{sw}=R_{swp}F_s
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Phase Behavior and ThermodynamicsFluid Properties

McCain Pure-Water Solution Gas-Water Ratio

Rswp=A+BP+CP2R_{swp}=A+BP+CP^2
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Phase Behavior and ThermodynamicsFluid Properties

McCain Saturated Water Compressibility with Gas Liberation

cwsat=cwunder+BgBw(RswP)Tc_{wsat}=c_{wunder}+\frac{B_g}{B_w}\left(\frac{\partial R_{sw}}{\partial P}\right)_T
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Phase Behavior and ThermodynamicsFluid Properties

McCain Solution Gas-Water Pressure Derivative

(RswP)T=Fs(B+2CP)\left(\frac{\partial R_{sw}}{\partial P}\right)_T=F_s(B+2CP)
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Phase Behavior and ThermodynamicsPVT Properties

McCain Water Formation Volume Factor

Bw=(1+ΔVwT)(1+ΔVwP)B_w=(1+\Delta V_{wT})(1+\Delta V_{wP})
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Phase Behavior and ThermodynamicsFluid Properties

McCain Water Viscosity at Atmospheric Pressure

μw1=ATB\mu_{w1}=AT^B
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Phase Behavior and ThermodynamicsFluid Properties

McCain Water Viscosity at Reservoir Pressure

μw=μw1(0.9994+4.0295×105p+3.1062×109p2)\mu_w=\mu_{w1}\left(0.9994+4.0295\times10^{-5}p+3.1062\times10^{-9}p^2\right)
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Phase Behavior and ThermodynamicsGas Properties

Necessary Inhibitor Concentration Required in Liquid Phase to Reduce Hydrate Point

X=100dMdM+2335X=\frac{100dM}{dM+2335}
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Phase Behavior and ThermodynamicsFluid Properties

Newtonian Shear Stress from Viscosity

τ=μdudy\tau=\mu\frac{du}{dy}
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Phase Behavior and ThermodynamicsFluid Properties

Osif Water Isothermal Compressibility

cw=17.033P+0.5415Cmg/L537T+403300c_w=\frac{1}{7.033P+0.5415C_{mg/L}-537T+403300}
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Phase Behavior and ThermodynamicsGas Properties

Papay Gas Z-Factor Correlation

z=13.53Ppr100.9813Tpr+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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Phase Behavior and ThermodynamicsPVT Properties

Peng-Robinson Characterization Factor

kCi=0.0289+0.0001633Mk_{Ci}=0.0289+0.0001633M
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Phase Behavior and ThermodynamicsPVT Properties

Peng-Robinson PVT Equation

P=RTVbaTV(V+b)+b(Vb)P=\frac{RT}{V-b}-\frac{aT}{V(V+b)+b(V-b)}
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Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Bubble Point Pressure

pb=112.727[Rsb0.5774γg0.843910x12.34]p_b=112.727\left[\frac{R_{sb}^{0.5774}}{\gamma_g^{0.8439}}10^x-12.34\right]
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Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Saturated Oil Formation Volume Factor

Bob=1.0113+7.2046×105F3.0936B_{ob}=1.0113+7.2046\times10^{-5}F^{3.0936}
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Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Solution Gas-Oil Ratio from Pressure

Rs=[(p112.727+12.34)γg0.843910x]1.73184R_s=\left[\left(\frac{p}{112.727}+12.34\right)\gamma_g^{0.8439}10^x\right]^{1.73184}
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Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Undersaturated Oil Compressibility

co=1.705×107Rsb0.69357γg0.1885API0.3272T0.6729p0.5906c_o=1.705\times10^{-7}R_{sb}^{0.69357}\gamma_g^{0.1885}API^{0.3272}T^{0.6729}p^{-0.5906}
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Phase Behavior and ThermodynamicsPVT Properties

Petrosky-Farshad Undersaturated Oil Formation Volume Factor

Bo=Bobexp[co(pbp)]B_o=B_{ob}\exp[c_o(p_b-p)]
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Phase Behavior and ThermodynamicsGas Properties

Pseudo-Reduced Conditions

Pr=P(PcAPcB)0.5P_r = \frac{P}{(P_{cA}P_{cB})^{0.5}}
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Phase Behavior and ThermodynamicsGas Properties

Pseudo-Reduced Gas Properties from Critical Properties

Ppr=PPpcP_{pr}=\frac{P}{P_{pc}}
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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=1P1z(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 Derivative

dmdp=2pμgz\frac{dm}{dp}=\frac{2p}{\mu_g z}
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Phase Behavior and ThermodynamicsGas Properties

Real Gas Pseudopressure Difference for Constant Mu-Z

Δm=p22p12μgz\Delta m=\frac{p_2^2-p_1^2}{\mu_g z}
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Phase Behavior and ThermodynamicsGas Properties

Real Gas Pseudopressure Trapezoidal Increment

Δm=12(D1+D2)(p2p1)\Delta m=\frac{1}{2}(D_1+D_2)(p_2-p_1)
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Phase Behavior and ThermodynamicsPVT Properties

Redlich-Kwong PVT Equation

P=RTVbaT0.5V(V+b)P=\frac{RT}{V-b}-\frac{a}{T^{0.5}V(V+b)}
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Phase Behavior and ThermodynamicsPVT Properties

Saturated Oil Compressibility from FVF and Solution GOR Derivatives

co=1BodBodp+BgBodRsdpc_o=-\frac{1}{B_o}\frac{dB_o}{dp}+\frac{B_g}{B_o}\frac{dR_s}{dp}
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Phase Behavior and ThermodynamicsPVT Properties

Solution Gas-Oil Ratio - Beggs-Standing Correlation Below Bubble Point

Rso=γg(p1810Yg)1.204R_{so} = \gamma_g\left(\frac{p}{18\cdot10^{Y_g}}\right)^{1.204}
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Phase Behavior and ThermodynamicsPVT Properties

Solution Gas-Oil Ratio - Standing Correlation

Rs=γg[p18100.0125API100.00091t]1.2048R_s=\gamma_g\left[\frac{p}{18}\frac{10^{0.0125API}}{10^{0.00091t}}\right]^{1.2048}
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Phase Behavior and ThermodynamicsPVT Properties

Solution Gas-Water Ratio

Rsw=Rswp100.0840655ST0.285854R_{sw}=R_{swp}10^{-0.0840655ST^{-0.285854}}
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Phase Behavior and ThermodynamicsGas Properties

Specific Gravity of Gas Hydrate Forming Components

Γh=mh28.96\Gamma_h=\frac{m_h}{28.96}
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Phase Behavior and ThermodynamicsFluid Properties

Standard Discharge Time for Saybolt Viscosimeter Measurements

ts=to[1+0.000064(ToTs)]t_s=t_o\left[1+0.000064(T_o-T_s)\right]
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Phase Behavior and ThermodynamicsFluid Properties

Standing Dead Oil Viscosity Correlation

μod=(0.32+1.8×107API4.53)(360t+200)a\mu_{od}=\left(0.32+\frac{1.8\times10^7}{API^{4.53}}\right)\left(\frac{360}{t+200}\right)^a
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Phase Behavior and ThermodynamicsGas Properties

Standing Dry Gas Pseudo-Critical Properties

Tpc=168+325γg12.5γg2T_{pc}=168+325\gamma_g-12.5\gamma_g^2
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Phase Behavior and ThermodynamicsFluid Properties

Standing Live Oil Density Correlation

ρo=62.4γo+0.0136Rsγg0.972+0.000147(Rsγg/γo+1.25t)1.175\rho_o=\frac{62.4\gamma_o+0.0136R_s\gamma_g}{0.972+0.000147\left(R_s\sqrt{\gamma_g/\gamma_o}+1.25t\right)^{1.175}}
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Phase Behavior and ThermodynamicsPVT Properties

Standing Oil Formation Volume Factor

Bo=0.9759+0.00012F1.2B_o=0.9759+0.00012F^{1.2}
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Phase Behavior and ThermodynamicsGas Properties

Standing Wet Gas Pseudo-Critical Properties

Tpc=187+330γg71.5γg2T_{pc}=187+330\gamma_g-71.5\gamma_g^2
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Phase Behavior and ThermodynamicsFluid Properties

Stock-Tank Oil Density from API Gravity

ρo,st=ρw141.5API+131.5\rho_{o,st}=\rho_w\frac{141.5}{API+131.5}
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Phase Behavior and ThermodynamicsGas Properties

Sutton Pseudo-Critical Gas Properties

Tpc=169.2+349.5γg74.0γg2T_{pc}=169.2+349.5\gamma_g-74.0\gamma_g^2
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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Attraction Parameter from Critical Properties

a=27R2Tc264Pca = \frac{27R^2T_c^2}{64P_c}
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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Covolume from Critical Properties

b=RTc8Pcb = \frac{RT_c}{8P_c}
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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Critical Molar Volume

vc=3bv_c = 3b
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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Critical Pressure from Parameters

Pc=a27b2P_c = \frac{a}{27b^2}
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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Critical Temperature from Parameters

Tc=8a27RbT_c = \frac{8a}{27Rb}
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Phase Behavior and ThermodynamicsPVT Properties

Van der Waals Equation of State Pressure

P=RTvmbavm2P = \frac{RT}{v_m-b} - \frac{a}{v_m^2}
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Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Bubble Point Pressure from Solution GOR

pb=[RsbC1γgexp(C3API/(T+460))]1/C2p_b=\left[\frac{R_{sb}}{C_1\gamma_g\exp(C_3API/(T+460))}\right]^{1/C_2}
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Phase Behavior and ThermodynamicsFluid Properties

Vasquez-Beggs Oil Viscosity Above Bubble Point

μo=μob(ppb)m\mu_o=\mu_{ob}\left(\frac{p}{p_b}\right)^m
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Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Saturated Oil Formation Volume Factor

Bo=1+A1Rs+A2(T60)APIγgc+A3Rs(T60)APIγgcB_o=1+A_1R_s+A_2(T-60)\frac{API}{\gamma_{gc}}+A_3R_s(T-60)\frac{API}{\gamma_{gc}}
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Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Solution Gas-Oil Ratio from Pressure

Rs=C1γgpC2exp(C3APIT+460)R_s=C_1\gamma_g p^{C_2}\exp\left(\frac{C_3API}{T+460}\right)
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Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Undersaturated Oil Compressibility

co=1433+5Rsb+17.2T1180γg+12.61API105pc_o=\frac{-1433+5R_{sb}+17.2T-1180\gamma_g+12.61API}{10^5p}
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Phase Behavior and ThermodynamicsPVT Properties

Vasquez-Beggs Undersaturated Oil Formation Volume Factor

Bo=Bobexp[co(pbp)]B_o=B_{ob}\exp[c_o(p_b-p)]
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Phase Behavior and ThermodynamicsPVT Properties

Villena-Lanzi Saturated Oil Compressibility

co=exp[0.6641.430lnp0.395lnpb+0.390lnT+0.455lnRsb+0.262lnAPI]c_o=\exp[-0.664-1.430\ln p-0.395\ln p_b+0.390\ln T+0.455\ln R_{sb}+0.262\ln API]
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Phase Behavior and ThermodynamicsFluid Properties

Viscosibility

cv=1μdμdPc_v = \frac{1}{\mu}\frac{d\mu}{dP}
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Phase Behavior and ThermodynamicsGas Properties

Water Content of Sour Gas

W=yWhc+yCO2WCO2+yH2SWH2SW=yW_{hc}+y_{CO2}W_{CO2}+y_{H2S}W_{H2S}
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Phase Behavior and ThermodynamicsPVT Properties

Watson Characterization Factor from Boiling Point and Specific Gravity

Kw=Tb1/3γ60K_w=\frac{T_b^{1/3}}{\gamma_{60}}
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Phase Behavior and ThermodynamicsGas Properties

Wichert-Aziz Sour Gas Pseudo-Critical Correction

Tpc=TpcϵT'_{pc}=T^*_{pc}-\epsilon
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