## SusaProp

SusaProp is a correlation-based PVT package for dry-gas, wet-gas, black-oil and water samples. It generates a list of properties in a tabular format at a constant temperature from atmospheric pressure up to the pressure of interest. All the predictions can be generated by only two functions: **pvt_lst()** and **pvt_predict()**.

**pvt_lst()** generates a **list object** with a fluid type, a PVT model, a viscosity model, and all the required input parameters. The generated **list object** is used by the **pvt_predict()** function which creates a matrix of physical properties over a wide range of pressures at a constant temperature.

The SusaProp package also has a list of sub-functions, defined internally, that generate different properties for gas, oil, and water. In the following sections all the correlations are explained.

## pvt_lst() parameters

input_unit: Unit of input parameters, either “Field” or “SI”.

output_unit: Unit of output predictions, either “Field” or “SI”.

fluid: Type of fluid, it can be “dry_gas”, “wet_gas”, “black_oil”, or “water”.

pvt_model: There is only one model for dry_gas or wet_gas samples, “Sutton”. There are five models for black_oil samples, “Standing”, “Vasquez_Beggs”, “Farshad_Petrosky”, “Al_Marhoun”, and “Glaso”. There are two models for water samples, “McCain”, and “Meehan”.

visc_model: There is only one model for dry_gas or wet_gas samples, “Sutton”. There are two models for black_oil samples, “Beggs_Robinson”, and “Al_Marhoun”. There are two models for water samples, “McCain”, and “Meehan”.

t: Reservoir temperature in C or F depending on input_unit.

p: Reservoir pressure in kPag or Psig depending on input_unit.

spgr: Gas specific gravity (air = 1) used in dry_gas, wet_gas, or black_oil models.

nhc_composition: $N_{2}$-$H_{2}S$-$CO_{2}$ mole fractions in gas samples, respectively.

cgr: condensate_to_gas ratio in m3/m3 or STB/MMSCF depending on input_unit, used only for wet_gas samples. It must be zero for dry_gas and black_oil samples.

api: Oil API gravity used in wet_gas and black_oil samples.

rsi: Gas solubility in oil (initial solution gas) in m3/m3 or SCF/STB depending on input_unit, used only for black_oil samples. Either “rsi” or “pb” must be entered for black_oil samples.

pb: Bubble point pressure of black_oil samples in kPag or Psig depending on input_unit. Either “rsi” or “pb” must be entered for black_oil samples.

water_saturated: Used only for water samples and checks whether it is gas saturated or not. Either “yes” or “no” must be chosen for water samples.

salinity: Used only for water samples and is water salinity in weight percent TDS.

warning: Shows warning messages for input parameters outside the range of correlations. Either “yes” or “no” must be chosen.

## pvt_predict() parameter

- lst: A list object with pvt_model, visc_model, fluid, and all other required parameters.

## Gas PVT Correlations

Gas properties are estimated using **Sutton’s** correlations(Sutton 2007).

### Pseudoreduced Properties ($T_{pc}, P_{pc}$):

${y_{HC} = 1 - y_{H_{2}S} - y_{CO_{2}} - y_{N_{2}}}$

$\gamma_{gHC} = \frac{\gamma_{g} - (y_{H_{2}S}Mw_{H_{2}S} - y_{CO_{2}}Mw_{CO_{2}} - y_{N_{2}}Mw_{N_{2}})}{y_{HC}}$

For dry gas:

$p_{pcHC} = 671.1 + 14.0 \gamma_{gHC} - 34.3 \gamma_{gHC}^2$

$T_{pcHC} = 120.1 + 429.0 \gamma_{gHC} - 62.9 \gamma_{gHC}^2$

For wet/condensate gas:

$p_{pcHC} = 744.0 - 125.4 \gamma_{gHC} + 5.9 \gamma_{gHC}^2$

$T_{pcHC} = 164.3 + 357.7 \gamma_{gHC} - 67.7 \gamma_{gHC}^2$

The estimated pseudoreduced properties are adjusted due to presence of nonhydrocarbons(Wichert and Aziz 1972):

$p_{pc}^* = y_{HC}P_{pcHC} + y_{H_{2}S}P_{cH_{2}S} + y_{CO_{2}}P_{cCO_{2}} + y_{N_{2}}P_{cN_{2}}$

$T_{pc}^* = y_{HC}T_{pcHC} + y_{H_{2}S}T_{cH_{2}S} + y_{CO_{2}}T_{cCO_{2}} + y_{N_{2}}T_{cN_{2}}$

$\epsilon = 120[(y_{H_{2}S} + y_{CO_{2}})^{0.9} - (y_{H_{2}S} + y_{CO_{2}})^{1.6}] + 15 (y_{H_{2}S}^{0.5} - y_{H_{2}S}^{4})$

$T_{pc} = T_{pc}^* - \epsilon$

$p_{pc} = \frac{p_{pc}^* (T_{pc}^* - \epsilon)}{T_{pc}^* + y_{H_{2}S} (1 - y_{H_{2}S}) \epsilon}$

$y_{i}$ is mole fraction of component $i$, $Mw_{i}$ is molecular weight of component $i$ in ($\frac {lb}{lbmole}$), $T_{ci}$ is critical temperature of component $i$ in R, and $P_{ci}$ is critical pressure of component $i$ in Psia.

### Gas Compressibility Factor (Z):

$Z = 1 + (A_{1} + \frac{A_{2}}{T_{r}} + \frac{A_{3}}{T_{r}^3} + \frac{A_{4}}{T_{r}^4} + \frac{A_{5}}{T_{r}^5})\rho_{r} + (A_{6} + \frac{A_{7}}{T_{r}} + \frac{A_{8}}{T_{r}^2}) \rho_{r}^2 - A_{9} (\frac{A_{7}}{T_{r}} + \frac{A_{8}}{T_{r}^2}) \rho_{r}^5 + A_{10} (1 + A_{11} \rho_{r}^2) \frac{\rho_{r}^2}{T_{r}^3} exp(-A_{11} \rho_{r}^2)$

where $\rho_{r}$ is reduced density and is defined as:

$\rho_{r} = \frac{0.27P_{r}}{ZT_{r}}$

$T_{r}$ is reduced temperature, $P_{r}$ is reduced pressure, $Z$ is gas compressibility factor, and $A_{1} = 0.3265, A_{2} = -1.0700, A_{3} = -0.5339, A_{4} = 0.01569, A_{5} = -0.05165, A_{6} = 0.5475, A_{7} = -0.7361, A_{8} = 0.1844, A_{9} = 0.1056, A_{10} = 0.6134, A_{11} = 0.7210$

### Gas Density ($\rho_{g}$):

$\rho = \frac{P Mw}{ZRT}$

where $\rho$ is density in ($\frac{lb}{ft^3}$), P is pressure in Psia, Mw is molecular weight in ($\frac {lb}{lbmole}$), Z is gas compressibility factor, $R=10.73159$ is universal gas constant in ($\frac{ft^3.Psia}{lbmole.R}$), and T is temperarure in R.

### Gas Formation Volume Factor ($B_{g}$):

$B_{g} = \frac{ZP_{sc}T}{5.615PT_{sc}}$

where $B_{g}$ is gas formation volume factor in ($\frac{bbl}{scf}$), Z is gas compressibility factor, P is pressure in Psia, T is temperature in R, $P_{sc} = 14.696$ is pressure at standard conditions in Psia, and $T_{sc} = 519.67$ is temperature at standard conditions in R.

### Gas Compressibility ($C_{g}$):

$C_{g} = \frac{1}{P} - \frac{1}{Z} (\frac{\partial Z}{\partial P})_{T}$

which can be expressed as:

$C_{g} = \frac{C_{r}}{p_{pc}}$

where $C_{r}$ is pseudo-reduced gas compressibility and is defined as:

$C_{r} = \frac{1}{P_{r}} - \frac{1}{Z} (\frac{\partial Z}{\partial P_{r}})_{T_{r}} = 1 - \frac{P_{r}}{ZT_{r}} (\frac{0.27(\frac{\partial Z}{\partial \rho_{r}})_{T_{r}}} {Z + \rho_{r}(\frac{\partial Z}{\partial \rho_{r}})_{T_{r}}})$

$\rho_{r} = \frac{0.27P_{r}}{ZT_{r}}$

and

$(\frac{\partial Z}{\partial \rho_{r}})_{T_{r}} = (A_{1} + \frac{A_{2}}{T_{r}} + \frac{A_{3}}{T_{r}^3} + \frac{A_{4}}{T_{r}^4} + \frac{A_{5}}{T_{r}^5}) + 2(A_{6} + \frac{A_{7}}{T_{r}} + \frac{A_{8}}{T_{r}^2}) \rho_{r} - 5A_{9}(\frac{A_{7}}{T_{r}} + \frac{A_{8}}{T_{r}^2}) \rho_{r}^4+ (\frac{2A_{10}\rho_{r}}{T_{r}^3}+2A_{10}A_{11}\frac{\rho_{r}^3}{T_{r}^3}-2A_{10}A_{11}^2\frac{\rho_{r}^5}{T_{r}^3})exp(-A_{11} \rho_{r}^2)$

where $C_{g}$ is gas compressibility in ($\frac{1}{Psai}$), and $A_{i}$ values are the same as $A_{i}$ values reported for the gas compressibility factor (Z Factor).

### Gas Viscosity ($\mu_{g}$):

$\mu_{g} = \mu_{gsc} exp (X\rho_{g}^Y)$

where

$X = 3.47 + \frac{1588}{T} + 0.0009Mw$

$Y = 1.66378 - 0.04679X$

$\mu_{gsc}\zeta = 10^{-4}[0.807T_{r}^{0.618} - 0.357 exp(-0.449 T_{r}) + 0.340 exp(-4.058 T_{r}) + 0.018]$

$\zeta = 0.9490(\frac{T_{pc}}{Mw^3P_{pc}^4})^{\frac{1}{6}}$

in the above equations, $\mu_g$ is gas viscosity in centipoise (cp), $\rho_g$ is gas density in ($\frac{gr}{cm^3}$), T is temperature in R, and P is pressure in Psia.

### Gas Pseudo-Pressure ($\Psi(p)$):

$\Psi(p) = 2\int_0^{p}\frac{p}{\mu_{g} Z}$

where $\Psi(p)$ is gas pseudo-pressure in ($\frac{Psia^2}{cp}$), $\mu_g$ is gas viscosity in centipoise (cp), and Z is gas compressibility factor.

## Oil PVT Correlations

There are five correlations available for estimating black oil properties: **Standing**, **Vasquez_Beggs**, **Farshad_Petrosky**, **Al_Marhoun**, and **Glaso**. Two correlations are available for estimating black oil viscosity: **Beggs_Robinson**, and **Al_Marhoun**. Oil compressibility above bubble point is estimated by **Spivey et. al.** correlation.

### 1. Standing Oil Properties Model(Standing 1947):

### Bubble Point Pressure ($P_{b}$):

$P_{b} = 18.2 * [(\frac{R_{sob}}{\gamma_{g}})^{0.83} 10^{0.00091 t - 0.0125 API} - 1.4]$

$P_{b}$ is bubble point pressure in Psia, t is temperature in F, $R_{sob}$ is gas solubility in oil at bubble point in ($\frac{scf}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Gas Solubility in Oil ($R_{so}$):

$R_{so} = \gamma_{g} [(\frac{p}{18.2} + 1.4) 10^{0.0125 API - 0.00091 t}]^{\frac{1}{0.83}}$

$R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), t is temperature in F, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Oil Formation Volume Factor ($B_{o}$):

if P > $P_{b}$:

$B_{o} = B_{ob} exp[C_{o}(P_{b}-P)]$

and if P <= $P_{b}$:

$B_{o} = 0.9759 + 0.00012 (R_{so}(\frac{\gamma_{g}}{\gamma_{o}})^{0.5} + 1.25 t)^{1.2}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), t is temperature in F, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), API is oil API gravity, and $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$).

### Oil Compressibility ($C_{o}$):

if P > $P_{b}$:

$C_{o} = C_{o,Spivey}$

and if P <= $P_{b}$:

$C_{o} = (B_{g} - \frac{\partial B_{o}}{\partial R_{so}}) \frac{\frac{\partial R_{so}}{\partial P}}{B_{o}}$

$C_{o}$ is oil compressibility in ($\frac{1}{Psia}$), $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), and $B_{g}$ is gas formation volume factor in ($\frac{bbl}{stb}$).

### Oil Density ($\rho_{o}$):

$\rho_{o}= \frac{62.37 \gamma_{o} + 0.0136 \gamma_{g} R_{so}}{B_{o}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$\rho_{o}$ is oil density in ($\frac{lbm}{ft^3}$), $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### 2. Vasquez_Beggs Oil Properties Model(Vasquez and Beggs 1980):

### Bubble Point Pressure ($P_{b}$):

$P_{b} = [\frac{R_{sob}}{C_{1}\gamma_{g}exp(\frac{C_{3}API}{t + 459.67})}]^{\frac{1}{C_{2}}}$

if oil API <= 30:

$C_{1} = 0.0362$, $C_{2} = 1.0937$, $C_{3} = 25.7240$

if oil API > 30:

$C_{1} = 0.0178$, $C_{2} = 1.1870$, $C_{3} = 23.9310$

$P_{b}$ is bubble point pressure in Psia, t is temperature in F, $R_{sob}$ is gas solubility in oil at bubble point in ($\frac{scf}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Gas Solubility in Oil ($R_{so}$):

$R_{so} = C_{1} \gamma_{g} p^{C_{2}} exp(\frac{C_{3}API}{t + 459.67})$

$R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), t is temperature in F, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Oil Formation Volume Factor ($B_{o}$):

if P > $P_{b}$:

$B_{o} = B_{ob} exp[C_{o}(P_{b}-P)]$

and if P <= $P_{b}$:

$B_{o} = 1 + A_{1} R_{so} + A_{2}(t-60)(\frac{API}{\gamma_{g}}) + A_{3}R_{so}(t-60)(\frac{API}{\gamma_{g}})$

if oil API <= 30:

$A_{1} = 4.677 * 10^{-4}$, $A_{2} = 1.751 * 10^{-5}$, $A_{3} = -1.811 * 10^{-8}$

if oil API > 30:

$A_{1} = 4.670 * 10^{-4}$, $A_{2} = 1.100 * 10^{-5}$, $A_{3} = 1.337 * 10^{-9}$

$B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), t is temperature in F, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), API is oil API gravity, and $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$).

### Oil Compressibility ($C_{o}$):

if P > $P_{b}$:

$C_{o} = C_{o,Spivey}$

and if P <= $P_{b}$:

$C_{o} = (B_{g} - \frac{\partial B_{o}}{\partial R_{so}}) \frac{\frac{\partial R_{so}}{\partial P}}{B_{o}}$

$C_{o}$ is oil compressibility in ($\frac{1}{Psia}$), $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), and $B_{g}$ is gas formation volume factor in ($\frac{bbl}{stb}$).

### Oil Density ($\rho_{o}$):

$\rho_{o}= \frac{62.37 \gamma_{o} + 0.0136 \gamma_{g} R_{so}}{B_{o}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$\rho_{o}$ is oil density in ($\frac{lbm}{ft^3}$), $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### 3. Farshad_Petrosky Oil Properties Model(Petrosky Jr. and Farshad 1998):

### Bubble Point Pressure ($P_{b}$):

$P_{b} = 112.727 * (\frac{R_{sob}^{0.5774}}{\gamma_{g}^{0.8439}} 10^{x} - 12.34)$

$x = 4.561 * 10^{-5} t^{1.3911} - 7.916 * 10^{-4} API^{1.541}$

$P_{b}$ is bubble point pressure in Psia, t is temperature in F, $R_{sob}$ is gas solubility in oil at bubble point in ($\frac{scf}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Gas Solubility in Oil ($R_{so}$):

$R_{so} = ([\frac{P}{112.727}+12.34]\gamma_{g}^{0.8439} 10^x)^{1.73184}$

$R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), t is temperature in F, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Oil Formation Volume Factor ($B_{o}$):

if P > $P_{b}$:

$B_{o} = B_{ob} exp[C_{o}(P_{b}-P)]$

and if P <= $P_{b}$:

$B_{o} = 1.0113 + 7.2046 * 10^{-5} (R_{so}^{0.3738} \frac{\gamma_{g}^{0.2914}}{\gamma_{o}^{0.6265}} + 0.24626 t^{0.5371})^{3.0936}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), t is temperature in F, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), API is oil API gravity, and $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$).

### Oil Compressibility ($C_{o}$):

if P > $P_{b}$:

$C_{o} = C_{o,Spivey}$

and if P <= $P_{b}$:

$C_{o} = (B_{g} - \frac{\partial B_{o}}{\partial R_{so}}) \frac{\frac{\partial R_{so}}{\partial P}}{B_{o}}$

$C_{o}$ is oil compressibility in ($\frac{1}{Psia}$), $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), and $B_{g}$ is gas formation volume factor in ($\frac{bbl}{stb}$).

### Oil Density ($\rho_{o}$):

$\rho_{o}= \frac{62.37 \gamma_{o} + 0.0136 \gamma_{g} R_{so}}{B_{o}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$\rho_{o}$ is oil density in ($\frac{lbm}{ft^3}$), $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### 4. Al_Marhoun Oil Properties Model(Al-Marhoun 1988):

### Bubble Point Pressure ($P_{b}$):

$P_{b} = a_{0} R_{sob}^{a_{1}} \gamma_{g}^{a_{2}} \gamma_{o}^{a_{3}} T^{a_{4}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$a_{0}= 0.00538088$, $a_{1}= 0.715082$, $a_{2}= -1.87784$, $a_{3}= 3.1437$, $a_{4}= 1.32657$

$P_{b}$ is bubble point pressure in Psia, T is temperature in R, $R_{sob}$ is gas solubility in oil at bubble point in ($\frac{scf}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Gas Solubility in Oil ($R_{so}$):

$R_{so} = a_{0} \gamma_{g}^{a_{1}} P^{a_{2}} \gamma_{o}^{a_{3}} T^{a_{4}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$a_{0}= 1490.28$, $a_{1}= 2.62605$, $a_{2}= 1.398441$, $a_{3}= -4.396279$, $a_{4}= -1.85513$

$R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), T is temperature in R, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### Oil Formation Volume Factor ($B_{o}$):

if P > $P_{b}$:

$B_{o} = B_{ob} exp[C_{o}(P_{b}-P)]$

and if P <= $P_{b}$:

$B_{o} = 0.497069 + 0.862963 * 10^{-3} T + 0.182594 * 10^{-2} f + 0.318099 * 10^{-5} f^2$

$f = R_{so}^{0.74239} \gamma_{g}^{0.323294} * \gamma_{o}^{-1.20204}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), T is temperature in R, p is pressure in Psia, $\gamma_{g}$ is gas specific gravity (air = 1), API is oil API gravity, and $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$).

### Oil Compressibility ($C_{o}$):

if P > $P_{b}$:

$C_{o} = C_{o,Spivey}$

and if P <= $P_{b}$:

### Oil Density ($\rho_{o}$):

$\rho_{o}= \frac{62.37 \gamma_{o} + 0.0136 \gamma_{g} R_{so}}{B_{o}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

### 5. Glaso Oil Properties Model(Glaso 1980):

### Bubble Point Pressure ($P_{b}$):

$P_{b} = 10^a$

$a = -0.30218 log10(x)^2 + 1.7447 log10(x) + 1.7669$

$x = \frac{(\frac{R_{sob}}{\gamma_{g}})^{0.816} t^{0.172}} {API^{0.989}}$

### Gas Solubility in Oil ($R_{so}$):

$R_{so} = A^{\frac{1}{0.816}} \gamma_{g};$

$A = B \frac{API^{0.989}}{t^{0.172}}$

$B = 10^x$

$x = min(\frac{-b \pm \sqrt{b^2-4ac} }{2a})$

$a = -0.30218$

$b = 1.7447$

$c = -log10(p) + 1.7669$

### Oil Formation Volume Factor ($B_{o}$):

if P > $P_{b}$:

$B_{o} = B_{ob} exp[C_{o}(P_{b}-P)]$

and if P <= $P_{b}$:

$B_{o} = 10^f + 1$

$f = -6.58511+2.91329log10(y)-0.27683(log10(y))^2$

$y = R_{so} (\frac{\gamma_{g}}{\gamma_{o}})^{0.526} + 0.968 t$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

### Oil Compressibility ($C_{o}$):

if P > $P_{b}$:

$C_{o} = C_{o,Spivey}$

and if P <= $P_{b}$:

### Oil Density ($\rho_{o}$):

$\rho_{o}= \frac{62.37 \gamma_{o} + 0.0136 \gamma_{g} R_{so}}{B_{o}}$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

### 6. Spivey et. al. Oil Compressibility Model(Spivey, Valko, and McCain 2007):

### Oil Compressibility ($C_{o}$) for pressures above bubble point pressure:

$C_{o} = C_{ofb} + (P - P_{b}) \frac{\partial C_{ofb}}{\partial P}$

$C_{ofb} = exp(2.434 + 0.475 Z + 0.048 Z^2)$

$Z = \sum_{k=1}^6 z_{n}$

$z_{n} = C_{0n} + C_{1n}x_{n}+C_{2n}x_{n}^2$

$C_{0n} = [3.011, -0.0835, 3.51, 0.327, -1.918, 2.52]$

$C_{1n} = [-2.6254, -0.259, -0.0289, -0.608, -0.642, -2.73]$

$C_{2n} = [0.497, 0.382, -0.0584, 0.0911, 0.154, 0.429]$

$x_{n} = [ln(API), ln(\gamma_{g}), ln(P_{b}), ln(\frac{P}{P_{b}}), ln(R_{so}), ln(t)]$

$\frac{\partial C_{ofb}}{\partial P} = C_{ofb} (0.475+0.096Z) \frac{\partial Z}{\partial P}$

$\frac{\partial Z}{\partial P} = \frac{-0.608+0.1822ln(\frac{P}{P_{b}})}{P}$

$C_{o}$ is undersaturated oil compressibility in ($\frac{1}{Psia}$), t is temperature in F, p is pressure in Psia, $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### 7. Beggs_Robinson Viscosity Model(Beggs and Robinson 1975):

If P > $P_{b}$:

$\mu_{o} = A \mu_{od}^B (\frac{P}{P_{b}})^w$

$w = 2.60 P^{1.187} exp(-11.513 -8.98 * 10^{-5} P)$

If P <= $P_{b}$:

$\mu_{o} = A \mu_{od}^B$

All other parameters are defined below as:

$A = 10.715 (R_{so} + 100)^{-0.515}$

$B = 5.44 (R_{so} + 150)^{-0.338}$

$\mu_{od} = 10^x - 1$

$x = y t^{-1.163}$

$y = 10^{3.0324-0.02023API}$

$\mu_{o}$ is oil viscosity in centipoise (cp), t is temperature in F, p is pressure in Psia, $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

### 8. Al_Marhoun Viscosity Model(Al-Marhoun 2004):

$\mu_{o} = exp[ln(\mu_{o}^*) + 0.000151292 \gamma_{oo}^2 (P - P_{b})]$

$\mu_{o}^* = a_{o} \mu_{od}^{b_{o}}$

$\mu_{od} = exp[a_{1} + a_{2} ln(t) + a_{3} ln(ln(API)) + a_{4} ln(t) ln(ln(API))]$

$\gamma_{o} = \frac{141.5}{131.5 + API}$

$\gamma_{oo} = \frac{(\gamma_{o} + 0.000218 R_{so} \gamma_{g})}{B_{o}}$

$a_{o} = b_{1} (R_{so} + b_{2})^{b_{3}}$

$b_{o} = b_{4} (R_{so} + b_{5})^{b_{6}}$

$a = [54.56805426,-7.179530398,-36.447,4.478878992]$

$b = [10.715,100.0,-0.515,5.44,150.0,-0.338]$

$\mu_{o}$ is oil viscosity in centipoise (cp), t is temperature in F, p is pressure in Psia, $R_{so}$ is gas solubility in oil in ($\frac{scf}{stb}$), $B_{o}$ is oil formation volume factor in ($\frac{bbl}{stb}$), $\gamma_{g}$ is gas specific gravity (air = 1), and API is oil API gravity.

## Water PVT Correlations

There are two correlations available for estimating Water properties: **McCain** and **Meehan**.

### 1. McCain Water Properties Model(McCain Jr. 1991):

### Water Formation Volume Factor ($B_{w}$):

$B_{w} = (1 + dVp)(1+dVt)$

$dVp = -1.95301*10^{-9}tp - 1.72834*10^{-13}tp^2 - 3.58922*10^{-7}p - 2.25341*10^{-10}p^2$

$dVt = -1.0001*10^{-2} + 1.33391*10^{-4}t + 5.50654*10^{-7}t^2$

where $B_{w}$ is water formation volume factor in ($\frac{bbl}{stb}$), t is temperature in F and p is pressure in Psia.

### Water Density ($\rho_{w}$):

$\rho_{w} = \frac{\rho_{w,st}}{(B_{w})}$

$\rho_{w,st} = 62.368 + 0.438603 S + 1.60074 * 10^{-3} S^2$

where $\rho_{w}$ is water density in ($\frac{lbm}{ft^3}$), $\rho_{w,st}$ is density of water at standard conditions in ($\frac{lbm}{ft^3}$), and S is water salinity in weight percent TDS.

### Gas Solubility in Water Density ($R_{sw}$):

$R_{sw} = R_{sw}^* * 10^{-0.0840655t^{-0.285854}S}$

$R_{sw}^* = A + B p + C p^2$

$A = 8.15839 - 6.12265*10^{-2} t + 1.91663*10^{-4} t^2 - 2.1654*10^{-7} t^3$

$B = 1.01021*10^{-2} - 7.44241*10^{-5} t + 3.05553*10^{-7} t^2 - 2.94883*10^{-10} t^3$

$C = -1 * 10^{-7} * (9.02505 - 0.130237 t + 8.53425 * 10^{-4} t^2 - 2.34122 * 10^{-6} t^3 + 2.37049 * 10^{-9} t^4)$

where $R_{sw}$ is gas solubility in water in ($\frac{scf}{stb}$), t is temperature in F, p is pressure in Psia, and S is water salinity in weight percent TDS.

### Water Compressibility ($C_{w}$):

$C_{w} = C_{w1} + C_{w2}$

$C_{w1} = 1 / (7.033 p + 0.5415 S^* - 537 t + 403300)$

$C_{w2} = \frac{B_{g}}{B_{w}} \frac{\partial R_{sw}}{\partial p}$ if water is gas_saturated.

$C_{w2} = 0$ if water is not gas_saturated.

$S^* = 10000S \rho_{w}$

where $C_{w}$ is water compressibility in ($\frac{1}{Psia}$), t is temperature in F, p is pressure in Psia, S is water salinity in weight percent TDS, $S^*$ is water salinity in ($\frac{mg}{lit}$), $\rho_{w}$ is water density in ($\frac{gr}{cm^3}$), $B_{g}$ is gas formation volume factor in ($\frac{bbl}{stb}$), $B_{w}$ is water formation volume factor in ($\frac{bbl}{stb}$), and $R_{sw}$ is gas solubility in water in ($\frac{scf}{stb}$).

### Water Viscosity ($\mu_{w}$):

$\mu_{w} = \mu_{w}^* (0.9994 + 4.0295 * 10^{-5} p + 3.1062 * 10^{-9} p^2)$

$\mu_{w}^* = A^{t^{-B}}$

$A = 109.574 - 8.40564 S + 0.313314 S^2 + 8.72213 * 10 ^{-3} S^3$

$B = 1.12166 - 2.63951*10^{-2} S + 6.79461* 10 ^{-4} S^2 + 5.47119* 10 ^{-5} S^3 - 1.55586* 10 ^{-6} S^4$

where $\mu_{w}$ is water viscosity in centipoise (cp), t is temperature in F, p is pressure in Psia, and S is water salinity in weight percent TDS.

### 2. Meehan Water Properties Model(Meehan 1980a, 1980b):

### Water Formation Volume Factor ($B_{w}$):

$B_{w} = (a + b p + c p^2) S^*$

$S^* = 1 + S [5.1 * 10^{-8} p + (5.47 * 10^{-6} - 1.96 * 10^{-18} p) (t - 60) + (-3.23 * 10^{-8} + 8.5 * 10^{-13} p) (t - 60)^2]$

if water is gas_saturated:

$a = 0.9911 + 6.35 * 10^{-6} t + 8.5 * 10^{-7} t^2$

$b = -1.093 * 10^{-6} - 3.497 * 10^{-9} t + 4.57 * 10^{-12} t^2$

$c = -5 * 10^{-11} + 6.429 * 10^{-13} t - 1.43 * 10^{-15}t^2$

and if water is not gas_saturated:

$a = 0.9947 + 5.8 * 10^{-6} t + 1.02 * 10^{-6} t^2$

$b = -4.228 * 10^{-6} + 1.8376 * 10^{-8} t - 6.77 * 10^{-11} t^2$

$c = 1.3 * 10^{-10} - 1.3855 * 10^{-12} t + 4.285 * 10^{-15} t^2$

$B_{w}$ is water formation volume factor in ($\frac{bbl}{stb}$), t is temperature in F and p is pressure in Psia, and S is water salinity in weight percent TDS.

### Water Density ($\rho_{w}$):

$\rho_{w} = \frac{\rho_{w,st}}{B_{w}}$

$\rho_{w,st} = 62.368 + 0.438603 S + 1.60074 * 10^{-3} S^2$

where $\rho_{w}$ is water density in ($\frac{lbm}{ft^3}$), $\rho_{w,st}$ is density of water at standard conditions in ($\frac{lbm}{ft^3}$), and S is water salinity in weight percent TDS.

### Gas Solubility in Water Density ($R_{sw}$):

$R_{sw} = R_{sw}^* * 10^{-0.0840655t^{-0.285854}S}$

$R_{sw}^* = A + B p + C p^2$

$A = 8.15839 - 6.12265*10^{-2} t + 1.91663*10^{-4} t^2 - 2.1654*10^{-7} t^3$

$B = 1.01021*10^{-2} - 7.44241*10^{-5} t + 3.05553*10^{-7} t^2 - 2.94883*10^{-10} t^3$

$C = -1 * 10^{-7} * (9.02505 - 0.130237 t + 8.53425 * 10^{-4} t^2 - 2.34122 * 10^{-6} t^3 + 2.37049 * 10^{-9} t^4)$

where $R_{sw}$ is gas solubility in water in ($\frac{scf}{stb}$), t is temperature in F, p is pressure in Psia, and S is water salinity in weight percent TDS.

### Water Compressibility ($C_{w}$):

$C_{w} = C_{w1} + C_{w2}$

$C_{w1} = C_{w}^* S^*$

$C_{w}^* = C_{wf} (1 + 8.9*10^{-3} R_{sw})$

$C_{wf} = 1*10^{-6} (C_{0} + C_{1} t + C_{2} t^2)$

$C_{0} = 3.8546 - 0.000134 p$

$C_{1} = -0.01052 + 4.77 * 10^{-7} p$

$C_{2} = 3.9267 * 10^{-5} - 8.8* 10^{-10} p$

$S^* = 1 + (-0.052 + 2.7 * 10^{-4} t - 1.14 * 10^{-6} t^2 + 1.121 * 10^{-9} t^3) S^{0.7}$

if water is gas_saturated:

$C_{w2} = \frac{B_{g}}{B_{w}} \frac{\partial R_{sw}}{\partial p}$

and if water is not gas_saturated:

$C_{w2} = 0$

$C_{w}$ is water compressibility in ($\frac{1}{Psia}$), t is temperature in F, p is pressure in Psia, S is water salinity in weight percent TDS, $B_{g}$ is gas formation volume factor in ($\frac{bbl}{stb}$), $B_{w}$ is water formation volume factor in ($\frac{bbl}{stb}$), and $R_{sw}$ is gas solubility in water in ($\frac{scf}{stb}$).

### Water Viscosity ($\mu_{w}$):

$\mu_{w} = f \mu_{w}^*$

$f = 1 + 3.5 * 10^{-12} p^2 (t - 40)$

$\mu_{w}^* = A + \frac{B}{t}$

$A = -0.04518 + 0.009313 S - 0.000393 S^2$$

$B = 70.634 + 0.09576 S^2$

where $\mu_{w}$ is water viscosity in centipoise (cp), t is temperature in F, p is pressure in Psia, and S is water salinity in weight percent TDS.

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