Solution Gas-Water Ratio (Rsw) Calculation

Overview

The Solution Gas-Water Ratio (Rsw) represents the volume of gas dissolved in water at reservoir conditions, expressed as standard cubic meters of gas per standard cubic meter of water (Sm³/Sm³). This property is essential for:

The SolutionGasWaterRatio class in NeqSim provides three calculation methods with varying levels of complexity and accuracy.

Physical Background

Gas Solubility in Water

Gas solubility in water is governed by Henry’s Law at low pressures:

\[x_g = \frac{P_g}{H}\]

where:

At higher pressures, deviations from Henry’s Law become significant, and equation of state methods are required.

Key Factors Affecting Rsw

  1. Pressure: Rsw increases approximately linearly with pressure at moderate conditions
  2. Temperature: Shows a minimum around 70-100°C for hydrocarbons
    • At low T: solubility decreases with increasing T (entropy effect)
    • At high T: solubility increases with T (approaching critical point)
  3. Salinity: Dissolved salts reduce gas solubility (“salting-out” effect)
  4. Gas Composition: CO₂ is 20-50× more soluble than methane; H₂S is even more soluble

Typical Values

Condition Rsw (Sm³/Sm³)
Shallow reservoir (50 bar, 50°C) 0.5 - 1.0
Medium depth (150 bar, 80°C) 1.5 - 3.0
Deep reservoir (300 bar, 120°C) 3.0 - 6.0
CO₂-rich gas (100 bar, 50°C) 5.0 - 15.0

Available Calculation Methods

1. McCain (Culberson-McKetta) Correlation

Best for: Quick estimates, pure methane systems, engineering screening

The McCain correlation is based on the Culberson-McKetta experimental data (1951) with coefficients from McCain (1990).

Formulation

For pure water: \(R_{sw,pure} = A + B \cdot P + C \cdot P^2\)

where coefficients A, B, C are temperature-dependent polynomials:

\[A = 8.15839 - 6.12265 \times 10^{-2}T + 1.91663 \times 10^{-4}T^2 - 2.1654 \times 10^{-7}T^3\] \[B = 1.01021 \times 10^{-2} - 7.44241 \times 10^{-5}T + 3.05553 \times 10^{-7}T^2 - 2.94883 \times 10^{-10}T^3\] \[C = (-9.02505 + 0.130237T - 8.53425 \times 10^{-4}T^2 + 2.34122 \times 10^{-6}T^3 - 2.37049 \times 10^{-9}T^4) \times 10^{-7}\]

where T is in °F and P is in psia.

Salinity Correction

\[R_{sw,brine} = R_{sw,pure} \times 10^{-C_s \cdot S}\]

where:

Validity Range

Parameter Range
Temperature 60-350°F (15-177°C)
Pressure 14.7-10,000 psia (1-690 bar)
Salinity 0-30 wt% NaCl
Gas type Methane (use with caution for other gases)

2. Søreide-Whitson Method

Best for: Multi-component gas mixtures, moderate salinity, process simulation

Uses the modified Peng-Robinson equation of state with Søreide-Whitson alpha function and mixing rules specifically developed for hydrocarbon-water systems.

Key Features

Mixing Rule

The Søreide-Whitson mixing rule (mixing rule 11 in NeqSim) uses:

\[a_m = \sum_i \sum_j x_i x_j \sqrt{a_i a_j}(1 - k_{ij})\]

with special binary interaction parameters for water-hydrocarbon pairs that account for salinity.

Validity Range

Parameter Range
Temperature 273-473 K (0-200°C)
Pressure 1-1000 bar
Salinity 0-6 mol/kg (0-26 wt% NaCl)
Gas type Any hydrocarbon mixture with CO₂, N₂, H₂S

3. Electrolyte CPA Method

Best for: High-accuracy predictions, electrolyte systems, research applications

Uses the Cubic-Plus-Association (CPA) equation of state with electrolyte extensions for rigorous modeling of ion-water-gas interactions.

Key Features

CPA Equation

\[P = \frac{RT}{V_m - b} - \frac{a}{V_m(V_m + b)} - \frac{1}{2}\frac{RT}{V_m}\left(1 + \rho\frac{\partial \ln g}{\partial \rho}\right)\sum_A x_A(1 - X_A)\]

where the last term accounts for hydrogen bonding associations.

Validity Range

Parameter Range
Temperature 273-473 K (0-200°C)
Pressure 1-1000 bar
Salinity 0-6 mol/kg NaCl equivalent
Gas type Any composition

Usage Examples

Basic Usage with McCain Correlation

import neqsim.thermo.system.SystemInterface;
import neqsim.thermo.system.SystemSrkCPAstatoil;
import neqsim.pvtsimulation.simulation.SolutionGasWaterRatio;

// Create gas system
SystemInterface gas = new SystemSrkCPAstatoil(350.0, 100.0); // 350 K, 100 bar
gas.addComponent("methane", 0.95);
gas.addComponent("CO2", 0.05);
gas.setMixingRule(10);

// Create Rsw calculator
SolutionGasWaterRatio rswCalc = new SolutionGasWaterRatio(gas);

// Set conditions
double[] temperatures = {350.0, 360.0, 370.0}; // K
double[] pressures = {100.0, 150.0, 200.0};    // bar
rswCalc.setTemperaturesAndPressures(temperatures, pressures);

// Set salinity (pure water)
rswCalc.setSalinity(0.0);

// Use McCain method
rswCalc.setCalculationMethod(SolutionGasWaterRatio.CalculationMethod.MCCAIN);
rswCalc.runCalc();

// Get results
double[] rsw = rswCalc.getRsw();
for (int i = 0; i < rsw.length; i++) {
    System.out.printf("T=%.1f K, P=%.1f bar: Rsw = %.4f Sm³/Sm³%n", 
                      temperatures[i], pressures[i], rsw[i]);
}

Using Søreide-Whitson for Multi-Component Gas

// Create gas with multiple components
SystemInterface gas = new SystemSrkCPAstatoil(373.15, 200.0);
gas.addComponent("methane", 0.85);
gas.addComponent("ethane", 0.05);
gas.addComponent("propane", 0.03);
gas.addComponent("CO2", 0.05);
gas.addComponent("nitrogen", 0.02);
gas.setMixingRule(10);

SolutionGasWaterRatio rswCalc = new SolutionGasWaterRatio(gas);
rswCalc.setTemperaturesAndPressures(new double[]{373.15}, new double[]{200.0});

// Use Søreide-Whitson method
rswCalc.setCalculationMethod(SolutionGasWaterRatio.CalculationMethod.SOREIDE_WHITSON);
rswCalc.runCalc();

System.out.printf("Rsw (Søreide-Whitson) = %.4f Sm³/Sm³%n", rswCalc.getRsw(0));

Accounting for Salinity

SolutionGasWaterRatio rswCalc = new SolutionGasWaterRatio(gas);
rswCalc.setTemperaturesAndPressures(new double[]{350.0}, new double[]{100.0});

// Compare pure water vs seawater vs formation water
double[] salinities = {0.0, 3.5, 10.0}; // wt% NaCl
String[] waterTypes = {"Pure water", "Seawater", "Formation water"};

rswCalc.setCalculationMethod(SolutionGasWaterRatio.CalculationMethod.ELECTROLYTE_CPA);

for (int i = 0; i < salinities.length; i++) {
    rswCalc.setSalinity(salinities[i], "wt%");
    rswCalc.runCalc();
    System.out.printf("%s (%.1f wt%% NaCl): Rsw = %.4f Sm³/Sm³%n", 
                      waterTypes[i], salinities[i], rswCalc.getRsw(0));
}

Salinity Unit Conversions

The class supports multiple salinity units:

// Set salinity in different units
rswCalc.setSalinity(0.5);           // Default: molality (mol NaCl / kg water)
rswCalc.setSalinity(3.5, "wt%");    // Weight percent NaCl
rswCalc.setSalinity(35000, "ppm");  // Parts per million

Method Selection Guide

Scenario Recommended Method Reason
Quick screening McCain Fast, simple
Pure methane system McCain Optimized for CH₄
Multi-component gas Søreide-Whitson Accounts for composition
CO₂-rich gas (>20% CO₂) Søreide-Whitson or CPA McCain underestimates
High salinity (>5 wt%) Electrolyte CPA Best ion modeling
Research/validation Electrolyte CPA Most rigorous
Process simulation Søreide-Whitson Good balance

Comparison with Literature

Methane Solubility in Pure Water

T (°C) P (bar) Literature (Sm³/Sm³) McCain Søreide-Whitson CPA
25 100 1.8-2.2 2.20 1.02 2.52
50 100 1.5-1.8 1.78 1.03 1.94
75 100 1.4-1.7 1.57 1.13 1.65
100 100 1.5-1.8 1.59 1.31 1.52

Salinity Effect

The salting-out coefficient ($k_s$) represents the reduction in solubility per unit salinity:

\[\log_{10}\left(\frac{R_{sw,brine}}{R_{sw,pure}}\right) = -k_s \cdot m_{salt}\]
Method Typical $k_s$ (L/mol)
McCain 0.10-0.15
Søreide-Whitson 0.12-0.18
Electrolyte CPA 0.10-0.16
Experimental (Duan & Mao, 2006) 0.11-0.14

API Reference

Constructor

public SolutionGasWaterRatio(SystemInterface inputSystem)

Creates a new Rsw calculator using the given thermodynamic system as the gas composition source.

Key Methods

Method Description
setCalculationMethod(CalculationMethod method) Set calculation method (MCCAIN, SOREIDE_WHITSON, ELECTROLYTE_CPA)
setSalinity(double salinity) Set salinity in mol/kg water
setSalinity(double salinity, String unit) Set salinity with unit (“wt%”, “ppm”)
setTemperaturesAndPressures(double[] T, double[] P) Set calculation conditions
runCalc() Execute calculation
getRsw() Get array of calculated Rsw values
getRsw(int index) Get Rsw at specific index
calculateRsw(double T, double P) Single-point calculation

Calculation Methods Enum

public enum CalculationMethod {
    MCCAIN,           // Empirical correlation (fast)
    SOREIDE_WHITSON,  // Modified PR-EoS (recommended)
    ELECTROLYTE_CPA   // CPA with electrolytes (most accurate)
}

References

  1. Culberson, O.L. and McKetta, J.J. (1951). “Phase Equilibria in Hydrocarbon-Water Systems III - The Solubility of Methane in Water at Pressures to 10,000 psia.” Journal of Petroleum Technology, 3(08), 223-226.

  2. McCain, W.D. Jr. (1990). The Properties of Petroleum Fluids, 2nd Edition. PennWell Publishing Company.

  3. Søreide, I. and Whitson, C.H. (1992). “Peng-Robinson Predictions for Hydrocarbons, CO₂, N₂, and H₂S with Pure Water and NaCl Brine.” Fluid Phase Equilibria, 77, 217-240.

  4. Duan, Z. and Mao, S. (2006). “A Thermodynamic Model for Calculating Methane Solubility, Density and Gas Phase Composition of Methane-Bearing Aqueous Fluids from 273 to 523 K and from 1 to 2000 bar.” Geochimica et Cosmochimica Acta, 70(13), 3369-3386.

  5. Haghighi, H., Chapoy, A., and Tohidi, B. (2009). “Methane and Water Phase Equilibria in the Presence of Single and Mixed Electrolyte Solutions Using the Cubic-Plus-Association Equation of State.” Oil & Gas Science and Technology, 64(2), 141-154.

See Also