Material_H2 class

This class defines the material properties and behavior for a porous medium involving liquid and gas phases. It includes methods for computing relative permeabilities, saturation degrees, permeability matrices, and compressibility coefficients for the liquid and gas phases.

Contents

Methods

Author

Danilo Cavalcanti

Version History

Version 1.00.

Class definition

classdef Material_H2 < handle

Public attributes

    properties (SetAccess = public, GetAccess = public)
        liqRelativePermeability = [];
        gasRelativePermeability = [];
        capillaryPressure       = [];
        liquidFluid             = Fluid();
        gasFluid                = Fluid();
        porousMedia             = PorousMedia();
    end

Constructor method

    methods
        %------------------------------------------------------------------
        function this = Material_H2(matData)
            this.liquidFluid = matData.liquidFluid;
            this.gasFluid    = matData.gasFluid;
            this.porousMedia = matData.porousMedia;
            % Liquid phase relative permeability function
            if strcmp('BrooksCorey',matData.porousMedia.liqRelPermeability)
                this.liqRelativePermeability = RelativePermeabilityBrooksCoreyLiquid();
            elseif strcmp('Liakopoulos',matData.porousMedia.liqRelPermeability)
                this.liqRelativePermeability = RelativePermeabilityLiakopoulosLiquid();
            elseif strcmp('PolynomialLiquid',matData.porousMedia.liqRelPermeability)
                this.liqRelativePermeability = RelativePermeabilityPolynomialLiquid();
            elseif strcmp('UMAT',matData.porousMedia.liqRelPermeability)
                curve = matData.porousMedia.klr_umat;
                this.liqRelativePermeability = RelativePermeabilityUMAT(curve(:,1),curve(:,2));
            end
            % Gas phase relative permeability function
            if strcmp('BrooksCorey',matData.porousMedia.gasRelPermeability)
                this.gasRelativePermeability = RelativePermeabilityBrooksCoreyGas();
            elseif strcmp('PolynomialGas',matData.porousMedia.gasRelPermeability)
                this.gasRelativePermeability = RelativePermeabilityPolynomialGas();
            elseif strcmp('UMAT',matData.porousMedia.gasRelPermeability)
                curve = matData.porousMedia.kgr_umat;
                this.gasRelativePermeability = RelativePermeabilityUMAT(curve(:,1),curve(:,2));
            end
            % Saturation degree function
            if strcmp('BrooksCorey',matData.porousMedia.capillaryPressure)
                this.capillaryPressure = CapillaryPressureBrooksCorey();
            elseif strcmp('UMAT',matData.porousMedia.capillaryPressure)
                curve = matData.porousMedia.SlPc_umat;
                this.capillaryPressure = CapillaryPressureUMAT(curve(:,1),curve(:,2));
            elseif strcmp('Liakopoulos',matData.porousMedia.capillaryPressure)
                this.capillaryPressure = CapillaryPressureLiakopoulos();
            end
        end
    end

Public methods

    methods
        %------------------------------------------------------------------
        % Get the liquid saturation degree
        function Sl = saturationDegree(this,pc)
            Sl = this.capillaryPressure.saturationDegree(pc, this.porousMedia);
        end

        %------------------------------------------------------------------
        % Compute the permeability matrices
        function [Kll, Klg, Kgl, Kgg] = permeabilityMtrcs(this,Sl,pl,pg)
            K = this.porousMedia.intrinsicPermeabilityMatrix();
            % Get fluids dynamic viscosity
            mul = this.liquidFluid.mu;
            mug = this.gasFluid.mu;
            % Compute relative permeability coefficients
            klr = this.liqRelativePermeability.calculate(Sl, this.porousMedia);
            kgr = this.gasRelativePermeability.calculate(Sl, this.porousMedia);
            % Permeability matrices
            Kll = K * klr / mul;
            Klg = zeros(2);
            Kgl = zeros(2);
            Kgg = K * kgr / mug;
        end

        %------------------------------------------------------------------
        % Compute the permeability matrices
        function [Kll, Klg, Kgl, Kgg] = permeabilityMtrcsPgPc(this,Sl,pl,pg)
            K = this.porousMedia.intrinsicPermeabilityMatrix();
            % Get fluids dynamic viscosity
            mul = this.liquidFluid.mu;
            mug = this.gasFluid.mu;
            % Get fluid densities
            rhol = this.liquidFluid.getDensity(pl);
            rhog = this.gasFluid.getDensity(pg);
            % Compute relative permeability coefficients
            klr = this.liqRelativePermeability.calculate(Sl, this.porousMedia);
            kgr = this.gasRelativePermeability.calculate(Sl, this.porousMedia);
            % Permeability matrices
            Kll = - K * klr / mul;
            Klg = K * klr / mul;
            Kgl = zeros(2);
            Kgg = K * kgr / mug * (rhog / rhol);
        end

        %------------------------------------------------------------------
        % Compute the compressibility coefficients
        function [cll, clg, cgl, cgg] = compressibilityCoeffs(this,Sl,pl,pg)
            % Get porous media parameters
            biot = this.porousMedia.biot;
            phi  = this.porousMedia.phi;
            Ks   = this.porousMedia.Ks;
            % Get the fluids bulk modulus
            Klb  = this.liquidFluid.K;
            Kgb  = this.gasFluid.K;
            % Gas saturation degree
            Sg   = 1.0 - Sl;
            % Capillary pressure
            pc = pg - pl;
            % Derivative of the liquid saturation degree wrt pc
            dSldpc = this.capillaryPressure.derivativeSaturationDegree(pc, this.porousMedia);
            % Compressibility coefficients
            cll = Sl * ((biot - phi) / Ks) * (Sl + dSldpc * pc) - phi * dSldpc + phi * Sl / Klb;
            clg = Sl * ((biot - phi) / Ks) * (Sg - dSldpc * pc) + phi * dSldpc;
            cgl = Sg * ((biot - phi) / Ks) * (Sl + dSldpc * pc) + phi * dSldpc;
            cgg = Sg * ((biot - phi) / Ks) * (Sg - dSldpc * pc) - phi * dSldpc + phi * Sg / Kgb;
        end

        %------------------------------------------------------------------
        % Compute the compressibility coefficients
        function [ccc, ccg, cgc,cgg] = compressibilityCoeffsPgPc(this,Sl,pl,pg)
            % Get porous media parameters
            phi  = this.porousMedia.phi;
            % Get fluid densities
            rhol = this.liquidFluid.getDensity(pl);
            rhog = this.gasFluid.getDensity(pg);
            % Capillary pressure
            pc = pg - pl;
            % Derivative of the liquid saturation degree wrt pc
            dSldpc = this.capillaryPressure.derivativeSaturationDegree(pc, this.porousMedia);
            % Derivative of the gas density wrt to pg
            drhogdpg = this.derivativeGasDensityWrtGasPressure(rhog,pg);
            % Compressibility coefficients
            ccc =  phi * dSldpc;
            ccg = 0.0;
            cgc = -phi * dSldpc * (rhog / rhol);
            cgg =  phi * (1.0 - Sl) * drhogdpg / rhol;
        end
        %------------------------------------------------------------------
        % Compute the derivative of the gas density wrt to the gas pressure
        function drhogdpg = derivativeGasDensityWrtGasPressure(this,rhog,pg)
            % Pertubation value
            pert = sqrt(eps);
            % Compute the gas density given a pertubation at the gas pressure
            rhogPert = this.gasFluid.getDensity(pg + pert);
            % Compute the derivative
            drhogdpg = (rhogPert - rhog)/(pert);
        end

    end

end

Published with MATLAB® R2022a