ResInsight/ApplicationLibCode/ReservoirDataModel/RigTransmissibilityEquations.cpp

/////////////////////////////////////////////////////////////////////////////////
//
//  Copyright (C) 2017-     Statoil ASA
//
//  ResInsight is free software: you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation, either version 3 of the License, or
//  (at your option) any later version.
//
//  ResInsight is distributed in the hope that it will be useful, but WITHOUT ANY
//  WARRANTY; without even the implied warranty of MERCHANTABILITY or
//  FITNESS FOR A PARTICULAR PURPOSE.
//
//  See the GNU General Public License at <http://www.gnu.org/licenses/gpl.html>
//  for more details.
//
/////////////////////////////////////////////////////////////////////////////////

#include "RigTransmissibilityEquations.h"

#include <cmath>
#include <limits>

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::wellBoreTransmissibilityComponent( double cellPerforationVectorComponent,
                                                                        double permeabilityNormalDirection1,
                                                                        double permeabilityNormalDirection2,
                                                                        double cellSizeNormalDirection1,
                                                                        double cellSizeNormalDirection2,
                                                                        double wellRadius,
                                                                        double skinFactor,
                                                                        double cDarcyForRelevantUnit )
{
    double K = cvf::Math::sqrt( permeabilityNormalDirection1 * permeabilityNormalDirection2 );

    const double lowerLimit = 1.0e-9;
    if ( std::fabs( permeabilityNormalDirection1 * permeabilityNormalDirection2 ) < lowerLimit )
    {
        // Guard further computations to avoid nan values
        return 0.0;
    }

    double nominator = cDarcyForRelevantUnit * 2 * cvf::PI_D * K * cellPerforationVectorComponent;

    double peaceManRad =
        peacemanRadius( permeabilityNormalDirection1, permeabilityNormalDirection2, cellSizeNormalDirection1, cellSizeNormalDirection2 );

    double denominator = log( peaceManRad / wellRadius ) + skinFactor;

    double trans = nominator / denominator;
    return trans;
}

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::totalConnectionFactor( double transX, double transY, double transZ )
{
    return cvf::Math::sqrt( pow( transX, 2.0 ) + pow( transY, 2.0 ) + pow( transZ, 2.0 ) );
}

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::totalKh( double            cellPermX,
                                              double            cellPermY,
                                              double            cellPermZ,
                                              const cvf::Vec3d& internalCellLengths,
                                              double            lateralNtg,
                                              double            ntg )
{
    // Compute kh for each local grid cell axis
    // Use permeability values for the two other axis
    double khx = sqrt( cellPermY * cellPermZ ) * internalCellLengths.x() * lateralNtg;
    double khy = sqrt( cellPermX * cellPermZ ) * internalCellLengths.y() * lateralNtg;
    double khz = sqrt( cellPermX * cellPermY ) * internalCellLengths.z() * ntg;

    const double totKh = cvf::Math::sqrt( khx * khx + khy * khy + khz * khz );

    return totKh;
}

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::effectiveK( double            cellPermX,
                                                 double            cellPermY,
                                                 double            cellPermZ,
                                                 const cvf::Vec3d& internalCellLengths,
                                                 double            lateralNtg,
                                                 double            ntg )
{
    // Compute kh for each local grid cell axis
    // Use permeability values for the two other axis

    double lx = internalCellLengths.x() * lateralNtg;
    double ly = internalCellLengths.y() * lateralNtg;
    double lz = internalCellLengths.z() * ntg;

    double khx = sqrt( cellPermY * cellPermZ ) * lx;
    double khy = sqrt( cellPermX * cellPermZ ) * ly;
    double khz = sqrt( cellPermX * cellPermY ) * lz;

    double nominator   = khx + khy + khz;
    double denominator = lx + ly + lz;

    const double effK = nominator / denominator;

    return effK;
}

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::effectiveH( const cvf::Vec3d& internalCellLengths, double lateralNtg, double ntg )
{
    double lx = internalCellLengths.x() * lateralNtg;
    double ly = internalCellLengths.y() * lateralNtg;
    double lz = internalCellLengths.z() * ntg;

    double effH = cvf::Math::sqrt( lx * lx + ly * ly + lz * lz );

    return effH;
}

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::permeability( const double conductivity, const double width )
{
    double threshold = 1e-7;

    if ( std::fabs( width ) > threshold )
    {
        double perm = conductivity / width;

        return perm;
    }
    else
    {
        return 0.0;
    }
}

//--------------------------------------------------------------------------------------------------
///
//--------------------------------------------------------------------------------------------------
double RigTransmissibilityEquations::peacemanRadius( double permeabilityNormalDirection1,
                                                     double permeabilityNormalDirection2,
                                                     double cellSizeNormalDirection1,
                                                     double cellSizeNormalDirection2 )
{
    double numerator =
        cvf::Math::sqrt( pow( cellSizeNormalDirection2, 2.0 ) * pow( permeabilityNormalDirection1 / permeabilityNormalDirection2, 0.5 ) +
                         pow( cellSizeNormalDirection1, 2.0 ) * pow( permeabilityNormalDirection2 / permeabilityNormalDirection1, 0.5 ) );

    double denominator = pow( ( permeabilityNormalDirection1 / permeabilityNormalDirection2 ), 0.25 ) +
                         pow( ( permeabilityNormalDirection2 / permeabilityNormalDirection1 ), 0.25 );

    double r0 = 0.28 * numerator / denominator;

    return r0;
}