Method for determining capillary pressure and relative permeability by imaging

A method for determining mobilities of a sample of a material having a known porosity, comprising:

• providing said sample with at least two preselected fluids,
• imaging a preselected volume of said sample to determine the saturations of said fluids in said preselected volume,
• calculating time and spatial derivatives of said saturations,
• determining total superficial velocity for said fluids,
• determining the individual superficial velocities of said fluids from said porosity, said total superficial velocity, and said time derivatives,
• calculating mobility coefficients from said individual and total superficial velocities, saturations and spatial derivatives of saturations,
• measuring the differential pressures of one of said fluids, and
• calculating a mobility of one of said fluids from said pressures and individual superficial velocities.

A method for determining mobility coefficients of a sample of a material having a known porosity, comprising:

• providing said sample with at least two preselected fluids,
• imaging a preselected volume of said sample to determine the saturations of said fluids in said preselected volume,
• calculating time and spatial derivatives of said saturations,
• determining total superficial velocity for said fluids,
• determining the individual superficial velocities of said fluids from said porosity, said total superficial velocity, and said time derivatives, and
• calculating said mobility coefficients from said individual and total superficial velocities, saturations and spatial derivatives of saturations.

A method for determining relative permeability of a sample of a material having a known porosity and absolute permeability, comprising:

• providing said sample with at least two preselected fluids having known viscosities,
• imaging a preselected volume of said sample to determine the saturations of said fluids in said preselected volume,
• calculating time and spatial derivatives of said saturations,
• determining total superficial velocity for said fluids,
• determining the individual superficial velocities of said fluids from said porosity, said total superficial velocity, and said time derivatives,
• calculating mobility coefficients from said individual and total superficial velocities, saturations and spatial derivatives of saturations,
• measuring the differential pressures of one of said fluids,
• calculating a mobility of said one of said fluids from said pressures, and individual velocities,
• determining the mobilities of said other fluids from said mobility coefficients, and
• calculating relative permeabilities from said mobilities, viscosity and absolute permeability for said fluids.

A method for determining capillary pressure of a sample of a material having a known porosity and absolute permeability, comprising:

• providing said sample with at least two preselected fluids,
• imaging a preselected volume of said sample to determine the saturations of said fluids in said preselected volume,
• calculating time and spatial derivatives of said saturations,
• determining total superficial velocity for said fluids,
• determining the individual superficial velocities of said fluids from said porosity, said total superficial velocity, and said time derivatives,
• calculating mobility coefficients from said individual and total superficial velocities, saturations and spatial derivatives of saturations,
• measuring the differential pressures of one of said fluids,
• calculating a mobility of said one of said fluids from said pressures, and individual superficial velocities,
• calculating the saturation derivatives of capillary pressures from said mobilities, and mobility coefficients for one of said fluids, and
• integrating said derivaties of capillary pressures to obtain said capillary pressures.