Material point method modeling in oil and gas reservoirs

A method of operating a computer system to simulate the fluid and structural behavior of a volume of the earth near a wellbore, comprising the steps of:

• retrieving, from a memory resource in the computer system, parameters defining properties defining at least one fluid phase within each of a plurality of mesh nodes in a sub-surface formation in the volume to be simulated, the parameters comprising a velocity parameter for fluid at each mesh node;
• retrieving, from a memory resource in the computer system, parameters defining properties for each of a plurality of particles of a frangible material within the volume, the parameters comprising a velocity parameter for each particle, and a damage parameter having possible states comprising undamaged and damaged;
• selecting initial pressure conditions at each of the plurality of mesh nodes;
• then, at each of a first plurality of time steps separated by a first time period:
• setting the velocity parameter to zero for each particle having a damage parameter in the undamaged state;
• setting an elastic stress term in a state equation for particle behavior to a constant for each particle having a damage parameter in the undamaged state;
• then solving a state equation for fluid flow at each of the plurality of mesh nodes;
• and
• solving the state equation for particle behavior for each of the plurality of particles;
• after the first plurality of time steps, for each of a second plurality of time steps separated by a second time period, the second time period being shorter than the first time period:
• setting a velocity parameter for fluid at each mesh node to a constant value corresponding to a recent value of the velocity parameter in that mesh node;
• then solving the state equation for particle behavior for each of a subset of the plurality of particles within a selected portion of the volume;
• and
• then, for each particle in the subset, evaluating a damage model responsive to one or more stress values determined in the solving step, to determine the state of the damage parameter for that particle;
• and
• processing the results of the solving steps to estimate fluid flow and changes in the sub-surface structure over the simulation time period.

A computer system for simulating the fluid and structural behavior of a volume of the earth near a wellbore, comprising:

• a processing unit for executing program instructions;
• a memory resource, coupled to the processing unit, for storing data representative of properties of at least one fluid phase at each of a plurality of mesh nodes in a grid representative of a sub-surface formation in the volume to be simulated, and data representative of properties for each of a plurality of particles of a frangible material within the volume;
• and
• program memory, coupled to the processing unit, for storing a computer program including program instructions that, when executed by the one or more processing units, causes the computer system to perform a sequence of operations comprising:
• retrieving, from the memory resource, at least a portion of the data defining properties of at least one fluid phase at each of a plurality of mesh nodes in a grid representative of a sub-surface formation in the volume to be simulated;
• retrieving, from the memory resource, at least a portion of the data defining properties for each of a plurality of particles of a frangible material within the volume;
• selecting initial pressure conditions at each of the plurality of mesh nodes;
• then, at each of a plurality of time steps over a simulation time period, solving a system of equations comprising a state equation for fluid flow at each of the plurality of mesh nodes and a state equation for particle behavior for each of the plurality of particles;
• and
• processing the results of the solving steps to estimate fluid flow and changes in the sub-surface structure over the simulation time period.

A non-transitory computer-readable medium storing a computer program that, when executed on a computer system, causes the computer system to perform a sequence of operations for simulating the fluid and structural behavior of a volume of the earth near a wellbore, the sequence of operations comprising:

• retrieving, from a memory resource of a computer system, data representative of properties of at least one fluid phase at each of a plurality of mesh nodes in a grid representative of a sub-surface formation in the volume to be simulated;
• retrieving, from a memory resource of a computer system, data representative of properties for each of a plurality of particles of a frangible material within the volume;
• selecting initial pressure conditions at each of the plurality of mesh nodes;
• then, at each of a plurality of time steps over a simulation time period, solving a system of equations comprising a state equation for fluid flow at each of the plurality of mesh nodes and a state equation for particle behavior for each of the plurality of particles;
• and
• processing the results of the solving steps to estimate fluid flow and changes in the sub-surface structure over the simulation time period.