Material point method modeling in oil and gas reservoirs

9,378,310

13/649655

October 11, 2012

A computer system and method of simulating the behavior of an oil and gas reservoir including changes in the margins of frangible solids. A system of equations including state equations such as momentum, and conservation laws such as mass conservation and volume fraction continuity, are defined and discretized for at least two phases in a modeled volume, one of which corresponds to frangible material. A material point model technique for numerically solving the system of discretized equations, to derive fluid flow at each of a plurality of mesh nodes in the modeled volume, and the velocity of at each of a plurality of particles representing the frangible material in the modeled volume. A time-splitting technique improves the computational efficiency of the simulation while maintaining accuracy on the deformation scale. The method can be applied to derive accurate upscaled model equations for larger volume scale simulations.

Vanderheyden, William Brian (Katy, TX, US); Zhang, Duan (Los Alamos, NM, US)

Los Alamos National Security, LLC (Los Alamos, NM, US), BP Corporation North America Inc. (Houston, TX, US)

1. 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 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, 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 for each particle comprising a velocity parameter, 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 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 formation over the simulation time period; wherein the solving step comprises: for 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 to a constant for each particle having a damage parameter in the undamaged state; then solving the 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; and 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 the velocity parameter for fluid in 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.

2. The method of claim 1 , wherein the retrieved parameters defining at least one fluid phase represent hydraulic fracturing fluid; and wherein the retrieved parameters defining particles of a frangible material represent a gas shale.

3. The method of claim 1 , wherein the retrieved parameters defining at least one fluid phase represent heavy oil; wherein the retrieved parameters defining particles of a frangible material represent unconsolidated sand; wherein the state equation for fluid flow expresses momentum of the heavy oil at a mesh node in terms of a pressure gradient at the mesh node, viscous stress of the heavy oil at the mesh node, and material interaction with the unconsolidated sand at the mesh node; wherein the state equation for particle behavior expresses momentum of unconsolidated sand in terms of a pressure gradient at the particle, elastic stress at the particle, viscous stress at the particle, and material interaction of the particle with heavy oil; and wherein the system of equations further comprises equations corresponding to mass conservation laws for the heavy oil and the unconsolidated sand, and an equation corresponding to a volume fraction continuity constraint.

4. The method of claim 3 , wherein the processing step comprises: volume averaging the system of equations to a first volume scale; executing a simulation of the behavior of a volume corresponding to the first volume scale using the volume averaged system of equations; setting values of constants in the volume averaged equations responsive to a comparison of the results of the executing step and a first instance of the step of solving the system of equations; and upscaling the volume averaged system of equations to a larger volume scale; and executing a simulation of the behavior of a volume corresponding to the larger volume scale using the upscaled system of equations.

5. The method of claim 1 , wherein the retrieved parameters defining at least one fluid phase represent heavy oil; and wherein the retrieved parameters defining particles of a frangible material represent unconsolidated sand.

6. The method of claim 5 , wherein the step of evaluating the damage model comprises: determining a shear stress value and a normal stress value resulting from the solving step; responsive to the shear stress value exceeding a limit corresponding to the normal stress value, setting the damage parameter of the particle to the damaged state.

7. The method of claim 5 , further comprising: after the second plurality of time steps, repeating the setting and solving steps for a third plurality of time steps separated by the first time period.

8. The method of claim 1 , wherein the step of evaluating the damage model comprises: determining a shear stress value and a normal stress value resulting from the solving step; responsive to the shear stress value exceeding a limit corresponding to the normal stress value, setting the damage parameter of the particle to the damaged state.

9. The method of claim 1 , further comprising: after the second plurality of time steps, repeating the setting and solving steps for a third plurality of time steps separated by the first time period.

10. The method of claim 1 , wherein the retrieved parameters defining at least one fluid phase represent heavy oil; and wherein the retrieved parameters defining particles of a frangible material represent unconsolidated sand; wherein the state equation for fluid flow expresses momentum of the heavy oil at a mesh node in terms of a pressure gradient at the mesh node, viscous stress of the heavy oil at the mesh node, and material interaction with the unconsolidated sand at the mesh node; and wherein the state equation for particle behavior expresses momentum of an unconsolidated sand particle in terms of a pressure gradient at the particle, elastic stress at the particle, viscous stress at the particle, and material interaction of the particle with heavy oil.

11. 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, each particle associated with a damage parameter having possible states comprising undamaged and damaged; 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 formation over the simulation time period; wherein the solving operation comprises: for each of a first plurality of time steps separated by a first time period: setting a velocity parameter to zero for each particle having a damage parameter in the undamaged state; setting an elastic stress term to a constant for each particle having a damage parameter in the undamaged state; then solving the 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; and 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 in 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.

12. The computer system of claim 11 , wherein the at least one fluid phase comprises hydraulic fracturing fluid; and wherein the frangible material comprises a gas shale.

13. The computer system of claim 11 , wherein the at least one fluid phase comprises heavy oil; wherein the frangible material comprises unconsolidated sand. wherein the state equation for fluid flow expresses momentum of the heavy oil at a mesh node in terms of a pressure gradient at the mesh node, viscous stress of the heavy oil at the mesh node, and material interaction with the unconsolidated sand at the mesh node; wherein the state equation for particle behavior expresses momentum of unconsolidated sand in terms of a pressure gradient at the particle, elastic stress at the particle, viscous stress at the particle, and material interaction of the particle with heavy oil; and wherein the system of equations further comprises equations corresponding to mass conservation laws for the heavy oil and the unconsolidated sand, and an equation corresponding to a volume fraction continuity constraint.

14. The computer system of claim 13 , wherein the processing operation comprises: volume averaging the system of equations to a first volume scale; executing a simulation of the behavior of a volume corresponding to the first volume scale using the volume averaged system of equations; setting values of constants in the volume averaged equations responsive to a comparison of the results of the executing step and a first instance of the step of solving the system of equations; and upscaling the volume averaged system of equations to a larger volume scale; and executing a simulation of the behavior of a volume corresponding to the larger volume scale using the upscaled system of equations.

15. The computer system of claim 11 , wherein the at least one fluid phase comprises heavy oil; and wherein the frangible material comprises unconsolidated sand.

16. The computer system of claim 15 , wherein the operation of evaluating the damage model comprises: determining a shear stress value and a normal stress value resulting from the solving step; responsive to the shear stress value exceeding a limit corresponding to the normal stress value, setting the damage parameter of the particle to the damaged state.

17. 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, each particle associated with 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 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 formation over the simulation time period; and wherein the solving operation comprises: for each of a first plurality of time steps separated by a first time period: setting a velocity parameter to zero for each particle having a damage parameter in the undamaged state; setting an elastic stress term to a constant for each particle having a damage parameter in the undamaged state; then solving the 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 in each mesh node to a constant value corresponding to a recent value of the velocity parameter in that mesh node; and 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.

18. The computer-readable medium of claim 17 , wherein the at least one fluid phase comprises hydraulic fracturing fluid; and wherein the frangible material comprises a gas shale.

19. The computer-readable medium of claim 17 , wherein the at least one fluid phase comprises heavy oil; wherein the frangible material comprises unconsolidated sand. wherein the state equation for fluid flow expresses momentum of the heavy oil at a mesh node in terms of a pressure gradient at the mesh node, viscous stress of the heavy oil at the mesh node, and material interaction with the unconsolidated sand at the mesh node; wherein the state equation for particle behavior expresses momentum of unconsolidated sand in terms of a pressure gradient at the particle, elastic stress at the particle, viscous stress at the particle, and material interaction of the particle with heavy oil; and wherein the system of equations further comprises equations corresponding to mass conservation laws for the heavy oil and the unconsolidated sand, and an equation corresponding to a volume fraction continuity constraint.

20. The computer-readable medium of claim 19 , wherein the processing operation comprises: volume averaging the system of equations to a first volume scale; executing a simulation of the behavior of a volume corresponding to the first volume scale using the volume averaged system of equations; setting values of constants in the volume averaged equations responsive to a comparison of the results of the executing step and a first instance of the step of solving the system of equations; and upscaling the volume averaged system of equations to a larger volume scale; and executing a simulation of the behavior of a volume corresponding to the larger volume scale using the upscaled system of equations.

21. The computer-readable medium of claim 17 , wherein the at least one fluid phase comprises heavy oil; and wherein the frangible material comprises unconsolidated sand.

22. The computer-readable medium of claim 21 , wherein the operation of evaluating the damage model comprises: determining a shear stress value and a normal stress value resulting from the solving step; responsive to the shear stress value exceeding a limit corresponding to the normal stress value, setting the damage parameter of the particle to the damaged state.

Tremblay, B., and K. Oldakowski. “Modeling of wormhole growth in cold production.” Transport in porous media 53.2 (2003): 197-214. cited by examiner
Vittoratos et al., “Deliberate Sand Production from Heavy Oil Reservoirs: Potent Activation of Both Solution Gas and Aquifer Drives”, Proceedings for the World Heavy Oil Congress 2008, Paper 2008-501. cited by applicant
Zhang et al., “Material point method applied to multiphase flows”, J. Computational Physics 227 (Elsevier, 2008), pp. 3159-3173. cited by applicant
Zhang et al., “CartaBlanca Theory Manual: Multiphase Flow Equations and Numerical Methods”, Los Alamos National Laboratory Report No. LAUR-07-3621 (2007), available at http://www.lanl.gov/projects/CartaBlanca/. cited by applicant
Kamp et al., “A New Modeling Approach for Heavy Oil Flow in Process Media”, SPE paper 69270, SPE International Thermal Operations and Heavy Oil Symposium (SPE, 2001). cited by applicant
Giguere et al., “CartaBlanca User's Manual”, Los Alamos National Laboratory Report No. LA-UR-07-8214 (2007), available at http://www.lanl.gov/projects/CartaBlanca/. cited by applicant
Zhang et al., “Averaged equations for inviscid two-phase flow”, J. Fluid Mechanics, vol. 267 (1994), pp. 185-219. cited by applicant
Zhang et al., “The effects of mesoscale structures on phase interaction forces in two-phase flows and macroscopic equations”, Int. J. Multiphase Flow, vol. 28 (2002), pp. 805-822. cited by applicant
Zhang et al., “Pressure calculation in disperse and continuous multiphase flows”, Int. J. Multiphase Flow, vol. 33 (2007), pp. 86-100. cited by applicant
Zhang, “Ensemble phase averaged equations for multiphase flows in porous media; Part 2: a general theory”, Int. J. Multiphase Flow, vol. 35 (2009), pp. 640-649. cited by applicant
“CartaBlanca: A High-Efficiency, Object-Oriented, General-Purpose Computer Simulation Environment”, Los Alamos National Laboratory Report No. LAUR-05-6574 (2005). cited by applicant
Wang et al., “Numerical Modeling of Massive Sand Production”, SPE 147110, SPE Annual Technical Conference (SPE, Oct. 30, 2011). cited by applicant
Vanderheyden et al., “Modeling Wormhole Growth and Wormhole Networks in Unconsolidated Sand Media Using the BP CHOPS Model”, Paper WHOC11-427, 2011 World Heavy Oil Congress (Mar. 14-17, 2011). cited by applicant
Vanderheyden et al., “A New Pressure Field Based Model for Cold Heavy Oil Production with Sand”, Paper WHOC12-383, 2012 World Heavy Oil Congress (Sep. 10-13, 2012). cited by applicant

edspgr.09378310