[미국특허]
Method for solving implicit reservoir simulation matrix equation
원문보기
IPC분류정보
국가/구분
United States(US) Patent
등록
국제특허분류(IPC7판)
G06G-007/48
G06G-007/50
출원번호
UP-0579966
(2005-04-13)
등록번호
US-7672818
(2010-04-21)
국제출원번호
PCT/US2005/012629
(2005-04-13)
§371/§102 date
20061110
(20061110)
국제공개번호
WO05/121840
(2005-12-22)
발명자
/ 주소
Watts, III, James W.
출원인 / 주소
ExxonMobil Upstream Research Company
대리인 / 주소
ExxonMobil Upstream Research Company - Law Department
인용정보
피인용 횟수 :
5인용 특허 :
133
초록▼
A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector. In one embodiment, the method includes receiving the block sparse matrix and the right hand side block vector, constructing a
A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector. In one embodiment, the method includes receiving the block sparse matrix and the right hand side block vector, constructing a reduced transformed block sparse matrix from the block sparse matrix, constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector, and solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector.
대표청구항▼
What is claimed is: 1. A computer-implemented method for simulating fluid flow in a hydrocarbon reservoir, the method comprising: constructing a system of fluid flow equations relating to the hydrocarbon reservoir; representing the system of fluid flow equations as a matrix equation AX=B, wherein A
What is claimed is: 1. A computer-implemented method for simulating fluid flow in a hydrocarbon reservoir, the method comprising: constructing a system of fluid flow equations relating to the hydrocarbon reservoir; representing the system of fluid flow equations as a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector, and X represents a solution block vector; receiving the block sparse matrix and the right hand side block vector; constructing a reduced transformed block sparse matrix from the block sparse matrix; constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector; wherein constructing the reduced transformed block sparse matrix comprises: assembling one or more coefficients of one or more mass change terms from a column of the block sparse matrix into a column matrix; performing a singular value decomposition on the column matrix to generate a left matrix, a diagonal matrix and a right matrix; and discarding one or more singular values that are less than a predetermined threshold value to generate a reduced diagonal matrix; solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector simulating fluid flow rate in the hydrocarbon reservoir based on the solution block vector; and displaying, on a display, results of fluid flow rates for the reservoir simulation based on the solution block vector. 2. The method of claim 1, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms. 3. The method of claim 1, wherein constructing the reduced transformed block sparse matrix further comprises constructing a transformed block sparse matrix having the same block structure and submatrix form as the block sparse matrix. 4. The method of claim 1, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms, and wherein the diagonal matrix comprises one or more singular values arranged in ascending order. 5. The method of claim 1, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms, and wherein constructing the reduced transformed block sparse matrix comprises multiplying the left matrix by the reduced diagonal matrix to generate a temporary column matrix. 6. The method of claim 1, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms, and wherein constructing the reduced transformed block sparse matrix comprises: multiplying the left matrix by the reduced diagonal matrix to generate a temporary column matrix having a plurality of mass change terms coefficients; and assembling the mass change terms coefficients of the temporary column matrix into one or more temporary mass change terms coefficient submatrices that correspond to the mass change terms coefficients of the column matrix. 7. The method of claim 6, wherein constructing the reduced transformed block sparse matrix comprises premultiplying each temporary mass change terms coefficient submatrix by the transpose of the right matrix to generate a transformed temporary mass change terms coefficient submatrix. 8. The method of claim 7, wherein constructing the reduced transformed block sparse matrix comprises premultiplying each subvector containing the pressure change terms coefficients in the block sparse matrix by the transpose of the right matrix to generate a transformed pressure change terms coefficients subvector. 9. The method of claim 8, wherein constructing the reduced transformed block sparse matrix comprises postmultiplying each fluid partial volumes subvector in the block sparse matrix by the right matrix to generate a transformed fluid partial volumes vector. 10. The method of claim 9, wherein constructing the reduced transformed block sparse matrix comprises constructing a transformed block sparse matrix from one or more of the transformed temporary mass change terms coefficient submatrix, the transformed pressure change terms coefficients subvector and the transformed fluid partial volumes vector. 11. The method of claim 10, wherein constructing the reduced transformed block sparse matrix comprises eliminating one or more transformed fluid partial volumes that correspond to the discarded singular values in the transformed block sparse matrix to generate the reduced transformed block sparse matrix. 12. The method of claim 1, wherein constructing the reduced transformed block sparse matrix comprises: determining a column matrix norm for the column matrix; skipping the singular value decomposition if the column matrix norm is equal to or less than the predetermined threshold value; setting the singular values to zero if the column matrix norm is equal to or less than the predetermined threshold value; and setting the right matrix to the identity matrix if the column matrix norm is equal to or less than the predetermined threshold value. 13. The method of claim 12, wherein determining the column matrix norm comprises calculating the Frobenius norm of the column matrix. 14. The method of claim 1, wherein the reduced transformed block sparse matrix comprises one or more reduced transformed diagonal submatrices and one or more reduced transformed off-diagonal submatrices, wherein each reduced transformed diagonal submatrix comprises mass change terms coefficients and pressure change terms coefficients only within the bottom ri+1 rows and right most ri+1 columns of each transformed diagonal submatrix. 15. The method of claim 14, wherein each reduced transformed off-diagonal submatrix comprises mass change terms coefficients and pressure change terms coefficients only within the bottom ri+1 rows and the right most rj+1 columns of each transformed off-diagonal submatrix. 16. The method of claim 1, wherein constructing the reduced transformed residual block vector comprises constructing a transformed residual block vector. 17. The method of claim 1, wherein constructing the transformed residual block vector comprises constructing a transformed residual block vector having a transformed mass balance residual subvector and a transformed volume constraint residual subvector. 18. The method of claim 1, wherein constructing the reduced transformed residual block vector comprises premultiplying a mass balance residual subvector by the transpose of the right matrix to generate a transformed mass balance residual subvector. 19. The method of claim 1, wherein solving for the solution block vector comprises solving for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector. 20. The method of claim 1, wherein solving for the solution block vector comprises: solving for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector; and converting the reduced transformed solution change block vector to a solution change block vector. 21. The method of claim 1, wherein solving for the solution block vector comprises: adding the solution change block vector to a current estimate of the solution block vector to update the solution block vector. 22. The method of claim 1, wherein solving for the solution block vector comprises: solving for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector; and converting the reduced transformed solution change block vector to a solution change block vector having one or more changes in mass unknowns and one or more changes in pressure unknowns. 23. A computer-implemented method for solving a matrix equation AX=B that represents a system of fluid flow equations, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector, the method comprising: constructing a reduced transformed block sparse matrix from the block sparse matrix; constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector wherein constructing the reduced transformed block sparse matrix comprises: assembling one or more coefficients of one or more mass change terms from a column of the block sparse matrix into a column matrix; performing a singular value decomposition on the column matrix to generate a left matrix, a diagonal matrix and a right matrix; discarding one or more singular values that are less than a predetermined threshold value to generate a reduced diagonal matrix; solving for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector; converting the reduced transformed solution change block vector to a solution change block vector having one or more changes in mass unknowns and one or more changes in pressure unknowns; adding the solution change block vector to a current estimate of the solution block vector to update the solution block vector simulating fluid flow rate in the hydrocarbon reservoir based on the solution block vector; and displaying on a display, results of fluid flow rates for the reservoir simulation based on the solution block vector. 24. A computer-implemented method for solving a matrix equation AX=B in a hydrocarbon reservoir simulation, wherein A represents a block sparse matrix, B represents a first block vector and X represents a solution block vector, the method comprising: receiving the block sparse matrix and the first block vector; constructing a reduced transformed block sparse matrix from the block sparse matrix; constructing a reduced transformed residual block vector from the block sparse matrix and the first block vector; wherein constructing the reduced transformed block sparse matrix comprises: assembling at least one coefficient associated with the at least one mass change term from a column of the block sparse matrix into a column matrix; performing a singular value decomposition on the column matrix to generate a first matrix, a second matrix and a third matrix; and discarding each singular value less than a predetermined threshold value to generate a reduced diagonal matrix; solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector simulating fluid flow rate in the hydrocarbon reservoir based on the solution block vector; and outputting results of fluid flow rates for the reservoir simulation based on the solution block vector. 25. The method of claim 24, wherein the matrix equation represents fluid flow equations in a reservoir having at least one pressure change term and at least one mass change term, wherein the block sparse matrix has at least one coefficient associated with the at least one pressure change term and at least one coefficient associated with the at least one mass change term. 26. The method of claim 24, wherein constructing the reduced transformed block sparse matrix comprises: determining a column matrix norm for the column matrix; skipping the singular value decomposition if the column matrix norm is equal to or less than a predetermined threshold value; setting the singular values to zero if the column matrix norm is equal to or less than the predetermined threshold value; and setting the third matrix to the identity matrix if the column matrix norm is equal to or less than the predetermined matrix threshold. 27. The method of claim 26, wherein determining the column matrix norm comprises calculating the Frobenius norm of the column matrix. 28. A system comprising: a computer; program instructions executed by the computer and configured to: receive a block sparse matrix and a right hand side block vector for a matrix equation AX=B that represents a system of fluid flow equations in a hydrocarbon reservoir, wherein A represents the block sparse matrix, B represents the right hand side block vector and X represents a solution block vector; construct a reduced transformed block sparse matrix from the block sparse matrix; construct a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector; wherein to construct the reduced transformed block sparse matrix the program instructions are configured to assemble one or more coefficients of one or more mass change terms from a column of the block sparse matrix into a column matrix, perform a singular value decomposition on the column matrix to generate a left matrix, a diagonal matrix and a right matrix, discard one or more singular values that are less than a predetermined threshold value to generate a reduced diagonal matrix, and solve for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector simulate fluid flow rate in the hydrocarbon reservoir based on the solution block vector; and a graphics display coupled to the computer and configured to display results based on the solution block vector on a graphics display. 29. The system of claim 28, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms. 30. The system of claim 28, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to construct a transformed block sparse matrix having the same block structure and submatrix form as the block sparse matrix. 31. The system of claim 28, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms, and wherein the diagonal matrix comprises one or more singular values arranged in ascending order. 32. The system of claim 28, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms, and wherein to construct the reduced transformed block sparse matrix the program instructions are configured to multiply the left matrix by the reduced diagonal matrix to generate a temporary column matrix. 33. The system of claim 28, wherein the matrix equation represents a system of fluid flow equations in one or more dimensions having one or more pressure change terms and the one or more mass change terms, wherein the block sparse matrix contains one or more coefficients of the pressure change terms and the one or more coefficients of the mass change terms, and wherein to construct the reduced transformed block sparse matrix the program instructions are configured to multiply the left matrix by the reduced diagonal matrix to generate a temporary column matrix having a plurality of mass change terms coefficients, and assemble the mass change terms coefficients of the temporary column matrix into one or more temporary mass change terms coefficient submatrices that correspond to the mass change terms coefficients of the column matrix. 34. The system of claim 33, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to premultiply each temporary mass change terms coefficient submatrix by the transpose of the right matrix to generate a transformed temporary mass change terms coefficient submatrix. 35. The system of claim 34, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to premultiply each subvector containing the pressure change terms coefficients in the block sparse matrix by the transpose of the right matrix to generate a transformed pressure change terms coefficients subvector. 36. The system of claim 35, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to postmultiply each fluid partial volumes subvector in the block sparse matrix by the right matrix to generate a transformed fluid partial volumes vector. 37. The system of claim 36, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to construct a transformed block sparse matrix from one or more of the transformed temporary mass change terms coefficient submatrix, the transformed pressure change terms coefficients subvector and the transformed fluid partial volumes vector. 38. The system of claim 37, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to eliminate one or more transformed fluid partial volumes that correspond to the discarded singular values in the transformed block sparse matrix to generate the reduced transformed block sparse matrix. 39. The system of claim 28, wherein to construct the reduced transformed block sparse matrix the program instructions are configured to determine a column matrix norm for the column matrix, skip the singular value decomposition if the column matrix norm is equal to or less than the predetermined threshold value, set the singular values to zero if the column matrix norm is equal to or less than the predetermined threshold value, and set the right matrix to the identity matrix if the column matrix norm is equal to or less than the predetermined threshold value. 40. The system of claim 39, wherein to determine the column matrix norm the program instructions are configured to calculate the Frobenius norm of the column matrix. 41. The system of claim 28, wherein the reduced transformed block sparse matrix comprises one or more reduced transformed diagonal submatrices and one or more reduced transformed off-diagonal submatrices, wherein each reduced transformed diagonal submatrix comprises mass change terms coefficients and pressure change terms coefficients only within the bottom ri+1 rows and right most ri+1 columns of each transformed diagonal submatrix. 42. The system of claim 41, wherein each reduced transformed off-diagonal submatrix comprises mass change terms coefficients and pressure change terms coefficients only within the bottom ri+1 rows and the right most rj+1 columns of each transformed off-diagonal submatrix. 43. The system of claim 28, wherein to construct the reduced transformed residual block vector the program instructions are configured to construct a transformed residual block vector. 44. The system of claim 28, wherein to construct the transformed residual block vector the program instructions are configured to construct a transformed residual block vector having a transformed mass balance residual subvector and a transformed volume constraint residual subvector. 45. The system of claim 28, wherein to construct the reduced transformed residual block vector the program instructions are configured to premultiply a mass balance residual subvector by the transpose of the right matrix to generate a transformed mass balance residual subvector. 46. The system of claim 28, wherein to solve for the solution block vector the program instructions are configured to solve for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector. 47. The system of claim 28, wherein to solve for the solution block vector the program instructions are configured to: solve for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector; and convert the reduced transformed solution change block vector to a solution change block vector. 48. The system of claim 28, wherein to solve for the solution block vector the program instructions are configured to add the solution change block vector to a current estimate of the solution block vector to update the solution block vector. 49. The system of claim 28, wherein to solve for the solution block vector the program instructions are configured to: solve for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector; and convert the reduced transformed solution change block vector to a solution change block vector having one or more changes in mass unknowns and one or more changes in pressure unknowns. 50. The system of claim 28 comprising a printer coupled to the computer and configured to provide the solution block vector to a user.
Schaeffer Arnold ; Anderson David R. ; Palevich Jack H., Apparatus and method for allowing computer systems with different input/output devices to collaboratively edit data.
Rogers William L. (Rijswijk TX NLX) Good Paul A. (Houston TX) Smith Richard A. (Missouri City TX), Dynamic visual display of reservoir simulator results.
Pita, Jorge A.; Tan, James C. T.; Fung, Larry S.; Dogru, Ali H., Highly-parallel, implicit compositional reservoir simulator for multi-million-cell models.
Henninger Derek P. (Cupertino CA) Jensen Richard H. (Redwood City CA) Keene Christopher T. (San Francisco CA), Method and apparatus for automatic generation of object oriented code for mapping relational data to objects.
Kapur Sharad ; Long David Esley ; Zhao Jingsong, Method and apparatus for designing interconnections and passive components in integrated circuits and equivalent structures by efficient parameter extraction.
Gunasekera Dayal L.,GBX, Method and apparatus for generating more accurate earth formation grid cell property information for use by a simulator to display more accurate simulation results of the formation near a wellbore.
Gunasekera Dayal L.,GBX, Method and apparatus for generating more accurate earth formation grid cell property information for use by a simulator to display more accurate simulation results of the formation near a wellbore.
Neff, Dennis B.; Grismore, John R.; Singleton, Jacquelyn K.; Layton, Jesse E., Method and apparatus for interactive curved surface borehole interpretation and visualization.
King Adrian S. (Albuquerque NM), Method and apparatus for solving dense systems of linear equations with an iterative method that employs partial multipl.
Saji Miyuki (Funabashi JPX) Konno Chisato (Inagi JPX) Umetani Yukio (Hachioji JPX), Method and device for displaying information on simulation result in a numerical simulation system.
Grace, John D., Method and system for creating irregular three-dimensional polygonal volume models in a three-dimensional geographic information system.
Kennon, Stephen R.; Canann, Scott A.; Ward, Steven B., Method and system for modeling geological structures using an unstructured four-dimensional mesh.
Neff Dennis B. ; Runnestrand Scott A. ; Butler Edgar L. ; Vienot Michael E., Method for determining distribution of reservoir permeability, porosity and pseudo relative permeability.
Bennis Chakib,FRX ; Sassi William,FRX, Method for generating a 3D-grid pattern matching the geometry of a body in order to achieve a model representative of th.
Manceau, Emmanuel; Sarda, Sylvain; Cosentino, Luca; Cacas, Marie-Christine; Bourbiaux, Bernard, Method for modelling flows in a fractured medium crossed by large fractures.
Vladimir Pisetski RU; Valeri B. Kormilcev RU; Aleksander N. Ratushnak RU, Method for predicting dynamic parameters of fluids in a subterranean reservoir.
Guerillot Dominique,FRX ; Roggero Frederic,FRX, Method for predicting, by means of an inversion technique, the evolution of the production of an underground reservoir.
Roggero, Frederic; Mezghani, Mokhles, Method of constraining by dynamic production data a fine model representative of the distribution in the reservoir of a physical quantity characteristic of the subsoil structure.
Mainguy, Marc; Longuemare, Pascal; Lemonnier, Patrick; Chalon, Florent, Method of constructing a geomechanical model of an underground zone intended to be coupled with a reservoir model.
Hinchman Steven B. (Houston TX) Brickey Raymond T. (Anchorage AK) Heymans Michael J. (Highlands Ranch CO), Method of extrapolating reservoir performance.
Balaven,Sophie; Boissonnat,Jean Daniel; Bennis,Chakib; Sarda,Sylvain, Method of generating a grid on a heterogenous formation crossed by one or more geometric discontinuities in order to carry out simulations.
Bennis, Chakib; Sarda, Sylvain; Pain, Eric; Balaven, Sophie, Method of generating a hybrid grid allowing modelling of a heterogeneous formation crossed by one or more wells.
Sagawa Nobutoshi (Kokubunji JPX) Finn Donal (Dublin IEX) Hurley Neil (Sligo IEX), Method of generating partial differential equations for simulation, simulation method, and method of generating simulati.
Anders Malthe-Sorenssen NO; Thomas Walmann NO; Torstein Jossang NO; Jens Feder NO; Humphrey H. Hardy, Method of modeling of faulting and fracturing in the earth.
Austvold Shawn M. ; Legler Rebecca B. ; Cline Marshall P. ; Dahl Daniel R. ; Evans Jim ; Gaertner Peter M. ; Hale Neal ; Pothireddy Sujatha, Object oriented application program development framework mechanism.
Stoisits Richard F. ; Crawford Kelly D. ; MacAllister Donald J. ; McCormack Michael D., Petroleum production optimization utilizing adaptive network and genetic algorithm techniques.
Dalal Mukesh (Piscataway NJ) Gangopadhyay Dipayan (Brewster NY), Query optimization by type lattices in object-oriented logic programs and deductive databases.
Dhond Umesh R. ; LaSala Carl J. ; Rubenstein Jeffrey D., Software utility for creating and editing a multidimensional oil-well log graphics presentation.
Migdal Alexander ; Lebedev Alexei, System and method for computer modeling of 3D objects or surfaces by mesh constructions having optimal quality character.
Jacob Thomas ; Craig William Godfrey ; William Launey Vidrine ; Jerry Wayne Wauters ; Douglas Donald Seiler, System and method for real time reservoir management.
Thomas Jacob ; Godfrey Craig ; Vidrine William Launey ; Wauters Jerry Wayne ; Seiler Douglas Donald, System and method for real time reservoir management.
Thomas, Jacob; Godfrey, Craig William; Vidrine, William Launey; Wauters, Jerry Wayne; Seiler, Douglas Donald, System and method for real time reservoir management.
Wason Cameron B. (Plano TX) King Geoffrey A. (Garland TX) Shuck Edward L. (Dallas TX) Breitenbach E. Allen (Littleton CO) McFarlane Robert C. (Englewood CO), System for monitoring the changes in fluid content of a petroleum reservoir.
※ AI-Helper는 부적절한 답변을 할 수 있습니다.