# US 11,906,697 B2 · Method and system for a multi-level nonlinear solver for reservoir simulations > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,906,697 B2 - Document ID: US11906697B2 - Status: Granted - Kind: B2 - Application number: 17/193,639 - Filed: 2021-03-05 - Published: 2022-09-08 - Granted: 2024-02-20 - Earliest claimed: 2021-03-05 - Assignees: Saudi Arabian Oil Company - Applicants: Saudi Arabian Oil Company - Inventors: Tareq Shaalan; Zhen Chen - Web page: https://patentgrep.com/patent/US11906697B2 ## CPC - E21B 49/00: Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells - G01V 20/00: Geomodelling in general - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - E21B 2200/20: Computer models or simulations, e.g. for reservoirs under production, drill bits - G06F 2111/04: Constraint-based CAD - G06F 2111/10: Numerical modelling - G06F 2113/08: Fluids - E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS - G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A method may include obtaining grid model data for a geological region of interest and well data for various wells in the geological region of interest. A well among the wells may correspond to a simulated well network in a reservoir simulation. The method may further include determining, based on the grid model data and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method. The method may further include determining, based on the grid model data, the well data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method. The method may further include performing, based on the grid model data, and the second simulation solution, the reservoir simulation. ## Claims ### Claim 1 A method, comprising: obtaining wellbore pressure data from a plurality of pressure sensors in a wellbore for a first well in a geological region of interest; obtaining flow rate data from at least one flow rate sensor that measures a production rate for the first well; obtaining, by a computer processor, grid model data for the geological region of interest and well data for a plurality of wells in the geological region of interest, wherein the first well is among the plurality of wells; determining, by the computer processor, a simulated well network for the first well in the geological region of interest for a reservoir simulation, wherein the simulated well network comprises a well source node, a plurality of wellbore links, and a plurality of reservoir perforation links, and wherein at least one reservoir perforation link among the plurality of reservoir perforation links corresponds to a perforation operation that perforates a casing in the wellbore for the first well; determining, by the computer processor and based on the grid model data, the wellbore pressure data, the flow rate data, and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method; determining, by the computer processor and based on the grid model data, the well data, the wellbore pressure data, the flow rate data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method; performing, by the computer processor and based on the grid model data, and the second simulation solution, the reservoir simulation of the geological region of interest for a predetermined period of time using a third search method; and determining, by the computer processor, a predicted production rate for the first well based on the reservoir simulation. ### Claim 2 (depends on 1) The method of claim 1, further comprising: updating, iteratively using the second search method, a first value of the second simulation solution to produce a second value of the second simulation solution, determining whether the second simulation solution has converged based on a comparison between the first value and the second value, and wherein, in response to the second simulation solution converging, the reservoir simulation of the geological region of interest is performed using a final value of the second simulation solution. ### Claim 3 (depends on 1) The method of claim 1, wherein the first search method is a secant method, wherein the second search method is a first Newton-Raphson method, and wherein the third search method is a second Newton-Raphson method. ### Claim 4 (depends on 1) The method of claim 1, wherein the first constraint rate equation is a fixed equation that comprises a boundary condition with a constant predetermined surface flow rate. ### Claim 5 (depends on 1) The method of claim 1, further comprising: determining, using a linear solver, a plurality of fluid properties regarding the simulated well network, wherein the plurality of fluid properties comprise at least one density value, at least one viscosity value, at least one phase volume value, and at least one pressure drop value, and wherein determining the first simulation solution comprises using the at least one viscosity value, the at least one phase volume value, and the at least one pressure drop value. ### Claim 6 (depends on 1) The method of claim 1, wherein first simulation solution for the first constraint rate equation is updated until a value of the first simulation solution satisfies a predetermined criterion, and wherein the predetermined criterion corresponds to a predetermined minimum amount of change between updates of the value of the first simulation solution. ### Claim 7 (depends on 1) The method of claim 1, wherein the reservoir simulation of the geological region of interest is performed by coupling the second simulation solution to a grid model network using implicit coupling. ### Claim 8 A system, comprising: a plurality of wells in a geological region of interest, wherein the plurality of wells comprises a first well; a plurality of pressure sensors in a wellbore for the first well in the geological region of interest; at least one flow rate sensor that measures a production rate for the first well; and a reservoir simulator comprising a computer processor and coupled to the plurality of wells, wherein the reservoir simulator is configured to perform a method comprising: obtaining wellbore pressure data from the plurality of pressure sensors; obtaining flow rate data from the at least one flow rate sensor; obtaining grid model data for the geological region of interest; obtaining, from the plurality of wells, well data determining a simulated well network for the first well in the geological region of interest for a reservoir simulation, wherein the simulated well network comprises a well source node, a plurality of wellbore links, and a plurality of reservoir perforation links, and wherein at least one reservoir perforation link among the plurality of reservoir perforation links corresponds to a perforation operation that perforates a casing in the wellbore for the first well; determining, based on the grid model data, the wellbore pressure data, the flow rate data, and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method; determining, based on the grid model data, the well data, the wellbore pressure data, the flow rate data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method; performing, based on the grid model data and the second simulation solution, the reservoir simulation of the geological region of interest for a predetermined period of time using a third search method; and determining a predicted production rate for the first well based on the reservoir simulation. ### Claim 9 (depends on 8) The system of claim 8, wherein the reservoir simulator further comprises functionality for: updating, iteratively using the second search method, a first value of the second simulation solution to produce a second value of the second simulation solution, determining whether the second simulation solution has converged based on a comparison between the first value and the second value, and wherein, in response to the second simulation solution converging, the reservoir simulation of the geological region of interest is performed using a final value of the second simulation solution. ### Claim 10 (depends on 8) The system of claim 8, wherein the reservoir simulator further comprises functionality for: determining, using a linear solver, a plurality of fluid properties regarding the simulated well network, wherein the plurality of fluid properties comprise at least one density value, at least one viscosity value, at least one phase volume value, and at least one pressure drop value, and wherein determining the first simulation solution comprises using the at least one viscosity value, the at least one phase volume value, and the at least one pressure drop value. ### Claim 11 (depends on 8) The system of claim 8, wherein first simulation solution for the first constraint rate equation is updated until a value of the first simulation solution satisfies a predetermined criterion, and wherein the predetermined criterion corresponds to a predetermined minimum amount of change between updates of the value of the first simulation solution. ### Claim 12 (depends on 8) The system of claim 8, wherein the reservoir simulation of the geological region of interest is performed by coupling the second simulation solution to a grid model network using implicit coupling. ### Claim 13 A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions being configured to perform a method comprising: obtaining wellbore pressure data from a plurality of pressure sensors in a wellbore for a first well in a geological region of interest; obtaining flow rate data from at least one flow rate sensor that measures a production rate for the first well; obtaining grid model data for flail the geological region of interest and well data for a plurality of wells in the geological region of interest, wherein the first well among the plurality of wells; determining a simulated well network for the first well in the geological region of interest for a reservoir simulation, wherein the simulated well network comprises a well source node, a plurality of wellbore links, and a plurality of reservoir perforation links, and wherein at least one reservoir perforation link among the plurality of reservoir perforation links corresponds to a perforation operation that perforates a casing in the wellbore for the first well; determining, based on the grid model data, the wellbore pressure data, the flow rate data, and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method; determining, based on the grid model data, the well data, the wellbore pressure data, the flow rate data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method; performing, based on the grid model data and the second simulation solution, the reservoir simulation of the geological region of interest for a predetermined period of time using a third search method; and determining a predicted production rate for the first well based on the reservoir simulation. ### Claim 14 (depends on 13) The non-transitory computer readable medium of claim 13, wherein the instructions further comprise functionality for: updating, iteratively using the second search method, a first value of the second simulation solution to produce a second value of the second simulation solution, determining whether the second simulation solution has converged based on a comparison between the first value and the second value, and wherein, in response to the second simulation solution converging, the reservoir simulation of the geological region of interest is performed using a final value of the second simulation solution. ### Claim 15 (depends on 13) The non-transitory computer readable medium of claim 13, wherein the first search method is a secant method, wherein the second search method is a first Newton-Raphson method, and wherein the third search method is a second Newton-Raphson method. ### Claim 16 (depends on 13) The non-transitory computer readable medium of claim 13, wherein the first constraint rate equation is a fixed equation that comprises a boundary condition with a constant predetermined surface flow rate.