# US 2022/0035071 A1 · Pore-scale, multi-component, multi-phase fluid model and method > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2022/0035071 A1 - Document ID: US20220035071A1 - Status: Published application - Kind: A1 - Application number: 17/298,969 - Filed: 2019-11-05 - Published: 2022-02-03 - Earliest claimed: 2018-12-17 - Assignees: King Abdullah University of Science and Technology - Applicants: King Abdullah University of Science and Technology - Inventors: Shuyu SUN; Tao ZHANG; Xiaolin FAN; Yiteng LI; Jingfa LI - Web page: https://patentgrep.com/patent/US20220035071A1 ## 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 30/28: using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD] - E21B 47/10: Locating fluid leaks, intrusions or movements - 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 for calculating a fluid flow in a given underground medium, the method including receiving initial molar densities for components of the fluid; introducing a scalar auxiliary variable r into an inhomogeneous Helmholtz free energy equation F with a Peng-Robinson equation of state; calculating a molar density ni of each component of the fluid based on a discretized scalar auxiliary variable rk; and determining the flow of the fluid based on the calculated molar densities ni. ## Claims ### Claim 1 A method for calculating a fluid flow in a given underground medium, the method comprising: receiving initial molar densities for components of the fluid; introducing a scalar auxiliary variable r into an inhomogeneous Helmholtz free energy equation F with a Peng-Robinson equation of state; calculating a molar density ni of each component of the fluid based on a discretized scalar auxiliary variable rk; and determining the flow of the fluid based on the calculated molar densities ni. ### Claim 2 (depends on 1) The method of claim 1, further comprising: applying an inhomogeneous Helmholtz free energy equation for the fluid; and modifying the inhomogeneous Helmholtz free energy equation based on the Peng-Robinson equation of state to obtain the inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state. ### Claim 3 (depends on 2) The method of claim 2, further comprising: discretizing the inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state. ### Claim 4 (depends on 3) The method of claim 3, further comprising: solving the discretized inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state to obtain the discretized scalar auxiliary variable. ### Claim 5 (depends on 3) The method of claim 3, wherein the discretizing step includes applying a finite difference algorithm. ### Claim 6 (depends on 1) The method of claim 1, wherein the fluid is a multi-component, multi-phase fluid. ### Claim 7 (depends on 1) The method of claim 1, wherein the scalar auxiliary variable r is equal to a square root of a sum of (1) a homogeneous Helmholtz energy part of the inhomogeneous Helmholtz free energy with the Peng-Robinson equation of state, and (2) a constant. ### Claim 8 (depends on 1) The method of claim 1, further comprising: iteratively calculating the scalar auxiliary variable and the molar density until the molar density converges. ### Claim 9 (depends on 1) The method of claim 1, further comprising: obtaining two linear equations for calculating the discretized scalar auxiliary variable and the discretized molar density. ### Claim 10 A computing device for calculating a fluid flow in a given underground medium, the computing device comprising: an interface for receiving initial molar densities for components of the fluid; and a processor connected to the interface and configured to, apply a scalar auxiliary variable r to an inhomogeneous Helmholtz free energy equation with a Peng-Robinson equation of state; calculate a molar density ni of each component of the fluid based on a discretized scalar auxiliary variable; and determine the flow of the fluid based on the calculated molar densities ni. ### Claim 11 (depends on 10) The device of claim 10, wherein the processor is further configured to: receive an inhomogeneous Helmholtz free energy equation for the fluid; and modify the inhomogeneous Helmholtz free energy equation based on Peng-Robinson equation of state to obtain the inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state. ### Claim 12 (depends on 11) The device of claim 11, wherein the processor is further configured to: discrete the inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state. ### Claim 13 (depends on 12) The device of claim 12, wherein the processor is further configured to: solve the discretized inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state to obtain the discretized scalar auxiliary variable. ### Claim 14 (depends on 12) The device of claim 12, wherein the discretizing step includes applying a finite difference algorithm. ### Claim 15 (depends on 10) The device of claim 10, wherein the fluid is a multi-component, multi-phase fluid. ### Claim 16 (depends on 10) The device of claim 10, wherein the scalar auxiliary variable r is equal to a square root of a sum of (1) a homogeneous Helmholtz energy part of the inhomogeneous Helmholtz free energy with the Peng-Robinson equation of state, and (2) a constant. ### Claim 17 (depends on 10) The device of claim 10, wherein the processor is further configured to: iteratively calculate the scalar auxiliary variable and the molar density until the molar density converges. ### Claim 18 (depends on 11) The device of claim 11, wherein the processor is further configured to: obtain two linear equations for calculating the discretized scalar auxiliary variable and the discretized molar density. ### Claim 19 A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement instructions for calculating a fluid flow in a given underground medium, the instructions comprising: receiving initial molar densities for components of the fluid; introducing a scalar auxiliary variable r into an inhomogeneous Helmholtz free energy equation F with a Peng-Robinson equation of state; calculating a molar density ni of each component of the fluid based on a discretized scalar auxiliary variable rk; and determining the flow of the fluid based on the calculated molar densities ni. ### Claim 20 (depends on 19) The medium of claim 19, further comprising: applying an inhomogeneous Helmholtz free energy equation for the fluid; modifying the inhomogeneous Helmholtz free energy equation based on Peng-Robinson equation of state to obtain the inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state; discretizing the inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state; and solving the discretized inhomogeneous Helmholtz free energy equation with the Peng-Robinson equation of state to obtain the discretized scalar auxiliary variable.