# US 10,309,812 B1 · System and method of using the same > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,309,812 B1 - Document ID: US10309812B1 - Status: Granted - Kind: B1 - Application number: 14/288,141 - Filed: 2014-05-27 - Granted: 2019-06-04 - Earliest claimed: 2013-05-24 - Applicants: University of Wyoming - Inventors: Ye Zhang; Jianying Jiao; Juraj Irsa - Web page: https://patentgrep.com/patent/US10309812B1 ## CPC - G01F 1/8436: {signal processing} - G01F 1/74: Devices for measuring flow of a fluid or flow of a fluent solid material in suspension in another fluid - G01F 1/86: Indirect mass flowmeters, e.g. measuring volume flow and density, temperature or pressure - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - G06F 2111/10: Numerical modelling - G01F: MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A system and method for parameter estimation of steady state flow in heterogeneous aquifers, and more particularly to a method and system for reducing uncertainty in calibrating aquifer flow and estimating aquifer hydraulic conductivities. ## Claims ### Claim 1 A method of approximating a steady-state flow of groundwater in an aquifer, comprising: determining, using computation equipment, an area representation of at least a portion of the aquifer, wherein the determining includes discretizing the area representation into elements, wherein each of the respective element includes a hydraulic head, wherein the determining considers a hydraulic flux of the flow at the respective element being a gradient of the hydraulic head scaled by a hydraulic conductivity to the flow at the respective element, and wherein the determining further considers there being no net change of the hydraulic flux within the respective element; and for each of the respective element, approximating the hydraulic head, the hydraulic flux, and the hydraulic conductivity, wherein the approximating comprises determining a numerical approximation to the hydraulic head, a numerical approximation to the hydraulic flux, and a numerical approximation to the hydraulic conductivity based on an approximate solution to a harmonic function. ### Claim 2 (depends on 1) The method of claim 1, wherein the harmonic function comprises a holomorphic function. ### Claim 3 (depends on 1) The method of claim 1, wherein the approximate solution is a linear or quadratic approximation. ### Claim 4 (depends on 1) The method of claim 1, further comprising, for each boundary between two adjacent elements of the elements, minimizing a residual of one or more of the approximation to the hydraulic head, the approximation to the hydraulic flux, and the approximation to the hydraulic conductivity. ### Claim 5 (depends on 4) The method of claim 4, wherein the residual is scaled by a weighting function. ### Claim 6 (depends on 5) The method of claim 5, wherein the weighting function approximates continuity at the boundary. ### Claim 7 (depends on 4) The method of claim 4, wherein the minimizing comprises minimizing the residual on a set of collocation points, wherein each of the collocation points lies on the boundary. ### Claim 8 (depends on 4) The method of claim 4, wherein the aquifer is heterogeneous, and wherein the minimizing comprises minimizing a residual of an approximation of a normal of the hydraulic flux. ### Claim 9 (depends on 1) The method of claim 1, wherein the aquifer is homogenous. ### Claim 10 A method of approximating, using computational equipment, a steady-state flow of groundwater in an aquifer, comprising: discretizing an area representative of at least a portion of the aquifer into elements, wherein each of the respective element includes a hydraulic head, wherein a hydraulic flux of the flow at the respective element is a gradient of the hydraulic head scaled by a hydraulic conductivity to the flow at the respective element, and wherein there is no net change of the hydraulic flux within the respective element; for each of the respective element, approximating the hydraulic head, the hydraulic flux, and the hydraulic conductivity, wherein the approximating comprises determining an approximation to the hydraulic head, an approximation to the hydraulic flux, and an approximation to the hydraulic conductivity based on an approximate solution to a harmonic function; and minimizing a residual of one or more of the approximation to the hydraulic head, the approximation to the hydraulic flux, and the approximation to the hydraulic conductivity, on a set of collocation points, wherein each of the collocation points lies on a boundary between two adjacent elements of the elements, wherein the residual is scaled by a weighting function, and wherein the weighting function approximates continuity at the boundary. ### Claim 11 (depends on 10) The method of claim 10, wherein the harmonic function comprises a holomorphic function. ### Claim 12 (depends on 10) The method of claim 10, wherein the approximate solution is a linear or quadratic approximation. ### Claim 13 (depends on 10) The method of claim 10, wherein the aquifer is homogenous. ### Claim 14 (depends on 10) The method of claim 10, wherein the aquifer is heterogeneous, and wherein the minimizing comprises minimizing a residual of an approximation of a normal of the hydraulic flux. ### Claim 15 A method of approximating, a steady-state flow of groundwater in an aquifer, comprising: determining discretizing an area representative representation of at least a portion of the aquifer, wherein the determining includes discretizing the area representation into elements, wherein each of the respective element includes a hydraulic head, wherein the discretizing considers a hydraulic flux of the flow at the respective element being a gradient of the hydraulic head scaled by a hydraulic conductivity to the flow at the respective element, and wherein the discretizing further considers there being no net change of the hydraulic flux within the respective element; for each of the respective element, approximating the hydraulic head, the hydraulic flux, and the hydraulic conductivity, wherein the approximating comprises determining an approximation to the hydraulic head, an approximation to the hydraulic flux, and an approximation to the hydraulic conductivity based on an approximate solution to a harmonic function; and for each boundary between two adjacent elements of the elements, minimizing a residual of one or more of the approximation to the hydraulic head, the approximation to the hydraulic flux, and the approximation to the hydraulic conductivity, wherein the minimizing comprises minimizing the residual on a set of collocation points, wherein each of the collocation points lies on the boundary. ### Claim 16 (depends on 15) The method of claim 15, wherein the residual is scaled by a weighting function, wherein the weighting function approximates continuity at the boundary. ### Claim 17 (depends on 15) The method of claim 15, wherein the harmonic function comprises a holomorphic function. ### Claim 18 (depends on 15) The method of claim 15, wherein the approximate solution is a linear or quadratic approximation. ### Claim 19 (depends on 15) The method of claim 15, wherein the aquifer is homogenous. ### Claim 20 (depends on 15) The method of claim 15, wherein the aquifer is heterogeneous, and wherein the minimizing comprises minimizing a residual of an approximation of a normal of the hydraulic flux.