Method for assessment of pore-throat size distribution and permeability in porous media

12025,576

15/734047

May 31, 2019

A computerized method and system include (a) estimating parameters that quantify rock fabric features (e.g., tortuosity, effective pore size, throat-size distribution) by joint interpretation of electrical resistivity, dielectric permittivity, and NMR measurements, (b) developing a new workflow for permeability assessment that incorporates the quantified rock fabric parameters, and (c) validating the reliability of the new permeability model in core-scale domain using electrical resistivity, dielectric permittivity, NMR, Mercury Injection Capillary Pressure (MICP), and permeability measurements.

BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM (Austin, TX, US)

BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM (Austin, TX, US)

1. A computerized system for estimating pore-throat-size distribution in a section of porous media, comprising: at least one computer comprising a processor and computerized memory; an imaging device configured to collect nuclear magnetic resonance (NMR) data pertaining to the section of porous media and transmitting the NMR data to the memory; a holder configured for attaching the section of porous media between an anode and a cathode; a voltage source connected to the anode; an impedance analysis circuit connected to the cathode and receiving current through the section of porous media, wherein the impedance analysis circuit transmits at least one of impedance data and dielectric permittivity data regarding the current to the computer, and wherein the processor calculates an effective pore-throat size from the NMR data, the impedance data, and the permittivity data, wherein the processor is further configured for: storing, in the computerized memory, measurements performed on the section of the porous media, wherein the measurements comprise (i) the nuclear magnetic resonance (NMR) data comprising transverse magnetization decay values (T 2), (ii) the dielectric permittivity data, and (iii) the impedance data; and using the processor to implement software stored in the computerized memory, wherein the software is configured to independently calculate the effective pore-throat size from rock fabric parameters, comprising (a) electric tortuosity (τ E) calculated from the dielectric permittivity and the NMR data which correlates to hydraulic tortuosity (τ H), (b) an electrical constriction factor (C E) calculated from the measurements (i)-(iii) which correlates to hydraulic constriction factor (C H), and (c) pore-size distribution (r P) and effective pore radii ( r P ) calculated from the NMR data; wherein the software is further configured to calculate the pore-throat-size distribution (r T) according to the formula: [mathematical expression included]

2. A computerized system according to claim 1 , wherein the electrical constriction factor CE is calculated according to the formula: [mathematical expression included] wherein C E correlates to C H , σ F is the electrical conductivity of the section of the brine-saturated porous media, σ w is the conductivity of the brine, ϕ c is a connected porosity, and τ E is an electrical tortuosity which correlates to a dielectric tortuosity and a hydraulic tortuosity.

3. A computerized system of estimating effective pore-throat size according to claim 1 , wherein an effective pore-throat radius is calculated according to the formula: [mathematical expression included] wherein SM is a statistical mean operator.

4. A computerized system according to claim 1 , wherein an effective pore-throat radius is calculated from the T 2 distribution of the porous media fully saturated with a single fluid according to the formula: [mathematical expression included] wherein T 2b is the bulk relaxation time of the fluid and ρ is the surface relaxivity of the pores wherein SM is a statistical mean operator.

5. A computerized system according to claim 4 , wherein the porous media is partially saturated with water, and the T 2 distribution of the brine-saturated porous media is inferred from the measurements (i)-(iii).

6. A computerized method according to claim 1 , wherein the dielectric tortuosity is calculated from the dielectric permittivity of the porous media using the formula: [mathematical expression included] wherein F c is a capacitive formation factor, ε f is the relative dielectric permittivity of the fluid, ε R is the relative dielectric permittivity of the rock, ϕ T is the total porosity, and τ eW corresponds to the dielectric tortuosity which correlates to the hydraulic and electrical tortuosities.

7. A computerized system according to claim 1 , wherein the correlations between connected and effective porosity to total porosity are estimated from three-dimensional pore-scale images of the section of the porous media, and wherein the connected porosity of the porous media is calculated by a connected component labeling algorithm.

8. A computerized system for estimating pore-throat-size distribution in the section of porous media, comprising: at least one computer comprising a processor and computer readable memory; an imaging device configured to collect nuclear magnetic resonance (NMR) data pertaining to the section of porous media and transmitting the NMR data to the memory; a holder comprising opposite attachment points configured to connect to opposite ends of the section of porous media, wherein the opposite attachment points are further configured to provide, simultaneously, current flow and fluid flow through the attachment points in at least one electrical circuit and at least one fluid circuit; an anode connected to one of the attachment points and a cathode connected to another the other attachment point, defining an electrical circuit connected to the holder; a pressure regulating assembly connected to the cathode; a voltage source connected to the anode; an impedance analysis circuit connected to the cathode and receiving current through the section of porous media, wherein the impedance analysis circuit transmits at least one of impedance data and permittivity data regarding the current to the computer, and wherein the processor calculates an effective pore-throat size from the NMR data, the impedance data, and the permittivity data; wherein the processor is configured with software to estimate directional permeability (k) of a section of the porous media that is either fully or partially saturated with water by implementing a method of: storing, in the memory, measurements performed on the section of the porous media, wherein the measurements comprise (i) the nuclear magnetic resonance (NMR) data comprising transverse magnetization decay values (T 2), (ii) the permittivity data; and (iii) at least one directional electrical conductivity measurement (σ P); using the processor to implement software stored in the memory, wherein the software is configured to calculate the directional permeability from fabric parameters comprising (a) electric tortuosity (τ E) calculated from the permittivity data and the NMR data which correlates to hydraulic tortuosity (τ H), (b) an electrical constriction factor (C E) from the measurements (i)-(iii) which correlates to hydraulic constriction factor (C H), and (c) pore-size distribution (r P) and effective pore radii calculated from the NMR data, and (d) a connected porosity (ϕ c) estimated from the NMR data, in porous medias where total pore volume is approximately equal to the connected pore volume or estimated from NMR data displayed as three-dimensional pore-scale images of the section of the porous media, and wherein the connected porosity of the porous media is calculated by a connected component labeling algorithm in porous medias where total pore volume is greater than the connected pore volume; wherein the software is further configured to calculate a statistical mean of directional permeability of the section of the porous media using the formula: [mathematical expression included]  wherein SM is a statistical mean operator.

9. A computerized system of estimating directional permeability of the section of a porous media according to claim 8 , wherein the directional permeability is determined in a same direction as dielectric permittivity and impedance measurements for the porous media.

10. A computerized system of estimating directional permeability of the section of a porous media according to claim 8 , according to the formula: [mathematical expression included] wherein σ r is an electrical conductivity of the section of the porous media fully saturated with brine and σ w is conductivity of the brine.

11. A computerized system of estimating directional permeability of the section of porous media according to claim 10 , wherein the porous media is partially saturated with the brine, and the conductivity of a brine saturated section of porous media can be inferred from conductivity measurements of the partially brine saturated rock.

12. A computerized system of estimating directional permeability of the section of a porous media according to claim 11 , wherein a statistical mean of a distribution of the pore radius squared is a harmonic mean, in the pore-scale domain, and the effective pore radius is calculated from the T 2 distribution of the porous media fully saturated with a single fluid according to the formula: [mathematical expression included] wherein T 2b is a bulk relaxation time of the fluid and ρ is a surface relaxivity of the pores, wherein SM is a statistical mean operator.

13. A computerized system of estimating directional permeability of the section of a porous media according to claim 12 , wherein a statistical mean of a distribution of the pore radius squared is a geometric mean, in the core-scale domain, and the effective pore radius is calculated from the T 2 distribution of the porous media saturated with a single fluid according to the formula: [mathematical expression included] wherein T 2b is the bulk relaxation time of the fluid and ρ is the surface relaxivity of the pores, wherein SM is a statistical mean operator.

14. A computerized system of estimating directional permeability of a section of a porous media according to claim 13 , wherein the correlations between connected and effective porosity to total porosity are estimated from three-dimensional pore-scale images of the section of the porous media, and wherein the connected porosity of the porous media is calculated by a connected component labeling algorithm.

15. A computerized system of estimating directional permeability of a section of a porous media according to claim 14 , wherein a connected porosity is estimated as being equal to total porosity of the porous media.

16. A computerized system of estimating directional permeability of a section of a porous media according to claim 15 , wherein dielectric tortuosity is calculated from the dielectric permittivity of the porous media using the formula: [mathematical expression included] wherein F c is a capacitive formation factor, ε f is the relative dielectric permittivity of the brine, ε R is the relative dielectric permittivity of the porous media, ϕ T is a total porosity, and τ eW corresponds to the dielectric tortuosity which correlates to the hydraulic and electric tortuosities and the dielectric tortuosity is determined in a same direction as dielectric permittivity measurements for a porous media.

17. A system of estimating directional permeability of a section of a porous media according to claim 8 , wherein the electrical constriction factor is calculated according to the formula: [mathematical expression included] where C E is the electrical constriction factor which correlates to C H , ϕ c is the connected porosity, and τ E is the electrical tortuosity which correlates to the dielectric and hydraulic tortuosities.

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