Data-driven estimation of stimulated reservoir volume

Patent metadata

Field	Value
Publication number	US-10527744-B2
Application number	US-201415510029-A
Country	US
Kind code	B2
Filing date	Oct 13, 2014
Priority date	Oct 13, 2014
Publication date	Jan 7, 2020
Grant date	Jan 7, 2020

Abstract

A method for improved data-driven estimation of a stimulated reservoir volume may generate an optimized surface that encloses a set of data points including microseismic event data corresponding to a treatment of a subterranean formation. A Delaunay triangulation may be performed on the set of data points to generate a set of polytopes. A Voronoi polygon may be generated about each data point and used to obtain a local density measure that is locally and adaptively determined for each data point. Based on the local density measure, polytopes in the set of polytopes may be discriminated for inclusion in the optimized surface.

First claim

What is claimed is:

1. A computer-implemented method for determining a stimulated reservoir volume, the method comprising:
obtaining a set of data points including microseismic event data corresponding to a treatment of a subterranean formation;
triangulating the set of data points according to the Delaunay Triangulation algorithm to generate a set of polytopes, each of the polytopes P having vertices from the set of data points, and the set of polytopes being bounded by a convex hull;
for each point S in the set of data points, generating a Voronoi polygon V about S;
based on the Voronoi polygon V respectively for each point S, determining a value d for each point S, the value d being indicative of a local density associated with the set of data points near the point S; and
for each polytope P, determining whether the polytope P for an optimized surface is discarded, based on the values d for each point S corresponding to a vertex of P;
generating the optimized surface from the remaining polytopes P; and
identifying a stimulated reservoir volume (SRV) for the treatment based on the optimized surface.

2. The method of claim 1 , wherein each of the polytopes P is a triangle.

3. The method of claim 1 , wherein each of the polytopes P is a tetrahedron.

4. The method of claim 1 , wherein the optimized surface encloses the SRV for the subterranean formation.

5. The method of claim 1 , wherein determining the value d for each point S includes:
for each point S i in the set of data points not located at the convex hull and corresponding Voronoi polygon V i :
determining a line p i + S i , p i + being a positive pole of the Voronoi polygon V i , p i + being a first vertex of V i located farthest from S i ; and
determining a line segment D having a length corresponding to the value d, the line segment D corresponding to a projection of a vector p i + p i − on the line p i + S i , p i − being a negative pole p − of the Voronoi polygon V i , p i − being a second vertex of V i such that a vector S i p i − makes a maximum negative projection on a vector S i p i + among all vertices of V i .

6. The method of claim 1 , wherein determining the value d for each point S includes:
for each point S e in the set of data points located at the convex hull and corresponding Voronoi polygon V e :
estimating a line p e + S e given by an average direction of normal vectors directed outward from the convex hull for boundary facets of polytopes P adjacent to the point S e , such that p e + is a farthest point outward from the convex hull on the line p e + S e from S e ;
determining a line segment D having length d/2 corresponding to a projection of a vector S e p e − on the estimated line p e + S e , p e − being a negative pole p − of the Voronoi polygon V e , p e − being a vertex of V e such that a vector S e p e − makes a maximum negative projection on a vector S e p e + among all vertices of V e ; and
calculating d.

7. The method of claim 1 , wherein determining whether the polytope P for the optimized surface is discarded includes:
for each polytope P:
calculating a minimum value d min from values of d for each of the vertices S of the polytope P;
assigning the minimum value d min to a characteristic variable α for the polytope P; and
when α≤r c , where r c is a circumradius of the polytope P, discarding the polytope P from the optimized surface, else retaining the polytope P for the optimized surface.

8. The method of claim 1 , wherein the value d is inversely related to the local density.

9. An article of manufacture comprising a non-transitory computer-readable medium storing instructions for determining a stimulated reservoir volume, wherein the instructions, when executed by a processor, cause the processor to:
obtain a set of data points including microseismic event data corresponding to a treatment of a subterranean formation;
triangulate the set of data points according to the Delaunay Triangulation algorithm to generate a set of polytopes, each of the polytopes P having vertices from the set of data points, and the set of polytopes being bounded by a convex hull;
for each point S in the set of data points, generate a Voronoi polygon V about S;
based on the Voronoi polygon V respectively for each point S, determine a value d for each point S, the value d being indicative of a local density associated with the set of data points near the point S; and
for each polytope P, determine whether the polytope P for an optimized surface is discarded, based on the values d for each point S corresponding to a vertex of P;
generate the optimized surface from the remaining polytopes P; and
identify a stimulated reservoir volume (SRV) for the treatment based on the optimized surface.

10. The article of manufacture of claim 9 , wherein each of the polytopes P is a triangle.

11. The article of manufacture of claim 9 , wherein each of the polytopes P is a tetrahedron.

12. The article of manufacture of claim 9 , wherein the optimized surface encloses the SRV for the subterranean formation.

13. The article of manufacture of claim 9 , wherein the instructions to determine the value d for each point S include instructions to:
for each point S i in the set of data points not located at the convex hull and corresponding Voronoi polygon V i :
determining a line p i + S i , p i + being a positive pole of the Voronoi polygon V i , p i + being a first vertex of V i located farthest from S i ; and
determining a line segment D having a length corresponding to the value d, the line segment D corresponding to a projection of a vector p i + p i − on the line p i + S i , p i − being a negative pole p − of the Voronoi polygon V i , p i − being a second vertex of V i such that a vector S i p i − makes a maximum negative projection on a vector S i p i + among all vertices of V i .

14. The article of manufacture of claim 9 , wherein the instructions to determine the value d for each point S include instructions to:
for each point S e in the set of data points located at the convex hull and corresponding Voronoi polygon V e :
estimating a line p e + S e by an average direction of normal vectors directed outward from the convex hull for boundary facets of polytopes P adjacent to the point S e , p e + being a farthest point outward from the convex hull on the line p e + S e from S e ;
determining a line segment D having length d/2 corresponding to a projection of a vector S e p e − on the estimated line p e + S e , p e − being a negative pole p − of the Voronoi polygon V e , p e − being a vertex of V e such that a vector S e p e − makes a maximum negative projection on a vector S e p e + among all vertices of V e ; and
calculating d.

15. The article of manufacture of claim 9 , wherein the instructions to determine whether the polytope P for the optimized surface is discarded include instructions to:
for each polytope P:
calculate a minimum value d min from values of d for each of the vertices S of the polytope P;
assign the minimum value d min to a characteristic variable α for the polytope P; and
when α≤r c , where r c is a circumradius of the polytope P, discarding the polytope P from the optimized surface, else retaining the polytope P for the optimized surface.

16. The article of manufacture of claim 9 , wherein the value d is inversely related to the local density.

17. A computer system for determining a stimulated reservoir volume, the computer syste

Assignees

• Halliburton Energy Services Inc

Inventors

• Ray Baidurja
• Lin Avi
• Ma Jianfu

Classifications

• G06F30/20

  Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) · CPC title

• G01V1/306 Primary

  for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles · CPC title

• G01V1/288

  Event detection in seismic signals, e.g. microseismics (G01V1/36 takes precedence) · CPC title

• G01V2210/663

  Modeling production-induced effects · CPC title

• G01V2210/646

  Fractures · CPC title