Autonomous Uncertainty-Aware Engine For Pressure Gradient Identification Using A Discrete Optimization Framework

Abstract

A method and system for identifying a fluid within a subterranean formation. The method may comprise obtaining one or more pressure measurements at one or more depths with a downhole fluid sampling tool, forming a depth-pressure measurement set form the one or more pressure measurements, creating a solution novelty threshold from at least the depth-pressure measurement set, constraining a solution space with the solution novelty threshold, and finding a solution-space-inscribed simplex within the solution novelty threshold. The method may further comprise generating a simplicial decomposition for a convex hull of the solution-space-inscribed simplex up to the solution novelty threshold, identifying at least one inscribed simplex within the convex hull of the solution-space-inscribed simplex, determining a novel simplex interior with the at least one inscribed simplex, and forming a plurality of solutions with the novel simplex interior.

What is claimed is: 
     
         1 . A method comprising:
 obtaining one or more pressure measurements at one or more depths with a downhole fluid sampling tool;   forming a depth-pressure measurement set from the one or more pressure measurements;   creating a solution novelty threshold with a synthesis of at least one threshold;   generating a simplicial decomposition for a convex hull of a solution space up to the solution novelty threshold;   identifying at least one simplex within the convex hull of the solution space;   determining a novel simplex interior of the at least one simplex; and   forming a plurality of solutions within the novel simplex interior of the at least one simplex.   
     
     
         2 . The method of  claim 1 , wherein identifying the at least one simplex within the convex hull of the solution space is performed by adding a new simplex point that maximizes a hyperplane in a null space of a new simplex, wherein the new simplex is augmented by one dimension when the new simplex point is added. 
     
     
         3 . The method of  claim 1 , further comprising forming a simplex-decomposition-generating algorithm with the simplicial decomposition. 
     
     
         4 . The method of  claim 3 , further comprising applying the simplex-decomposition-generating algorithm to each of the at least one simplex. 
     
     
         5 . The method of  claim 4 , further comprising finding one or more interior points within each simplex from the novel simplex interior. 
     
     
         6 . (canceled) 
     
     
         7 . The method of  claim 1 , wherein the at least one threshold comprises a gradient slope differentiation threshold, a gradient offset differentiation threshold, or a partitioning differentiation threshold. 
     
     
         8 . The method of  claim 1 , further comprising, finding a solution-space-inscribed simplex within the solution novelty threshold. 
     
     
         9 . The method of  claim 1 , wherein the solution space is at least based in part on one or more inequalities. 
     
     
         10 . The method of  claim 9 , wherein the one or more inequalities are physical fluid gradient constraints. 
     
     
         11 . A system comprising:
 a downhole fluid sampling tool configured to obtain one or more pressure measurements at one or more depths; and   an information handling system configured to:
 form a depth-pressure measurement set from the one or more pressure measurements; 
 create a solution novelty threshold with a synthesis of at least one threshold; 
 generate a simplicial decomposition for a convex hull of a solution space up to the solution novelty threshold; 
 identify at least one simplex within the convex hull of the solution space; 
 determine a novel simplex interior of the at least one simplex; and 
 form a plurality of solutions within the novel simplex interior of the at least one simplex. 
   
     
     
         12 . The system of  claim 11 , wherein the information handling system is further configured to add a new simplex point that maximizes a hyperplane in a null space of a new simplex, wherein the new simplex is augmented by one dimension when the new simplex point is added. 
     
     
         13 . The system of  claim 11 , wherein the information handling system is further configured to form a simplex-decomposition-generating algorithm with the simplicial decomposition. 
     
     
         14 . The system of  claim 13 , wherein the information handling system is further configured to apply the simplex-decomposition-generating algorithm to each of the at least one simplex. 
     
     
         15 . The system of  claim 13 , wherein the information handling system is further configured to find one or more interior points within the novel simplex interior of each simplex. 
     
     
         16 . (canceled) 
     
     
         17 . The system of  claim 11 , wherein the system includes a gradient slope differentiation threshold, a gradient offset differentiation threshold, or a partitioning differentiation threshold. 
     
     
         18 . The system of  claim 11 , wherein the information handling system is further configured to find a solution-space-inscribed simplex within the solution novelty threshold. 
     
     
         19 . The system of  claim 11 , wherein the solution space is at least based in part on one or more inequalities. 
     
     
         20 . The system of  claim 19 , wherein the one or more inequalities are physical fluid gradient constraints. 
     
     
         21 . The system of  claim 19 , wherein the one or more inequalities are measurement constraints. 
     
     
         22 . The method of  claim 9 , wherein the one or more inequalities are measurement constraints.