A chemical compaction model for sandstone

Abstract

A method for modeling compaction in a reservoir including obtaining a profile of vertical burial depth, a profile of effective stress against the vertical burial depth, and approximating a plurality of rock grains with a hexagonal closed-packed arrangement of spheres to estimate compacted mechanical and chemical porosity profiles.

What is claimed: 
     
         1 . A method of modeling compaction in a reservoir, comprising:
 obtaining a profile of vertical burial depth against geological time within a subterranean region;   obtaining a profile of effective stress against the burial depth within the subterranean region;   approximating a plurality of rock grains in the subterraneous region with a hexagonal closed-packed arrangement of spheres having an approximated radius;   estimating a compacted porosity profile against the vertical burial depth for porosity greater than or equal to a threshold, using a mechanical compaction model incorporating the effective stress; and   estimating the compacted porosity profile against the vertical burial depth for porosity less than the threshold, using a chemical compaction model incorporating the geological time, the effective stress, and the arrangement of rock grains.   
     
     
         2 . The method of  claim 1 , wherein obtaining the effective stress comprises obtaining an average burial loading density for the subterranean region and determining an effective stress based on, at least in part, the vertical burial depth, a constant gravitational acceleration, and the average burial loading density. 
     
     
         3 . The method of  claim 1 , wherein the mechanical compaction model incorporates a depositional porosity, an exponential rate of porosity decline with effective stress, an initial proportion of matrix material, and a porosity of a stable packing configuration. 
     
     
         4 . The method of  claim 1 , wherein approximating the plurality of rock grains comprises obtaining the approximated radius. 
     
     
         5 . The method of  claim 4 , wherein obtaining the approximated radius comprises measuring an average size of core rock grains in a core sample from a well in the subterranean region. 
     
     
         6 . The method of  claim 1 , wherein the chemical compaction model incorporates calculating a removed thickness based on, at least in part, the threshold porosity and the approximated radius. 
     
     
         7 . The method of  claim 6 , wherein the chemical compaction model further incorporates iterating determining an additional removed thickness based on, at least in part a time differential, the effective stress, and the approximated radius; adding the additional removed thickness to the removed thickness to obtain an updated removed thickness; and determining a value of compacted porosity based, at least in part, on the updated removed thickness. 
     
     
         8 . The method of  claim 7 , wherein determining the additional removed thickness comprises determining a radius of a grain contact surface, a removed thickness due to dissolution at the grain contact surface, and an overgrowth thickness due to precipitation. 
     
     
         9 . The method of  claim 8 , wherein the overgrowth thickness due to precipitation is based on the approximated radius and the removed thickness according to a volume conservation relationship. 
     
     
         10 . The method of  claim 7 , wherein the additional removed thickness is further based on, at least in part, a strain rate, based, at least in part on the effective stress and the approximated radius. 
     
     
         11 . The method of  claim 10 , wherein the strain rate is further based on, at least in part, the removed thickness, the radius of a grain contact surface, the radius of a grain within the rock, and a diffusivity. 
     
     
         12 . The method of  claim 11 , wherein the diffusivity is determined based on a diffusivity constant extrapolated to infinite temperature, an activation energy, a universal gas constant, and an absolute temperature. 
     
     
         13 . The method of  claim 12 , further comprising obtaining profile of temperature against the geological time and determining the absolute temperature from the profile of temperature. 
     
     
         14 . A method of extracting petroleum from a reservoir, comprising:
 drilling a well in the reservoir;   modeling compaction in the reservoir according to  claim 1  to obtain the compacted porosity profile; and   adjusting a parameter of producing the petroleum from the well based on the compacted porosity profile.