Simple Zonation and Principal Component Analysis for Speeding Up Porosity and Permeability Estimation from 4D Seismic and Production Data

Simple Zonation and Principal Component Analysis for Speeding Up Porosity and Permeability Estimation from 4D Seismic and Production Data

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Abstract

Simple zonation and a mathematical transformation based on principal component analysis are used in a distributed computing environment for the estimation of porosity and permeability from production and 4D-seismic data, in the form of zero offset amplitudes and amplitude versus offset gradients. The parameter estimation problem is formulated as a least-squares minimization. The Gauss-Newton technique is used for this purpose which requires gradient information and derivatives are estimated numerically. The results show that with only a bound constraint the solution space cannot be properly limited, and therefore that the solutions found might not be geologically consistent. Although simple gradzone analysis can speed up the optimization, the resulting spatial distributions of porosity and permeability are not acceptable from a geological point of view. Principal component analysis gives us the opportunity to not only accelerate the optimization but also, by incorporating some more complex spatial constraints, to force the parameter estimation to honour geology. By considering both distributed computing and parameter space reduction techniques it is possible to apply the methodology presented to larger problems with practical relevance.
Content

Simple zonation and a mathematical transformation based on principal component analysis are used in a distributed computing environment for the estimation of porosity and permeability from production and 4D-seismic data, in the form of zero offset amplitudes and amplitude versus offset gradients. The parameter estimation problem is formulated as a least-squares minimization. The Gauss-Newton technique is used for this purpose which requires gradient information and derivatives are estimated numerically. The results show that with only a bound constraint the solution space cannot be properly limited, and therefore that the solutions found might not be geologically consistent. Although simple gradzone analysis can speed up the optimization, the resulting spatial distributions of porosity and permeability are not acceptable from a geological point of view. Principal component analysis gives us the opportunity to not only accelerate the optimization but also, by incorporating some more complex spatial constraints, to force the parameter estimation to honour geology. By considering both distributed computing and parameter space reduction techniques it is possible to apply the methodology presented to larger problems with practical relevance.

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