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Definition of the reservoir permeability field according to pressure measurements on wells with the use of spline function

A.V. Elesin, A.Sh. Kadyrova, A.I. Nikiforov

Original article

DOI https://doi.org/10.18599/grs.2018.2.102-107

102-107
rus.
eng.

open access

Under a Creative Commons license

The problem of reservoir permeability identification based on known well pressures under conditions of single-phase fluid filtration is considered in the article. The permeability field is identified in the spline function class from the solution of the inverse coefficient problem for the filtration equation. The problem of identification is reduced to the problem of minimizing the residual function, having the form of a sum of squares of the difference between the pressure values known from measurements at the wells and obtained with the help of a numerical model. Minimization of the residual function is carried out by the Levenberg-Marquardt method. The solutions of model problems of permeability identification for a two-dimensional reservoir, penetrated by a system of production and injection wells, are presented. The calculated permeability fields are close to the true fields. The example of a problem with errors in pressure measurements shows the stability of the solution.
 

permeability identification, spline function, residual function
 

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Andrey V. Elesin
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of the Russian Academy of Sciences
2/31, Lobachevsky St., Kazan, 420111, Russian Federation

Alfiya Sh. Kadyrova
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of the Russian Academy of Sciences
2/31, Lobachevsky St., Kazan, 420111, Russian Federation

Anatoly I. Nikiforov
Institute of Mechanics and Engineering, FRC Kazan Scientific Center of the Russian Academy of Sciences
2/31, Lobachevsky St., Kazan, 420111, Russian Federation
 

For citation:

Elesin A.V., Kadyrova A.Sh., Nikiforov A.I. (2018). Definition of the reservoir permeability field according to pressure measurements on wells with the use of spline function. Georesursy = Georesources, 20(2), pp. 102-107. DOI: https://doi.org/10.18599/grs.2018.2.102-107