Using total variation method to estimate the permeability model of a gas-fingering area in an Iranian carbonate reservoir

Abstract

A dozen of inversion methods are applied and tested to estimate the permeability of the area where gas-fingering event has taken place in an Iranian carbonate reservoir located southwest of Iran. In a previous work, the gas-fingering event was detected by inverting the 3D seismic data and in this study the permeability model in that area is estimated. Because the lateral area of the gas-fingering event is narrow, the whole system conducting the injected gas can be considered as one rock unit system and therefore the assumption of horizontal linear steady-state flow can be applied. Inversion methods are exploited to determine the permeability in the interval of interest. The interval of interest is located at the crest and involves four wells among which one is the gas-injection well. To investigate the feasibility of such an approach and select the best possible inversion method, first a controlled experiment for the system is designed and studied. The porosity values of the system are known from seismic data inversion and the permeability values are the desired parameters. The permeability values at well locations are known via well-test data and are used as constraints in the inversion procedure. The interval of interest is discretized and a simulator is used to simulate the fluid flow in the controlled system in order to apply and validate the inversion methods. All calculations are performed in the MATLAB environment. According to the results from the controlled experiment, the Maximum Entropy and Total Variation methods were found to be the best two inversion methods which were successful in retrieving the true permeability model. Similar comparative study using different inversion methods is performed for the real case for which the results retrieved by the Total Variation method is most reliable as it suggests the best recovery of the permeability value for the check-well. An estimation of the fracture permeabilities for the area under study also indicated that the inverted permeability values are most representing the fracture permeabilities rather than the matrix. The results of this study will be used to tune the field simulation model in terms of rock and fluid properties, consider the inverted permeability model as further constraints for the reservoir history-matching of the oil field, reconsider the factors involving the gas injection plan for the oil field, and obtain insights for further field development plans in other nearby oil fields.