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

Hosseini Mohammad

Acta Geophysica

2021

Vol. 69, no. 3

821--839

A dozen of inversion methods are applied and tested to estimate the permeability of the area where gas-fngering 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 fow 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, frst 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 fuid fow 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 diferent 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 feld simulation model in terms of rock and fuid properties, consider the inverted permeability model as further constraints for the reservoir history-matching of the oil feld, reconsider the factors involving the gas injection plan for the oil feld, and obtain insights for further feld development plans in other nearby oil felds.

New criterion of regularisation parameter choice in Tikhonov's method

Kojdecki M. A.

Biuletyn Wojskowej Akademii Technicznej

2000

Vol. 49, nr 1

47-126

This work presents methods of solving linear operator equations of the first kind in real Hilbert's spaces and is aimed to present a new criterion of parameter choice in Tikhonov's regularisation mthod. The Tikhonov method is developed here from smoothing functional with zero-order stabilising term. The properties of such regularisation method are briefly analysed. The convergence rates for sequences of regularised solutions of test source problem are estimated. The criteria of a-priori regularisation parameter choice are analysed.On this background the new criterion of a-posteriori parameter choice is presented and studied in detail. The numerical algorithm for practical application of the method is also proposed and analysed. The theoretical considerations are updated with an algorithm of olving Fredholm's integral equations of the first kind and with examples of numerical experiments with such equations.

W niniejszej pracy przedstawiono metody rozwiązywania liniowych równań operatorowych pierwszego rodzaju w przestrzeniach Hilberta; jej celem jest przedstawienie nowego kryterium wyboru parametru w metodzie regularyzacji Tichonowa. Metoda Tichonowa wyprowadzona jest tu od funkcjonału wygładzającego z członem stabilizującym zerowego rzędu. Oszacowano rzędy zbieżności dla ciągów rozwiązań zregulayzowanych testowego zadania o postaci źródłowej. Przeanalizowano kryteria wyboru parametru regularyzacji z góry. Na tym tle przedstawiono i zbadano szczegółowo nowe kryterium wyboru parametru z dołu. Zaproponowano i przeanalizowano numeryczny algorytm dla praktycznego zastosowania metody. Rozważania teoretyczne uzupełniono algorytmem rozwiązywania równań całkowych Fredholma pierwszego rodzaju i przykładami eksperymentów numerycznych z takimi równaniami.