The paper introduces new results regarding the spectral approach to geological modelling which extends it by providing means to involve data on horizontal wells in the process of spectral simulation. An analytical algorithm for conditioning random fields of 3D geological property simulated by the spectral method on horizontal wells data is described. The algorithm is based on generalization of kriging and two-step conditioning of stationary stochastic fields, based on that generalization. Numerical algorithms are provided for analytical derivations and implemented in program code in order to assess practical applicability of the method.
In order to demonstrate efficiency of the new method two models of sand distribution for a reservoir containing significant number of horizontal wells were simulated. The first one was simulated by means of conventional spectral approach, based only on vertical wells, and the second one was simulated by new method, based on all wells, including horizontal ones. Comparison of the two models showed that the second model, while preserving statistical characteristics of the well data as good as the first model, precisely reproduced data along horizontal well, thus increasing prognostic ability of the geological model. The results presented in the paper eliminate one of the main limitations of the spectral approach to geological modelling and significantly widen its practical application scope.
1. Baykov V.A., Bakirov N.K., Yakovlev A.A., New methods in the theory of geostatistical modelling (In Russ.), Vestnik Ufimskogo gosudarstvennogo aviatsionnogo tekhnicheskogo universiteta, 2010, V. 14, no. 2 (37), pp. 209-215.
2. Baykov V.А., Bakirov N.K., Yakovlev A.A., Matematicheskaya geologiya (Mathematical geology), Part 1. Vvedenie v geostatistiku (Introduction to geostatistics), Moscow – Izhevsk: Publ. of Institute of Computer Science, 2012, 228 p.
3. Khasanov M.M., Belozerov B.V., Bochkov A.S. et al., Application of the spectral theory to the analysis and modelling of the rock properties of the reservoir (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2014, no. 12, pp. 60–64.
4. Ismagilov N.S., Lifshits M.A., Conditioning spectral simulation method by horizontal well data, Proceedings of ECMOR XVI-16th European Conference on the Mathematics of Oil Recovery, 2018. – http://earthdoc.eage.org/publication/result?edid=561