The purpose of this research is to determine an actual optimal solution through cyclic optimization of CO2-Gas Assisted Gravity Drainage (GAGD) process in a heterogeneous sandstone reservoir under geological uncertainties. We propose an integrated approach to optimize durations of gas injection, soaking, and oil production under geological uncertainties. Therefore, 100 stochastic reservoir realizations of the 3D permeability and porosity distributions were created honouring geological constraints. Ranking was applied through quantifying of reservoir oil response to select P10, P50, and, P90 that represent the overall reservoir uncertainty. More than 400 training simulation runs were created including the durations and geological uncertainty parameters through Latin Hypercube Design to build the second-order proxy model along with approximately 200 extra verification runs. The verification runs led to keep the solutions in global optima and obtain satisfactory proxy model through an iterative validation procedure. The cyclic optimization has shown its feasibility to increase oil recovery through the GAGD process from 71.5% to 75.5% with incremental cumulative oil production of 225 million barrels. The presented robust optimization workflow under geological uncertainties led to higher recovery factor than nominal realization optimization with providing degrees of freedom for the decision-maker to significantly reduce the project risk. @en

In this paper, we present a methodology to condition the prior probability field of the facies to the facies observations collected at the well locations. The prior probability field of the facies usually comes from seismic inversion and the facies observations are the result of the examination of the cores extracted at the well locations. Consequently, the prior probability field is not directly conditioned to facies observations. The presented methodology relies on a regularized form of the element-free Galerkin (EFG) method. The regularization has been introduced in order to account for the prior, whereas the EFG is an interpolation technique with a moving least squares criterion. The methodology presented here consistently updates the prior probability field of facies with the facies data collected at some locations in the reservoir domain. We present two case studies: one in which hard facies data are considered and a second where hard and soft facies observations are involved in the conditioning.@en

Prior to any estimation process of channelized reservoirs, in the context of an Assisted History Matching method, the parameterization of facies fields is a necessary task. The parameterization of channelized reservoirs consists of defining a numerical field (parameter field) so that a projection function recovers the facies field from the parameter field. Mostly, the dimension of parameter field is equal to the dimension of reservoir domain. The issue of dimensionality is becoming relevant when the history matching method is applied, especially due to the tremendous number of parameters involved in the estimation process of the channelized reservoirs. In addition, one of the most important issue encountered is the loss of the multi-point geostatistical properties in the updates (channel continuity). In this study, we start from an initial parameterization of the channelized fields and infer from it a low-dimensional parameterization obtained after a high order singular value decomposition of a tensor built with the parameter fields. We show how the facies fields are fully characterized by a linear combination of a small number of coefficients with "basis functions". The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective. This new parameterization is further introduced in the estimation process of facies fields, using the ensemble smoother with multiple data assimilation (ES-MDA), updating the coefficients of decomposition. For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional singular value decomposition and the original parameterization. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions (oil and water rates). We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other two parameterizations, while the prediction capabilities are the same.@en