Proxy-Based Metamodeling Optimization of the Gas-Assisted Gravity Drainage GAGD Process in Heterogeneous Sandstone Reservoirs
Authors: Al-Mudhafar Watheq J. , Rao Dandina N. 
Published: April 2017

Abstract
Unlike these Continuous Gas Injection (CGI) and Water-Alternating-Gas (WAG) injection modes, the Gas-Assisted Gravity Drainage (GAGD) process takes advantage of the natural segregation of reservoir fluids to provide gravity-stable oil displacement. Specifically, the gas is injected through vertical wells to formulate a gas cap to allow oil and water drain down to the horizontal producer (s) and that would lead to improving oil recovery. Therefore, the GAGD process was implemented through immiscible injection modes to improve oil recovery in a sector of the main pay/upper sandstone member in the South Rumaila oil field, located in Iraq. Design of Experiments (DoE) and Proxy Modeling were adopted to obtain the optimal future oil recovery through the GAGD process.
The CO2-GAGD process feasibility was investigated for the immiscible injection mode through the EOS-compositional reservoir simulation with Design of Experiments and Proxy Modeling to obtain the optimal future performance scenario. After conducting the acceptable history matching, the Latin Hypercube Sampling (LHS) was employed as a low-discrepancy and more uniform DoE approach to create hundreds of simulation runs (experiments) in order to construct a proxy-based optimization approach. More specifically, the proxy model represents a metamodel used to evaluate the various designed experiments in the optimization procedure rather than the simulator itself. Then, the second-order polynomial equation was iteratively constructed and validated based on the least mismatch between the oil response calculated by the proxy model and by the simulator. The optimization process searches for the optimal future oil recovery by optimizing the levels of the operational decision factors, which constrain the production and injection activities. These decision factors include maximum oil production, minimum BHP, maximum water cut, and skin factor in the production wells in addition to the maximum gas injection rate and maximum injection pressure in the injection wells. The cumulative oil production was handled as the response parameter that is initially calculated by the compositional reservoir simulation for 10 years of future prediction. The optimal cumulative oil production, by the end of the prediction period, led to obtaining 4.6039 MMMSTB of oil production, while the base case of the GAGD process evaluation of default parameters setting resulted to obtain 4.3887 MMMSTB of oil production. Therefore, the current optimization approach has led to increasing the oil recovery by 215.2 million STB in 10 years of future prediction.
The polynomial proxy model was re-validated in a different procedure in comparison with three more proxy models: Multivariate Additive Regression Splines, Fuzzy Logic-Genetic Algorithm, and Generalized Boosted Modeling. The validation procedure integrates cross-validation with Root Mean Square Error to find the optimal proxy model that can be considered as a perfect metamodel for the nonlinear CO2-EOR flooding through the GAGD process. For the least mismatch obtained between the simulator- and proxy-based cumulative oil production, each of GBM and FUzzy-GEnetic can be adopted as an accurate simplified alternative metamodel to the full resolution compositional reservoir simulator through the GAGD Process evaluation and prediction.