Model-based field development optimization typically requires a large number of simulations. Consequently, this process may face challenges as model size and complexities increase. The objective of this paper is to apply a reduced-physics model with response surface approach for replacing full field simulation runs to reduce the time and resources required during a search for optimal solutions. The streamline technique is used to develop a reduced-physics model in this study. There are number of previous studies that demonstrated the use of streamlines for production optimization (e.g. well placement and/or rate allocation optimization). In a recent work (SPE 187298), an approximate equation was formulated to estimate the expected economic value based on streamlines and was applied into rate allocation optimization of a given well pattern. Our approach is to use this formulation to improve the efficiency of field development optimization by potentially screening out poor performing development designs without performing full simulations. The streamline-based surrogate model workflow was first applied and validated using a synthetic SPE-10 case study. The workflow was then applied to the Olympus field waterflood study. The study goal is to maximize the economic value by optimizing the well count, injector and producer locations, and completion design. The validation performed using random field development designs provided a rank correlation coefficient of 0.92 between the NPV values of full field simulations and streamline-based approximation from the Olympus field application. The streamline-surrogate model was then adopted with an optimization workflow (Genetic Algorithm) and response surface method with 2-stage approach. First, Genetic Algorithm (GA) optimization was performed using the streamline-surrogate as an initial stage to screen out suboptimal field development design. Then, a second GA optimization was performed using full simulations coupled with the response surface method, starting with results from the first stage. Response surfaces that were developed using samples through GA improved the process of screening poor economic cases at later stages, as the predictability of solution improved with more training. We demonstrated that the streamline-based surrogate formulation combined with the response surface approach will improve the optimization process of field development scenarios. The applicability of using the response surface approach by itself is limited for field applications due to the large number of simulations required for training and the risk of convergence at local minima. Multiple tests from the Olympus field development application demonstrated that the sequential combination of streamline-based surrogate formulation with response surface method had the best performance.
Streamline-based history matching techniques have provided significant capabilities in integrating field-scale water-cut and tracer data into high resolution geologic models. The effectiveness of the streamline approach lies in the fact that parameter sensitivities can be computed analytically as one-dimensional integrals along streamlines and requires little additional computational overhead beyond the forward simulation. However, application of the streamline-based approach for simultaneous integration of water-cut and bottomhole pressure has been rather limited. This is partly because the convective streamlines appear to offer no particular advantage while computing parameter sensitivities for the bottomhole pressure data. This limits the utility of streamline-based history matching particularly for three-phase black-oil and compositional systems where the integration of pressure data is a requirement to accurately model reservoir depletion mechanisms. In this paper we first introduce a novel semi-analytic approach to compute the sensitivity of the bottomhole pressure data with respect to grid block properties. The approach takes advantage of the streamline trajectories and yields results that are comparable to sensitivities computed from adjoint methods, at a fraction of the computational cost. The bottomhole pressure sensitivities can be easily integrated with the water-cut, gas oil ratio or composition sensitivities for a joint inversion of pressure data using high resolution geologic models. An iterative least squared method (LSQR) is used to minimize a penalized objective function that includes the data misfit and appropriate ‘norm’ and ‘roughness’ penalty terms to preserve the prior model characteristics during the inversion. The proposed approach is well suited for both streamline and finite difference methods with access to streamlines, and has been generalized for application to three-phase and compositional systems by integrating water-cut, gas oil ratio, and bottomhole pressure data. We demonstrate the power and utility of our proposed method using synthetic and field examples. The synthetic examples include black-oil and compositional cases involving gas injection. The streamline-based sensitivities are compared with adjoint methods for verification purposes. We then apply the method to the Brugge benchmark case and the Norne field to demonstrate the practical feasibility of the proposed method.
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