Waterflooding Optimization Using Gradient Based Methods

Abstract

Abstract Finding the best strategy for production optimization is currently an important research task for closed-loop reservoir management. The closed-loop reservoir management consists of two main tasks: history matching and production optimization. A comparative closed loop reservoir management exercise was performed in connection with the SPE Applied Technology Workshop "Closed-loop reservoir management" in Bruges June 2008. The model used in this exercise was a synthetic reservoir with typical geological features of Northern Sea fields and considerably larger than those used in most previous studies. In a previous work (Lorentzen et al., 2009), a set of history matched models were obtained using the ensemble Kalman filter. We will use these models to investigate the effect of formulation and initial guess on gradient based optimization methods. Within production optimization, most of the works are focused on optimizing the reservoir performance under waterflooding. We will review the waterflooding optimization studies so far. The mathematical theories of an optimization problem as well as the practical issues regarding reactive and proactive approaches are discussed. The formulation of a waterflooding optimization problem is investigated using three different optimization variables: bottomhole pressure, oil and liquid production rates. Results show that proper formulation improves the performance of gradient based methods considerably. Then it is verified that manual optimization of the initial guess based on reservoir concepts enhances both the result and efficiency of the gradient based optimization. The manual optimization saves the gradient based methods from a number of local optima and also decreases the simulation costs substantially. Two line search methods, steepest descent and conjugate gradient, are used and compared in the adjoint based optimization approach. The conjugate gradient acts slightly faster than the steepest descent method. However, the selection of a proper initial guess is far more important for the performance. Finally, the optimal solution is applied on ten more history matched realizations to check the robustness of the solution. It is shown that the well liquid rates are the best variables used for maximizing the net present value using gradient based optimization. In previous works, well bottomhole pressure has been suggested. Introduction Reservoir management, as a practical science, uses elements of geology and petroleum engineering to predict and optimize the future production of the oil or gas fields. The goal is to determine the most cost-effective strategy of developing a new field or to bring new life to an older field with enhanced oil recovery methods. Through the use of a suite of technologies, including remote sensors and simulation modeling, reservoir management can improve production rates and increase the total amount of hydrocarbons that is ultimately recovered from a field. Closed loop reservoir management (CLRM) is defined as "a combination of model-based optimization and history matching (or data assimilation), also known as real time or smart reservoir management, closed loop optimization or self learning reservoir management" (Jansen et al., 2009). Recently, growing attention has been given to the closed loop approaches in the industry with different names as smart fields, i-fields, e-fields, field of the future, digital fields, next generation fields or integrated operations (see e.g. Jansen et al., 2005; Unneland et al., 2005; Red-dick, 2006). The main elements of the CLRM process are shown in Figure 1. The physical system consists of the reservoir, wells and facilities, each of these represented by models. The main task of the data assimilation is to update the reservoir mod-els based on the measurements, whereas reservoir optimization is concerned with finding the best production strategy for the producing field based on these updated models. The CLRM is well described elsewhere (Jansen et al., 2009). In this work, we will focus on the optimization task in the context of the CLRM.