Reservoir management uses the geological and petroleum engineering knowledge to predict and maximize the future production of the oil and gas reservoirs. Finding an optimal production strategy has always been a key task in reservoir...
moreReservoir management uses the geological and petroleum engineering knowledge to predict and maximize the future production of the oil and gas reservoirs. Finding an optimal production strategy has always been a key task in reservoir management. The main aim is to determine the most cost-effective strategy to develop a new field or to optimize the production from an existing field using improved oil recovery methods. Through the use of a suite of technologies, including remote sensors and reservoir simulation, reservoir management can improve the well placement as well as well controls (production/injection rates) and increase the total amount of hydrocarbons that is ultimately recovered from a field.
Most optimized strategies are model-based and are effective if the model predicts the future reservoir behavior correctly. The updated reservoir models are used to determine the best field development and production plan in the future. Traditionally, this task was done manually by a large number of trials and errors. During the last few years, a number of optimization strategies were developed to assist this decision making process, e.g. well placement optimization or rate optimization in a given well configuration. The optimization problem requires the maximization of net present value, or recovery factor, by manipulation of some parameters in the reservoir system, e.g. well location, liquid production/injection rates or valve settings in an on/off mode. These parameters are usually subject to some limitations (also known as constraints) due to operational conditions, surface process facilities etc. These constraints pose substantial complication while solving the optimization problem. Although production optimization can be applied to any kind of recovery method in the reservoir, most of the works focus on optimizing the reservoir performance under waterflooding. The most important reason is that waterflooding is the most widely applied improve recovery method among the secondary and tertiary recovery methods in the oil reservoirs.
The injected water may reach from the injectors to the producers without touching a large region of the reservoir, thus resulting to a low recovery factor. Intelligent or smart wells are equipped with downhole valves to control the fluid flow from the reservoir to the well and sensors to monitor the downhole pressure and saturation changes. This technology has the capability to significantly improve the recovery from the reservoir. Determination of the optimal rates, or valve settings, is the main challenge in the intelligent fields.
The main focus of this thesis was finding an efficient workflow to determine the optimal production/injection strategy for a reservoir waterflooding project in a given well configuration. A comparative closed loop reservoir management exercise was performed in connection with the SPE Applied Technology Workshop in Brugge June 2008. The model used in this exercise was a synthetic reservoir with typical geological features of North Sea fields and considerably larger than those used in most previous studies. The Brugge model was used to explore a cost-effective workflow for waterflooding of an intelligent oil field. The effect of a proper formulation on the waterflooding optimization problem was investigated and two different formulations were presented.
In the first formulation, the production/injection rates of producer/injector completions were selected as the optimization variables to maximize NPV value of the Brugge field. In the original Brugge optimization problem, the parameters were asked to be updated on monthly basis (20,160 variables). In this thesis, these variables were optimized monthly and every 6 months (3,360 variables), depending on the memory requirements of the chosen optimization algorithms. For the steepest descent and conjugate gradient methods, the variables were updated on monthly basis. For the interior point and active set methods the variables were optimized every 6 months. The optimization constraints were maximum production/injection rates and minimum/maximum production/injection bottomhole pressures in each well. The adjoint approach in combination with a multiscale estimation technique was proposed to solve the rate formulation. The main advantages of the multiscale optimization were acceleration of the optimization process and increasing the chance of finding a better optimal solution. Gradient based algorithms were used to utilize the adjoint gradients for finding an optimal solution. Different gradient based optimization methods, interior point and active set algorithms were evaluated for the adjoint optimization solution. Among the gradient based optimization algorithms, the active-set method outperformed all other methods used in this thesis. The multiscale optimization approach improved the computational efficiency of the optimization algorithms for initial optimization iterations. Combination of the multiscale optimization with interior-point algorithm accelerated the optimization process and improved the quality of the obtained optimal point by this method.
In the second formulation, the shut-in water-cuts were proposed as the optimization variables to maximize NPV. The optimal injection strategy was chosen to be the unity voidage replacement ratio, to maintain the reservoir pressure. The decision was to close the completions producing too much water by optimizing the maximum water-cut level. This formulation efficiently reduced the number of variables to 54 parameters, which was the number of initially open completions in the production wells, and avoided optimizing on the high dimensional rate optimization problem. The optimization constraints were changed to simple upper and lower bounds on water-cuts and the production/injection rate & pressure constraints were handled by the reservoir simulator. A guide rate approach was presented to distribute the production rates between the producers to penalize the production from the completions with higher water-cut values. Due to the existence of the noise in the finite difference gradients, several derivative free optimization algorithms were used to optimize the shut-in water-cuts: pattern search Hooke-Jeeves, reflection simplex Nelder-Mead, a generalized pattern search method and a line search derivative free method. Here, the line search derivative free method was developed based on an existing line search derivative free algorithm in combination with Hooke-Jeeves method. The fractional ranking method was utilized to rank the performance of these algorithms based on the convergence rate of the methods and the quality of the objective function in the optimal point. Among these methods, the developed line search derivative free was the most efficient and the highest NPV value was achieved by both Hooke-Jeeves and line search derivative free methods. Overall, the line search derivative free method performed better than the other derivative free methods used in here.
Comparing two above mentioned formulations, high optimal NPV values were achieved, on the history matched model used in this thesis: 4.52 B$ & 4.54 B$ for the adjoint and guide rate approaches respectively. Based on the reactive case in Peters et al. (2010), the obtained NPV on the same history matched model was 3.94 B$. The NPV were improved approximately 15%, assuming the reactive control as the base case. Also, the average reservoir pressure was compared for the optimal solutions from these two approaches. In the guide rate approach, the main aim was reservoir pressure maintenance all through the life of the reservoir to maintain the performance of the waterflooding project. The adjoint solution suggested repressurization of the reservoir in the beginning and cutting the field injection rate in the end of the optimization horizon, which is not advisable in practice. In terms of availability of computing resources, the memory requirement for the guide rate approach is trivial and for the adjoint optimization it is dependent on the size of the optimization problem (number of variables) and the choice of the mathematical algorithm. It is simple and easy to implement the guide rate approach for every single reservoir simulator, while the implementation of the adjoint approach is a major programming effort and requires a proper knowledge of the reservoir simulator.
