Smart wells provide great potential to improve the recovery from hydrocarbon resources. Smart wells provide the ability to control uncertainties associated with reservoir heterogeneity. One example is to mitigate unexpected water production due to fractures and hence increase the ultimate recovery. This is achieved by selectively controlling production from multiple laterals. Due to subsurface communication between laterals that have different productivity indices, it is difficult in practice to optimize production from smart wells. The optimization of smart wells involves adjusting parameters including the settings of the downhole inflow control valves (ICV) that act as subsurface chokes.This paper focused on the reservoir engineering aspects of finding the optimum ICV configuration that optimizes reservoir performance parameters such as recovery factor and net present value. Also, the work studied the effect of heterogeneity, mainly fractures, on the optimization process. This paper also proposes a technique to quantify the effect of fractures on the optimization process and to provide recommendations of further analysis.Genetic algorithm (GA) was used as the main optimization engine to find the optimum ICV configuration. The GA was accompanied by a data library (proxy) to reduce the number of required simulation runs. A commercial reservoir simulator was used as the objective function evaluator that assesses the outcome of candidate ICV configurations.Several examples are presented to show the improvement in reservoir performance made using the optimization process. These examples include a synthetic model, and a real onshore model. Various objective functions were optimized such as water cut, and net present value. IntroductionWell design and planning have advanced tremendously during the last two decades, from the use of conventional vertical wells to nonconventional horizontal wells (NCWs) using directional drilling technology. Nonconventional wells range from simple horizontal wells with single wellbore to complex multilaterals with multiple sublaterals (fishbone wells).Nonconventional wells offer more cost-effective alternatives to conventional wells in terms of drilling, completion, surface equipment, and long-term operation costs. Production targets are achieved with fewer nonconventional wells as they provide better reservoir exposure. From a reservoir management point of view, nonconventional wells improve the productivity index (PI) by maximizing reservoir contact, minimizing water coning by operating at lower drawdown, and increasing sweep efficiency by distributing production along the horizontal section.A 'smart' or 'intelligent' well is considered one of the most advanced types of nonconventional wells. A typical smart well is equipped with a special completion that has packers or sealing elements that allow partitioning of the wellbore, as well as pressure and temperature sensors and downhole inflow control valves (ICV) installed on the production tubing, Figure 1. The sensors allow continuous m...
Reduced-order models (ROM) are considered powerful techniques to address computational challenges associated with reser-voir management decision-making. In this sense, they represent perfect alternatives that trade off accuracy for speed in a controllable manner. In this paper, we describe a model-order reduction technique that entails the use of proper orthogonal decomposition (POD), truncated balanced realization (TBR) and discrete empirical interpolation (DEIM) to accurately re-produce the full-order model (FOM) input/output behavior. POD allows for a concise representation of the FOM in terms of relatively small variables while TBR improves the overall stability and accuracy. DEIM improves the shortcomings of POD and TBR in the case of nonlinear PDEs, i.e.; saturation equation, by retaining nonlinearities at lower dimensional space. In this work, the use of ROM reduced the computational time by O(100) while providing good overall agreement with FOM. The use of large reservoir simulation models is expected to add additional speedup factors. ROMs are potentially perfect alternatives to FOMs in reservoir management intensive studies such as production optimization. However, ROMs presented in this paper and the overall physics-based ROMs have the tendency to perform well within a restricted zone. This zone is generally dictated by the training simulations used to build the ROM. Therefore, special care is considered when implementing these training runs. To mitigate the heuristic process of implementing the training runs, we apply a ROM based trust-region method that provides an adaptive framework to systemically retrain ROM during the optimization run. The ROM approach with trust-region methodology is applied to a heterogeneous model containing 13,200 grid blocks and five wells. The accuracy of the ROM is first demonstrated for several testing simulations in which the injection and production rates for each well differ from those used to build the ROM. A waterflood optimization case is then considered to determine the optimum injection and production rates for four producers and one injector at five different times (total of 25 control variables). Results for optimized net present value using ROM based trust-region is shown to be very close to those achieved using the full order model with a difference of only 0.2%. The runtime speedup factor for this case was about 31. The ROM approach thus appears to be well suited for use in applications in which many simulations must be performed such as production optimization and uncertainty assessment.
For applications of numerical reservoir simulators such as production optimization or uncertainty assessment, hundreds or thousands of reservoir simulation runs must be performed. Such huge computational cost is a major problem in petroleum engineering, and reduced-order model (ROM) based on proper orthogonal decomposition (POD) has been intensively studied in recent decade to overcome it. While POD-based methods have been shown to be efficient compared to full order model (FOM), it is not as efficient when it is applied to a typical large dimensional nonlinear reservoir system. One of the reasons for the inefficiency is that in a typical nonlinear reservoir system ROM based only on POD is still dependent on the dimension of FOM. This is due to the fact that to compute the reduced nonlinear term in mass balance equation of a reservoir system, one must first reconstruct the full-order state solution such as pressure and saturation, evaluate the full-order nonlinear term before projecting it onto a reduced subspace. Therefore, we developed a reduced-order reservoir model based on a discrete empirical interpolation method (DEIM) to approximate nonlinear phase potential terms so that the repeated online evaluations of the ROM in Newton iteration are independent of full-order dimension. The independence comes from the fact that DEIM just needs to evaluate the nonlinear term only at interpolation indices that represent grid blocks that are important in terms of preserving the continuity properties of the mass balance equation. A case study was carried out to investigate the performance of DEIM compared POD. Although the testing schedule of well controls is far apart from the training schedule of well controls, close matches are obtained. Thus, the ROM using DEIM is expected to enable the practical application of reservoir simulator, such as production optimization in which many simulation runs must be performed, in a reasonable time frame by significantly relieving the required numerical effort.
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