Dynamic water flood optimization with smart wells using optimal control theory

During the oil production process water is generally injected into the reservoir to maintain reservoir pressure and to displace the oil towards the production wells. Ideally, as the production process continues the injected water will slowly move through the reservoir in the direction of the producers, in the meantime sweeping the oil in between. However, because the rock properties vary spatially, the displacement generally does not occur uniformly. There may be preferential, high permeability flow paths through which the injected water channels to the producer. Oil outside these channels may as a result not be displaced by the injected water. Because of this non-uniform displacement water production often starts at an early stage. With conventional wells there is little that can be done to remedy this early water production without significant costs. This early water production can also hardly be prevented, because identification of possible preferential flow paths is difficult due to the reservoir's limited accessibility. As a result of the uncertainty and the lack of control on the production process typically only a relatively small percentage (30-40 percent) of the oil present in the reservoir can be recovered economically. Hence, the world's recoverable reserves may be increased if a larger percentage of oil can be recovered from the reservoir. In de last few years a variety of technologies to better measure and control the production process through the wells have been developed. These technologies are typically installed within the well and they can be operated remotely. A well equipped with this type of measurement and control technology is generally referred to as a smart, intelligent or instrumented well. With down-hole control valves and isolating packers a well can be split up in segments that can be controlled separately. This enables an increased control on fluid flow into or out of the well. By manipulating the valve-settings it is to some degree possible to change the pressure distribution and thereby the fluid flow direction in the reservoir. The objective of this thesis work is to examine if by doing this it is possible to increase the percentage of oil recovered from the reservoir. An important part of this study comprises the calculation of the valve-settings that will optimize the net present value of the displacement process. To be able to do this for various reservoirs a numerical reservoir model was used, instead of a real reservoir. The calculation of the optimal valve-settings was done with a gradient-based optimization routine, the derivative information was calculated with optimal control theory. The results show that significant improvement in the water flooding process can be achieved by dynamically controlling the valve-settings in the injection and production wells. In fields equipped with smart wells this is realized by controlling the down-hole valves, in fields equipped with vertical conventional wells by controlling the valves at the surface. The degree of improvement depends on the fluid properties and on the spatial variation in the rock properties. The scope for improvement also depends on constraints on the well operating conditions, it generally increases with increasing pressure available to inject or produce fluids. In addition the scope for improvement depends on the relative well locations, because these partly determine to what extent the fluid flow direction in the reservoir can be affected. The improvement partly results from the fact that through dynamic flow control the negative impact of geological features can be mitigated. Because the rock properties are poorly known in reality, the displacement optimization must be calculated based on estimated reservoir properties. We investigated if significant improvement in the water flooding process can also be realized if some of the reservoir properties must be estimated from production data. To this end the gradient-based optimization routine was combined with an ensemble Kalman filter data-assimilation method, developed in RFRogaland Research. The Kalman filter was used to frequently update the estimated pressure-, saturation, and permeability distribution in the reservoir, based on production data. After each update of the reservoir model, the optimum valve-settings were recalculated for the remaining producing period. First results indicate that significant improvements may be possible with this closed-loop approach.Civil Engineering and Geoscience