| In modern reservoir management, optimizing the recovery efficiency of displacement processes is a fundamental problem with important economic ramifications. Given a well configuration, the optimum displacement efficiency may be achievable through controlling injection rates. Smart wells and intelligent completion have gained significant attention in recent years in the field of dynamic optimization of Enhanced Oil Recovery processes. Implementing separate downhole control valves enables the application of optimal rate control in real time, through the appropriate valve settings in injection and production wells. In this thesis, we consider a fundamental question in rate-control flow problems, namely the control of a displacement front via flow-rate partition in a horizontal well.;The specific question we address is how to partition the flow rate within the well, so that the displacement front can be steered according to pre-determined dynamics, or as is necessary. The ability to steer a front at will is of obvious significance. Given the reservoir geology, one can for example, steer the front away from flow obstacles, affect a piston-like displacement in heterogeneous formations or otherwise control the displacement process as needed.;The objective of this thesis is to investigate the steering of the front by partitioning the injection rates along the well. First, the problem is addressed in a simple rectangular geometry based on potential flow. It is assumed that the flow is potential and that the displacement is at a unit mobility ratio. These assumptions are for mathematical convenience only and can be relaxed. They allow, however, significant insight into the problem. When the reservoir is homogeneous and isotropic, an integral equation in an analytical form is derived, the solution of which determines the desired injection rate profile. A similar approach applies for an anisotropic or a heterogeneous system, except that the kernel in the integral equation must be determined numerically. This is done either by repeated calculations of the Green's function in a heterogeneous system or for a modified two well system. For the solution of the integral (Fredholm) equation, a regularization technique is necessary. However, it is found that numerical instabilities do develop, even with the use of regularization, for later times, when transverse cross-flow is large. Conversely, the instabilities diminish with a more stratified structure. The application of the technique is highlighted and extended to heterogeneous systems where its complexity and the solution were studied. Also in a forward displacement problem, the effect of rate fluctuations on the front dynamics were analyzed in a semi-infinite porous media. We considered the special case of injection rate with one harmonic term. It was found that the front is less sensitive to the fluctuations in rate for larger harmonic terms.;The results of this study find applications to the rapidly emerging field of smart wells and the optimization of displacement problems in oil reservoirs using flow rate control. |
