No abstract

Experiments on the instability of the interface in two-phase displacements in Hele-Shaw cells were conducted using air and a viscous oil as the working fluids. The experiments had two objectives: (i) to provide quantitative measurements of the growth constants of the instability which occurs when a less-viscous fluid displaces a more-viscous one, and (ii) to compare the measured dispersion relations with the predictions of the recent theory of Park & Homsy (1984). The experiments were made by analysing the growth characteristics of between 10 and 20 Fourier modes describing the shape of the interface between displaced and displacing fluids, using still photography. For capillary numbers Ca = μU/γ less than approximately 4 × 10−3 the agreement is only fair, owing to substantial edge effects produced by a nearly static contact line near the lateral boundaries of the cell. For 4 × 10−3 < Ca < 1 × 10−2 theory and experiment agree to within the accuracy of the measurements. Location and verification of the behaviour of modes near the predicted cut-off wavenumber give partial verification of the theory of Park & Homsy.

The stability of the displacement of a viscous fluid in a porous medium by a less viscous fluid containing an additive is considered. For the case in which the total amount of injected additive is fixed, a theory has been formulated to find the graded mobility profile which minimizes the instability due to an adverse mobility ratio. The result is a constrained nonlinear eigenvalue problem in which the mobility ratio of the fluids, a, and the total dimensionless amount of additive, N , appear as parameters. Estimates show N is typically large for practical situations. An asymptotic solution for large N is developed which shows that the optimal mobility profile is always an exponential curve at leading order. It is shown that although the optimal mobility profile is nearly exponential, the optimal concentration profile is not necesarily so, contrary to previous suggestions in the literature. Furthermore, it is shown that, unlike the case of a mobility jump, a graded mobility process under optimal conditions has amplifications independent of displacement velocity. We also discuss a possibile stabilization mechanism due to the very long wavelength disturbances which occur under optimal conditions.

The paper presents a process for determining optimal subsurface locations for producing and injecting wells in a field to improve reservoir performance and value. The process is illustrated by optimizing well locations in an initial development planning context. The process involves planning a set of wells on a static reservoir model using an automated well planner. These locations are then optimized with dynamic flow simulation to achieve higher recovery or economic benefit. In this work, we present the framework for optimizing many well locations simultaneously, with reservoir simulation and economic analysis. This method is demonstrated byapplying it to a field-scale simulation model with water injection. Introduction Forecasting optimal number, type, subsurface locations, and design parameters for a new set of wells, considering field uncertainty, is a complex and often a time-consuming set of challenges for field development planning. But it is a necessary and critical part of the field development planning workflow. Sub-optimal decisions on the number of wells, the size and configuration of platforms, the processing capacity of facilities, etc which are made early in the field life may constrain field operations for years. The problem is often addressed through a tedious process of locating one well at a time in a static model, and then validating a set of well locations through case studies with reservoir simulation; then repeating this process until some convergence to a "good" set of wells is reached. With only a small number of cases investigated, there may be little confidence by an asset team that an overlooked alternative could be more attractive. Previous reseachers have proposed using mathematical optimization on this problem. All previous work recognized that the well location problem is a highly combinatorial, nonlinear optimization problem with integer variables. Early work experimented with integer programming[1,2] and ranking on static reservoir models[3]. Beckner and Song[4] used simulated annealing optimization with reservoir simulation, and Seifert et al[5] used exhaustive sampling and uncertainty analysis with simulation. More recent advances,[6,7,8,9] have shown that a genetic algorithm or a hybrid genetic algorithm coupled with flow simulation can be used to optimize and configure well plans. The more recent work demonstrated locating a small number of new wells or configuring a complex well, such as a multilateral well. The problem of locating many wells simultaneously when formulated as an optimization problemis that it can result in innumerable solution combinations. Thus, a practical procedure for locating many wells in a full-field development plan has been elusive. In this current work, we present a framework for optimizing many well locations with design constraints simultaneously. Rather than solve the full problem all at once, the method identifies a set of target and well plan locations based on the static reservoir model and then uses the locations to "seed" the global optimization as initial guesses. The method locates initial target perforation intervals using static reservoir properties, e.g., porosity, pore volume, or saturation, with a greedy-search algorithm.These locations are used as initial decision varaiables by the optimizer, which tunes the variables using a global, metaheuristic optimizer and flow simulation. The locations are risked, based on subsurface uncertainty, through analysis of the statistical character of the oil recovery or net present value within the optimization procedure. The mean recovery can be maximized with requirements on the statistical risk, e.g., the standard deviation. A key to the success of the optimization is efficiently running optimizer simulations on a computer cluster or grid. The paper discusses the architecture that enables efficient execution of hundreds or thousands of full-field simulations and the nature of the parallel optimizer We demonstrate the methodby applying it on a field-scale simulation model with water injection. We show that dynamic simulation was critical to improving well locations for this example.