Representing Wells in Numerical Reservoir Simulation: Part 2 - Implementation

Abstract

Abstract A reservoir simulation system uses an analytical model to represent flow within a grid block as it enters or leaves a well, This model is called a well model. This paper presents a succinct but comprehensive description of the installation of a well model in a simulator, including problems which may be encountered and possible remedies. This and the preceding paper, SPE 7697, present possible remedies. This and the preceding paper, SPE 7697, present a unified viewpoint of material, some of which may be already familiar to simulator developers. Introduction Our concern in this paper is the inclusion of a well model and well boundary conditions in a reservoir simulator. The source representation and the wellbore flow model are the basic components of the well model. The usefulness of the working version finally installed in a reservoir simulator depends greatly on the numerical implementation. We accordingly discuss numerical aspects of the well model for black-oil, compositional, and thermal well models.We have omitted a discussion of the incorporation into well models of surface gathering facilities and what could be called "well group constraints" such as lease, platform or pipeline constraints. These subjects easily could be the topics of several other papers.A satisfactory well model is frequently a key to successful simulation. Many of the details of well model development have not appeared in the petroleum literature. It is our hope that this paper may provide a basis for further work and discussion of this paper may provide a basis for further work and discussion of this essential topic. Implementation We shall discuss the implementation of the following equation (developed in Part 1) for the flow of each phase per completion interval. (1) Here, p is the phase (either oil, water, or gas). We note here certain aspects of this well model.1. The rates are in standard units.2. The relative permeability is calculated using the grid-block (average) fluid saturation from a well (i.e., not necessarily the grid-block) relative permeability table. It is at this point that the saturation boundary condition is imposed.3. The oil pressure is used to calculate the potential for all phases. Thus, capillarity, is not treated (i.e., no capillary end effect or water block). Also, the difference in phase pressures within a grid block due to gravity segregation is ignored.4. Zk is the vertical distance from the center of the kth completion interval to the center of the (k + 1)th completion interval (positive downward).5. The viscosity, formation volume factor, solution GOR, and density are calculated at gridblock pressure. Only the grid block for the completion interval is used.6. The skin and well radius are the same for every completion interval for each well.7. The external radius re of the grid block is a function of the grid-block, geometry. JPT P. 339