Abstract

This paper describes COSMOS, a new equation-of-state, compositional simulator. COSMOS is designed for full-field studies of hydrocarbon gas and carbon dioxide injection for miscible flooding, gas condensate reservoirs and volatile oil reservoirs. The numerical procedures in this simulator are based on Newton's method and couple together the phase equilibrium constraints and species continuity equations. The transport flux terms in the flow equations may depend on pressure alone, or may be treated as implicit functions of both pressure and saturation. With this latter option, COSMOS contains the coupling terms which give fully-implicit, black-oil simulators their stability. The well management package is flexible and provides for platform and field limits as well as individual well controls. The coupling of the well flow equations with the continuity equations parallels the implicit treatment of the transport terms. This implicit option also affects our linear algebra routines which are capable of solving matrices with one or three unknowns per grid block.

COSMOS was constructed as an efficient vector code which can be easily modified as simulation needs or capabilities arise. Structured design methodologies were employed to achieve as high a degree of modularity as is consistent with extensive vectorization. COSMOS contains a resource manager to efficiently run large and small problems within a limited central memory. Additional resource management software determines a critical path to optimally schedule computations and data traffic. We have also developed a flexible, hierarchical data base package for the storage and retrieval of data which provides printing and restarting capabilities. Although the COSMOS code and these software packages were targeted for the CRAY-1, the simulator is designed to run on other machines with a minimal number of changes.

Introduction

Reservoir simulators are the modern tools that engineers use to develop an optimal exploitation scheme for a given hydrocarbon reservoir. Black oil simulators have been the most widely used of these mathematical models and have studied conventional recovery techniques by assuming the hydrocarbon system consists of two components, oil and gas, with properties that depend only on pressure. The development properties that depend only on pressure. The development and sophistication of these simulators has been quite impressive, and their utility in reservoir engineering seems certain for many years. However, compositional models have been receiving an increasing amount of attention which can be explained by two recent events. First, as the petroleum industry has proposed the use of tertiary processes and the development of more complex reservoirs, the engineer requires a model which treats the hydrocarbon system as a multicomponent mixture. These simulators use the principles of mass conservation and phase equilibrium to principles of mass conservation and phase equilibrium to track in time and space the pressure, saturation and composition of each phase. The multicomponent nature of compositional models makes it ideal for simulating a broad variety of recovery processes such as a) miscible flooding by carbon dioxide, nitrogen or hydrocarbon gas injection; b) cycling of gas- condensate reservoirs with dry gas; c) gas injection into volatile oil reservoirs; d) primary depletion of volatile oil or gas condensate reservoirs.

The second reason for the increased activity in compositional simulation is the availability of larger and faster computers such as the CRAY series of machines. Compositional models require considerably more storage and computational speed than black-oil programs simply because the number of equations and programs simply because the number of equations and unknowns is much larger. Before the availability of large vector computers, full-field studies with compositional simulators were impractical due to the extremely crude grid resolution that was dictated by a relatively large number of hydrocarbon components and the limited storage capacities. Even with the CRAY computer and its fixed memory system, studies using large numbers of grid cells and hydrocarbon components will require data storage outside of central memory. This requirement has been discussed in an earlier paper by Kendall et al. and will be further paper by Kendall et al. and will be further examined in this work.

The heart of any reservoir simulator is its numerical algorithm, and several different methods have appeared in the literature.

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