|Publisher||Society of Petroleum Engineers||Language||English|
|Content Type||Conference Paper|
|Title||A Fully-Implicit Thermal Reservoir Simulator|
|Authors||Naccache, P.F., GeoQuest|
SPE Reservoir Simulation Symposium, 8-11 June 1997, Dallas, Texas
|Copyright||Copyright 1997, Society of Petroleum Engineers, Inc.|
This paper describes a 3D thermal reservoir simulator that models the injection of steam into heavy oil. The variables are pressure, energy and molar densities, and the equations are volume balance and component and energy conservation. The use of energy and molar densities means that there is no variable-switching, and the formulation combines the advantages of volume balance with a fully-implicit code.
A number of example problems are presented, including a large full-field fine-grid model run on parallel processors. Introduction
We describe a full-featured thermal simulator that works in a number of coordinate systems: cartesian or radial, rectangular or corner-point geometry, and PEBI grids. It calculates non-neighbor connections, and will solve both single- and dual-porosity models. Local grid refinements can be defined, and these are treated simultaneously and fully coupled in the linear solver. A nine-point method can be used to reduce grid orientation effects. Computer memory requirements are minimized by only storing properties and derivatives for active cells.
The new simulator is based on an existing simulator that runs in either compositional or black oil mode. A choice has been maintained and we can either model dead or live oil. We define live oil as having at least one volatile component and dead oil as having none. This paper will describe the general formulation then give examples for the dead oil case. In practice, the dead oil model can be applied to oils that have a small proportion of volatile components as long as these components do not have a significant effect on the simulation.
To solve the thermal effects in the reservoir we choose energy rather than temperature as our new variable. The main advantage of an energy variable is that we avoid the problems of variable switching. In the dead-oil case, for instance, we can use energy to describe the boiling of water at a constant pressure and temperature. By adding an energy variable and an energy conservation equation to the existing formulation, we can simulate the injection of steam or hot or cold water (or hot or cold gas) into the reservoir. The formulation differs from many others in calculating energy bounds for each state in each grid block. The energy in the grid block then defines its state and a flash is performed within that state. We use a conventional fully-implicit discretization of the flow equations. Once the non-linear equations have been set up, they are iterated using Newton's method. The linear equations are solved using nested factorization. The simulator can be run either in scalar or parallel mode, and results are presented for both cases.
Variables and Equations
The primary solution variables X are the pressure P, the reservoir molar densities mc and the bulk internal energy density e. The system is made up of N-1 oleic components and one aqueous component. There are N+2 variables.
The N+2 equations are one volume balance equation, one energy conservation equation, and N component conservation equations. P. 97^
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