Reservoir Simulation Using Mixed Models
Authors: Ganzer L.J. , Heinemann Z.E. 
Published: December 2007

Abstract
A multipurpose reservoir simulator should be able to solve a wide range of reservoir problems, ranging from single-phase, isothermal flow, to three-phase, black-oil depletion, to miscible or thermal displacement requiring multi-component, non-isothermal models.
This paper describes the combination of cubic EOS compositional formulation with black-oil formulation. One or more parts of a reservoir can be converted to a compositional model at a chosen time. The areas with different formulations are strongly coupled, i.e. a black-oil block can have a compositional neighbor and vice versa.
The flow terms between the different model regions are treated implicitly. The resulting linear equation system is solved without splitting or iteration for the boundary blocks. Adaptive implicitness can be applied with automatic selection of IMPES, IMPEC and fully implicit blocks.
The paper includes the mathematical formulation of the fluxes between black-oil and compositional blocks, the constraints for the fluid characterization and some practical aspects of the implementation.
The idea and the applied solution for mixed models are validated using fully black-oil and compositional calculations.

Introduction
Since reservoir simulation has evolved to be the main tool for understanding the dynamic behavior of reservoirs and predicting their future performance, there has been an ever increasing number of tasks for a reservoir simulator to fulfill. In the past at least two factors hampered the users of reservoir simulators from 'keeping their models alive.' On the one hand the grid construction was too rigid and fixed to allow the required resolution at the right place at the right time. The introduction of the windowing technique solved this problem for most of the practical cases.
On the other hand one major problem that still remained was the formulation of the simulation model itself. Once the model was set up and history-matched, the formulation determined the results in a qualitative manner and thus restricted the purposes for which this model could be used. This limitation was most serious when studying an improved oil recovery (IOR) pilot test using an already matched reservoir model. In this case the engineer still had to isolate the specific region from the full-scale model to use a different formulation, or -even worse- re-run the history match using a different formulation with possibly different software.
The advent of multipurpose simulators brought only a partial solution to the problem. They allowed the engineer to use the software he was accustomed to for a wide variety of problems but the restriction of a single formulation throughout the entire reservoir model and entire simulation run usually still remained.
In this paper we will show that it is possible to combine different model formulations within one simulation model - we call them mixed models. The goal of the approach is to solve the problem of choosing the appropriate model formulation. Certain areas of the reservoir grid may be assigned to different model formulations and the assignment can be altered at any time during the simulation.
The combination of a black-oil formulation with a compositional formulation will be shown. Whenever the hydrocarbon reservoir fluids can be approximated by a black-oil description, the basic formulation will be black-oil type and will apply to most of the grid-blocks. However, in certain areas of special interest (e.g. CO2- or gas-injection) where the effects are limited in space, specific model formulations can be assigned and will be fully coupled to the basic black-oil formulation. In every respect, a full-field compositional model is much more expensive than a black-oil model with say, 10 percent compositional grid-blocks. Savings in CPU-time and storage will be considerable.