Compositional and Black Oil Modelling with Emphasis on the Volume Balance Method
Abstract/Contents
- Abstract
- This report examines the relationship between previously published isothermal compositional numerical simulation models. To facilitate comparison, a general set of equations and a basic solution methodology are laid out. Then the various models are related to the basic one.A large number of the models considered are based on the standard Newton-Raphson method of solving sets of nonlinear equations. In this method, the partial derivatives of all the pertinent equations with respect to a selected set of primary variables are written in a Jacobian matrix. This model can be solved fully implicitly as Coats did, or implicitly for pressure and explicitly for saturation and composition (IMPEM) as Fussell and Fussell or Young and Stephenson did. An alternative set of models, first proposed by Acs et al, is based on the fact that in each simulator block, the pore volume should be equal to the fluid volume. As originally proposed, this method was also an IMPEM one, but Watts later extended it to include a sequential step implicit in saturation. As yet, no computational results have been published for this volume balance method.At first glance, the volume balance models appear to be completely different than Newton-Raphson based ones. Upon further analysis, however, it is revealed that while the models have been developed from fundamentally different viewpoints, the end result is virtually identical. In short, the volume balance model is a scheme which executes only a single Newton-Raphson iteration per timestep. Total moles instead of mole fractions are used as the primary variables. Before proceeding to the next timestep, a separate equilibrium flash calculation is carried out. Any difference existing between the pore and fluid volumes is carried forward to the next timestep. The development of a black oil model from a compositional model format is also presented. The black oil system is developed in such a way as to preserve the compositional appearance of the model.Numerical results are presented for both the fully compositional case, and the simplified black oil case. Two models were actually constructed - one based on the volume balance method and the other based on a Newton-Raphson scheme. These models were constructed before the full extent of the similarity between the two models was understood, so that the numerical comparison between them is somewhat limited in value. However, the results do show that the volume balance methodology is a viable alternative to the standard Newton-Raphson procedure. The phase behaviour of the compositional models in these programs can be calculated from either the Peng-Robinson, Soave-Redlich-Kwong, or Schmidt-Wenzel equations of state. All the derivatives needed in the model have been derived analytically from all three equations of state, and the simulator solves these derivatives explicitly from these equations.
Description
| Type of resource | text |
|---|---|
| Date created | February 1988 |
Creators/Contributors
| Author | Wong, Terry W. |
|---|---|
| Primary advisor | Aziz, Khalid |
| Degree granting institution | Stanford University, Department of Petroleum Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
Bibliographic information
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Preferred citation
- Preferred Citation
- Wong, Terry W. (1988). Compositional and Black Oil Modelling with Emphasis on the Volume Balance Method. Stanford Digital Repository. Available at: https://purl.stanford.edu/ch707km8499
Collection
Master's Theses, Doerr School of Sustainability
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