Abstract
This paper examines the relative strengths and weaknesses of solving a fully compositional isothermal three phase numerical simulator by two fundamentally different approaches. One of the methods considered is based on the standard Newton-Raphson procedure where the partial derivatives for all the pertinent equations are written with respect to a selected set of primary variables 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. The alternative method, first proposed by Acs et al., is based on a volume balance where in each simulator block, the pore volumes are equated with the fluid volumes. 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.
The Young and Stephenson model is compared with the IMPEM method of Acs et al. as well as the sequential method of Watts. The main area of comparison is the relative ease or difficulty with which each simulator handles various compositional problems. The advantages and disadvantages of using either method under different circumstances are discussed. As well, the performance of these simulators in their corresponding black oil forms is compared.
Both models can be run using either the Peng Robinson, Soave-Redlich-Kwong, or Schmidt-Wenzel equations of state. All the derivatives needed in both models can be solved explicitly from analytical expressions that have been derived from these equations of state.
