Rapid Flash Calculations for Compositional Modeling

Abstract

Abstract The computational time for conventional flash calculations increasessignificantly with the number of components making it impractical for use inmany finely-grided compositional simulations.Previous research toincrease flash calculation speed has been limited to those with zero binaryinteraction parameters (BIPs) or approximate methods based on an eigenvalueanalysis of the binary interaction matrix.Practical flash calculations, however, nearly always have some nonzero BIPs.Further, the accuracy andspeed of the eigenvalue methods varies depending on the choice and number ofthe dominant eigenvalues. This paper presents a new method for significantly increasing the speed offlash calculations for any number of nonzero BIPs.The approach requiresthe solution of up to six reduced parameters regardless of fluid complexity orthe number of components and is based on decomposing the BIPs into twoparameters using a simple quadratic expression.The new approach is exactin that the equilibrium phase compositions for the same BIPs are identical tothose with the conventional flash calculation; no eigenvalue analysis isrequired. Further, the new approach eliminates the Rachford-Riceprocedure and is more robust than the conventional flash calculationprocedure.We demonstrate the new approach for several example fluids, andshow that speed up by a factor of about 3 – 20 is obtained over conventionalflash calculations depending on the number of components. Introduction Gas injection into oil reservoirs results in complex interactions of flowwith phase behavior that are often not modeled accurately by black oilsimulation. This is especially true for miscible or nearly misciblefloods where significant mass transfer occurs between the hydrocarbonphases.Such floods are best modeled by compositionalsimulation. A significant disadvantage of compositional simulation, however, is that itis more computationally intensive than black-oil simulation.The primaryreason for the increased computational time is the result of solving repeatedflash calculations with cubic equations-of-state (EOS).Research has shownthat EOS flash calculations can occupy 50–70% of total computational time incompositional simulation.[1,2] The use of fewer pseudocomponents can reduce the flash computation time, butfewer components results in less accuracy.[3–5] This is especially truein MCM displacements, in which miscibility is developed by a combinedcondensing/vaporizing (CV) drive process.[6–9]Fluid characterization bypseudocomponent models can be improved by tuning to the analytical MME orMMP,[9] but those models still require significant computational time even forfewer pseudocomponents. Another way to reduce computation time is to reduce the number of gridblocks. With coarse grids, however, numerical dispersion is large, which maycloud the results.[10] More recently, methods have been examined to find reduced parameters forflash calculations.Michelsen[11–13] significantly increased flashcalculation speed by finding three reduced parameters, regardless of the numberof components.His method, however, assumes zero BIPs, which is toorestrictive for real fluid characterization. Michelsen also gave apractical method for stability calculations using the tangent plane distance(TPD).[12] Jensen and Fredenslund[14] extended Michelsen's research by the addition oftwo reduced parameters for every column of the BIP matrix with at least onenonzero element.Thus, there are a total of five reduced parameters forthe case when one column contains a single nonzero BIP. All other BIPs, however, must be zero in their approach, which again limits itsusefulness. In 1988, Hendricks[15] used an eigenvalue analysis to identify the dominantBIPs in flash calculations. The BIP matrix is recalculated by settingsmall eigenvalues to zero, using some predetermined criterion.Theprocedure was applied later by Hendricks and van Bergen[16] usingNewton-Raphson (NR) iteration. Although the method is faster thanconventional flash calculations, the reduction in eigenvalues can lead tonon-physical BIPs in that the diagonal elements of the BIP matrix can havesmall nonzero values. Their method is only an approximation to theoriginal phase behavior characterization.