An integrated approach for rapid phase behavior calculations in compositional modeling

The solution of the hydrocarbon phase equilibria problem through the use of an Equation of State (EoS) requires substantial computational power due to the complexity and iterative nature of the calculations particularly when the reservoir fluid needs to be described with a significant number of components. This high CPU time demand becomes particularly acute during the execution of compositional reservoir simulations as the phase equilibria problem needs to be solved repeatedly for each discretization block and at each iteration of the non-linear solver. Solving the hydrocarbon phase equilibrium problem is often reported to consume more than 50% of the simulation's total CPU time, thus making the speeding up of these calculations a challenge of great interest. In this work, an integrated approach is presented which utilizes classification and regression models to provide direct answers to both the phase stability and phase split problems during compositional modeling. The models are generated offline, in an automated way, once the selected EoS model is tuned and finalized and prior to setting up and running the reservoir or process simulator. First, classifiers are trained, as previously presented in the literature, utilizing the fluid's tuned EoS model, which label the fluid's state as stable or unstable for given feed composition, pressure and temperature. Second, regression models are generated so as to provide the prevailing reduced variables values, thus emulating the unknown closed-form solution of the Equation-of-State based reduced flash formulation. An unsupervised training technique is proposed to optimize the usage of the regression model's learning capacity. Once the models are generated an unlimited number of compositional modeling calculations can be made during which the models developed beforehand are simply called to determine directly both the stability state of the feed and the phase split reduced variables values, if the mixture is found unstable, which, in turn, will lead to the equilibrium phases properties and molar ratios. By providing the reduced variables values instead of the full equilibrium coefficients set, the regression model expression is kept simple, thus very fast to evaluate compared to the conventional iterative algorithms. The method is applicable to any type of simulation models requiring a great number of phase behavior calculations. The proposed approach is presented in two-phase equilibria formulation although it can be directly extended to multi-phase equilibria applications. Examples demonstrate the accuracy of the calculations and the very significant performance improvement achieved with respect to currently used methods. (C) 2014 Elsevier B.V. All rights reserved.