No abstract

No abstract

No abstract

Compositional reservoir simulation is the most powerful tool available to the reservoir engineer upon which, nowadays, most reservoir development decisions rely on. According to the number of components used to describe the fluids, there is a very high demand for computational power due to the complexity and to the iterative nature of the phase behavior problem solution process. Phase stability and phase split computations often consume more than 50% of the simulation's total CPU time as both problems need to be solved repeatedly for each discretization block at each iteration of the non-linear solver. Therefore, the speeding up of these calculations is a challenge of great interest. In this work, machine learning methods are proposed for the solving of the phase equilibrium problem. It is shown that by using proper transformations, the unknown closed-form solution of the Equation-of-State based formulation can be emulated by proxy models. The phase stability problem is treated by classifiers which label the fluid's state in each block as either stable or unstable. For the phase-split problem, regression models provide the prevailing equilibrium coefficients values given the feed composition, pressure and temperature. The development of both models is performed rapidly and offline in an automated way, by utilizing the fluid's tuned-EoS model, prior to running the reservoir simulator. During the simulation run, the proxy models are called to provide direct answers of the phase equilibrium problem at a very small CPU charge instead of solving iteratively the phase behavior problem. The proposed approach is presented in two-phase equilibria formulation but it can be extended to multi-phase equilibria applications. Examples demonstrate the accuracy of the calculations and the very significant CPU time reduction achieved with respect to currently used methods.

No abstract

No abstract

The gas compressibility factor, also known as the deviation or Z-factor, is one of the most important parameters in the petroleum and chemical industries involving natural gas, as it is directly related to the density of a gas stream, hence its flow rate and isothermal compressibility. Obtaining accurate values of the Z-factor for gas mixtures of hydrocarbons is challenging due to the fact that natural gas is a multicomponent, non-ideal system. Traditionally, the process of estimating the Z-factor involved simple empirical correlations, which often yielded weak results either due to their limited accuracy or due to calculation convergence difficulties. The purpose of this study is to apply a hybrid modeling technique that combines the kernel ridge regression method, in the form of the recently developed Truncated Regularized Kernel Ridge Regression (TR-KRR) algorithm, in conjunction with a simple linear-quadratic interpolation scheme to estimate the Z-factor. The model is developed using a dataset consisting of 5616 data points taken directly from the Standing–Katz chart and validated using the ten-fold cross-validation technique. Results demonstrate an average absolute relative prediction error of 0.04%, whereas the maximum absolute and relative error at near critical conditions are less than 0.01 and 2%, respectively. Most importantly, the obtained results indicate smooth, physically sound predictions of gas compressibility. The developed model can be utilized for the direct calculation of the Z-factor of any hydrocarbon mixture, even in the presence of impurities, such as N 2 , CO 2 , and H 2 S, at a pressure and temperature range that fully covers all upstream operations and most of the downstream ones. The model accuracy combined with the guaranteed continuity of the Z-factor derivatives with respect to pressure and temperature renders it as the perfect tool to predict gas density in all petroleum engineering applications. Such applications include, but are not limited to, hydrocarbon reserves estimation, oil and gas reservoir modeling, fluid flow in the wellbore, the pipeline system, and the surface processing equipment.

No abstract