An upscaling approach using adaptive multi-resolution upgridding and automated relative permeability adjustment

The upscaling process of a high-resolution geostatistical reservoir model to a dynamic simulation grid model plays an important role in a reservoir study. Several upscaling methods have been proposed in order to create balance between the result accuracy and computation speed. Usually, a high-resolution grid model is upscaled according to the heterogeneities assuming single phase flow. However, during injection processes, the relative permeability adjustment is required. The so-called pseudo-relative permeability curves are accepted, if their corresponding coarse model is a good representation of the fine-grid model. In this study, an upscaling method based on discrete wavelet transform (WT) is developed for single-phase upscaling based on the multi-resolution analysis (MRA) concepts. Afterwards, an automated optimization method is used in which evolutionary genetic algorithm is applied to estimate the pseudo-relative permeability curves described with B-spline formulation. In this regard, the formulation of B-spline is modified in order to describe the relative permeability curves. The proposed procedure is evaluated in the gas injection case study from the SPE 10th comparative solution project’s data set which provides a benchmark for upscaling problems [1]. The comparisons of the wavelet-based upscaled model to the high-resolution model and uniformly coarsened model show considerable speedup relative to the fine-grid model and better accuracy relative to the uniformly coarsened model. In addition, the run time of the wavelet-based coarsened model is comparable with the run time of the uniformly upscaled model. The optimized coarse models increase the speed of simulation up to 90% while presenting similar results as fine-grid models. Besides, using two different production/injection scenarios, the superiority of WT upscaling plus relative permeability adjustment over uniform upscaling and relative permeability adjustment is presented. This study demonstrates the proposed upscaling workflow as an effective tool for a reservoir simulation study to reduce the required computational time.     

Multi-level Optimization of Reservoir Scheduling Using Multi-resolution Wavelet-Based Up-scaled Models

This paper presents a multi-level procedure for production and injection scheduling through a numerical model-based optimization of well control variables. To calculate the net present value (NPV), the objective function of optimization, this procedure uses a number of discretized systems for a reservoir model with different degrees of up-scaling prepared according to a multi-resolution wavelet technique. These up-scaled models were incorporated into optimization based on a probability function. In early optimization iterations, due to the necessity to explore the search space quickly, the coarsest grid model has a higher chance for selection than the others; however, by a selection (with a low probability) of the finest up-scaled grid model in these iterations, solutions and objective function were tuned. In the later iterations of optimization, the finest up-scaled grid model probability was the highest in order to ensure the reliability of the final solution. The optimization algorithm is an adaptive simulated annealing algorithm coupled with a polytope. This procedure was evaluated in two case studies. The first case study was a horizontal 2D oil model with water flooding. The second case study was a vertical 2D oil model with gas injection. The results show that the proposed optimization procedure provides approximately the same accuracy compared to the situation in which the fine grid model is used for all the optimization iterations. Also, the run-time for the proposed optimization procedure is comparable to the run-time of the optimization in which only the coarsest grid model is used to calculate objective function. Moreover, the superiority of the wavelet-based up-scaling over an analogous multiple grid system optimization using uniformly up-scaled models is presented.

     

Improved Minimum Miscibility Pressure Prediction for Gas Injection Process in Petroleum Reservoir

Determination of gas–oil minimum miscibility conditions is one of the important design parameters to improve the displacement efficiency of the hydrocarbon reservoir during enhanced oil recovery with gas injection. In this work, a support vector regression (SVR) model is developed using experimental data to estimate the minimum miscibility pressure (MMP) for various reservoir fluids and injection gases. Experimental MMP data taken from the reliable literature were used as input. Each data point input includes methane and intermediate components mole percent, plus fraction properties and reservoir temperature related to reservoir fluid and CO₂, H₂S, N₂ and intermediate mole fractions, and intermediate properties of the injected gas. Experimental MMP is regarded as the model output. The database contains 135 datasets, from which 125 datasets were used for model development, and the rest were used for model evaluation. Genetic algorithm was implemented to optimize the SVR model parameters. The proposed data-driven model was verified by statistical validation data. The model results illustrate a correlation coefficient (R²) of 0.999. In addition, the SVR results demonstrate the proposed model to be a fast tool and a robust approach to map input space to output features. The SVR model was compared to popular data-driven MMP estimation models as well. This comparison presents an acceptable accuracy relative to this estimation model. Finally, the presented model was evaluated against a comprehensive theoretical model of slim tube compositional simulation on a trusted literature dataset.