Optimization of Oil Production Using Reduced Order Modeling in Hydrocarbon Reservoir Simulation

Document Type : Research Paper

Authors

1 Department of Petroleum Engineering, Amirkabir University of Technology, Tehran, Iran

2 Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

Production-injection optimization has been the subject of various researches due to its complicated and expensive computations. The main reason for this complexity is number of reservoir simulation runs is needed to predict reservoir performance. These numerical reservoir simulations are computationally expensive and time consuming. Therefore, finding a way to reduce the computational burden of reservoir simulation will facilitate the optimization process. One of the methods for reducing the complexity of reservoir simulation is Reduced Order Modeling (ROM) which has been recently introduced for improving efficiency of open source reservoir simulators. In this paper, an ROM method based on Artificial Neural Networks (ANN) and Discrete Empirical Interpolation Method (DEIM) is proposed to resolve the curse of dimensionality while simulating reservoir dynamics with acceptable accuracy. This method is also applicable to black box reservoir simulators. The performance of the suggested ANN-DEIM algorithm has been investigated on a case study on Brugge field. The reduced model well represent the reservoir dynamic behavior while reducing run time by a factor of eight comparing with that of a full order reservoir simulator. ANN-DEIM also has been applied in production-injection optimization of Brugge filed using a Pattern Search optimization algorithm. The proposed method can reduce optimization time by 7 times while leading  to %11 improvement in Net Present Value (NPV) over the initial solution used in the optimization process.

Keywords


[1]. Frangos M., Marzouk Y. and Willcox K., “Surrogate and reduced-order modelling: a comparison of approaches for large-scale statistical inverse problems,” John Wiley and Sons Ltd, 2001.##
[2]. Foroud T., seifi A. and Hassani H., “Surrogate-based optimization of horizontal well placement in a mature oil reservoir,” JPST, Vol. 30, No. 11, pp. 1091-1101, 2012. ##
[3]. Mohammadi H., seifi A. and Foroud T., “A Robust Kriging model for predicting accumulative outflow fram a mature reservoir considering a new horizontal well,” JPSE, Vol. 82-83, pp. 113-119, 2012.##
[4]. Lumley J. L., “Atmospheric turbulence and radio wave propagation”, Journal of Computational Chemistry, Vol. 23, No. 13, pp. 1236–1243, 1967.##
[5]. Vermeulen P. T., Heemink A. W. and Stroet C. B., “Reduced models for linear groundwater flow models using empirical orthogonal functions”, Advances in Water Resources, Vol. 27, pp. 57–69, 2004.##
[6]. Cardoso M. A, Durlofsky L. and Sarma P., “Development and application of reduced order modelling procedures for subsurface flow simulation”, International Journal for Numerical Methods in Engineering, Vol. 77, No. 9, pp. 1322-1350, 2009.##
[7]. Dong N. and Roychowdhury J., “Piecewise polynomial nonlinear model reduction”, Design Automation Conference, IEEE Computer Society, Los Alamitos, CA, 2003.##
[8]. Cardoso M. A. and Durlofsky L. J., “Linearized reduced-order models for subsurface flow simulation”, J. Comput. Phys., Vol. 229, pp. 681–700, 2010.##
[9]. Chaturantabut S. and Sorensen D. C., “Discrete empirical interpolation for nonlinear model reduction”, Joint 48th Conference on Decision and Control, 2009.##
[10]. Chaturantabut S. and Sorensen D. C., “Nonlinear model reduction via discrete empirical interpolation”, SIAM J. Sci. Comput., Vol. 32, No. 5, pp. 2737-2764, 2010.##
[11]. Barrault M., Maday Y., Nguyen N. C. and Patera A. T., “An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations”, Comptes Rendus Mathematique, Vol. 339, No. 9, pp. 667–672, 2004.##
[12]. Sava D., “Model-reduced gradient based production optimization”, M.S.c Thesis, Delft University, The Netherlands, 2012.##
[13]. Peters E. et al., “Results of the Brugge benchmark study for flooding optimization and history matching,” SPE Reservoir Evaluation & Engineering, Vol. 13, No. 3, pp. 391-405, 2010.##
[14]. Foroud T., Seifi A. and AminShahidy B., “Assisted history matching using artificial neural network based global optimization method – Applications to Brugge field and a fractured Iranian reservoir”, JPSE, Vol. 123, pp. 46–61, 2014.##