A major part of the uncertainty for shale reservoirs comes from the distribution and properties of the fracture network. However, explicit fracture models are rarely used in uncertainty quantification due to their high computational cost. This paper presents a workflow to match the history of reservoirs with complex fracture network with a novel forward model. By taking advantage of the efficiency of the model, fractures can be explicitly characterized, and the corresponding uncertainty about the distribution and properties of fractures can be evaluated. No upscaling of the fracture properties is necessary, which is usually a required step in a traditional workflow.
The embedded discrete fracture model (EDFM) has recently been studied by many researchers due to its high efficiency compared to other explicit fracture models. By assuming a linearly distributed pressure near fractures, EDFM can provide a sub-grid resolution that lifts the requirement to refine near the fractures to a comparable size as the fracture aperture. Although efficient, considerable error is reported when applying this method to simulate flow barriers, especially when dominant flux direction is across instead of along the fractures. In this work, a novel discrete fracture model, compartmental EDFM (cEDFM) is developed based on the original EDFM framework. However, different from the original method, in cEDFM the fracture would split matrix grid blocks when intersecting them. The new model is benchmarked for single phase as well as multi-phase cases, and the accuracy is evaluated by comparing to fine explicit cases. Results indicate the improved model yields much better accuracy even for multi-phase flow simulation with flow barriers.
In the second part of the work, we applied the model in history matching and performed uncertainty quantification to the fracture network for two synthetic cases. We used Ensemble Kalman Filter (EnKF) as the data assimilation algorithm due to its robustness for cases with large uncertainty. The initial state does not need to be close to the truth to achieve convergence. Also EnKF performs well for the history matching of reservoirs with complex fracture network, where the number of parameters can be large. Therefore, it is advantageous compared to using Ensemble Smoother (ES) or Markov Chain Monte Carlo (MCMC) for fractured reservoirs. After the final step of data assimilation, a good match is obtained that can predict the production reasonably well. The proposed cEDFM model shows its robustness to be incorporated into the EnKF workflow, and benefit from the efficiency of the model, this work made it practical to perform history matching with explicit fracture models.
Ahmed Elfeel, M., Jamal, S., Enemanna, C., Arnold, D., & Geiger, S. (2013, June 10). Effect of DFN Upscaling on History Matching and Prediction of Naturally Fractured Reservoirs. Society of Petroleum Engineers. doi:10.2118/164838-MSChai, Z., Yan, B., Killough, J. E., & Wang, Y. (2017, May 15). An efficient method for fractured shale reservoir history matching: The embedded discrete fracture multi-continuum approach. Journal of Petroleum Science and Engineering, 160, 170–181. doi: 10.1016/j.petrol.2017.10.055Chai, Z., Yan, B., Killough, J. E., & Wang, Y. (2016, November 12). Dynamic Embedded Discrete Fracture Multi-Continuum Model for the Simulation of Fractured Shale Reservoirs. International Petroleum Technology Conference. doi:10.2523/IPTC-18887-MSChen, Y., & Oliver, D. S. (2013, May 08). Levenberg–Marquardt Forms of The Iterative Ensemble Smoother for Efficient History Matching and Uncertainty Quantification. Computational Geosciences, 17(4), 689–703. doi: 10.1007/s10596-013-9351-5Coats, K. H. (1989, January 1). Implicit Compositional Simulation of Single-Porosity and Dual-Porosity Reservoirs. Society of Petroleum Engineers. doi:10.2118/18427-MSDing, D. Y., Farah, N., Bourbiaux, B., Wu, Y.-S., & Mestiri, I. (2017, February 20). Simulation of Matrix-Fracture Interaction in Low-Permeability Fractured Unconventional Reservoirs. Society of Petroleum Engineers. doi:10.2118/182608-MSEvensen, G. (2003, May 7). The ensemble Kalman filter: Theoretical Formulation and Practical Implementation. Ocean Dynamics, 53(4), 343–367. doi: 10.1007/s10236-003-0036-9EGang, T., & Kelkar, M. G. (2006, January 1). Efficient History Matching in Naturally Fractured Reservoirs. Society of Petroleum Engineers. doi:10.2118/99578-MSHeinemann, Z. E., Brand, C., Munka, M., & Chen, Y. M. (1989, January 1). Modeling Reservoir Geometry With Irregular Grids. Society of Petroleum Engineers. doi:10.2118/18412-MSHinkley, R., Gu, Z., Wong, T., & Camilleri, D. (2013, November 5). Multi-Porosity Simulation of Unconventional Reservoirs. Society of Petroleum Engineers. doi:10.2118/167146-MSJiang, J., & Younis, R. M. (2016, June 1). Hybrid Coupled Discrete-Fracture/Matrix and Multicontinuum Models for Unconventional-Reservoir Simulation. Society of Petroleum Engineers. doi:10.2118/178430-PAKarimi-Fard, M., Durlofsky, L. J., & Aziz, K. (2004, June 1). An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators. Society of Petroleum Engineers. doi:10.2118/88812-PAKazemi, H., Merrill, L. S., Porterfield, K. L., & Zeman, P. R. (1976, December 1). Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs. Society of Petroleum Engineers. doi:10.2118/5719-PAKazemi, H., Gilman, J. R., & Elsharkawy, A. M. (1992, May 1). Analytical and Numerical Solution of Oil Recovery From Fractured Reservoirs With Empirical Transfer Functions (includes associated papers 25528 and 25818). Society of Petroleum Engineers. doi:10.2118/19849-PALee, S. H., Jensen, C. L., & Lough, M. F. (2000, September 1). Efficient Finite-Difference Model for Flow in a Reservoir With Multiple Length-Scale Fractures. Society of Petroleum Engineers. doi:10.2118/65095-PALi, L., & Lee, S. H. (2008, August 1). Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media. Society of Petroleum Engineers. doi:10.2118/103901-PALu, L., & Zhang, D. (2015, October 1). Assisted History Matching for Fractured Reservoirs by Use of Hough-Transform-Based Parameterization. Society of Petroleum Engineers. doi:10.2118/176024-PAMoinfar, A., Varavei, A., Sepehrnoori, K., & Johns, R. T. (2014, April 1). Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs. Society of Petroleum Engineers. doi:10.2118/154246-PANejadi, S., Leung, J. Y. W., Trivedi, J. J., & Virues, C. J. J. (2014, September 30). Integrated Characterization of Hydraulically Fractured Shale Gas Reservoirs Production History Matching. Society of Petroleum Engineers. doi:10.2118/171664-MSOuenes, A., & Saad, N. (1993, January 1). A New, Fast Parallel Simulated Annealing Algorithm for Reservoir Characterization. Society of Petroleum Engineers. doi:10.2118/26419-MSPing, J., Al-Hinai, O., & Wheeler, M. F. (2017, May 19). Data Assimilation Method for Fractured Reservoirs Using Mimetic Finite Differences and Ensemble Kalman Filter. Computational Geosciences, 21(4), 781–794. doi: 10.1007/s10596-017-9659-7Ping, J., & Zhang, D. (2013, May 18). History Matching of Fracture Distributions by Ensemble Kalman Filter Combined with Vector Based Level Set Parameterization. Journal of Petroleum Science and Engineering, 108, 288–303. doi: 10.1016/j.petrol.2013.04.018Sarda, S., Jeannin, L., Basquet, R., & Bourbiaux, B. (2002, April 1). Hydraulic Characterization of Fractured Reservoirs: Simulation on Discrete Fracture Models. Society of Petroleum Engineers. doi:10.2118/77300-PASandve, T. H., Berre, I., & Nordbotten, J. M. (2012, May 1). An Efficient Multi-Point Flux Approximation Method for Discrete Fracture-Matrix Simulations. Journal of Computational Physics, 231, 3784–3800. doi:10.1016/j.jcp.2012.01.023Schulze-Riegert, R. W., Axmann, J. K., Haase, O., Rian, D. T., & You, Y.-L. (2002, April 1). Evolutionary Algorithms Applied to History Matching of Complex Reservoirs. Society of Petroleum Engineers. doi:10.2118/77301-PATafti, T. A., & Aminzadeh, F. (2013, January 1). A New Way to Characterize the Fracture Network Using Seismic Velocity Volumes. Society of Exploration Geophysicists. doi: 10.1190/segam2013-1264.1Tang, H., Killough, J. E., Heidari, Z., & Sun, Z. (2017, August 1). A New Technique To Characterize Fracture Density by Use of Neutron Porosity Logs Enhanced by Electrically Transported Contrast Agents. Society of Petroleum Engineers. doi:10.2118/181509-PATene, M., Bosma, S. B., Al Kobaisi, M. S., & Hajibeygi, H. (2017, May 15). Projection-based Embedded Discrete Fracture Model (pEDFM). Advances in Water Resources, 105, 205–216. doi: 10.1016/j.advwatres.2017.05.009Warren, J. E., & Root, P. J. (1963, September 1). The Behavior of Naturally Fractured Reservoirs. Society of Petroleum Engineers. doi:10.2118/426-PAYang, D., Xue, X., & Chen, J. (2018, April 22). High Resolution Hydraulic Fracture Network Modeling Using Flexible Dual Porosity Dual Permeability Framework. Society of Petroleum Engineers. doi:10.2118/190096-MS
