Application of Flow Diagnostics to Rapid Production Data Integration in Complex Grids and Dual-Permeability Models
- Feyi Olalotiti-Lawal (Quantum Reservoir Impact) | Gil Hetz (Quantum Reservoir Impact) | Amir Salehi (Quantum Reservoir Impact) | David Castineira (Quantum Reservoir Impact)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2020
- Document Type
- Journal Paper
- 2020.Society of Petroleum Engineers
- flow diagnostics, geologic model update, naturally fractured reservoirs, inverse problems, streamline simulation
- 23 in the last 30 days
- 236 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Streamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models.
Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, on the basis of a defined flux field, are computed on the native finite-volume grid. The information embedded in these metrics are used in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival-time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation used in the well-established generalized travel-time inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR (sparse least-squares with QR factorization) system composed of the computed analytical sensitivity and the optimal water travel-time shift, augmented with regularization and smoothness constraints.
The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatiotemporal trends. Furthermore, the desirable quasilinear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multicontinuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models.
This work presents, for the first time, an application of the GTTI to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel-time sensitivity computations directly on finite-volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.
|File Size||9 MB||Number of Pages||21|
Aanonsen, S. I. 2008. Efficient History Matching Using a Multiscale Technique. SPE Res Eval & Eng 11 (1): 154–164. SPE-92758-PA. https://doi.org/10.2118/92758-PA.
Aanonsen, S. I., Naevdal, G., Oliver, D. S. et al. 2009. The Ensemble Kalman Filter in Reservoir Engineering—A Review. SPE J. 14 (3): 393–412. SPE-117274-PA. https://doi.org/10.2118/117274-PA.
Al-Huthali, A. H. and Datta-Gupta, A. 2004. Streamline Simulation of Water Injection in Naturally Fractured Reservoirs. Paper presented at the SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma, USA, 17–21 April. SPE-89443-MS. https://doi.org/10.2118/89443-MS.
Al-Ramadan, K. A., Hussain, M., Imam, B. et al. 2004. Lithologic Characteristics and Diagenesis of the Devonian Jauf Sandstone at Ghawar Field, Eastern Saudi Arabia. Mar Pet Geol 21 (10): 1221–1234. https://doi.org/10.1016/j.marpetgeo.2004.09.002.
Al Harbi, M. H. 2005. Streamline-Based Production Data Integration in Naturally Fractured Reservoirs. Doctoral dissertation, Texas A&M University, College Station, Texas, USA.
Barenblatt, G., Zheltov, I. P., and Kochina, I. 1960. Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks [Strata]. J Appl Math Mech 24 (5): 1286–1303. https://doi.org/10.1016/0021-8928(60)90107-6.
Bhark, E., Rey, A., Datta-Gupta, A. et al. 2012. A Multiscale Workflow for History Matching in Structured and Unstructured Grid Geometries. SPE J. 17 (3): 828–848. SPE-141764-PA. https://doi.org/10.2118/141764-PA.
Chen, H., Onishi, T., Olalotiti-Lawal, F. et al. 2018. Streamline Tracing and Applications in Naturally Fractured Reservoirs Using Embedded Discrete Fracture Models. Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, 24–26 September. SPE-191475-MS. https://doi.org/10.2118/191475-MS.
Chen, W. H., Gavalas, G. R., Seinfeld, J. H. et al. 1974. A New Algorithm for Automatic History Matching. SPE J. 14 (6): 593–608. SPE-4545-PA. https://doi.org/10.2118/4545-PA.
Chen, Y. and Oliver, D. S. 2014. History Matching of the Norne Full-Field Model with an Iterative Ensemble Smoother. SPE Res Eval & Eng 17 (2): 244–256. SPE-164902-PA. https://doi.org/10.2118/164902-PA.
Cheng, H., Datta-Gupta, A., and He, Z. 2005a. A Comparison of Travel-Time and Amplitude Matching for Field-Scale Production-Data Integration: Sensitivity, Nonlinearity, and Practical Implications. SPE J. 10 (1): 75–90. SPE-84570-PA. https://doi.org/10.2118/84570-PA.
Cheng, H., Kharghoria, A., He, Z. et al. 2005b. Fast History Matching of Finite-Difference Models Using Streamline-Based Sensitivities. SPE Res Eval & Eng 8 (5): 426–436. SPE-89447-PA. https://doi.org/10.2118/89447-PA.
Cheng, H., Wen, X.-H., Milliken, W. J. et al. 2004. Field Experiences with Assisted and Automatic History Matching Using Streamline Models. Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 26–29 September. SPE-89857-MS. https://doi.org/10.2118/89857-MS.
Christie, M. and Blunt, M. 2001. Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques. Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, USA, 11–14 February. SPE-66599-MS. https://doi.org/10.2118/66599-MS.
Datta-Gupta, A. and King, M. J. 2007. Streamline Simulation: Theory and Practice. Richardson, Texas, USA: Society of Petroleum Engineers.
Datta-Gupta, A., Kulkarni, K. N., Yoon, S. et al. 2001. Streamlines, Ray Tracing and Production Tomography: Generalization to Compressible Flow. Pet Geosci 7 (Supp): 75–86. https://doi.org/10.1144/petgeo.7.S.S75.
Di Donato, G. and Blunt, M. J. 2004. Streamline-Based Dual-Porosity Simulation of Reactive Transport and Flow in Fractured Reservoirs. Water Resour Res 40 (4): W04203, 12 pages. https://doi.org/10.1029/2003WR002772.
Emerick, A. A. and Reynolds, A. C. 2013. Ensemble Smoother with Multiple Data Assimilation. Comp Geosci 55: 3–15. https://doi.org/10.1016/j.cageo.2012.03.011.
Evensen, G. 2009. Data Assimilation: The Ensemble Kalman Filter. Berlin, Germany: Springer Science & Business Media.
Farshbaf Zinati, F., Jansen, J.-D., and Luthi, S. M. 2012. Estimating the Specific Productivity Index in Horizontal Wells from Distributed-Pressure Measurements Using an Adjoint-Based Minimization Algorithm. SPE J. 17 (3): 742–751. SPE-135223-PA. https://doi.org/10.2118/135223-PA.
Fernández-Martínez, J., García-Gonzalo, M., Fernández-Alvarez, J. et al. 2008. Particle Swarm Optimization (PSO): A Simple and Powerful Algorithm Family for Geophysical Inversion. SEG Technical Program Expanded Abstracts 2008: 3568–3571. https://doi.org/10.1190/1.3064068.
Foresee, F. D. and Hagan, M. T. 1997. Gauss-Newton Approximation to Bayesian Learning. Proc., International Conference on Neural Networks (ICNN'97), Houston, Texas, USA, 12 June, 1930–1935. https://doi.org/10.1109/ICNN.1997.614194.
Hajizadeh, Y., Christie, M. A., and Demyanov, V. 2011. Towards Multiobjective History Matching: Faster Convergence and Uncertainty Quantification. Paper presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 21–23 February. SPE-141111-MS. https://doi.org/10.2118/141111-MS.
Harris, S., Santoshini, S., Kashem, S. et al. 2018. Complex Geological Modeling and Quality Assurance Using Unstructured Grids. Paper presented at the Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 12–15 November. SPE-193202-MS. https://doi.org/10.2118/193202-MS.
He, Z., Datta-Gupta, A., and Vasco, D. 2006. Rapid Inverse Modeling of Pressure Interference Tests Using Trajectory-Based Travel Time and Amplitude Sensitivities. Water Resour Res 42 (3): W03419, 15 pages. https://doi.org/10.1029/2004WR003783.
He, Z., Datta-Gupta, A., and Yoon, S. 2002. Streamline-Based Production Data Integration with Gravity and Changing Field Conditions. SPE J. 7 (4): 423–436. SPE-81208-PA. https://doi.org/10.2118/81208-PA.
Ibrahima, F., Maqui, A., Negreira, A. S. et al. 2017. Reduced-Physics Modeling and Optimization of Mature Waterfloods. Paper presented at the SPE Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, 13–16 November. SPE-188313-MS. https://doi.org/10.2118/188313-MS.
Jenny, P., Lee, S., and Tchelepi, H. 2003. Multi-Scale Finite-Volume Method for Elliptic Problems in Subsurface Flow Simulation. J Comput Phys 187 (1): 47–67. https://doi.org/10.1016/S0021-9991(03)00075-5.
Kang, S., Bhark, E., Datta-Gupta, A. et al. 2015. A Hierarchical Model Calibration Approach with Multiscale Spectral-Domain Parameterization: Application to a Structurally Complex Fractured Reservoir. J Pet Sci Eng 135: 336–351. https://doi.org/10.1016/j.petrol.2015.09.024.
Kazemi, H., Mwrrill, L. S. Jr., Porterfield, K. L. et al. 1976. Numerical Simulation of Water-Oil Flow in Naturally Fractured Reservoirs. SPE J. 16 (6): 317–326. SPE-5719-PA. https://doi.org/10.2118/5719-PA.
Landa, J. L. and Horne, R. N. 1997. A Procedure to Integrate Well Test Data, Reservoir Performance History and 4-D Seismic Information into a Reservoir Description. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 5–8 October. SPE-38653-MS. https://doi.org/10.2118/38653-MS.
Lantz, R. 1971. Quantitative Evaluation of Numerical Diffusion (Truncation Error). SPE J. 11 (3): 315–320. SPE-2811-PA. https://doi.org/10.2118/2811-PA.
Li, D., Wang, J. Y., Zha, W. et al. 2018. Pressure Transient Behaviors of Hydraulically Fractured Horizontal Shale-Gas Wells by Using Dual-Porosity and Dual-Permeability Model. J Pet Sci Eng 164: 531–545. https://doi.org/10.1016/j.petrol.2018.01.016.
Li, R., Reynolds, A. C., and Oliver, D. S. 2001. History Matching of Three-Phase Flow Production Data. Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, USA, 11–14 February. SPE-66351-MS. https://doi.org/10.2118/66351-MS.
Lie, K. A., Møyner, O., and Krogstad, S. 2015. Application of Flow Diagnostics and Multiscale Methods for Reservoir Management. Paper presented at the SPE Reservoir Simulation Symposium, Houston, Texas, USA, 23–25 February. SPE-173306-MS. https://doi.org/10.2118/173306-MS.
Luo, Y. and Schuster, G. T. 1991. Wave-Equation Traveltime Inversion. Geophysics 56 (5): 645–653. https://doi.org/10.1190/1.1443081.
Ma, X., Al-Harbi, M., Datta-Gupta, A. et al. 2008. An Efficient Two-Stage Sampling Method for Uncertainty Quantification in History Matching Geological Models. SPE J. 13 (1): 77–87. SPE-102476-PA. https://doi.org/10.2118/102476-PA.
Mallison, B., Sword, C., Viard, T. et al. 2014. Unstructured Cut-Cell Grids for Modeling Complex Reservoirs. SPE J. 19 (2): 340–352. SPE-163642-MS. https://doi.org/10.2118/163642-MS.
Matringe, S. F., Juanes, R., and Tchelepi, H. A. 2007. Streamline Tracing on General Triangular or Quadrilateral Grids. SPE J. 12 (2): 217–233. SPE-96411-PA. https://doi.org/10.2118/96411-PA.
Mirzabozorg, A., Nghiem, L., Chen, Z. et al. 2013. Differential Evolution for Assisted History Matching Process: SAGD Case Study. Paper presented at the SPE Heavy Oil Conference Canada Calgary, Alberta, Canada, 11–13 June. SPE-165491-MS. https://doi.org/10.2118/165491-MS.
Mohamed, L., Christie, M. A., Demyanov, V. et al. 2010. Application of Particle Swarms for History Matching in the Brugge Reservoir. Paper presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September, SPE-135264-MS. https://doi.org/10.2118/135264-MS.
Møyner, O., Krogstad, S., and Lie, K.-A. 2015. The Application of Flow Diagnostics for Reservoir Management. SPE J. 20 (2): 306–323. SPE-171557-PA. https://doi.org/10.2118/171557-PA.
Møyner, O. and Lie, K.-A. 2014. The Multiscale Finite-Volume Method on Stratigraphic Grids. SPE J. 19 (5): 816–831. SPE-163649-PA. https://doi.org/10.2118/163649-PA.
Møyner, O. and Lie, K.-A. 2016. A Multiscale Restriction-Smoothed Basis Method for High Contrast Porous Media Represented on Unstructured Grids. J Comput Phy 304: 46–71. https://doi.org/10.1016/j.jcp.2015.10.010.
Narr, W. and Flodin, E. 2012. Fractures in Steep-Rimmed Carbonate Platforms: Comparison of Tengiz Reservoir, Kazakhstan, and Outcrops in Canning Basin, NW Australia. Paper presented at the American Association of Petroleum Geologists, Annual Convention and Exhibition, Long Beach, California, USA. https://doi.org/10.3997/2214-4609.20132005.
Natvig, J. R. and Lie, K.-A. 2008. Fast Computation of Multiphase Flow in Porous Media by Implicit Discontinuous Galerkin Schemes with Optimal Ordering of Elements. J Comput Phys 227 (24): 10108–10124. https://doi.org/10.1016/j.jcp.2008.08.024.
Olalotiti-Lawal, F. and Datta-Gupta, A. 2018. A Multiobjective Markov Chain Monte Carlo Approach for History Matching and Uncertainty Quantification. J Pet Sci Eng 166: 759–777. https://doi.org/10.1016/j.petrol.2018.03.062.
Olalotiti-Lawal, F., Onishi, T., Kim, H. et al. 2019. Post-Combustion Carbon Dioxide Enhanced-Oil-Recovery Development in a Mature Oil Field: Model Calibration Using a Hierarchical Approach. SPE Res Eval & Eng 22 (3): 998–1014. SPE-187116-PA. https://doi.org/10.2118/187116-PA.
Oliver, D. S., Reynolds, A. C., and Liu, N. 2008. Inverse Theory for Petroleum Reservoir Characterization and History Matching. Cambridge, England, UK: Cambridge University Press.
Oyerinde, A., Datta-Gupta, A., and Milliken, W. J. 2009. Experiences with Streamline-Based Three-Phase History Matching. SPE Res Eval & Eng 12 (4): 528–541. SPE-109964-PA. https://doi.org/10.2118/109964-PA.
Paige, C. C. and Saunders, M. A. 1982. LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Trans Math Softw 8 (1): 43–71. https://doi.org/10.1145/355984.355989.
Pan, Y., Hui, M.-H., Narr, W. et al. 2016. Integration of Pressure-Transient Data in Modeling Tengiz Field, Kazakhstan—A New Way To Characterize Fractured Reservoirs. SPE Res Eval & Eng 19 (1): 5–17. SPE-165322-PA. https://doi.org/10.2118/165322-PA.
Parker, R. L. 1994. Geophysical Inverse Theory. Princeton, New Jersey, USA: Princeton University Press.
Peters, L., Arts, R., Brouwer, G. et al. 2010. Results of the Brugge Benchmark Study for Flooding Optimization and History Matching. SPE Res Eval & Eng 13 (3): 391–405. SPE-119094-PA. https://doi.org/10.2118/119094-PA.
Pollock, D. W. 1988. Semianalytical Computation of Path Lines for Finite-Difference Models. Ground Water 26 (6): 743–750. https://pubs.er.usgs.gov/publication/70013303.
Prevost, M., Edwards, M. G., and Blunt, M. J. 2002. Streamline Tracing on Curvilinear Structured and Unstructured Grids. SPE J. 7 (2): 139–148. SPE-78663-PA. https://doi.org/10.2118/78663-PA.
Romero, C., Carter, J., Gringarten, A. et al. 2000. A Modified Genetic Algorithm for Reservoir Characterisation. Paper presented at the International Oil and Gas Conference and Exhibition in China, Beijing, China, 7–10 November. SPE-64765-MS. https://doi.org/10.2118/64765-MS.
Santoshini, S., Harris, S., Kashem, S. et al. 2018. Depogrid: Next Generation Unstructured Grids for Accurate Reservoir Modeling and Simulation. Paper presented at the SPE Russian Petroleum Technology Conference, Moscow, Russia, 15–17 October. SPE-191615-18RPTC-RU. https://doi.org/10.2118/191615-18RPTC-RU.
Schlumberger. 2014. Technical Description. Schlumberger.
Shahvali, M., Mallison, B., Wei, K. et al. 2012. An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids. SPE J. 17 (3): 768–778. SPE-146446-PA. https://doi.org/10.2118/146446-PA.
Spooner, V., Geiger, S., and Arnold, D. 2018. Flow Diagnostics for Naturally Fractured Reservoirs. Paper presented at the SPE Europec featured at 80th EAGE Conference and Exhibition, Copenhagen, Denmark, 11–14 June. SPE-190877-MS. https://doi.org/10.2118/190877-MS.
Stenerud, V. R., Kippe, V., Lie, K.-A. et al. 2008. Adaptive Multiscale Streamline Simulation and Inversion for High-Resolution Geomodels. SPE J. 13 (1): 99–111. SPE-106228-PA. https://doi.org/10.2118/106228-PA.
Stenerud, V. R., Lie, K.-A., and Kippe, V. 2009. Generalized Travel-Time Inversion on Unstructured Grids. J Pet Sci Eng 65 (3–4): 175–187. https://doi.org/10.1016/j.petrol.2008.12.030.
Tanaka, S., Kam, D., Datta-Gupta, A. et al. 2015. Streamline-Based History Matching of Arrival Times and Bottomhole Pressure Data for Multicomponent Compositional Systems. Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 28–30 September. SPE-174750-MS. https://doi.org/10.2118/174750-MS.
Tarantola, A. 2005. Inverse Problem Theory. Methods for Model Parameter Estimation. Philadelpha, Pennsylvania, USA: SIAM.
Vasco, D., Seongsik, Y., and Datta-Gupta, A. 1999. Integrating Dynamic Data into High-Resolution Reservoir Models Using Streamline-Based Analytic Sensitivity Coefficients. SPE J. 4 (4): 389–399. SPE-49002-MS. https://doi.org/10.2118/49002-MS.
Vasco, D. W., Datta-Gupta, A., Behrens, R. et al. 2004. Seismic Imaging of Reservoir Flow Properties: Time-Lapse Amplitude Changes. Geophysics 69 (6): 1425–1442. https://doi.org/10.1190/1.1836817.
Warren, J. E. and Root, P. J. 1963. The Behavior of Naturally Fractured Reservoirs. SPE J. 3 (3): 245–255. SPE-426-PA. https://doi.org/10.2118/426-PA.
Wender, L. E., Bryant, J. W., Dickens, M. F. et al. 1998. Paleozoic (Pre-Khuff Hydrocarbon Geology of the Ghawar Area, Eastern Saudi Arabia. GeoArabia 3 (2): 273–302.
Willhite, G. 1986. Waterflooding, Vol. 3. Richardson, Texas, USA: SPE Textbook Series, Society of Petroleum Engineers.
Williams, G., Mansfield, M., MacDonald, D. et al. 2004. Top-Down Reservoir Modelling. Paper presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 26–29 September. SPE-89974-MS. https://doi.org/10.2118/89974-MS.
Wu, Z. and Datta-Gupta, A. 2002. Rapid History Matching Using a Generalized Travel-Time Inversion Method. SPE J. 7 (2): 113–122. SPE-66352-MS. https://doi.org/10.2118/66352-MS.
Yin, J., Park, H.-Y., Datta-Gupta, A. et al. 2011. A Hierarchical Streamline-Assisted History Matching Approach with Global and Local Parameter Updates. J Pet Sci Eng 80 (1): 116–130. https://doi.org/10.1016/j.petrol.2011.10.014.
Zhang, Y., King, M. J., and Datta-Gupta, A. 2012. Robust Streamline Tracing Using Inter-Cell Fluxes in Locally Refined and Unstructured Grids. Water Resour Res 48 (6): W06521, 19 pages. https://doi.org/10.1029/2011WR011396.
Zuo, L., Lim, J., Chen, R. et al. 2016. Efficient Calculation of Flux Conservative Streamline Trajectories on Complex and Unstructured Grids. Paper presented at the Proceedings of 78th EAGE Conference and Exhibition. https://doi.org/10.3997/2214-4609.201600779.