Imperial College Consortium on Pore-Scale Modelling

Transcription

1 Imperial College Consortium on Pore-Scale Modelling Martin Blunt Department of Earth Science and Engineering Imperial College London Executive summary Over the last six years the Imperial College Consortium on Pore-Scale Modelling has developed a suite of software to predict two- and three-phase transport properties for geologically realistic networks. We have used pore-scale modelling to predict, successfully, many different properties, such as two- and three-phase relative permeability, dispersion coefficients and non-newtonian flow. We have imaged a series of rock samples provided to us by sponsors and have developed methods to analyze the pore space and extract geologically realistic networks. We have then applied these methods to analyze recovery at the field scale, demonstrating the waterflood potential of transition zone reservoirs and explaining the apparently contradictory recovery trends with wettability in fractured and unfractured reservoirs. Pore-scale modelling is now established as a theoretical compliment to special core analysis. It is being used in the industry to assign multiphase flow properties in reservoir models and to predict how these properties vary with rock type and wettability. This proposal describes a third phase of the research for the next three years that is focused on three topics: three-phase flow, network extraction and validation. In three-phase flow we will use our unique state-of-the-art code to develop a physically-based predictive model for three-phase relative permeability with an emphasis on the study of gas and oil trapping. This has applications in enhanced oil recovery, including CO 2 injection and storage. For network extraction we will continue our research on using the topological properties of grain contacts to construct an unambiguous network. To validate our models we will perform benchmark experimental measurements of relative permeability on well-characterized sands and sandstones and compare the results with network predictions. We will use a combination of capillary pressure, NMR and electrical measurements to pin down the pore-scale distribution of contact angle. Budget Funding from a consortium of companies is requested at 30,000 per year per company. It is anticipated that with six members of the consortium and leverage from Government funding through the Department of Trade and Industry, the overall project will support two postdoctoral research associates and two PhD students. The initial period of funding will be for three years. Deliverables Access to all software developed. Six-monthly project meetings. Copies of all preprints and theses. Yearly progress reports. Page 1 of 10

2 Imperial College Consortium on Pore-Scale Modelling Abstract The aim of the proposed work is to apply pore-scale modelling to three important areas of research: three-phase flow, network extraction and validation. In three-phase flow we will use our unique state-of-the-art code to develop a physically-based predictive model for threephase relative permeability with an emphasis on the study of gas and oil trapping. For network extraction we will continue our research on using the topological properties of grain contacts to construct an unambiguous network. To validate our models we will perform benchmark experimental measurements of relative permeability on well-characterized sands and sandstones and compare the results with network predictions. We will use a combination of capillary pressure, NMR and electrical measurements to pin down the pore-scale distribution of contact angle. Previous work and expertise of the consortium Prof. Blunt is Head of the Department of Earth Science and Engineering at Imperial College London. He has considerable expertise in the numerical modelling of flow in porous media, both at the macroscopic (core and reservoir scale), and at the pore scale. He has written over 100 scientific papers on flow in porous media and reservoir engineering. He has performed research on pore-scale modelling for almost 20 years and has worked on the development of predictive methods, three-phase flow and the effects of wettability. Description of the problem One the key uncertainties in reservoir characterization and simulation is the assignment of multiphase flow properties. Relative permeabilities are measured on only a few core samples and then assigned in reservoir simulation to large heterogeneous grid blocks that may contain many rock types. As a consequence, relative permeabilities are rarely considered to be reliable and are often modified with little physical justification during history matching. However, the relative permeabilities assigned in field-scale simulation can have a dramatic impact on predictions of recovery. The use of physically-based properties that properly capture the pore structure and wettability variations in the reservoir give very different predictions than using empirical relative permeability models [1,2]. This problem is important in many enhanced oil recovery (EOR) applications, such as CO 2 flooding; while the waterflood response of a field may be understood, with gas present the behaviour is often poorly understood. An appealing approach to tackling the problem of multiphase flow characterization is to simulate flow processes directly at the pore scale. In recent years it has been demonstrated that by combining geologically realistic networks with a coherent description of pore-scale phase distributions and displacement accurate predictions of two- and three-phase transport properties can be made (see, for instance [3-8]). Now that pore-scale modelling is becoming established as a useful technique to compliment special core analysis, our research will focus on specific areas where there are still significant gaps in our knowledge. We still have very little quantitative understanding of three-phase flow and rely on empirical models to predict relative permeability. We plan to use our pore-scale code to develop a physically-based model of three-phase relative permeability with an emphasis on predicting the amount of gas and oil trapping for any displacement path for any wettabilty. This work will have specific application to EOR, such as CO 2 injection and longterm storage. The second topic concerns network extraction from pore-space images. While considerable progress has been made in finding the topology of the pore space using skeletonization and maximal ball algorithms, current methods still suffer from significant ambiguities. We will continue to develop an alternative approach that uses grain contacts to determine a pore-space topology. Last, while our comparisons of literature experimental data with prediction have been promising, such validation has been quite limited. We plan to perform a series of benchmark experiments on well-characterized samples and use porescale modelling to predict the results. The emphasis of the work will be on the assignment of Page 2 of 10

3 contact angles using a combination of capillary pressure, NMR and electrical measurements on the same sample. The research programme 1. Three-phase flow and trapping. Our current three-phase pore-scale model [7,8] can simulate any displacement sequence in a geologically realistic network for media of arbitrary wettability. It has been used to predict experimentally measured three-phase relative permeabilities, including displacements with multiple cycles of water and gas flooding [9] see Fig. 1. The code at present, however, is difficult to run and has not been fully debugged. To make good use of this unique tool, our first priority is to debug the code and make it more robust. In addition, at present, the model does not use thermodynamically consistent capillary pressures. Recently, the appropriate expressions for capillary entry pressures have been worked out and we plan to incorporate these in an improved code [10,11]. At present our model tends to over-predict the presence of oil layers which means that at present we cannot make reliable predictions of oil trapping in many circumstances. Once we have a robust code with proper consideration of capillary entry pressures, we will run a suite of simulations for media of different wettability and different displacement paths. We will first attempt to find a closed-form analytical expression that relates the amount of gas and oil trapped to saturation path and wettability index. Preliminary results see Fig. 2 demonstrate that the amount of trapping is subtly dependent on initial non-wetting phase saturation and wettability and that current simple empirical models based on water-wet systems are inadequate. Then, using the hypothesis that relative permeability is a unique function of the flowing (non trapped) phase saturation [12], we will develop a model of threephase relative permeability. Again this is not straightforward, as even as a function of flowing saturation, the isoperms do not necessarily have a simple form. This work will be carried out in collaboration with Prof. Mohammad Piri at the University of Wyoming, who is the original author of the three-phase network model. Prof. Piri plans to measure steady-state three-phase relative permeabilities for media of different wettability, extending the benchmark experiments of Oak [13]. These results will be used to test and validate our model. Oak, 1990 Sg predicted experimental Water2 k rw Gas1 Water1 So Sw k rg k ro Fig. 1. Predictions of three-phase relative permeability. We are able to make accurate predictions of three-phase relative permeability for water-wet media [11]. Page 3 of 10

4 Fig. 2. We can use the network model to predict the amount of oil and gas that is a trapped as a function of wettability and initial gas or oil saturation. Note that there are no simple trends and that the conventional Land model, based on water-wet media is inadequate in most cases. 2. Network extraction from pore-space images. We will continue our recent research on the topological analysis of grain packings. This is a complimentary approach to maximal ball and medial axis methods [14-16] and uses the contact points of grain packs to identify the topology of the pore space directly. Fig. 3 shows examples in two and three dimensions where sphere packs are defined in terms of networks of contact points. It is then possible to identify pores as the largest spaces between grains and how these pores are connected to each other. From this a network can be constructed without the ambiguities inherent in other methods. The problem is that the material needs to be analyzed in terms of discrete grains. For granular media it is possible to identify these grains, even in consolidated materials, from micro-ct scanning with erosion of voxels identified as solid. Once the pore-space topology is known, other network properties, such as inscribed radius and shape factor can be defined on the original image. While this is not a general method it cannot be applied to most carbonates, for instance, and may fail for low porosity systems it is a potentially powerful technique for a wide range of materials, including sands, sandstones and some granular carbonates. 3. Benchmark experiments and model validation. The final topic concerns the careful validation of our current models through comparison with experiment. Existing experimental facilities at Imperial College will be used to measure, on the same samples, two-phase relative permeability (both steady and unsteady state), capillary pressure, NMR response and resistivity index. In addition, the media studied sand-packs and simple sandstones will be imaged at a resolution of a few microns using micro-ct scanning to resolve the pore space. Using the tools developed in topic 2, representative networks representing the studied media will be generated. Then the predictive power of our two-phase code will be tested by an attempt to predict the measured properties. We will study the effect of wettability by ageing the systems in crude oil for different amounts of time. In particular we will determine how a combination of wettability index (from capillary pressure measurements), NMR response and resisitivity index can be used to determine the pore-scale distribution of contact angle. Page 4 of 10

5 Fig. 3. Grain packings in two and three dimensions can be analyzed as networks of grain contacts. From this pore spaces and the topology of the pore space can be determined unambiguously. This is a powerful way to generate geologically realistic networks for granular systems. The deliverables and milestones of the project will be: 1. A workable, debugged three-phase network model with thermodynamically consistent capillary pressures. 2. A physically-based model of three-phase relative permeability, validated against porescale modelling and experimental data that contains a prediction of oil, water and gas trapping for systems of arbitrary wettability for any displacement path. 3. Results of benchmark measurements of capillary pressure, relative permeability, resistivity index and NMR response for simple sand packs and sandstones of different wettability with validated network model predictions. 4. Guidelines on how to relate a combination of measurements to assign pore-scale contact angle. 5. An unambiguous methodology and code for network extraction for granular packings. Project management Prof. Martin Blunt of Imperial College will be the Project Manager. He will be in overall charge of coordinating the activity and links with the sponsoring oil companies. In addition, a postdoctoral research fellow will supervise the research on a day-today basis. Every six months there will be a project meeting for all the industrial sponsors of the project. At that meeting Page 5 of 10

6 research results will be presented and plans for the future will be discussed. The views of the sponsors will be taken into account when planning future work. The important issue is to keep the research focussed on practical applications while pursuing new ideas. In addition, a project report will be given to the sponsors every year that details the progress made. Means of dissemination All the research carried out in the consortium will be described in project reports that will be made available to sponsors before publication in the open literature. The reports will explain in detail the approaches used and the results. This will help in both the design of improved oil recovery methods and in the possible incorporation of the ideas developed into commercial software. Budget The project will support two post-doctoral research associates and two PhD students for three years, together with travel and computer costs. The full economic costs of staff are shown. Year 1 Year 2 Year 3 2 post-docs 180, , ,000 2 PhD students 28,000 30,000 32,000 (bursary) Student fees* 26,000 26,000 26,000 Computing 4,000 2,000 0 Travel 2,000 2,000 2,000 Total 240, , ,000 *Assuming one EU and one non-eu student. Fees will cover costs of computers for the students. Income: 6 sponsors at 30,000 per year plus the DTI at 30,000 per year plus matching funds from other sources of 30,000 per year = 240,000 per year. If more than 6 sponsors join, then the scope of the work will be expanded and additional PhD students recruited. The new topics of interest will be discussed with sponsors, but are likely to include the use of multiple-point statistics for pore-space characterization and generation, non-newtonian flow in porous media and upscaling. If fewer than 6 sponsors join, attempts will be made to obtain direct funding of PhD students and post-docs from individual companies. References 1. M D Jackson, P H Valvatne and M J Blunt, Prediction of Wettability Variation Within an Oil/Water Transition Zone and Its Impact on Production, SPE Journal 10(2), , June (2005). 2. H Behbahani and M J Blunt, Analysis of Imbibition in Mixed-Wet Rocks Using Pore- Scale Modeling, SPE Journal, 10(4) , December (2005). 3. M J Blunt, M D Jackson, M Piri and P H Valvatne, Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow, Advances in Water Resources, , P-E Øren, S Bakke and O J Arntzen, Extending Predictive Capabilities to Network Models, SPE Journal, (1998). 5. P-E Øren and S Bakke Process based reconstruction of sandstones and prediction of transport properties. Transport in Porous Media, (2002). 6. P H Valvatne and M J Blunt, Predictive pore-scale modeling of two-phase flow in mixed wet media, Water Resources Research, 40, W07406, doi: /2003wr (2004). 7. M Piri and M J Blunt, Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. I. Model description, Physical Review E 71, (2005). 8. M Piri and M J Blunt, Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. II. Results, Physical Review E 71, (2005). Page 6 of 10

7 9. V S Suicmez, M Piri and M J Blunt, Pore Scale Modeling of Three-Phase WAG Injection: Prediction of Relative Permeabilities and Trapping for Different Displacement Cycles, SPE 95594, proceedings of the SPE/DOE Symposium on Improved Oil Recovery held in Tulsa, Oklahoma, April (2006). 10. M Piri and M J Blunt, Three-phase threshold capillary pressures in noncircular capillary tubes with different wettabilities including contact angle hysteresis, Physical Review E 70, (2004). 11. M I J van Dijke, M Piri, K S Sorbie and M J Blunt, Criterion for three-fluid configurations including layers in a pore with non-uniform wettability, proceedings of CMWRXVI, Copenhagen, June (2006). 12. M J Blunt, An Empirical Model for Three-Phase Relative Permeability SPE Journal December (2000). 13. Oak, M.J., Three-Phase Relative Permeability of Water-Wet Berea. SPE 20183, proceedings of the SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, April (1990). 14. D B Silin, G Jin and T W Patzek. Robust Determination of the Pore Space Morphology in Sedimentary rocks. SPE 84296, proceedings of the SPE Annual Conference, Denver, Colorado, October (2003). 15. W B Lindquist and A Venkatarangan, Investigating 3D geometry of porous media from high resolution images, Physics and Chemistry of the Earth (A), 25(7) (1999). 16. A P Sheppard, R M Sok and H Averdunk, Improved pore network extraction methods, proceedings of the International Symposium of the Society of Core Analysts, Toronto, August (2005). Page 7 of 10

8 CV of the Lead Investigator Prof. Martin J. Blunt Professor of Petroleum Engineering Head of the Department of Earth Science & Engineering Imperial College London SW7 2AZ, UK Tel. +44(0) Fax +44(0) Education 1985 BA Natural Sciences, Cambridge University (First Class Honours) 1988 PhD, Theoretical Physics, Cambridge University. The Growth and Properties of Fractal Boundaries. Employment Research Physicist, BP Research, Sunbury-on-Thames Faculty member, Department of Petroleum Engineering, Stanford University: Assistant Professor ; Associate Professor ; sabbatical at Imperial College Professor of Petroleum Engineering and head of the Petroleum Engineering and Rock Mechanics research group (PERM), Imperial College London present Head of the Department of Earth Science and Engineering. Honours and Awards 1985 Research Scholarship, Trinity College Cambridge 1985 Clerk Maxwell and ver Heyden de Lancey Prizes, Cambridge University 1991 Tallow Chandlers Prize, BP 1996 Teaching award, School of Earth Sciences, Stanford University 1996 Cedric Ferguson Medal, Society of Petroleum Engineers 2001 Distinguished Lecturer, Society of Petroleum Engineers TEACHING AND RESEARCH INTERESTS Prof. Blunt s research concentrates on the fundamentals of multiphase flow in porous media, with application to improving hydrocarbon recovery from reservoirs, understanding pollutant migration and clean-up and geological carbon storage. The research covers experimental, theoretical and numerical investigations of fluid transport in porous media, from detailed investigations of chemical and physical processes at the pore scale, to field-scale simulations. Prof. Blunt has studied of two- and three-phase flow in granular sediments, flow in fractured media, and the use of streamline methods for efficient numerical modelling of multiphase flow in oil reservoirs and contaminant transport. Overall, Prof. Blunt has 100 publications dealing with various aspects of flow in porous media. Page 8 of 10

9 Journal publications J J Hastings, A H Muggeridge and M J Blunt, A New Streamline Method for Evaluating Uncertainty in Small-Scale, Two-Phase Flow Properties, SPE Journal 8(1) 32-40, March (2003). 2. B Bijeljic, A H Muggeridge and M J Blunt, Multicomponent Mass Transfer across Water Films During Hydrocarbon Gas Injection, Chem. Eng. Sci. 58(11) , June (2003). 3. G Di Donato, E I Obi and M J Blunt, Anomalous transport in heterogeneous media demonstrated by streamline-based simulation, Geophysics Research Letters 30(12) , June (2003). 4. B Agarwal and M J Blunt, Streamline-Based Method with Full-Physics Forward Simulation for History Matching Performance Data of a North Sea Field, SPE Journal 8(2) , June (2003). 5. X Lopez, P H Valvatne, and M J Blunt, Predictive network modeling of single-phase non-newtonian flow in porous media, Journal of Colloid and Interface Science, 264(1) , August (2003). 6. M D Jackson, P H Valvatne and M J Blunt, Prediction of wettability variation and its impact on flow using pore- to reservoir-scale simulations, Journal of Petroleum Science and Engineering, , (2003). 7. P Audigane and M J Blunt, Dual Mesh Method for Upscaling in Waterflood Simulation, Transport in Porous Media, , (2004). 8. G Di Donato and M J Blunt, Streamline-based dual-porosity simulation of reactive transport and flow in fractured reservoirs, Water Resources Research, 40, W04203, doi: /2003wr (2004). 9. W Huang, G Di Donato and M J Blunt, Comparison of streamline-based and gridbased dual porosity simulation, Journal of Petroleum Science and Engineering, 43, (2004). 10. P H Valvatne and M J Blunt, Predictive pore-scale modeling of two-phase flow in mixed wet media, Water Resources Research, 40, W07406, doi: /2003wr (2004). 11. E-O Obi and M J Blunt, Streamline-based simulation of advective dispersive solute transport, Advances in Water Resources, , (2004). 12. B Bijeljic, A H Muggeridge and M J Blunt, Pore-scale modeling of longitudinal dispersion, Water Resources Research, 40, W11501, doi: /2004wr (2004). 13. M Piri and M J Blunt, Three-phase threshold capillary pressures in noncircular capillary tubes with different wettabilities including contact angle hysteresis, Physical Review E 70, (2004). 14. H Okabe and M J Blunt, Prediction of permeability for porous media reconstructed using multiple-point statistics, Physical Review E 70, (2004). 15. B Agarwal and M J Blunt, A Streamline-Based Method for Assisted History Matching Applied to an Arabian Gulf Field, SPE Journal 9, , December (2004). 16. M S Al-Gharbi and M J Blunt, Dynamic network modeling of two-phase drainage in porous media, Physical Review E 71, (2005). 17. H Okabe and M J Blunt, Pore space reconstruction using multiple-point statistics, Journal of Petroleum Science and Engineering (2005). 18. M Piri and M J Blunt, Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. I. Model description, Physical Review E 71, (2005). 19. M Piri and M J Blunt, Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. II. Results, Physical Review E 71, (2005). 20. P H Valvatne, M Piri, X Lopez and M J Blunt, Predictive Pore-Scale Modeling of Single and Multiphase Flow, Transport in Porous Media 58, 23 41, doi: /s (2005). 21. Z Tavassoli, R W Zimmerman and M J Blunt, Analytic Analysis for Oil Recovery During Counter-Current Imbibition in Strongly Water-Wet Systems, Transport in Porous Media 58, , doi: /s (2005). 22. M D Jackson, P H Valvatne and M J Blunt, Prediction of Wettability Variation Within an Oil/Water Transition Zone and Its Impact on Production, SPE Journal 10(2), , June (2005) Page 9 of 10

10 23. Z Tavassoli, R W Zimmerman and M J Blunt, Analysis of counter-current imbibition with gravity in weakly water-wet Systems, Journal of Petroleum Science and Engineering 48, (2005). 24. H Behbahani and M J Blunt, Analysis of Imbibition in Mixed-Wet Rocks Using Pore- Scale Modeling, SPE Journal, 10(4) , December (2005). 25. H Behbahani, G Di Donato and M J Blunt, Simulation of counter-current imbibition in water-wet fractured reservoirs, Journal of Petroleum Science and Engineering 50, (2006). 26. B Bijeljic and M J Blunt, Pore-scale modeling and continuous time random walk analysis of dispersion in porous media, Water Resources Research 42, W01202, doi: /2005wr (2006). 27. E I Obi and M J Blunt, Streamline-based simulation of carbon dioxide storage in a North Sea aquifer, Water Resources Research 42, W03414, doi: /2004wr (2006). 28. M E Rhodes and M J Blunt, An exact particle tracking algorithm for advectivedispersive transport in networks with complete mixing at nodes, Water Resources Research 42, W04501, doi: /2005wr (2006). 29. R Juanes and M J Blunt, Analytical Solutions to Multiphase First-Contact Miscible Models with Viscous Fingering, Transport in Porous Media 64(3), , doi: /s z (2006). Page 10 of 10