SPE DISTINGUISHED LECTURER SERIES is funded principally through a grant of the SPE FOUNDATION

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1 SPE DISTINGUISHED LECTURER SERIES is funded principally through a grant of the SPE FOUNDATION The Society gratefully acknowledges those companies that support the program by allowing their professionals to participate as Lecturers. And special thanks to The American Institute of Mining, Metallurgical, and Petroleum Engineers (AIME) for their contribution to the program.

2 Acknowledgements SPE International for the opportunity to participate in the Distinguished Lecturer Program BP America, Inc. for permission, and the Professional Recognition Program which has provided the time and resources to prepare and present this material Colleagues whose work is represented Local SPE chapters worldwide for their efforts in hosting these presentations 2of 57

3 Upgridding and Upscaling: Current Trends and Future Directions Dr. Michael J. King Senior Advisor, Reservoir Modelling and Simulation BP America, Inc. SPE Distinguished Lecturer

4 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility: Yes, Permeability: No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What To Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 4of 57

5 Introduction: What is Upscaling? What is Upscaling? Assign effective properties to coarse scale cells from properties on fine scale grid Capture flow features of fine scale model DW GOM Resolution? Why Upscale? Reduce CPU time for uncertainty analysis and risk assessment Make fine-scale simulation practical Image from Mike Christie geological models: ~ million cells 5of 57

6 Why Upscale?: CPU Time Reduction Waterflood Field Example CPU Ratio (Coarse Scale / Fine Scale) ( ) Uniform Layer Coarsening Flexible 3D Coarsening Uniform Layering Coarsen Optimum Layering Coarsen Optimal Layer MCoarsen Active Cell Ratio (Coarse Scale / Fine Scale) SPE 95759, King et.al. Coarsening 6of 57

7 Upgridding and Upscaling: Context Upgridding & Upscaling in the overall 3D Modelling Workflow (After Roxar RMS) 3D Detailed Geologic Static Model Structure from well picks &/or seismic horizons Properties from well logs &/or seismic attributes &/or field performance data Geologic description from facies, analogues and field data Upscaled flow simulation model Performance prediction in the absence of dynamic data Starting point for a history match when dynamic data is available When done well, upscaling will preserve the most important flow characteristics of a geologic model 7of 57

8 Why Upscale?: Length & Area Lateral resolution of geologic and simulation grids are set by well spacing miles miles 30 mile length of ACG reservoirs with the London M25 loop used to set the scale Simulation Grid Cells: 200m x 200m or 100m x 100m Geologic Grid Cells: 100m x 100m or 50m x 50m 8of 57

9 Kanaalkop: Tanqua Karoo basin, South Africa Deepwater channel w/splay at top of photo ~250ft, which is about the size of a single cell in the areal direction of many simulation grids ~10ft exposure ~15ft windmill 9of 57

10 10ft thick exposure of channel With 5 Components of a Bouma sequence ~10ft 10 of 57

11 Why Upscale?: Thickness Upscaling is dominated by loss of vertical resolution Geologic grid will typically have 1 ft or 50 cm vertical resolution Simulation grid may include only a single layer per geologic unit 600 ft section of a North Slope reservoir, with the 190 ft BP Anchorage office for scale 11 of 57

12 Reservoir Zones, Well Logs & Outcrop No Vertical Exaggeration 12 of 57

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15 15 meters Geologist at Outcrop 30 geologic model layers 1-5 simulation model layers 15 of 57

16 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility: Yes, Permeability: No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What To Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 16 of 57

17 Summary: What Works Well Preserve connectivity and flow within the reservoir using flow based transmissibility upscaling 1 2 Wide Pizza Box BC s preserve flow tortuosity &/or Sealed Side BC s preserve flow barriers Preserve flow between reservoir and wells using algebraic well index upscaling 3 Preserves reservoir quality This combination of techniques has worked well within BP & similarly elsewhere in the industry Streamline calculations provide detailed validation based on pressures, sweep, and time of flight Validation after upscaling is always necessary 17 of 57

18 Do We Have an Economic LKCF Waterflood Development? LKCF Limit MSM Limit M1 2 :A5 MSM C-G M16:A4 M5 :C4 B Shale 12A LKCF UKCF OWC He at he r / Brent MSM A km Yellow = Channel Red = Margins Blue = Non-pay 64x64x450 = 1,843,200 cells 50mx50mx0.5m resolution 18 of 57

19 Magnus LKCF Waterflood Development Study 19 of 57

20 Cell Permeability Upscaling: Laboratory and Reservoir Model A laboratory coreflood Darcy s Law: Q K P = A µ L In three dimensions, we have three numerical corefloods Coreflood follows the coarse cell shapes 3 4 No flow side boundary conditions are the most common (others are possible) k* of 57

21 Streamlines in the Upscaled LKCF Model How Well Did 2x2x6 Upscaling Work? Fine Scale Time of Flight Coarse Scale Time of Flight Coarse Pressure 3D Streamlines, Time of Flight & Pressures calculated in the fine scale geologic model 2xInjectors & 2xProducers at a typical waterflood well spacing Fence diagram traced within the 3D geologic model Pressure constrained wells used to validate permeability Time of Flight & Pressures after conventional 2x2x6 upscaling: Loss of 95% of effective permeability Loss of internal reservoir heterogeneity 21 of 57

22 Cell Permeability Upscaling What Went Wrong? Sealed Side coreflood boundary conditions systematically expand barriers and reduce the continuity of pay Example 12x12=>4x4 (3x3 Upscaling): KX Permeability Continuous channel replaced by marginal sands Highly productive well replaced by poor producer 22 of 57

23 Cell Permeability Upscaling Streamline Flow Visualization Each cell in isolation No cross-flow Equilibrium at cell faces Preserves & expands barriers 12x12 => 3x3 4x4 Upscaling Example KX Cell Permeability KY Cell Permeability 23 of 57

24 Cell Permeability Upscaling Errors & More Subtle Errors Sealed Side Boundary Conditions do not adequately represent fluid flow in the fine scale model Reservoir quality is not preserved This is the most significant error However, there are more subtle errors Well Productivity (or Injectivity) is not preserved Well Index Upscaling Needless loss of spatial resolution Transmissibility Upscaling 24 of 57

25 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility: Yes, Permeability: No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What To Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 25 of 57

26 Boundary Conditions and Upscaled Permeability - 1/2 Upscale a simple sand / shale reservoir Sealed side BC s expand barriers Open linear pressure BC s allow barriers to leak Pizza box (Wide BC s) allow global flow tortuosity One Cell 26 of 57

27 Boundary Conditions and Upscaled Permeability 2/2 Question: Which permeability is right? Answer: Wide Pizza Box (or tortuous) boundary conditions provide the best representation of fluid flow capacity, but Sealed side boundary conditions preserve barriers. Barriers are often very important for modelling gas displacement, especially for vertical permeability They are also important in preserving channel margins Both answers are useful Use your judgement as engineers What is most important in your reservoir processes? Use both choices of boundary conditions as a sensitivity Mix and match horizontal and vertical treatments? 27 of 57

28 Transmissibility Upscaling 1/3 Preserves Spatial Resolution Transmissibility can be calculated by direct upscaling instead of from the harmonic average of cell permeabilities TX i+ 1 2 = TX A i+ 1 2 i+ 1 2 ( KX DX ) i ( KX DX ) i+ 1 ( KX DX ) + ( KX DX ) 1 2 = A i+ 1 2 i 2 KX DX i + i+ 1 2 DX Link Permeability is upscaled from cell center to cell center and has double the lateral resolution compared to cell permeability upscaling KX Harmonic average of a zero cell permeability is always zero i+ 1 i+ ( Plus) i = KX i+ 1 2 = KX ( Minus) i+ 1 i i + 1 i of 57

29 Transmissibility Upscaling 2/3 KX Streamline Flow Comparisons KX Sealed Cell KX Wide Shifted KXY Wide No Shift KX Sealed Shifted 29 of 57

30 Permeability Upscaling Determines Cell Properties 50 MD 50 MD 50 MD 50 MD 50 MD 30 of 57

31 Transmissibility Upscaling 3/3 Captures fine scale juxtaposition 50 MD 0 MD 0 MD 38 MD 0 MD 50 MD 31 of 57

32 Well Index Upscaling Used to Preserve Reservoir Quality Well productivity / injectivity & sealed side coreflood permeability? Does not describe radial flow and logarithmic pressure drop near a well Instead, use three (hypothetical) X, Y, and Z wells for each coarse cell WI WI WI Z X Y ( KX KY ) 2π = µ ln ( r r ) 0 w ( KY KZ ) 2π = µ ln ( KX KZ ) 2π = µ ln ( r r ) 0 ( r r ) 0 w w H H H Z X Y 32 of 57

33 Improved Upscaling: Well Index + Transmissibility Lack of pay continuity resolved through Well Index Upscaling Preserves injectivity and productivity of horizontal and vertical wells But, expands channels and removes barriers KX Permeability Contrast and barriers reintroduced through Transmissibility Upscaling Repeat in all three directions for 2x2x2=8-fold factor of improved flow resolution compared to cell permeabilities 33 of 57

34 Coreflood Cell Permeability OR Well Index + Transmissibility Upscaling Coreflood Cell Permeability Upscaling Well Index + Transmissibility Upscaling 600 KX Permeability of 57

35 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility: Yes, Permeability: No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What To Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 35 of 57

36 LKCF Upscaling Validation Well Index + Transmissibility Fine Scale Time of Flight 3D Streamlines & Time of Flight Comparison of: Fine Scale Model Coreflood Cell Perm Upscaling WI + Transmissibility Upscaling Coarse Scale Time of Flight Coarse Scale Time of Flight Coarse Pressure Coarse Pressure 36 of 57

37 Transmissibility Multipliers: Double the Spatial Resolution A transmissibility multiplier can represent a barrier without using a cell In contrast, zero vertical permeability prevents flow both up AND down and impacts flow in three layers 37 of 57

38 Andrew Reservoir: Validation & Impact of Thin Barriers Well Index + Transmissibility upscaling tracks fine scale prediction & early field performance 38 of 57

39 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility: Yes, Permeability: No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What to Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 39 of 57

40 Summary: What Works Well Preserve connectivity and flow within the reservoir using flow based transmissibility upscaling Wide Pizza Box BC s preserve flow tortuosity &/or Sealed Side BC s preserve flow barriers Preserve flow between reservoir and wells using algebraic well index upscaling Preserves reservoir quality This combination of techniques has worked well within BP & similarly elsewhere in the industry Streamline calculations provide detailed validation based on pressures, sweep, and time of flight Validation after upscaling is always necessary 40 of 57

41 Summary: What to Avoid Flow based coreflood upscaling for cell permeabilities Sealed side boundary conditions will not preserve flow tortuosity & will under-estimate reservoir quality Open linear pressure boundary conditions will not preserve reservoir barriers A single upscaling calculation cannot be used to preserve: Reservoir quality Reservoir barriers Tortuosity of reservoir fluid flow around barriers Unfortunately, using coreflood permeability upscaling is the most common practice in the industry 41 of 57

42 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility Yes, Permeability No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What To Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 42 of 57

43 Future Trends: A Priori Error Analyses & Designer Grids Wouldn t it be nice to know if an upscaling calculation would be a good approximation before you performed the upscaling calculation? Sources of Upscaling Error Assumption Pressure equilibrium within the coarse cell Fluid velocity is parallel to the pressure drop Single velocity within a coarse cell Source of Error (Missing Physics) Disconnected pay within the coarse cell will not be in equilibrium Flow may depend upon the transverse pressure drop on the coarse grid Distribution of multiphase frontal velocities replaced by a single value Designer Grids: Upscale in the Simulator at Initialization Calculate Transmissibility and Pore Volume for Composite Cells 43 of 57

44 Error from Layer Coarsening: Flood Front Progression Error in the velocity distribution is introduced while upscaling Different fluid velocities are replaced by a single value ( ) ( ) * F (S) F S W Kx/Phi K X φ is the frontal speed in each layer This is the property whose heterogeneity we will analyze Analysis applies to the net sands Vertical equilibrium within each coarse cell Medium Fast Slow 44 of 57

45 Designer Grids within the Flow Simulator Static Boundary Conditions Source of A Priori Error: Multiphase frontal velocities are replaced by a single value Design simulation layering from 3D geologic model to minimize variation in local multiphase frontal velocities %-Heterogeneity , 80% 336, 86% Optimal Layering Li & Beckner % Heterogeneity % Heterogeneity ; B-Variation % Heterogeneity: Uniform Coarsen Diagonal Guide Solution Total RMS Regression Solution Weighted RMS Regression Total RMS Regression Weighted RMS Regression Uniform Coarsening: Not Efficient 18 RMS Regression Error RMS Regression - Error Model Layers Number of Coarse Layers 45 of 57

46 Designer Grids within the Flow Simulator Upscale During Initialization (Static) 30 Tight Gas Layer Coarsening Fine Scale Model 22x23x1715 (Geological Scenario 5) Cum. Gas Prod. (BCF) MCOARSE Li and Beckner Optimal Optimal Layering Uniform Coarsening Regular-Coarsen NextVar-OneStep NextVar-Sequential Optimal-12L Optimal Li-Map-12L Li-Ave-MaxL Li-Ave-12L MCOARSE Fine Scale ,000 1,200 1,400 1,600 1,800 Model Layers General trend shows that uniform coarsening does not perform well Optimal (293 layers) is the best layering scheme Flexible 3D grid (MCOARSE) provides even better results 46 of 57

47 Layer Coarsening: Waterflood Example Fine Scale 124 Layers Optimal 22 Layers 7 Layers Too Coarse 22 Uniform Layers Too Coarse 47 of 57

48 Waterflood Field Example: Oil Recovery and Watercut 30% 25% Optimal Simulation Model has 22 layers 7 layers and 22 uniform layers are each too coarse Oil Production 30% 25% Oil Production 20% 20% 00% 90% 80% 70% 60% 50% 40% 30% 20% 10% 15% 10% 5% 7 Layers FineScale Coarsen_54 Coarsen_22 Coarsen_31 Coarsen_19 Coarsen_07 Time 0% Water Cut 7 Layers FineScale Coarsen_54 Coarsen_22 Coarsen_22U Coarsen_31 Coarsen_19 Coarsen_07 22 Uniform Layers Time 0% % 10% 5% 7 Layers FineScale Coarsen_54 Coarsen_22 Coarsen_31 Coarsen_19 Coarsen_07 PVINJ 0% Average Reservoir Pressure FineScale Coarsen_22 Coarsen_22U Time 48 of 57

49 A Priori Error: Lack of Pressure Equilibrium Assumption Pressure equilibrium within the coarse cell Fluid velocity is parallel to the pressure drop Single velocity within a coarse cell Source of Error (Missing Physics) Disconnected pay within the coarse cell will not be in equilibrium Flow may depend upon the transverse pressure drop on the coarse grid Distribution of multiphase frontal velocities replaced by a single value 49 of 57

50 Designer Grids within the Flow Simulator Upscale During Initialization (Static) Source of A Priori Error: Pressure equilibrium in the coarse cell is not present on the fine grid Design 3D simulation grid to prevent different sands from merging 50 of 57

51 Designer Grids within the Flow Simulator Upscale During Initialization (Static) 30 Tight Gas Layer Coarsening Fine Scale Model 22x23x1715 (Geological Scenario 5) Cum. Gas Prod. (BCF) Li and Beckner MCOARSE Flexible Coarsening Uniform Optimal Regular-Coarsen NextVar-OneStep NextVar-Sequential Optimal-12L Optimal Li-Map-12L Li-Ave-MaxL Li-Ave-12L MCOARSE Fine Scale ,000 1,200 1,400 1,600 1,800 Model Layers General trend shows that uniform coarsening does not perform well Optimal (293 layers) is the best layering scheme Flexible 3D grid (MCOARSE) provides even better results 51 of 57

52 2-point Geostat Model, x10 λ x =1.0 λ y =0.1 σ logk = dx = 10.0 ft dy = 10.0 ft Observations Trans upscaling is better than k* T* (open) > T* (restricted) Linear pressure B.C. not good Line/ point average good restricted open ConstantPre PeriodicBC LinearPre LinearPre, vl LinearPre, ln LinearPre, pt PeriodicBC, vl PeriodicBC, ln PeriodicBC, pt ConstantPre, vl ConstantPre, ln ConstantPre, pt PeriodicBC, vl PeriodicBC, ln PeriodicBC, pt ConstantPre, vl ConstantPre, ln ConstantPre, pt ConstantPre PeriodicBC LinearPre LinearPre, vl LinearPre, ln LinearPre, pt T* K* restricted open -15% -10% -5% 0% Error to Fine-Scale Model Flow Rate, QX = % -20% -10% 0% 10% 20% Error to Fine-Scale Model Flow Rate, Qy = of 57

53 Upscaling within the Flow Simulator Dynamic Boundary Conditions Source of A Priori Error: Fluid flow may depend upon the transverse pressure drop on the coarse grid Utilize actual well positions, flow rates and an iterative global solution on the coarse simulation grid to provide local pressure boundary conditions for the upscaling calculation, including the transverse pressure drop Cell Permeability Transmissibility + Well PI Global Flow Rates 100x100x50 => 20x20x10 upscaling for a variogram-based fine scale model Material provided by Lou Durlofsky (Stanford) & Yuguang Chen (Chevron) 53 of 57

54 Future Trends: Upscale in the Simulator (Static) Workflow Implications Single Shared Earth Model used for both static and dynamic calculations Negligible time spent building coarse grid Extremely flexible grid design Simulation speed improvement comparable to model rebuild 3x3x3 coarsen used to reduce run-time Resolution re-introduced to preserve Fault block boundaries Resolution near wells Fluid contacts Heterogeneity via statistical measures More accurate flow simulation than with uniform coarsening 54 of 57

55 Outline Introduction: Change of Scale & Upscaling Case Study: Magnus LKCF Validation and Analysis: What Went Wrong? Improved Upscaling: Understanding Permeability Boundary Conditions and Permeability Upscaling Transmissibility Yes, Permeability No Maintain the Well Injectivity & Productivity Magnus LKCF & Andrew Reservoir Case Studies Summary: What Works Well & What To Avoid? Future Trends: A Priori Error Analyses & Designer Grids Summary: Best Practice in Upscaling 55 of 57

56 Summary: Best Practice in Upscaling Ensure that the fine and coarse grids are aligned Many to 1 logical relationship is very important Check transport properties in initial geologic model By Facies: NTG, Porosity, Horizontal Permeability, Kv/Kh ratio Conserve volumes when upscaling static properties & saturations Bulk Rock Volume, Net Rock Volume, Pore Volume, Fluid Volumes Both 3DGeo => 3DSimulation and 1DLog => 1DGeo (blocked wells) When upscaling transmissibility (or permeability) Preserve reservoir quality Preserve reservoir barriers Preserve flow around reservoir barriers Streamline-based flow validation after upscaling Iteration: Is there a need to change resolution? Future trends: A Priori Error analysis & Designer Grids 56 of 57

57 Summary: A Personal Literature Review John Barker Karam Burns Dominic Camilleri Tianhong Chen Mike Christie Lou Durlofsky Chris Farmer Kirk Hird Lars Holden Peter King Dave MacDonald Colin McGill Don Peaceman Jens Rolfsnes Kefei Wang Chris White John K Williams Mike Zerzan Individuals whose work and questions have shaped my understanding of permeability & upscaling 57 of 57