Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques

Transcription

1 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Yulin Jin Energy Resources Engineering CS Project Presentation Chevron Well Performance and Recovery Mechanisms

2 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Content Motivation and Background Information Connectivity Analysis and Sampling Heterogeneous Case Homogeneous Case Instinct Methods Performance Chevron WPRM Meeting, Aug -,

3 Reservoir Simulation Finite Volume Methods Computational cost is very expensive Computational time increases dramatically when the number of cells increases Chevron WPRM Meeting, Aug -,

4 Goal of Simulation: P-P-P Analysis Geostatistics Run multiple simulations to consider the uncertainty... -y y fw tim e, days -y Chevron WPRM Meeting, Aug -,

5 Fracture Modeling Workflow Fracture Characterization Gridding of Unstructured DFM M cells Save h/h = times! Chevron Simulation on DFM WPRM Meeting, Aug -, MSR & DPDP

6 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Content Motivation and Background Information Connectivity Analysis and Sampling Heterogeneous Case Homogeneous Case Instinct Methods Performance Chevron WPRM Meeting, Aug -,

7 Assumptions Injector in the center, producers on the corners fractures Injector connects to fracture Chevron WPRM Meeting, Aug -,

8 Different Fracture realizations with the Same Distribution Chevron WPRM Meeting, Aug -,

9 Different Fracture realizations with the Same Distribution Chevron WPRM Meeting, Aug -,

10 Results of Connectivity Analysis Chevron WPRM Meeting, Aug -,

11 Algorithm of well connectivity analysis.intersection Detection.Breadth Frist Search For each pair of Fracs Push the st Frac to queue In Box? Yes Break Yes Empty? No Intersected? Yes Deque top Frac Add Fracs to NB lists Continue No New? Yes Add to Frac list Enque NB- Fracs Chevron WPRM Meeting, Aug -,

12 Fractures Connecting to the Injector Chevron WPRM Meeting, Aug -,

13 Sampling Distance of points = coeff*l where coeff = L Chevron WPRM Meeting, Aug -,

14 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Content Motivation and Background Information Connectivity Analysis and Sampling Heterogeneous Case Homogeneous Case Instinct Methods Performance Chevron WPRM Meeting, Aug -,

15 Heterogeneous Permeability Field Log-Normal Distribution Chevron WPRM Meeting, Aug -,

16 Heterogeneous Permeability Field Log-Normal Distribution Chevron WPRM Meeting, Aug -,

17 WPRM Meeting, Aug -, Chevron Hausdorff Distance ) ( ) ( b a b a ab y y x x d + = )), ( ),supinf, ( max(sup inf : ), ( b a d b a d B A d A a B b B b A a Z H =

18 Result of Hausdorff Distance Zero diagonal # is very high Max is (#,#) Chevron WPRM Meeting, Aug -,

19 WPRM Meeting, Aug -, Chevron Connectivity Results

20 How to Choose realizations sort Chevron WPRM Meeting, Aug -,

21 Wasserstein Distance d W, p( A, B) : = inf d p µ M ( µ, µ L ( A B, µ ) A B ) d ( µ X p / W, p A, B) : = min( d( a, b) ( a, b)) a, b p d ab = e coeff K a K b ( xa xb) + ( ya yb ) where coeff >, Ka and Kb are permeability value at the (x a, y a ) and (x b, y b ) p =, p = and p = Remember that p = is also called EMD distance. Chevron WPRM Meeting, Aug -,

22 Advantage of Wasserstein Distance Chevron WPRM Meeting, Aug -,

23 Transportation Problem Sub sampling is needed. where w pi =/M w qi = /N d ab = e coeff K K a b M N i= j= f ij = ( xa xb) + ( ya yb ) Chevron WPRM Meeting, Aug -,

24 Results of Wasserstein Distance Zero diagonal # is not very high, Lower than Hausdorff Max are (#,#) and (#,#) Values when p Chevron WPRM Meeting, Aug -,

25 WPRM Meeting, Aug -, Chevron Connectivity Results

26 Different p of Wasserstein Distance P= Chevron P=.. WPRM Meeting, Aug -, P=

27 Wasserstein Distance using Diff Weights where w pi = Perm p (i)/sum(perm p ) w qi = Perm q (i)/sum(perm q ) Using different Perm EMD = Chevron WPRM Meeting, Aug -,

28 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Content Motivation and Background Information Connectivity Analysis and Sampling Heterogeneous Case Homogeneous Case Instinct Methods Performance Chevron WPRM Meeting, Aug -,

29 Homogeneous Permeability Field Everywhere is Chevron WPRM Meeting, Aug -,

30 Heterogeneity vs Homogeneity Chevron WPRM Meeting, Aug -,

31 Gromov-Hausdorff Distance dgh ( X, Y ) : = inf Z, f, g d Z H ( f ( X ), g( Y )) where f(x) = X g(y) = Rotate(Y, ), Rotate(Y, ), Rotate(Y, ), Rotate(Y, ) Chevron WPRM Meeting, Aug -,

32 Chevron WPRM Meeting, Aug -,

33 Results of Gromov-Hausdorff Distance Zero diagonal # is very high Much lower than Hausdorff.. Hausdorff Chevron WPRM Meeting, Aug -,

34 Gromov-Wasserstein Distance d Z ( X, Y ) : inf d, ( f ( X ), g( Y, p W p GW = Z, f, g )) where p =, p =, p = f(x) = X g(y) = Rotate(Y, ), Rotate(Y, ), Rotate(Y, ), Rotate(Y, ) Chevron WPRM Meeting, Aug -,

35 Results of Gromov-Wasserstein Distance Zero diagonal Lower than Gromov-Hausdorff and Wasserstein Max are (#,#) and (#,#) Chevron Values when p WPRM Meeting, Aug -, Gromov-Hausdorff......

36 WPRM Meeting, Aug -, Chevron Connectivity Results

37 Different p of Gromov-Wasserstein Distance p=..... p= p= Chevron WPRM Meeting, Aug -,

38 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Content Motivation and Background Information Connectivity Analysis and Sampling Heterogeneous Case Homogeneous Case Intrinsic Methods Performance Chevron WPRM Meeting, Aug -,

39 Shape Distribution Investigate the intrinsic method D: Measures the distance between two random points on the surface. Bhattacharyya: D( f, g) = fg Chevron WPRM Meeting, Aug -,

40 Results of Shape Distribution Zero diagonal # is extremely high Hard to discriminate values Eliminate High Value Chevron WPRM Meeting, Aug -,

41 Histogram of Shape Distribution Chevron WPRM Meeting, Aug -,

42 EMD using Shape Context where d ( a, b ) ij i j w pi =/M w qi = /N M N i= j= f ij = = aibj Chevron WPRM Meeting, Aug -,

43 Results of EMD using Shape Context Zero diagonal # is extremely high Better than Shape Distribution Eliminate High Value Chevron WPRM Meeting, Aug -,

44 EMD using Shape Context vs EMD using Euclidean Distance # is higher W... (#,#/#/#) is higher Values are higher.... EMD using Shape Context Gromov-W Chevron WPRM Meeting, Aug -,..

45 WPRM Meeting, Aug -, Chevron Connectivity Results

46 Systematically Accelerating the Fracture Simulation Workflow using Shape Matching Techniques Content Motivation and Background Information Connectivity Analysis and Sampling Heterogeneous Case Homogeneous Case Instinct Methods Performance Chevron WPRM Meeting, Aug -,

47 Performance Method GROMOV-Wasserstein Ave Time (s). # EMD using Shape Context. Wasserstein. GROMOV-HAUSDORFF. HAUSDORFF Shape Distribution. Chevron WPRM Meeting, Aug -,

48 Reduce from O(N ) to O(MN) M =, N = Bins are sorted by # Rs D < criterion?? Provider Chevron WPRM Meeting, Aug -,

49 Hausdorff Distance with Heterogeneity Hetero Coeff = Hetero Coeff = Hetero Coeff = Chevron d ab = e coeff K WPRM Meeting, Aug -, a K b ( xa xb) + ( ya yb )

50 Summary and Conclusions In the cases I studied, observations are below: In heterogeneous cases, use Wasserstein distance or Hausdorff distance using permeability information. In homogeneous cases, Gromov-Hausdorff distance is better than Gromov-Wasserstein distance because its values are higher and much faster. In both heterogeneous cases and homogeneous cases, EMD using Shape Context is better than Shape Distribution using D because its values are much higher and even better than Wasserstein distance (p=). The performance of Gromov-Wasserstein is low, practically, we had better avoid calculating Gromov- distance directly. Provided a systematic approach to accelerate the fracture simulation process. Chevron WPRM Meeting, Aug -,