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Siyao Xu Earth, Energy and Environmental Sciences (EEES)

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1 Siyao Xu Earth, Energy and Environmental Sciences (EEES)
Stanford Center for Reservoir Forecasting Integration of Geomorphic Experiment Data in Surface-based Modeling: Characterization and Simulation Siyao Xu Earth, Energy and Environmental Sciences (EEES)

2 Static Modeling Algorithms
Two points MPS Object based Surface based Process-based Geological Details Engineering Applicability & Simplicity Where we are  Rules imitate physics

3 The Work Structure 1. What data? 2. Which experiment? - Experiments
- Statistical External Similarity Real Experiment Similar? 3. How to make the appropriate algorithm? - Use Lobe Sequence from Experiments Experiment Realization Same Hierarchy Statistics & Rules T Sequential Surfaces 2D3D

4 Review of Surface-based Modeling
Positive-Negative Surfaces  Deposition-Erosion Channel Source Lobe Proximal Point Template

5 1. Erosion in Surface-based Modeling
A new lobe for time t+1 Surface at time t Changes sand body connectivity Requires Intermediate Records not maintained in real analogues Available in Experiments

6 1. Erosion in Surface-based Modeling
Experiment Settings

7 1. Erosion in Surface-based Modeling
Intermediate Records in Experiments  Along three lines per 2 min Infeed point 1.5 m 1.75 m 2 m

8 1. Erosion in Surface-based Modeling
Identify Erosion/Deposition Old Elevation New Elevation No event Erosion: New< old Deposition: New > old

9 1. Erosion in Surface-based Modeling
The Sequential Patterns Elevation Maintain Horizontal Location Negative Geometry Relative (to previous) T = 1 Sequence

10 1. Erosion in Surface-based Modeling
The Sequential Patterns Elevation Positive Geometry T = 2 The Vertical Axis Indicates the Order Sequence

11 1. Erosion in Surface-based Modeling
Example: 100 Records Positive-Negative Geometries Sequence Line

12 1. Erosion in Surface-based Modeling
Three Categories  Dimensionless measure

13 1. Erosion in Surface-based Modeling
Produced Erosion-Deposition Geometries Experiment Simulation

14 Summary - 1 Geomorphic Experimental Data
Provide information unavailable in real systems To Extract Dimensionless Information So it is rescalable to reservoirs New Question Is this the appropriate experiment?

15 … 2. Choose the Right Experiment Given a Field System Experiments
Saller et. al. 2008 … Experiments Which experiment? What part? Challenge Difficult to link with physics

16 2. Choose the Right Experiment
Scale-dependent Pattern Similarity Analysis Scale …… Hierarchy of Experimental Lobes P values Scale Scale-dependant Similarity Trend Saller et. al. 2008 Test Similarity at Every Scale

17 2. Choose the Right Experiment
Clustering Analysis on Experiments  Lobes at various scales Automatic Lobe Interpretation  Reachability Plot (Dendrogram) Source Direction Areal Shape Pairwise Interlobe Distance Time Interpretation Space 1 2 3 d13=d12+d23 d23 d12 Temporal Constrained Clustering Scale

18 2. Choose the Right Experiment
Quantify Lobe Patterns  G Functions Compare Lobe Patterns A Hypothesis Test (Specially Designed) on G Functions Lobe Pattern Spatial Point Process 𝐺 𝜃 𝐺 𝑀𝑃𝑃 𝐺 𝑃 𝐺 𝑆 G Functions Sample 1 Sample 2 Subset of 1 >> 0.58

19 2. Choose the Right Experiment
A Case Study Indonesia Amazon Real Exp. A – Extremely Unreal Exp. B Experiments Cross Comparison

20 2. Choose the Right Experiment
Experiments vs. Indonesia Param 1 Param 2 Exp. A vs. Indonesia Exp. B vs. Indonesia Similarity (P-Value) High p-values are consistent in all parameters Exp. B is similar to Indonesia Param 3 Param 4 One plot first ,then all Scale of Interpretation (km)

21 2. Choose the Right Experiment
Experiments vs. Amazon Param 1 Param 2 Exp. A vs. Amazon Exp. B vs. Amazon Similarity (P-Value) Neither is better Param 3 Param 4 Scale of Interpretation (km)

22 Summary - 2 Quantified Geology
Lobe patterns & hierarchy Pattern similarity Link Small Experiments to Large Reservoirs So experimental Information is applicable to specific reservoirs New Question: How to Simulate?

23 3. Simulate Input Lobe Sequence
Use a Lobe Pattern as Input Only X-Y pattern, no Z Peak Point 38 lobes 𝑮 𝑳𝒐𝒃𝒆 𝑺𝒐𝒖𝒓𝒄𝒆 Similarity Scale X Y Sequence

24 3. Simulate Lobe Sequence
A Correlated Random Walk (CRW) Lobe Migration Algorithm Relative migration Simple and fast Migration Distance ∆ 𝑟 𝑀 Migration Orientation ∆ 𝜃 𝑀 Lobe Orientation ∆ 𝜃 𝐿 ∆ 𝜃 𝑀 t t-1 t+1

25 Cross Sections Compensational Stacking
Aggradation: Spatial-Temporal Clustering SCRF 2013

26 3. Simulate Lobe Sequence
Quantify Lobe Sequence Similarity Scale Input Lobe Cophenetic Distance Simulated Lobes Scale

27 3. Simulate Lobe Sequence
Distance for Trees Cophenetic Distance 1 2 3 1.5 0.5 2.5 Heights of the Junction 𝐶𝐷 13 =2.5 𝐶𝐷 12 =1.2 𝐶𝐷 23 =2.5 3 Lobes

28 3. Simulate Lobe Sequence
A Tree  CDF of cophenetic distances L1-Norm of CDF  Dissimilarity of trees

29 3. Simulate Lobe Sequence
Input Seq. (TI)  Surface-based Model (MPS) Update Realization by Updating Input Seq. Input Seq. Controls Realizations

30 Summary - 3 Lobe Hierarchy  Dendrograms
Input to a simple but realistic algorithm appropriate for history matching Lobe Hierarchy is Implicitly Controlled Realizations can be updated by updating input lobe patterns

31 Contributions A Solution Tests Statistical Similarity between Small Experiments and Reservoir Scale Systems Quantitative Descriptions of Geological Concepts Easier for engineers A Realistic Lobe Model Simple & fast for engineering applications

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