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)

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

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

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

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

1. Erosion in Surface-based Modeling Experiment Settings

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

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

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

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

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

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

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

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?

… 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

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

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

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

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

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)

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)

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?

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

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

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

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

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

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

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

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

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