Modeling Sedimentary Heterogeneity

1. Modeling Sedimentary Heterogeneity Ye Zhang Geology & Geophysics http://faculty.gg.uwyo.edu/yzhang/ Strongly encourage students to also read the conclusions to tie the methods together from the earlier part of the text. 

2. Heterogeneity in sedimentary deposits: A review of structure-imitating, process-imitating, and descriptive approachesChristine E. Koltermann & Steven M. GorelickWATER RESOURCES RESEARCH, VOL. 32, NO. 9, PAGES 2617–2658, SEPTEMBER 1996 Statistical Methods (Page 2617~2632) + Conclusion Section

3. Introduction • Natural sedimentary rocks are heterogeneous (spatially varying) at multiple scales; • Heterogeneity formed as a result of complex geologic processes, e.g., deposition, erosion, diagenesis, structural deformation. • Subsurface heterogeneity is poorly known (most of the subsurface rock is inaccessible)

4. Sedimentary heterogeneity  heterogeneity of hydraulic parameter: porosity & permeability (or, hydraulic conductivity, transmissivity) • Permeability (K) varies over 13 orders of magnitude, whereas porosity (0—1) varies much less. • K heterogeneity controls fluid flow & solute transport in the subsurface  K is our focus!

5. K Heterogeneity controls subsurface fluid flow & solute transport, for example: • groundwater flow; • contaminant migration in groundwater; • oil/gas extraction; • geological waste disposal; • geothermal heat extraction. Solute transport video

6. CO2 Simulation CO2 migration video

7. Flow & Transport Modeling • Numerical models are used to simulate subsurface flow & transport processes & make recommendations for management; • Because of the importance of heterogeneity, models need to incorporate K variation; • But, how can heterogeneity be created for modeling, when we have so little data about the subsurface?

8. Image Creation Structure-imitating, process-imitating, & descriptive methods All approaches can mimic natural heterogeneity over a range of scales & consider geologic information. • Some approaches are strictly spatial; • Some are linked to the time evolution of sedimentation. • Some can be conditioned on measurements.

9. Structure-imitating methods Constrain the geometry of spatial patterns in sedimentary rocks: correlated random fields, probabilistic rules, and deterministic constraints (from facies relations). Approaches: spatial statistical algorithms & sedimentation pattern-matching.

10. Process-imitating models • Aquifer model calibration: • Use equations of flow and transport to relate K and porosity to hydraulic and solute information (fluid potential, flow rate, concentration) through history matching. • Geologic process models: • conservation of mass + conservation of momentum + sediment transport equations  simulate spatial patterns in grain size distributions.

11. Descriptive methods Couple geologic observations with facies relations to divide a subsurface reservoirs into zones of characteristic hydraulic properties(e.g., hydrofacies)

12. To summarize (1996): This talk! More has been done since 1996, including “hybrid” approaches. One approach popular in reservoir modeling is to integrate descriptive (deterministic) & structure-imitating (stochastic) methods

13. Spatial Statistical Methods • Gaussian methods; • Non-Gaussian methods.

14. Gaussian Methods • produce images of continuous distributions of K; • The joint multivariate probability density function (pdf) of K is Gaussian; • If actual sample values indicate that K is not normally distributed, then its frequency distribution can be modified by a normal scores transform, before the Gaussian methods are used.

15. Gaussian Methods • Gaussian methods can incorporate descriptive geologic information in 3 ways: • trends in the geology can be represented; • local values preserved by conditioning; • certain geologic features can be included in the variogram (a spatial correlation function) through statistical anisotropy & nested structures.

16. Gaussian Methods GEOL 5446 Fall, 2013 • Estimation (finding a “best” map): • Kriging; • Cokriging (including Collocated Cokriging) • Simulations (besides the “best”, evaluate uncertainty around the “best” with alternative realizations) • Nearest neighbor • Turning bands • Fourier transform methods • Fractal methods • LU Decomposition • Sequential Gaussian Simulation (SGS) • Co-Simulation (including Collocated CoSimulation) This Talk

17. Gaussian Methods --- Ordinary Kriging (OK) OK IDS IDS= Inverse Distance Squared (“Contouring”); OK=Ordinary Kriging (one type of Kriging)  gives a single “best” map  no alternatives from the best map  cannot be used to evaluate uncertainty

18. Gaussian Methods --Sequential Gaussian Simulation (SGS)

19. SGS  Multiple Realizations Realization 1 11 sampled f Realization 2 … Realization 10,000

20. SGS SGS – Limitation SGS is superior to IDS, but it has trouble delineating connected features IDS True

21. Gaussian Methods -- “Soft” Data Integration (Collocated CoSimulation)

22. Gaussian Methods -- Collocated CoSimulation

23. Gaussian Methods -- Collocated CoSimulation

24. Non-Gaussian Methods • Some use information from a training image, such as transition frequencies between rock types (e.g., MPS). • Indicator thresholds and variograms can be used to represent spatial structure of extreme values (e.g., indicator kriging or Sequential Indicator Simulation). • Probabilistic or geometric rules governing lithologic geometries can be incorporated. • Most non-Gaussian approaches can consider categorical variables, such as rock type.

25. Non-Gaussian Methods • Estimation (a single “best” map) • Indicator Kriging; • Indicator Principal components • Simulation (uncertainty around the “best” map) • Sequential Indicator Simulation (SIS) • Object-Based Modeling (Boolean Method; Marked Point Process) • Simulated Annealing • Markov Chains approaches This Talk

26. Non Gaussian Methods --- SIS Model the Nugget Sandstone in southwestern Wyoming for acid gas disposal from gas fields along the Moxa Arch

27. Non Gaussian Methods --- SIS • Data used: • Well logs (SP, Sonic, Porosity, Resistivity); • Core measurements; • Cross sections (AA’, BB’, CC’, DD’); • Isopach (one for each geological formation); • DD’ is outside the model domain; it helps us define the structure dip.

29. Correlating well logs: • Twin Creek Top • Nugget Top • Ankarah Top • Thaynes Top (= Ankarah Bottom)

30. Inferred structure tops from well logs

31. Petrofacies Modeling with SIS Facies Code 9 facies modeled: “0” clayey sandstone; “1” clay; etc. 3 reservoir zones (in gray color; no sufficient well data for SIS)

32. Acid Gas Injection End of Injection: 50 years from today End of Monitoring: 3000 years from today

33. SIS is sensitivity to variogram parameter & statistical anisotropy Same sample data, hand-contouring (deterministic; no uncertainty) Hand contour Hand contour SIS: assume “isotropic” pattern  isotropic variogram  isotropic SIS simulated pattern, vice versa; SIS (one realization) SIS (one realization)

34. Non Gaussian Methods --- Object-Based Modeling Geologic information  probabilistic rules and geometric constraints  object distribution, geometry, direction of elongation, and connectedness

35. 22 12 17 5 Object-Based Modeling: Deepwater Oil Reservoir Outcrop Observations of Facies relations High resolution seismic imaging of the channels at different reservoir depths

36. Object-Based Modeling of Facies http://faculty.gg.uwyo.edu/yzhang/Publications/SPE_114099.pdf

37. Porosity & K are then modeled within each facies object Porosity • Each facies has a distinct porosity/K distribution; • Petrophysical modeling is done for faciesby facies. Log10(k)

38. Once the image(s) are created, how are they used in subsurface modeling?

39. Estimate f at each unsampled location  evaluate its pdf (mean f; uncertainty from mean: sf) Created by collocated cosimulation

42. Where are the tools? • Many software have been developed for geostatistical modeling, e.g., • GSLIB (free) • Commercial (e.g., Petrel, GoCAD)

43. Petrel (Schlumberger 2009 Training Manual) SGS generated f conditioned to well data only (e.g., well-log-derived porosity) SGS generated f conditioned to well data & a facies probability cube (higher f are forced into the “channel belt” with a high channel facies probability)

44. Recent advances • Extract information from sedimentological facies models; • Incorporate qualitative geologic info into random field generators; • Simulate depositional processes; Bottomline: Better understanding of geological variability helps us build better models & make better management decisions.

45. Story of the “Missing Plume” Engineers first assumed homogenous aquifer with isotropic K  streamline perpendicular to head contours  plume migrates down hydraulic gradient  Install wells to intersect the plume for treatment, but no plume is found along the imaginedflow path! Heterogeneity due to buried “channels” in the aquifer  K is anisotropic  streamline is different (blue)  real plume Plainview

46. Extra Slides

47. Definitions: • Model: GEOL4444 • Simplified representation of reality; • A mathematical model: a set of PDEs used to describe fluid flow and transport. • Simulation (two definitions of “Simulation”) • Solve the flow and transport model with a computer code (GEOL4030) • Stochastic simulation: image creation using geostatistical techniques (GEOL 5446)

48. Definitions: • Facies: a rock assemblage of like characteristics, usually reflecting the origin of a rock unit; • Differentiating factors: • lithology lithofacies; • fossil content  biofacies, • geophysical log characteristics  petrophysical facies • hydraulic property  hydrofacies or hydrostratigraphic units (hydrogeology) or flow units (petroleum engineering)

49. Definitions: Connected high K units form conduits called preferential flow paths. The opposite of a preferential flow path is a flow barrier. When the spatial correlation between two variables disappears beyond a separation distance, that distance is called the correlation range(GEOL 5446). Conditioning: method of image generation exactly reproduces data values at measureddata locations.

50. Definitions Calibration: parameter values in a mathematical model are adjusted to achieve a best match between observed and simulated values. The volume of a measurement is its support or scale of support. In “upscaling,” values defined on a small support are used to create effective values related to a larger support. “Scale” refers to the extent of the field that is sampled, interpolated, viewed, or simulated.