History matching under geological control The probability perturbation method

1. Stanford Center for Reservoir Forecasting History matching under geological controlThe probability perturbation method Jef Caers Department of Petroleum Engineering Stanford University, Stanford, California, USA

2. Motivation • The goal of history matching is not just to match history • Prediction power of models cannot be verified • Geological realism enhances prediction • Interaction between geological model and flow model • Not all geology matters for flow • Iterative process between static/dynamic, not sequential

3. HM itself is not difficult Log Scale md 500 P3 P3 P3 I3 I3 I3 P4 P4 P2 P2 300 P4 P2 P5 P5 P5 I1 I1 I1 100 I2 I2 I2 P1 P1 P6 P6 P1 P6 0 Regions (SimOpt) Initial Model Proposed Matched Model Eclipse (SimOpt) Matched Model

4. Geological scenario prior geological scenario = set of decisions about the style of geological structures/features or about the parameterizations of these structures/features A prior geological scenario defines what remains constant during history matching Example geological scenario • permeability/porosity variogram • Boolean model with shape distributions • Training image model and seismic derived facies probabilities • Training image with unknown Net-to-Gross

5. Quantify geological scenario Prior geological scenario defines conditional probabilities P(A|B) A = “channel sand occurs” B = known “conditioning” data Key idea: Perturb the probability P(A|B) such that * a history match is achieved * the geological scenario remains unchanged

6. Probability perturbation Binary case: A=“channel occurs”, then i(o)(u)=1 P(A|D) = (1-rD) i(o)(u)+ rD P(A) prior information on A Perturb the conditional probabilities P(A|B) using another conditional probability that depends on the production data D Combine P(A|D) and P(A|B) into P(A|B,D) rD=0 P(A|B,D) = i(o)(u) : No perturbation rD=1 P(A|B,D) = P(A|B) : equiprobable realization is generated if random seed is changed

7. Example P Geological scenario 1. Two hard data 2. Training image I Assume permeability of each facies known (1500 vs 50mD)

8. Creating perturbations i(o)(u) Seed= 76845 P(A|D) = (1-rD) i(o)(u)+ rDP(A) Perturbations preserve geology Perturbation are between two equiprobable models Optimize on rD Seed= 36367

9. Graphical representation seed=76845 high seed=36367 low Space of All realizations rD=0 rD=1 Mismatch between simulated and field data

10. Basic Algorithm Inner Loop Change random seed Choose value for rD Done NO Define P(A|D) YES History match ? Generate a new realization and run flow simulation Outer Loop Converged to best rD ? YES NO Generate initial guess realization

11. Result Outer iteration 4

12. General method Match Reference Training image flow pressure

13. Multi-category

14. Junrae KimHistory matching on N/G History matching: Most critical : Finding a good geological model PP : searches within a fixed geological model Junrae: Critical parameters such as Net-to-Gross need to be part of the history matching process

15. Todd HoffmanRegional probability perturbation PP: one parameter creates same perturbation everywhere Todd: Create regions Attach a parameter rD to each region Regional perturbation method (RPP) Challenges: no artifact discontinuities at region border Solve a multiple-parameter problem P(A|D) = (1-rD) i(o)(u)+ rDP(A) P(A|D) = (1-rDk) i(o)(u)+ rDkP(A)

16. Satomi SuzukiHierarchical history matching 1) Perturb Facies by Prob. Perturbation 2) Perturb Perm within Facies END YES History Matched ? NO Perm Fixed Facies Fixed Change Random #

17. Inanc TureyenJoint fine and coarse scale HM Initial fine-scale realization Non-uniform coarsened realization History matched coarsened realization Initial coarsened realization Downscaled realization History Matching Static model : fine scale Flow simulations : coarse scale Traditional approach

18. Joint optimization History Matching Mismatch on coarse scale used for fine scale perturbations Grid Optimization Mismatch Between fine and coarse minimized Result: History matched non-uniform gridded model Fine-scale model also History matched

19. Joe VoelkerApplication to Ghawar Field Super-K determined By HM flow meter data Super-K= extreme flow But not caused by extreme K depth BBL/day/ft Driving mechanism = combined Facies and fracture model