1. Stanford Center for Reservoir Forecasting
History matching under geological control The 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
500
300
100
Log
Scale md
Regions (SimOpt)
Initial Model P1 P2 P6 P5 P4 P3 I1 I2 I3
Eclipse (SimOpt)
Matched Model
Proposed
Matched Model P1 P2 P6 P5 P4 P3 I1 I2 I3 P1 P2 P6 P5 P4 P3 I1 I2 I3

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
Perturb the conditional probabilities P(A|B)
using another conditional probability
that depends on the production data D
P(A|D) = (1-rD) i(o)(u)+ rD P(A)
prior information on A
Binary case: A=“channel occurs”, then i(o)(u)=1
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
Space of
All realizations
rD=0
high
low
rD=1
seed=36367
Mismatch between simulated and field data

10. Basic Algorithm Inner Loop Done Outer 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
Reference
Match
Training image
flow
pressure

13. Multi-category

14. Junrae Kim History matching on N/G
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 Hoffman Regional 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 Suzuki Hierarchical 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 Tureyen Joint fine and coarse scale HM
Static model : fine scale
Flow simulations : coarse scale
Traditional approach
Initial fine-scale
realization
Non-uniform
coarsened
realization
Initial coarsened
realization
History matched
coarsened
History
Matching
Downscaled
realization

18. Joint optimization Result: History matched non-uniform gridded model
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 Voelker Application 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