1. Measurement and Control of Reservoir Flow
FORCE seminar, October 2002
D.R. Brouwer, Delft University of Technology (DUT)
J.D. Jansen , DUT & Shell E&P

2. Outline Smart well research at Delft
Reduction of high order reservoir models
Identification of low order reservoir models
Optimisation of reservoir drainage

3. Smart Wells – Research at TU Delft
Cor van Kruijsdijk Prof.
Jan Dirk Jansen Ass. Prof.
Renato Markovinovic Ph.D
Joris Rommelse Ph.D
Roald Brouwer Ph.D
Paul van den Hof (Phys.) Prof.
Okko Bosgra (Mech. Eng.) Prof.
Arnold Heemink (Math.) Prof.

4. Smart well research at Delft
Assume hardware is working
How to use hardware to improve production process?
Measurement and control theory

5. Model-based closed-loop control
Output
System x = f(x,u,w)
(reservoir, wells & facilities)
Input .
Noise w
Noise v
Controllable input u
Sensors
y=h(x,v)
Optimization
Control
algorithms
Reduction
Low-order model
Identification
High-order model
Geology, seismics,
well logs, well tests,
fluid properties, etc.

6. Model reduction High order model: 103-106 state variables
geological model, reservoir model
Low order model: state variables
low order physical/mathematical description
Why reduction
Reduce computational burden of history matching and optimisation
Adjust model size to
what you can control
what you can ‘history match’ (information available)

7. black-box modelling: identification
Model reduction (2)
Two approaches:
high-order model
low-order model
white-box modelling
black-box modelling: identification
optimization
real reservoir

8. Model reduction methods
Linear
Modal Decomposition
eigenvalues of system matrix
Balanced Realisation
Input to output transfer function
Obervability and controllability energy functions
Others
Nonlinear
Proper Orthogonal Decomposition (POD)

9. Proper Orthogonal Decomposition
Nonlinear low order model
Based on large number of snapshots of states (X) over time
Compatible with all simulators

10. POD - numerical example
n =128, k = 5
prediction
reconstruction 1 2 3 4 5 6
permeability k 8 7
model order: 128

11. Model reduction - conclusions
First results promising; in particular POD.
Essential information may be of low-order!
Next question
Can we obtain this info directly from the measurements (outputs)?

12. Model-based closed-loop control
Optimization
Identification
Reduction
Controllable input u
Noise w
Output
System x = f(x,u,w)
(reservoir, wells & facilities)
Input .
Control
algorithms
Noise v
Sensors
y=h(x,v)
Low-order model
High-order model
Geology, seismics,
well logs, well tests,
fluid properties, etc.

13. Approach II: Black box modelling
Low order models directly from input-output data
Experimental data
Compatible with all simulators

14. Reservoir identification (1)
Idea: use smart well valves and pressure sensors for continuous cross-well pressure transient analysis
Obtain low order model from these input-ouput data
First try: Single-phase, linear, deterministic ‘reservoir’
Method: sub-space identification: (Linear input-output, black-box identification method)

15. Reservoir identification (2)
- 1 4
Fluid parameters:
c fluid compressibility [1/Pa]
m fluid viscosity [Pa.s]
r fluid density [Pa.s]
Reservoir dimensions:
# gridblocks in x and
y direction
h gridblock height [m]
Dx, Dy x,y-gridblock width [m]
injector
producer

16. Reservoir identification (3)
Injectors:
q = 10-8 or 0 [m3/ m3 s]
Producers:
q = or 0 [m3/ m3 s]

17. Reservoir identification (4)
Injectors:
q = 10-8 or 0 [m3/ m3 s]
Producers:
q = or 0 [m3/ m3 s]

18. Reservoir identification (5a)

19. Reservoir identification (5b)

20. Reservoir identification (5c)

21. Reservoir identification (5a)

22. Reservoir identification (6)
Injectors:
q = [m3/ m3 s]
Producers:
q = or 0 [m3/ m3 s]

23. Reservoir identification (7a)

24. Reservoir identification (7b)

25. Reservoir identification (7c)

26. Reservoir identification (7d)

27. Identification - conclusions
Works very well for single phase flow
Only valid for short time spans in multi-phase flow
Alternative to black box identification: Start with white-box model and ‘continuously’ update
Extended Kalman filtering on low-order (reduced) model
Ensemble Kalman filtering on high-order model – ‘data assimilation’ (Vefring et al. 2002)

28. Model-based closed-loop control
Controllable input u
Noise w
Output
System x = f(x,u,w)
(reservoir, wells & facilities)
Input .
Control
algorithms
Identification
Noise v
Sensors
y=h(x,v)
Low-order model
Optimization
High-order model
Reduction
Geology, seismics,
well logs, well tests,
fluid properties, etc.

29. Optimisation and Control
Optimise reservoir drainage based on description that is available
high order model
low order model

30. Current optimisation approach
Model:
Reservoir simulator
Objective:
Net Present Value (NPV)
Optimisation algorithm:
Optimal Control Theory

31. Waterflooding with smart wells

32. Water flooding optimization (1)
k [m2]
45 x 45 grid blocks
45 inj. & prod. segments
permeability contrast: factor 25-40
oil in streaks: 25%
1 PV injected, qinj = qprod
ro = 80 $/m3, rw = 20 $/m3
SPE (Europec 2002)

33. Water flooding optimization (2)
Conventional (equal pressure in all segments, no control)
Best possible (identical field rate, no pressure constraints)

34. Water flooding optimization (3)
Production data rate-constrained case

35. Water flooding optimization (4)
Production data pressure-constrained case

36. Example 2 3 injectors, 2 producers Pressure constrained
Rate constrained

37. Water flooding optimisation conclusions
Always scope to increase NPV
Pressure constraints: value is in reduced water production
Rate constraints: value is in reduced water production, accelerated oil production and increased oil recovery
Next steps:
3D, 3-phase
spatial (well placement)
closed-loop (‘real-time’)

38. Summary of Conclusions
Formal application of model-based control theory to smart wells/fields still in its infancy
Model reduction and identification techniques give encouraging first results
Closed-loop control can be based on low-order models (only model what you can observe and control!)
Large scope for drainage optimisation with smart wells (based on open-loop model)

39. Reservoir model
injectors
producers
<

40. Pressure constrained optimisation
4.4 PV production in base case
Maximum water cut 80%
<

41. Final saturation distribution
Ref case, PV=4.4
Opt case, PV=1.6
<

42. Results
90% of the reference case oil recovery achieved with only 36% of fluids injected
78% reduction in water production
max. profitable water cut
Reduction in number of wells possible?
Injector 3 closed for large part of time (50-60%).
Both producers closed for large part of time
<

43. <

44. Reservoir model
injectors
producers
<

45. Rate contrained optimisation
2 PV of injection/production
maximum water cut 80%
<

46. Final saturation distribution
Ref case, PV=2.0
Opt case, PV=2.0
<

47. Results For same pv injected
24% more oil
13% reduction in water production
Large number of well segments closed for large time intervals
smaller number of wells maybe sufficient?
<

48. <

49. <

50. Water flooding optimization conclusions
Always scope to increase NPV
Pressure constraints: value is in reduced water production
Rate constraints: value is in reduced water production, accelerated oil production and increased oil recovery
Scope for reduction in number of wells?
Next steps:
3D, 3-phase
spatial (well placement)
closed-loop (‘real-time’)

51. Summary of Conclusions
Formal application of model-based control theory to smart wells/fields still in its infancy
Model reduction and identification techniques give encouraging first results
Closed-loop control can be based on low-order models (only model what you can observe and control!)
Large scope for drainage optimisation with smart wells (based on open-loop model)