Measurement and Control of Reservoir Flow FORCE seminar, 23-24 October 2002 D.R. Brouwer, Delft University of Technology (DUT) J.D. Jansen , DUT & Shell E&P

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

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.

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

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.

Model reduction High order model: 103-106 state variables geological model, reservoir model Low order model: 101-102 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) www.win.tue.nl/macsi-net

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

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)

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

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

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)?

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.

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

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)

Reservoir identification (2) - 1 4 Fluid parameters: c fluid compressibility 10-9 [1/Pa] m fluid viscosity 10-3 [Pa.s] r fluid density 10-3 [Pa.s] Reservoir dimensions: # gridblocks in x and y direction 8 h gridblock height 10 [m] Dx, Dy x,y-gridblock width 100 [m] injector producer

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

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

Reservoir identification (5a)

Reservoir identification (5b)

Reservoir identification (5c)

Reservoir identification (5a)

Reservoir identification (6) Injectors: q = 1.25-9 [m3/ m3 s] Producers: q = -10-8 or 0 [m3/ m3 s]

Reservoir identification (7a)

Reservoir identification (7b)

Reservoir identification (7c)

Reservoir identification (7d)

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)

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.

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

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

Waterflooding with smart wells

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 78278 (Europec 2002)

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

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

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

Example 2 3 injectors, 2 producers Pressure constrained Rate constrained

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’)

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)

Reservoir model injectors producers <

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

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

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 <

<

Reservoir model injectors producers <

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

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

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? <

<

<

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’)

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)