Robust Production Optimization with Capacitance-Resistance Model as Proxy

Transcription

1 Robust Production Optimization with Capacitance-Resistance Model as Proxy

2 What is Robust Production Optimization? Production Optimization: To optimize the objective by tuning the control variables (e.g. maximize the NPV by tuning well water injection rates for a water-flooded reservoir). Robust: To consider uncertainties. one single realization with averaged parameter values an ensemble of realizations with possible parameter values Benefits: 1) We can identify the optimal decisions (settings of the control variables) given the uncertainties. 2) Production can be optimized in the face of uncertainty.

3 How do We Get the Ensemble of Realizations? The ensemble of realizations can be generated by history matching using the Ensemble Kalman Filter (EnKF) (Lorentzen et al. 2001). The EnKF is a recursive filter: re-uses its outputs as inputs; weighs the model prediction and the observation; can be used to continuously update the reservoir simulation models. Kalman Gain There are uncertainties in both model prediction and observation. The EnKF can tell us which one should we trust more. The updated model is a combined result of considering model prediction, observation and uncertainties in them.

4 EnKF Example True Case Unknown: the horizontal permeability field Observation: WBHP and Oil Production Rate Selected Realizations (Initial (Time Step Guess) = 10) 20)

5 EnKF Example

6 The objective function Robust Production Optimization (RO) max NNNNNN rrrrrr = EE[NNNNNN] = 1 NN rr NNNNNN(mm rr, uu rr ) Expected Net Present Value Model Control Parameters Variables describes the value of a project decided (e.g. water/chemical by history matching injection rates, (e.g. chemical permeabilities, concentrations, porosities, slug sizes, ) location of faults, contact levels, ) NN rr rr=1

7 The objective function Robust Production Optimization (RO) max NNNNNN rrrrrr = EE[NNNNNN] = 1 NN rr NNNNNN(mm rr, uu rr ) Ensemble based steepest ascent method (EnOpt) (Chen et al. 2009) NN rr rr=1

8 Using grid-based reservoir models for RO can be computationally expensive. Serial computation time for grid-based reservoir models: The solution is to use a proxy model which must be 1) able to capture the most important physics and mechanisms affecting production prediction, and 2) very computationally attractive.

9 Grid-Based Model vs. Proxy Model

10 A CRM is a potential candidate to serve as a proxy model for water-flooded reservoir. The Capacitance-Resistance Model (CRM) mimics the response of fluid production induced by fluid injection as an electrical representation. CRM Parameters: Connectivity (ff): describes the fraction of water injected by an injector that contributes to the fluid production of a producer. Time Constant (ττ): a characteristic time for the pressure wave to travel from an injector to a producer.

11 The CRM CRM Continuity Equation: qq tt = qq tt 0 ee tt tt 0 ττ + II tt 1 ee tt tt 0 ττ (cc tt VV pp )( PP wwww,tt PP wwww,0 ) 1 ee tt tt0 ττ tt tt 0 Primary Injection BHP It requires only production, injection and WBHP data to define its parameters. A fractional flow model needs to be used together with the CRM to separate oil/water production from fluid production.

12 Grid-Based Model vs. CRM Grid-Based Model Coupled CRMP Parameters (PERMX): 2025 Run Time (ECLIPSE): 4.1 s Parameters: 3 Run Time (MATLAB): 0.17 s

13 Matching Results Grid-Based Model vs. CRM

14 Matching Results Grid-Based Model vs. CRM

15 Validation Results Grid-Based Model vs. CRM

16 Validation Results Grid-Based Model vs. CRM

17 Grid-Based Model vs. CRM Workflow Base Traditional New Optimal Expected NPV [million $] Total Elapsed Time [seconds] (before opt.) (after opt.) (after opt.) - 24,805 2,027 The optimal expected NPV of the new workflow is only 0.65% lower than that of the traditional one. Total elapsed time is reduced by 12 times. In realfield cases, the reduction may be even more significant.

18 Further Work More Advanced Application: Using CRMs to Assess VOI for History Matching Why do we need to assess Value of Information (VOI) for history matching? Gather Data? No HM Prod. Scheme (RO) Realizations Outcome $56 million HM Observations $60 million VOI = $4 million max. cost of data History Matching Assessing VOI for history matching (Barros et al. 2015) Ca. 2,000,000 simulation runs. If 20 min./run, the computational cost will be 76 years! Proxy models as such CRMs is necessary to be used to reduce the computational cost for assessing the VOI for history matching. With 100 realizations

19 Summary Robust production optimization takes uncertainties into consideration. Using grid-based reservoir models for robust production optimization leads to high computational cost. Thus, a proxy model is required. The CRM is a potential candidate to be a proxy model because it significantly speeds up the optimization whilst still giving robust result. The further work is to investigate the impact of using CRMs to assess VOI for history matching.

20 References Lorentzen, Rolf J, Geir Nævdal An iterative ensemble Kalman filter (in Automatic Control, IEEE Transactions on 56 (8): Chen, Yan, Dean S Oliver, Dongxiao Zhang Efficient ensemble-based closed-loop production optimization (in SPE Journal 14 (04): de Holanda, R. W., Gildin, E., & Jensen, J. L. (2015). Improved Waterflood Analysis Using the Capacitance-Resistance Model Within a Control Systems Framework. Paper presented at the SPE Latin American and Caribbean Petroleum Engineering Conference. Barros, E. G. D., Jansen, J. D., & Van den Hof, P. M. J. (2015). Value of information in parameter identification and optimization of hydrocarbon reservoirs. IFAC- PapersOnLine, 48(6),