Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter
- Geir Naevdal (RF-Rogaland Research) | Liv Merete Johnsen (Norsk Hydro) | Sigurd I. Aanonsen (Norsk Hydro) | Erlend H. Vefring (RF-Rogaland Research )
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2005
- Document Type
- Journal Paper
- 66 - 74
- 2005. Society of Petroleum Engineers
- 1.6 Drilling Operations, 3.3 Well & Reservoir Surveillance and Monitoring, 5.4.2 Gas Injection Methods, 5.3.2 Multiphase Flow, 3 Production and Well Operations, 5.2.1 Phase Behavior and PVT Measurements, 7.2.2 Risk Management Systems, 4.6 Natural Gas, 5.6.9 Production Forecasting, 5.5 Reservoir Simulation, 4.3.4 Scale
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The use of ensemble Kalman filter techniques for continuous updating ofreservoir model is demonstrated. The ensemble Kalman filter technique isintroduced, and thereafter applied to a simplified 2-D field model, which aregenerated by using a single horizontal layer from a North Sea fieldmodel.By assimilating measured production data, the reservoir model iscontinuously updated. The updated models give improved forecasts and theforecasts improve as more data is included. Both dynamic variables, such aspressure and saturations, and static variables, such as the permeability, areupdated in the reservoir model.
In the management of reservoirs, it is important to utilize all availabledata in order to make accurate forecasts. For short time forecasts, inparticular, it is important that the initial values are consistent with recentmeasurements. The ensemble Kalman filter1 is a Monte Carlo approach, which ispromising with respect to achieving this goal through continuous model updatingand reservoir monitoring.
In this paper, the ensemble Kalman filter is utilized to update both staticparameters, such as the permeability, and dynamic variables, such as thepressure and saturation of the reservoir model. The filter computations arebased on an ensemble of realizations of the reservoir model, and when newmeasurements are available, new updates are obtained by combining the modelpredictions with the new measurements. Statistics about the model uncertaintyis built from the ensemble. When new measurements become available, the filteris used to update all the realizations of the reservoir model. This means thatan ensemble of updated realizations of the reservoir model is alwaysavailable.
The ensemble Kalman filter has previously been successfully applied forlarge-scale nonlinear models in oceanography2 and hydrology3. In thoseapplications, only dynamic variables were tuned. Tuning of model parameters anddynamic variables was done simultaneously in a well flow model used forunderbalanced drilling4. In two previous papers5,6, the filter has been used toupdate static parameters in near-well reservoir models, by tuning thepermeability field. In this paper, the filter has been further developed totune the permeability for simplified real field reservoir simulationmodels.
We present results from a synthetic, simplified real field model. Themeasurements are well bottom-hole pressures, water cuts and gas/oil ratios. Asynthetic model gives the possibility of comparing the solution obtained by thefilter to the true solution, and the performance of the filter can beevaluated. It is shown how the reservoir model is updated as new measurementsbecomes available, and that good forecasts are obtained. The convergence of thereservoir properties to the true solution as more measurements becomesavailable is investigated.
Since the members of the ensemble are updated independently of each other,the method is very suitable for parallel processing. It is also conceptuallystraightforward to extend the methodology to update other reservoir propertiesthan the permeability.
Based on the updated ensemble of models, production forecasts and reservoirmanagement studies may be performed on a single "average" model, whichis always consistent with the latest measurements. Alternatively, the entireensemble may be applied to estimate the uncertainties in the forecasts.
Updating reservoir models with ensemble Kalman filter
The Kalman filter was originally developed to update the states of linearsystems to take into account available measurements7. In our case, the systemis a reservoir model, using black oil, and three phases (water, oil and gas).For this model, the solution variables of the system are the pressure and thewater saturation, in addition to a third solution variable that depends on theoil and gas saturation. If the gas saturation is zero, the third solutionvariable becomes the solution gas/oil ratio, if the oil saturation is zero itbecomes the vapor oil/gas ratio. Otherwise the third solution variable is thegas saturation. The states of this system are the values of the solutionvariables for each grid block of the simulation model. This model isnon-linear.
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