Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter

Abstract

Summary The use of ensemble Kalman filter techniques for continuous updating of reservoir model is demonstrated. The ensemble Kalman filter technique is introduced, and thereafter applied to a simplified 2-D field model, which are generated by using a single horizontal layer from a North Sea field model. By assimilating measured production data, the reservoir model is continuously updated. The updated models give improved forecasts and the forecasts improve as more data is included. Both dynamic variables, such as pressure and saturations, and static variables, such as the permeability, are updated in the reservoir model. Introduction In the management of reservoirs, it is important to utilize all available data in order to make accurate forecasts. For short time forecasts, in particular, it is important that the initial values are consistent with recent measurements. The ensemble Kalman filter1 is a Monte Carlo approach, which is promising with respect to achieving this goal through continuous model updating and reservoir monitoring. In this paper, the ensemble Kalman filter is utilized to update both static parameters, such as the permeability, and dynamic variables, such as the pressure and saturation of the reservoir model. The filter computations are based on an ensemble of realizations of the reservoir model, and when new measurements are available, new updates are obtained by combining the model predictions with the new measurements. Statistics about the model uncertainty is built from the ensemble. When new measurements become available, the filter is used to update all the realizations of the reservoir model. This means that an ensemble of updated realizations of the reservoir model is always available. The ensemble Kalman filter has previously been successfully applied for large-scale nonlinear models in oceanography2 and hydrology3. In those applications, only dynamic variables were tuned. Tuning of model parameters and dynamic variables was done simultaneously in a well flow model used for underbalanced drilling4. In two previous papers5,6, the filter has been used to update static parameters in near-well reservoir models, by tuning the permeability field. In this paper, the filter has been further developed to tune the permeability for simplified real field reservoir simulation models. We present results from a synthetic, simplified real field model. The measurements are well bottom-hole pressures, water cuts and gas/oil ratios. A synthetic model gives the possibility of comparing the solution obtained by the filter to the true solution, and the performance of the filter can be evaluated. It is shown how the reservoir model is updated as new measurements becomes available, and that good forecasts are obtained. The convergence of the reservoir properties to the true solution as more measurements becomes available 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 conceptually straightforward to extend the methodology to update other reservoir properties than the permeability. Based on the updated ensemble of models, production forecasts and reservoir management studies may be performed on a single "average" model, which is always consistent with the latest measurements. Alternatively, the entire ensemble 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 linear systems to take into account available measurements7. In our case, the system is 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 the water saturation, in addition to a third solution variable that depends on the oil and gas saturation. If the gas saturation is zero, the third solution variable becomes the solution gas/oil ratio, if the oil saturation is zero it becomes the vapor oil/gas ratio. Otherwise the third solution variable is the gas saturation. The states of this system are the values of the solution variables for each grid block of the simulation model. This model is non-linear.

Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

“…Accurate prediction of groundwater flow and the fate of subsurface contaminants is one example (McLaughlin and Townley, 1996;Carrera et al, 2005). The multiphase flow of hydrocarbons in an oil reservoir is another example where accurate predictions have large economic impact (Naevdal et al, 2005;Fu and GomezHernandez, 2008). Subsurface domains are generally heterogeneous and shows wide range of heterogeneities in many physical attributes such as permeability and porosity fields.…”

Optimisation of costs and carbon savings in relation to the economic dispatch problem as associated with power system operation

“…As described by Naevdal et al [2003] Jahangiri [2012] are given below (note that only the key equations are provided). The EnKF comprises two main steps, forecast and analysis.…”

“…On the other hand, during the analysis step, new observations from the measurement sets are represented by another ensemble. In order to obtain consistent error propagation using the EnKF, the observations have to be considered as random variables [Naevdal et al, 2003]. This is accomplished by using the actual measurement (or whenever measurements are available) as the reference and the random measurement noise (d) is added to the measurement to obtain the perturbed observations denoted by d obs,j [Evensen, 2003, Naevdal et al, 2003, Jensen, 2007.…”

“…EnKF was first introduced by Evensen [1994] and further developed and applied in various branches of science (see Evensen [2003Evensen [ , 1994 and references therein). As described in Evensen [2003], Naevdal et al [2003], Jensen [2007], Altaf et al [2014], the EnKF is a recursive filter based on a Monte-Carlo approach to generate an ensemble of model representations. An ensemble is a system representation based on random sampling of system distribution [Evensen, 2003].…”

Multiscale ensemble filtering for reservoir engineering applications

“…Several publications have discussed the use of EnKF with oil reservoir models: Naevdal et al [19][20][21], Gu and Oliver [10], Gao and Reynolds [8], Liu and Oliver [15], Wen and Chen [27], and Skjervheim et al [24], showing promising results and, at the same time, raising some possible drawbacks.…”