Continuous Reservoir Model Updating Using Streamline Assisted Ensemble Kalman Filter

Abstract

This paper was presented as part of the student paper contest associated with the Annual Technical Conference and Exhibition. Abstract The recent use of the ensemble Kalman filter EnKF for data assimilation and assessment of uncertainties in future forecast in reservoir engineering seems to be very promising. It provides ways of incorporating any type of production data or time lapse seismic information in an efficient way; however, the use of the EnKF in history matching comes with its share of challenges and concerns. The overshooting of certain values in the permeability field, possible increase in the material balance errors of the updated phase(s), and limitation to work with non-Gaussian permeability distribution are some of the most critical problems of the EnKF. The use of larger ensemble size may mitigate some of these problems but are prohibitively expensive to implement. This paper presents a conditioning technique that can be implemented with the EnKF, which eliminates or reduces the magnitude of these problems. This allows for the use of a reduced ensemble size, thereby leading to significant saving in time during field scale implementation. Our approach involves no extra computational cost and is easy to implement. Additionally the final history matched model tends to preserve most of the geological features of the initial geologic model. A quick look at the procedure is provided here. It enables implementation of this approach into current EnKF algorithms. We demonstrate the power and utility of our approach with an example. Introduction Proper characterization of the reservoir and the assessment of uncertainty are crucial aspect of any optimal reservoir development plan and management strategy. To achieve this goal, it is necessary to reconcile geological models to the dynamic response of the reservoir through a process known as history matching. This procedure of history matching has been a topic of great interest1–5 and an area of active research in the oil industry. Some significant developments have been made in the area of dynamic data integration. Most of these techniques involve computation of sensitivities which relate changes in production response at a well to a change in reservoir parameters. Techniques of automatic history matching that do not use sensitivity or gradient based approaches are stochastic algorithms such as Markov Chain Monte Carlo (MCMC) and simulated annealing. A recent development in the field of production data integration without the use of sensitivities or gradients is known as the ensemble Kalman Filter6 (EnKF). EnKF is simulator independent; it can be linked to any existing reservoir simulator. Moreover, EnKF uses a sequential updating technique, that is, the data is assimilated as and when it becomes available. EnKF can assimilate the latest production data without re-running the simulator from the initial conditions. These characteristic makes it suitable for continuous model updating and clearly a more natural approach to reservoir characterization when compared to traditional history matching techniques. Furthermore, the increased application of downhole monitors, intelligent well systems and permanent sensors to continuously record pressure, well rates and temperature has provided a further boost to the sequential model updating approach via EnKF. These key features combined with the ease of implementation have generated significant interest7–12 in its applicability to the area of reservoir characterization. In addition to all the persuasive properties discussed above additional requirements are necessary in any history matching technique; a key requirement is that the final model should honor initial geological information and retain geologic realism. EnKF works pretty well when the initial distribution is Gaussian. It can have serious limitations with non-Gaussian distribution; it tends to transform multi-modal permeability distributions to a more normal or Gaussian distribution over a sequence of many updates16. This transformation leads to a loss of structure in the permeability field with the final model not conforming to geologic reality. The use of these ‘history matched’ suite of models for future forecasts or uncertainty analysis would lead to erroneous interpretation and inappropriate field development strategies. Failure of the EnKF to work with non-Gaussian distribution is related to the low moment statistics used to characterize the model state.