History matching is a type of inverse problem in which observed reservoir behavior is used to estimate reservoir model variables that caused the behavior. Obtaining even a single history-matched reservoir model requires a substantial amount of effort, but the past decade has seen remarkable progress in the ability to generate reservoir simulation models that match large amounts of production data. Progress can be partially attributed to an increase in computational power, but the widespread adoption of geostatistics and Monte Carlo methods has also contributed indirectly. In this review paper, we will summarize key developments in history matching and then review many of the accomplishments of the past decade, including developments in reparameterization of the model variables, methods for computation of the sensitivity coefficients, and methods for quantifying uncertainty. An attempt has been made to compare representative procedures and to identify possible limitations of each.

Recent progress on reservoir history matching: a review

The use of ensemble Kalman lter techniques for continuous updating of reservoir model is demonstrated. The ensemble Kalman lter technique is introduced, and thereafter applied on two 2-D reservoir models. One is a synthetic model with two producers and one injector. The other model is a simplied 2-D eld model, which is generated by using a horizontal layer from a North Sea eld model. By assimilating measured production data, the reservoir model is continuously updated. The updated models give im- proved forecasts. Both dynamic variables, as pressure and sat- urations, and static variables as the permeability are updated in the reservoir model. used to update static parameters in near-well reservoir models, by tuning the permeability eld. In this paper, the lter has been further developed to tune the permeability for simplied real eld reservoir simulation models. We present results from a synthetic model as well as a sim- plied real eld 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 lter to the true solution, and the performance of the lter can be evaluated. It is shown how the reservoir model is updated as new measurements becomes available, and that good fore- casts 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 indepen- dently 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 per- meability. Based on the updated ensemble of models, production fore- casts and reservoir management studies may be performed on a single iaveragei model, which is always consistent with the latest measurements. Alternatively, the entire ensemble may be applied to estimate the uncertainties in the forecasts.

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Reservoir Monitoring and Continuous Model Updating Using Ensemble Kalman Filter

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 on two 2-D reservoir models. One is a synthetic model with two producers and one injector. The other model is a simplified 2-D field model, which is generated by using a 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. Both dynamic variables, as pressure and saturations, and static variables 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. While 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 model as well as a simplified real field model. The measurements are well bottomhole 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, 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 Now with Centre for Integrated Petroleum Research, University of Bergen

Fluid Mechanics of Hydraulic Fracturing: a Review

In the management of reservoirs it is an important issue to utilize the available data in order to make accurate forecasts. In this paper a novel approach for frequent updating of the near-well reservoir model as new measurements becomes available is presented. The main focus of this approach is to have an updated model usable for forecasting. These forecasts should have initial values that are consistent with recent measurements. The novel approach is based on utilizing a Kalman filter technique. The idea behind the Kalman filter is to incorporate the information from the measurements into the current estimate of the state of the model, taking into account the uncertainty that belongs both to the state of the model and the measurements. The uncertainty of the model is updated simultaneously with the model itself. A benefit of this approach compared to usual history matching is that the initial values for the forecasts will be in better agreement with the current measurements. Originally, the Kalman filter had shortcomings for large, non-linear models. During the last decade, however, Kalman filter techniques has been further developed, and applied successfully for such models within oceanographic and hydrodynamic application. This work is based on use of the ensemble Kalman filter. The ensemble Kalman filter is easy to impl ement, and have some good properties for non-linear problems. Here, we demonstrate the use of this technique within nearwell reservoir monitoring, focusing on its performance in forecasting the future production.

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Near-Well Reservoir Monitoring Through Ensemble Kalman Filter

Hybrid flux-splitting schemes for a two-phase flow model

Underbalanced and Low-head Drilling Operations: Real Time Interpretation of Measured Data and Operational Support

On a rough AUSM scheme for a one-dimensional two-phase model

Real-Time Evaluation of Hole-Cleaning Conditions With a Transient Cuttings-Transport Model

The aim of this paper is to show how simple and traditional methods for simulating multi-phase flow can be improved by introducing higher order accuracy. Numerical diffusion is reduced to a minimum by using slopelimiter techniques, and better predictions of flow rates and pressure are obtained. Slopelimiter techniques, originally developed to achieve higher order of accuracy in Godunov's method, is applied to a method following a finite element approach and a predictor–corrector shooting technique. These methods are tested and compared to a Godunov-type scheme recently developed for multi-phase flow.

Implementation of Godunov-type schemes for multi-phase flow tends to be a complicated and challenging task. Introducing the slopelimiter techniques in the finite element approach and the predictor–corrector shooting technique is however simple, and provides an overall reduction of the numerical diffusion. The focus is on using these techniques to improve the mass transport description, since this is the main concern in the applications needed.

The presented schemes represent different semi-implicit approaches for simulating multi-phase flow. An evaluation of higher order extensions, as well as a comparison by itself, is of large interest. We present a model for two-phase flow in pipelines and wells, and an outline of the numerical methods and the extensions to second order spatial accuracy. Several examples motivated by applications in underbalanced drilling are presented, and the advantages of using higher order schemes are illustrated. Copyright © 2005 John Wiley & Sons, Ltd.

Kjell Kåre Fjelde

Papers

Hybrid flux-splitting schemes for a two-phase flow model

Underbalanced and Low-head Drilling Operations: Real Time Interpretation of Measured Data and Operational Support

On a rough AUSM scheme for a one-dimensional two-phase model

Real-Time Evaluation of Hole-Cleaning Conditions With a Transient Cuttings-Transport Model

Use of slopelimiter techniques in traditional numerical methods for multi-phase flow in pipelines and wells