Uncertainty management on a reservoir workflow
Authors: Feraille Mathieu Denis , Busby Daniel 
Published: March 2015

Abstract
In this paper, we determine a future development plan of a mature field to maximize the cumulated oil production. First, a probabilistic history matching of the simulation model is performed by integrating dynamic data. As a result, a posterior distribution of the uncertain parameters is obtained. To perform this step, an innovative statistical technique that combines non-parametric response surface modeling with adaptive design method is used to approximate the objective function. The adaptive design method allows us to reduce the number of necessary simulations while producing an accurate and predictive response surface in the areas of the input space where the OF is low (acceptable solutions region). This OF approximation is then used in a Markov Chain Monte Carlo algorithm to compute the posterior distribution of the parameters that respect the production data. At the end of the history period, a new development plan is performed and therefore new controllable parameters are added to the model. To optimize the new development plan under the remaining uncertainty, a new response surface model is built using both uncertain and controllable parameters. Then, the set of controllable parameters are optimized to maximize the cumulative oil production (or the Net Present Value) while minimizing the risk using the response surface model. In our test case, we show that the advanced statistical methods used to obtain the response surfaces allows us to address highly non-linear problems in an uncertain framework while doing an acceptable number of calls to the expensive fluid flow simulator.

Introduction
Recent works on mature fields are dealing with integration of all available data, such as, static data (well cores and log as well as 3D initial seismic) and dynamic data (well tests, production history and 4D seismic) in a consistent way to obtain a single and coherent matched model. Assisted history matching techniques involving reservoir engineering workflows, from seismic to fluid flow, are used to achieve this goal. The history matched model is then used to compute production forecasts and to define the future development scheme. This represents a huge improvement over previous history matching processes that were destroying the geological consistency. However, it is well known that considering only one deterministic production forecast to take development scheme decisions can be quite risky. In this work we propose to consider an uncertainty level on each possible production scenario. Then a reliable comparison between different options becomes possible to take the final decision. For mature fields we propose several possibilities, going from simplest to more complex one, to define the uncertainty level associated to a production scheme.
In case where only one matched model is used, different possible production forecasts can be obtained by taking into account some input parameters of the reservoir engineering workflow. Even if they did not have an influence on the match, they could impact the forecasts. As an example, if the production data are associated with the depletion duration, the history matching process will not be able to tune parameters that play a role only during a water injection process such as oil-water relative permeability. The uncertainty of these parameters can then be taken into account to compute different production forecasts.
A further step is to consider the history matching as a probabilistic inversion process. This results in considering all the possible history matched models and not just the best one. To compute the different possible production forecasts, we will consider both the uncertainty of parameters that do not influence the match and also a representative sample of all possible matched models.