Over the last twenty or more years of reservoir performance prediction through simulation there have been only two fundamental changes. First was the evolutionary increase in computing speed that has allowed larger, more detailed reservoir models to be built. Second was the revolutionary change in approach that involved the entire subsurface community in building integrated reservoir descriptions. The next big change may in time prove to be BP's Top-Down Reservoir Modelling (TDRM). This is a new pragmatic approach to fully incorporate reservoir uncertainty in model construction and performance prediction. TDRM is proprietary technology that has been developed in BP through extensive R&D, and consists of a philosophy and tools that enable a faster and more robust exploration of uncertainty than has hitherto been possible. The philosophy is to start investigations with the simplest possible model and simulator appropriate to the business decision. Detail is added later as required. The approach overcomes the problems of the conventional "bottom-up" process, which uses detailed models that are too slow and cumbersome to fully explore uncertainty and identify critical issues. Highly detailed models cannot overcome an underlying absence of information, and can have the negative effect of creating a false sense of understanding. The TDRM tools have been designed to minimise manual iterations by creating a semi automated, flexible workflow for case management, assisted history matching, depletion planning optimisation and post-analysis. TDRM has been successfully applied to eighteen oil and gas reservoirs that range from development appraisal stage to mature fields, and has resulted in up to 20% increase in estimated net present value for the projects. Background The business imperatives in developing oil and gas reservoirs are faster pace and less risk from subsurface uncertainties. Quantification of the uncertainties is difficult and time consuming because of a) the intrinsic subsurface complexity, requiring integration of data from core to seismic scales (cm to 10's m), b) the sparseness of information requiring estimation of unknown data for the construction of possible geological and simulation models, and c) the need to consider a large number of development scenarios. Processes used to estimate uncertainties vary, but the general trend is to start by building a large (multi-million cell) geological model. Often the type of model is independent of the business decision, timeframe and amount of data available. Due to the complex workflow and effort, the focus is on building only one, the "most likely", detailed model, even though evidence from the data indicates that there are many possible models. The next step is to build a simulation model that typically involves upscaling the geological model. If production data exist, this simulation model is history matched manually. Iterative rebuilding of the underpinning geological model is generally avoided. Exploration of the uncertainty in performance prediction using the simulation model is often limited to one-at-a-time sensitivities around a base case. These sensitivities are only a small sample from the factorially combined possibilities. The effort to reach this stage is significant and can be many months for a major reservoir decision. Overall, the focus of activity has been building ever more complex (hence apparently realistic) models and predicting performance from only a single realisation. Breaking away from this general approach and focusing on the real uncertainty breadth in performance prediction is a conceptual leap which requires new technology and understanding. Technology Improvements Technology improvements are providing better information about current and future reservoir performance and offer the opportunity to quantify the risk from subsurface uncertainties. Some of these advances are highlighted below.

Summary An improved heterogeneity/homogeneity index is introduced that uses the shear-strain rate of the single-phase-velocity field to characterize heterogeneity and rank geological realizations in terms of their impact on secondary-recovery performance. The index is compared with the Dykstra-Parsons coefficient (Dykstra and Parsons 1950) and the dynamic Lorenz coefficient (Shook and Mitchell 2009). The results show that the index's ranking ability is preserved for miscible and immiscible displacements at different viscosity/mobility ratios. Neither the Dykstra-Parsons coefficient (Dykstra and Parsons 1950) nor the dynamic Lorenz coefficient (Shook and Mitchell 2009) can consistently discriminate between different realizations in terms of breakthrough time and oil recovery at 1 pore volume injected (PVI) for tracer flow or adverse-viscosity-ratio miscible and immiscible floods.

Prudent decision making in subsurface assets requires reservoir uncertainty quantification. In a typical uncertainty quantification study, reservoir models must be updated using the observed response from the reservoir via a process known as history matching. This involves solving an inverse problem, finding reservoir models that produce, under simulation, a similar response to that of the real reservoir, requiring multiple expensive multiphase flow simulations. Thus uncertainty quantification studies employ optimization techniques to find acceptable models to be used in prediction. Different optimization algorithms and search strategies are presented in the literature, but they are generally unsatisfactory due to slow convergence to the optimal regions of the global search space, and, more importantly, failure in finding multiple acceptable reservoir models. In this context, a new approach is offered by Estimation of Distribution Algorithms (EDAs). EDAs are population-based algorithms, which use probability models to estimate the probability distribution of promising solutions, and then to generate new candidate solutions. This paper explores the application of EDAs including univariate and multivariate models. We discuss two histogram-based univariate models, and one multivariate model, Bayesian Optimization Algorithm (BOA), which employs Bayesian Networks for modelling. By considering possible interactions between variables and exploiting explicitly stored knowledge of such interactions, EDA can accelerate the search process, while preserving search diversity. Unlike most existing approaches applied to uncertainty quantification, the Bayesian Network allows BOA to build solutions using flexible rules learned from the models obtained, rather than fixed rules, leading to better solutions and improved convergence. BOA is naturally suited to finding good solutions in complex high-dimensional spaces, such as those typical in reservoir uncertainty quantification.We demonstrate the effectiveness of EDA by applying to the well-known synthetic PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a well controlled case. Results show better estimation of uncertainty when compared to some other traditional population-based algorithms.

The topic of automatically history-matched reservoir models has seen much research activity in recent years. History matching is an example of an inverse problem, and there is significant, active research on inverse problems in many other scientific and engineering areas. While many techniques from other fields such as Genetic Algorithms, Evolutionary Strategies, Differential Evolution, Particle Swarm Optimisation, and the Ensemble Kalman Filter have been tried in the oil industry, some more recent and effective ideas have yet to be tested. One of these relatively untested ideas is a class of algorithms known as Estimation of Distribution Algorithms (EDAs). EDAs are population-based algorithms, which use probability models to estimate the probability distribution of promising solutions, then to generate new candidate solutions. EDAs have been shown to be very efficient in very complex high-dimensional problems. An example of a state of the art EDA is the Bayesian Optimisation Algorithm (BOA), which is a multivariate EDA employing Bayesian Networks for modelling the relationships between good solutions. The use of a Bayesian Network leads to relatively fast convergence as well as high diversity in the matched models. Given relatively limited number of reservoir simulations used in history matching, EDA-BOA offers the promise of high quality history matches with a fast convergence rate. In this paper, we introduce EDAs and describe BOA in detail. We shows results of EDA-BOA algorithm on two history matching problems. First, we tune the algorithm and demonstrate convergence speed and search diversity on the PUNQ-S3 synthetic case. Secondly, we apply the algorithm to a real, North Sea, turbidite field with multiple wells. In both examples, we show improvements in performance over traditional population-based algorithms.

A new and improved heterogeneity index is introduced that uses the shear-strain rate of the single phase velocity field to characterise heterogeneity in terms of its impact on performance. This index's ability to rank heterogeneous reservoir models is compared with that of the Dykstra-Parsons coefficient and the dynamic Lorenz coefficient. The new index is able to rank reservoirs, both accurately and quickly, based on performance for both miscible and immiscible fluids at a range of different mobility ratios. In contrast both the Dykstra-Parsons coefficient and the dynamic Lorenz coefficient are found to lack the sensitivity needed to be able to estimate the time to breakthrough of the displacing fluid and the recovery of oil at one pore volume injected.