Realistic reservoir models are essential for efficient field management and accurate forecasting of hydrocarbon production. Such models, based on the physical description of the reservoir, need to be calibrated or conditioned to historical production data. The process of incorporating dynamic data in the generation of reservoir models, known as history matching, is traditionally done by hand and is a very tedious, time-consuming procedure that, in addition, returns only one single matched model. It has been shown that the best matched model may well not be a good predictor of future performance. In this work, one of the first field applications of the Neighbourhood Algorithm (NA) is presented. The NA is a stochastic sampling algorithm that explores the parameter space, finds an acceptable ensemble of data fitting models and extracts robust information from this ensemble in a Bayesian framework. The aim is to forecast hydrocarbon production accurately and to assess the related uncertainty by means of multiple reservoir models. The NA methodology was extensively applied to an offshore gas field and compared to a previously manually matched model. The Mistral field has been producing for 6 years from 7 wells. Gas and water productions and pressure data were available and the uncertainty quantification was consistently obtained. Algorithm control parameters and objective function definition effects were investigated. The posterior probability density functions of each unknown parameter, calculated taking into account the observed production data, were evaluated. The hydrocarbon production was forecast using Bayesian inference and the economic risk estimated. The overall process was carried out with a significant time reduction compared with the previous manual approach. The results presented suggest that use of stochastic sampling techniques in a Bayesian framework may well be a valid alternative methodology to the traditional industry workflow for the uncertainty quantification in producing fields. Introduction History matching is a very complex non-linear and ill-posed problem. Like most inverse problems, it is characterised by non-uniqueness of solution [24]. For this reason different combinations of the model parameters may lead to acceptable representations of the history of the reservoir. Traditionally, history matching is done by hand and is a very tedious, time-consuming procedure where the reservoir parameters are varied until a satisfactory match is obtained. In addition, this standard practice leads only to a single production forecast making unfeasible any assessment of uncertainty. Recently, thanks to increasing computer power and technology, computer-aided history matching techniques are becoming gradually more adopted by the oil industry. This is due to the great time-saving benefits they can offer over conventional trial-and-error approaches [25]. "Automatic" and "Assisted history match" techniques automatically vary reservoir parameters until a defined stopping criteria is achieved. In literature they can be divided into three main groups:Deterministic methods;Stochastic methods;Hybrid methods. During the last decades the application of stochastic methods has spread over all the disciplines of the oil industry [12, 13, 14, 15, 20]. However, even if the nature of the history matching problem has been widely recognized, the majority of the approaches adopted return only one matched model that eventually will be used to forecast production. Alternative solutions (i.e. other acceptable models) are usually not sought because of computational and human time constraints. However, neglecting the non-uniqueness of the inverse problem and selecting only one reservoir model could lead to errors in the prediction of the production as cleverly highlighted in the work of Tavassoli et al. [25]. In addition only one model does not allow an assessment of uncertainty in prediction.
The quantitative assessment of the risk associated with the economic exploitation of a hydrocarbon field is mandatory to support, in an efficient and comprehensive way, the decision process guiding the development management system of an oil company. The Full Range Risk Analysis (FRRA) approach developed in Eni E&P Division allows the identification of uncertainties arising from each step of an integrated reservoir study, and the evaluation of their impact on recoverable reserves and on the economic value of a project. This methodology has already been successfully applied in the concept selection and concept definition phases of field development projects. Recently it has been further improved to be employed both in the evaluation stage, of a new discovery, and in the revamping of mature fields with production history. Introduction The Full Range Risk Analysis is aimed at investigating the whole range of possible reservoir development combinations. Its main objectives are:the support of the sanction of an economic discovery, considering an acceptable and accepted risk; the estimation of the value of information (VOI) of new data acquirement and the comparison between different appraisal strategies; the choice of the best development plan taking into account the main impacting reservoir uncertainties (mainly during concept selection phase);the quantification of downside/upside potential of the reservoir and of residual risk associated to field with production history. The presented workflow is a valuable tool in assessing the risk associated to a particular development scenario taking into account the entire surface and sub-surface uncertainties and therefore a methodology to support decisions in development projects. The FRRA methodology is fully based on Montecarlo approach and massive simulations of 3D reservoir models. Full Range Risk Analysis Workflow The current paper describes in detail the standard FRRA workflow along with the latest developments of the methodology, starting from the uncertainty definition phase up to the frequency distribution of the target variable, i.e. ultimate recovery, plateau length, NPV.
It is becoming increasingly important to quantify uncertainty in reservoir performance. History matching is carried out to improve field knowledge and simulation reliability by ensuring that simulations match observed production. In real field cases at most a few reservoir scenarios are used to estimate production performance uncertainty and this leads to a lack of reliability of the uncertain forecasts. The Neighbourhood Algorithm (NA), originally developed for earthquake seismology, provides a framework for generating history matched models and assessing uncertainty in production forecasting. It is a stochastic approach approximating the structure of the likelihood function by Voronoi tessellation and using all information previously obtained about the model space. In this paper the first application of NA on a real oil reservoir is described. The case is the Rigel field, an undersaturated black-oil model producing since July 2001 with 6 producers and 2 water injection wells. The history-matched production data are static and flowing bottom-hole pressures and water cut. A previous manual history match had obtained good response at field level and acceptable responses at well by well level. We applied NA, using the same approach (varying fault transmissibilities) that had been used in the manual history match. We generated 640 Eclipse models that spanned the parameter space and obtained 396 matches that were better than those with the traditional history match. Those results have been achieved in a significant reduction of time. To correctly quantify the uncertainty in reservoir forecast, we have to obtain the posterior probability of each model - that is the probability of the model given the history data. This is accomplished with a separate code (NAB) running Markov Chain Monte Carlo. This paper will describe how we obtained the history match, the formulation and choice of misfit definition which is critical to obtain accurate predictions of uncertainty ranges and the use of NAB code to uncertainty estimation. Introduction A strong positive correlation between the complexity and sophistication of oil company's decision analysis and its financial performance exists. Underestimation of magnitude of reservoir uncertainties and their interdependencies can lead to sub-optimal decision making and financial underperformance of any project. Knowledge of the reservoir comes from cuttings and a limited number of cores extracted from wells but above all from indirect measurements and dynamic information. Uncertainty in producing reservoir modeling can be reduced by integrating observed data and then generating multiple reservoir descriptions conditioned to these ones. The dynamic data are a direct measure of the reservoir response to production process. Their integration in the model set-up is termed history matching and it can be mathematically defined and consists of minimizing an objective function M which quantifies the misfit between observed and simulated data. In the technical literature it is possible to encounter two distinct approaches to the history matching problem: the deterministic and the stochastic methods [1,2]. The former techniques, mainly based on gradient algorithms, have fast convergence rates for an optimal set of parameters but tends to be trapped in local minima. The latter approaches recognize that the dynamic data is a realization of a stochastic process and the solution is found by means of an ensemble of models generated using some hill-climbing rule in the attempt to avoid local entrapment. Moreover the ensemble of models can be used to assess uncertainty. In this work the Neighbourhood Algorithm (NA), developed for the solution of inverse problems in earthquake seismology [3], has been implemented for a first time to history match and asses the uncertainty of a real reservoir. NA exploits the properties of Voronoi diagrams to preferentially sample good data-fitting regions of the model parameter space. Voronoi tessellation is then combined with an hill-climbing rule to account for the ill-posed nature of history matching problems.
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