Production Data and Uncertainty Quantification: A Real Case Study

Abstract

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.

Mitigação de incertezas através da integração com ajuste de histórico de produção e técnicas de amostragem

“…Esse trabalho foi validado através da comparação das incertezas na previsão de produção obtidas, antes e depois do ajuste de histórico com parâmetros de produção fixos, para a solução ótima do Joint Modeling Method. Os resultados indicam que as incertezas na previsão são reduzidas em 75% quando são considerados os modelos ajustados, em relação aos modelos não submetidos ao ajuste de histórico Nicotra et al (2005). implementaram nesse trabalho um algoritmo da vizinhança (Neighbourhood Algorithm).…”