Combination of Experimental Design and Joint Modeling Methods for Quantifying the Risk Associated With Deterministic and Stochastic Uncertainties - An Integrated Test Study

Abstract

This paper presents a fully-integrated methodology for managing reservoir uncertainties during history matching, production forecasting and production scheme optimization. Based on the traditional experimental design methodology, this innovative approach, called the Joint Modeling Method, allows to model the production recovery as a function of both the deterministic uncertain parameters, such as petrophysical and production parameters, as well as non-continuous parameters such as geostatistical realizations and equiprobable matched models. In this new approach, the dispersion due to the non-continuous uncertainties is modeled in a rigorous statistical framework through the variance of the production recovery. The method was successfully applied on data derived from a North Sea real field case. The objective was to quantify the impact of the principle reservoir uncertainties on the cumulative oil production and to optimize future field development in a risk analysis approach. The uncertainties were mainly on petrophysical data, geostatistical facies distribution and aquifer strength. The study was performed in the following steps:sensitivity study. The most influential parameters were identified and the impact of geostatistical uncertainties was highlighted.history matching. The influential parameters were constrained to the available production data. In particular, the geostatistical model was locally modified using both FFTMA technique and the gradual deformation method.production scheme optimization. Experimental design and joint modeling were used to obtain probabilistic distributions of the optimized location of new wells in a non-producing zone.risk analysis: Finally, probabilistic incremental oil production was obtained using Monte-Carlo technique. Results show that this integrated methodology successfully enables to quantify the risk associated with the main reservoir uncertainties during the whole process of a reservoir engineering study (sensitivity, history match, production optimization and forecast). Introduction Thanks to growing measurement and computational facilities, reservoir modeling is getting more and more complex. Hence more and more prior uncertain parameters can be introduced in reservoir studies. The difficulty is then to identify the ones that are influential on production recovery and on economic field profitability and to quantify their impact. The "simplest" case where the reservoir engineer needs to deal with reservoir uncertainties is the appraisal case, when there is no production data to match. In that case, the uncertainty domain cannot be highly constrained and the impact on production forecasts may hence be very significant. To deal with those uncertainties, reservoir and production engineers commonly perform many reservoir simulations for different values of the uncertain parameters. This approach gives a qualitative idea of the influence of each uncertain parameter on the production response. However this method can quickly become very expensive when the number of uncertain parameters increases. Moreover, this is not a rigorous method since the impact of each uncertain parameter as well as the possible interactions between those uncertain parameters cannot be easily detected. Finally no direct quantitative relation between the responses and the uncertainties can be established.

Better Field Development Decisions from Multi-Scenario, Interdependent Reservoir, Well, and Facility Simulations

“…However, practical optimization solutions and formulations are a challenge. There should be an easy method to state the design could be used to reduce the number of simulations and thus the time needed for a decision analysis, but it can require a considerable number of simulations up front followed by extensive analysis 7,11 .…”

“…Scenario and Monte Carlo analyses reveal many aspects of the interrelationships of the decision variables to the state parameters. Experimental design can be used to reduce the number of simulations required 7,11 . The 480 iterations used in this work are too small to span all the combinations of scenarios and to span adequately the number and ranges of uncertainties encountered.…”

“…Compared to the sensitivity runs and the high resolution runs, the Monte Carlo simulations capture the uncertainty in the objective better (figures 11,12). Though the iterations with the high resolution more accurately model the flow of fluids through the reservoir, large uncertainty ranges, seen here from the Monte Carlo simulations, mean that a few iterations with fine resolution models will not be sufficient ( figure 11).…”

Quantification of Uncertainties for Drilling-Induced Formation Damage

“…Both are being used more extensively in reservoir engineering applications now because of their significant potential in uncertainty studies (Dejean and Blanc 1999;Manceau et al 2001;Zabalza-Mezghani et al 2001;White and Royer 2003;Cheong and Gupta 2005). The RSM method has been described in details by Dejean and Blanc (1999).…”

“…Experimental design approach combined with the RSM have found wide application in the industry. They have been recently used in oil/gas industry for uncertainty study in oil reserves, production forecasting, and development optimization (Dejean and Blanc 1999;Manceau et al 2001;Zabalza-Mezghani et al 2001;White and Royer 2003;Cheong and Gupta 2005). Applied to formation damage risk assessment, they allow identification of the most influential parameters on well produc-tivity and estimation of the possible range of formation damage.…”