by S.K. Mahjour, A.A.D.S. Dos Santos, M.G. Correia, D.J. Schiozer, presented at 17th European Conference on the Mathematics of Oil Recovery, September 2020
Well-positions in an oil field have a key role in production performance and financial interests. Defining the location of wells is challenging due to rock-fluid interaction, adjacent wells effects, petrophysical variables, and so on (Janiga et al., 2019). Hence, to overcome the problems and gain maximum economic profits, the optimization of well placement is required (Rahim and Li, 2015). In well placement optimization problems, reservoir flow simulation is normally used to integrate geological (static) and dynamic data, and evaluate the objective functions which are normally related to the economic performance of the field (i.e., the NPV). However, reservoir uncertainties strongly affect the accuracy and reliability of reservoir simulation and optimization outcomes. In the following subsections, we explained the required concepts in the robust well-placement optimization under uncertainties. Reservoir uncertainties arise when there are some constraints in the understanding of the reservoir properties (Hutahaean et al., 2019). Hence, instead of optimizing a deterministic model, robust well placement optimization is performed to optimize the objective functions over a reservoir model set (Badru and Kabir, 2003; van Essen et al., 2009; Yang et al., 2011and Chang et al., 2015). During robust optimization, the decision-maker looks for an optimal risk-weighted solution that has good performance for all reservoir models under reservoir uncertainty (Yang et al., 2011). Reservoir uncertainties can be divided into two groups including (1) geological (static) uncertainties related to geological and petrophysical properties, (2) dynamic uncertainties associated with flow properties, production system accessibility, and oil price fluctuation (Santos et al., 2018a). Static uncertainties in well placement optimization are commonly considered by generating numerous geological realizations (static reservoir models) while dynamic uncertainties are taken into account by building multiple simulation models (dynamic reservoir models). Monte Carlo (MC) and Latin Hypercube (LH) sampling methods are standard tools (Santos et al., 2018b) for generating the geological realization. To combine the static uncertainties with dynamic uncertainties and build the simulation model set, Discretized Latin Hypercube Sampling with Geostatistical realizations (DLHG) has been widely used during the last decade (Almeida et al., 2014; Avansi et al., 2015; Bertolini et al.,2015 and Schiozer et al., 2015).