Uncertainty Assessment of Well Placement Optimization

Abstract

TX 75083-3836, U.S.A., fax 01-214-952-9435. AbstractDetermining the best location for new wells is a complex problem that depends on reservoir and fluid properties, well and surface equipment specifications, and economic criteria. Numerical simulation is often the most appropriate tool to evaluate the feasibility of well configurations. However, since the data used to establish numerical models have uncertainty, so do the model forecasts. The uncertainties in the model reflect themselves in uncertainties of the outcomes of well configuration decisions.We never possess the true and deterministic information about the reservoir but we may have geostatistical realizations of the truth constructed from the information available. An approach that can translate the uncertainty in the data to uncertainty in the well placement decision in terms of monetary value was developed in this study. The uncertainties associated with well placement were addressed within the utility theory framework using numerical simulation as the evaluation tool. The methodology was evaluated using the PUNQ-S3 model, which is a standard test case that was based on a real field. Experiments were carried on 23 history-matched realizations and a truth case was also available. The results were verified by comparison to exhaustive simulations. Utility theory not only offered the framework to quantify the influence of uncertainties in the reservoir description in terms of monetary value but also provided the tools to quantify the otherwise arbitrary notion of the risk attitude of the decision maker. A Hybrid Genetic Algorithm (HGA) was used for optimization.In addition a computationally cheaper alternative was also investigated. The well placement problem was formulated as the optimization of a random function. The GA was used as the optimization tool. Each time a well configuration was to be evaluated, a different realization of the reservoir properties was selected randomly from the set of realizations all of which honored the geologic and dynamic data available from the reservoir. Numerical simulation was then carried out with this randomly selected realization to calculate the objective function value. This approach had the potential to incorporate risk attitudes of the decision maker and was observed to be approximate but computationally feasible.

On optimization algorithms for the reservoir oil well placement problem

“…If no such point can be found, the entire simplex is shrunk. This procedure was employed in [5,14] as part of a hybrid optimization strategy for the solution of the well placement problem. More information on the N-M algorithm can be found in [22] and in the original paper [28].…”

“…In the particular case of the well placement problem, the use of optimization algorithms began to be reported about 10 years ago (see, e.g., [4,37]). Since then, increasingly complicated cases have been reported in the literature, mainly in the directions of complex well models (type, number, orientation), characteristics of the reservoir under study, and the numerical approaches employed for its simulation [5,13,14,30,46,47]. From an optimization standpoint, most algorithms employed so far are either stochastic or heuristic approaches; in particular, this includes simulated annealing (SA) [4] and genetic algorithms (GA) [14,47].…”

“…Since then, increasingly complicated cases have been reported in the literature, mainly in the directions of complex well models (type, number, orientation), characteristics of the reservoir under study, and the numerical approaches employed for its simulation [5,13,14,30,46,47]. From an optimization standpoint, most algorithms employed so far are either stochastic or heuristic approaches; in particular, this includes simulated annealing (SA) [4] and genetic algorithms (GA) [14,47]. Some of them have also been combined with deterministic approaches to provide a fast convergence close to the solution; for instance, GA with polytope and tabu search [5] and GA with neural networks [7,14].…”

“…From an optimization standpoint, most algorithms employed so far are either stochastic or heuristic approaches; in particular, this includes simulated annealing (SA) [4] and genetic algorithms (GA) [14,47]. Some of them have also been combined with deterministic approaches to provide a fast convergence close to the solution; for instance, GA with polytope and tabu search [5] and GA with neural networks [7,14]. In all cases, the authors point out that all these algorithms are still computationally demanding for large-scale applications.…”

Well Placement Optimization Using a Basic Genetic Search Heuristics Algorithm and a Black Oil Simulator

“…This approach utilizes information from seismic surveys, measurement while drilling, special core analysis and also logging to create an electronic sample of the reservoir. This method is applied to establish the most efficient depletion scheme which may be utilized to produce a well [5].…”