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Summary Well-control management is nowadays frequently approached by means of mathematical optimization. However, in many practical situations the optimization algorithms used are still computationally expensive. In this paper, we present progressive optimization (PO), a simulator-nonintrusive four-stage methodology to accelerate optimal search substantially in well-control applications. The first stage of PO comprises a global exploration of the search space using design of experiments (DOEs). Thereafter, in the second stage, a fast-to-evaluate proxy model is constructed with the points considered in the experimental design. This proxy is based on generalized barycentric coordinates (GBCs), a generalization of the concept of barycentric coordinates used within a triangle. GBCs can be especially suited to problems in which nonlinearities are not strong, as is the case often for well-control optimization. This fact is supported by the good performance in these types of optimization problems of techniques that rely strongly on linearity assumptions, such as trajectory piecewise linearization, a procedure that is not always applicable due to its simulator-intrusive nature. In the third stage, the precision of the proxy model is iteratively improved and the enhanced surrogate model is reoptimized by means of manifold mapping (MM), a method that combines models with different levels of accuracy. MM has solid theoretical foundations and leads to efficient optimization schemes in multiple engineering disciplines. The final and fourth stage aims at additional improvement, resorting to direct optimization of the best solution from the previous stages. Nonlinear (operational) constraints are handled in PO with the filter method. The optimal search may be finalized earlier than at the fourth stage whenever the solution obtained is of satisfactory quality. PO is tested on two waterflooding problems built upon a synthetic model previously studied in well-control optimization literature. In these problems, which have 120 and 40 well controls and include nonlinear constraints, we observe for PO reductions in computational cost, for solutions of comparable quality, of approximately 30% and 50% with respect to Hooke-Jeeves direct search (HJDS), which, in turn, outperforms particle swarm optimization (PSO). HJDS and PSO are simulator-nonintrusive algorithms that usually perform well in optimization for oilfield operations. The novel concepts of GBC and MM within the framework of the PO paradigm can be extremely helpful for practitioners to efficiently deal with optimized well-control management. Savings of 50% in computing cost may be translated in practice into days of computations for just a single field and optimization run.

In this work we present a methodology for optimal management of brownfields that is illustrated on a real field. The approach does not depend on the particular reservoir flow simulator used although streamline-derived information is leveraged to accelerate the optimization. The method allows one to include (nonlinear) constraints (e.g., recovery factor larger than a given baseline value), which are very often challenging to address with optimization tools. We rely on robust (derivative-free) optimization combined with the filter method for nonlinear constraints. It should be noted that the approach yields not only a feasible optimized solution but also a set of alternative infeasible solutions that could be considered in case the constraints can be relaxed. The whole procedure is accelerated using streamline-derived information. Performance in terms of wall-clock time can be improved further if distributed-computing resources are available (the method is amenable to parallel implementation). The methodology is showcased using a real field in West Siberia where net present value (NPV) is maximized subject to a constraint for the recovery factor (RF). The optimization variables represent a discrete time series for well bottomhole pressure over a fraction of the production time frame. An increase in NPV of 7.9% is obtained with respect to an existing baseline. The optimization methods studied include local optimization algorithms (e.g., Generalized Pattern Search) and global search procedures (e.g., Particle Swarm Optimization). We provide solutions with different levels of approximation and computational efficiency. Without the acceleration achieved through streamline-derived information, the method, while effective, could be prohibitive in many practical scenarios. It is worthwhile noting that part of the solution determined in this work has been tested out on the real field. Optimal management of brownfields is typically addressed using bottomhole pressure values or rates as well control variables. Well controls given as bottomhole pressure values, although not directly implementable in the real field, are often much easier to put into practice than if they are given as rates. However, optimization algorithms that deal with well rates as control variables can be in many cases computationally faster than methods based on bottomhole pressure values. In this work we combine the two aforementioned desirable features for the optimal management of mature fields: well controls are given as bottomhole pressure values for a more practical implementation, and these values are also determined efficiently using concepts borrowed from optimization via well rates.

In this paper we present an enhanced and new optimization algorithm based on Particle Swarm Optimization (PSO) that can be used in reservoir characterization applications to determine multiple solutions that reproduce measurements within satisfactory accuracy. The method is illustrated on a history-matching problem where significant speed-up is obtained with respect to a standard PSO implementation. PSO is a global-search iterative technique where the solution space is explored using a swarm of particles. In every PSO iteration each particle is individually attracted to: the best point (in terms of objective function) in the swarm during last iteration, the best point visited by that particle in all iterations, and the best point found by any particle in all iterations. In the PSO variant proposed here, rather than single points, collections of points carefully selected are used as attractors. The algorithm ensures by a series of mechanisms that the number of attractors is adequate and that the solutions progressively determined are sufficiently different from one another. A series of experiments were performed with a synthetic model based on a real oil field for which nine years of historical data were generated. Both standard PSO and the PSO variant were tested to obtain several models that reproduced well rates within acceptable accuracy. In order to determine multiple solutions via standard PSO (which usually returns only one solution), a number of independent runs with different initial conditions were considered (i.e., standard PSO was run in multi-start fashion). In our experiments, which had a budget of 3,072 simulations in the two cases, the number of solutions found on average by standard PSO and by our PSO variant was 8 and 837, respectively. That is, multi-start standard PSO may require, on average, around 100 times more simulations than our PSO variant to compute a comparable number of models (possibly) distributed in similar manner in the solution space. These results may be explained by noticing that the search for multiple solutions may be more efficient when all information is considered simultaneously than separately by means of a number of independent runs. Standard PSO, when applied to many uncertainty quantification problems, may provide only one solution because the particles in the swarm generally tend to converge to essentially a single point. The Ensemble Kalman Filter (EnKF), which has lately become a very popular history-matching algorithm, presents a similar problem because the ensemble sometimes collapses into one solution. The PSO variant introduced in this work can be an efficient alternative to these algorithms in reservoir characterization since it has been designed to provide multiple and different solutions in a single run.

In this paper we present a methodology of automated optimal (in terms of NPV maximization) greenfield development strategy construction that takes into account geological uncertainties of the reservoir. The algorithm is based on ensemble of hydrodynamic models and uses the theory of probabilistic graphical models. The proposed methodology allows making dynamic (in the process of field development) decisions about well grid pattern change on the basis of information obtained from the studies on the oil reservoir carried out with the help of the appraisal wells: appraisal boreholes of the development wells and pre-drilling wells (drilling from current pad to the next one for refining geological targets). The decision of the wells pattern option change does not require any additional calculations. The proposed methodology was applied for creating optimal development strategy for one of the new assets (on production stage) of JSC "Gazprom neft". The reservoir development is complicated by the set of uncertain parameters related to the complex heterogeneous structure of the collector. The parameters have very high influence on the optimal decision choice. As result expected NPV is increased by 15%.

The paper describes an approach to selection of horizontal well placement. Given a field dynamic model we use advanced optimization techniques to select horizontal well length, well placement, well control that improve the field economics (as measured by the net present value, NPV) and increase field recoveries. Well-known problems of using optimization algorithms for field development are: (1) big number of variables, simplest well description assumes 5 variables: position, lateral length, orientation, bottom-hole pressure; (2) computational complexity of hydrodynamic simulation. In order to deal with high dimensionality and computation complexity we propose multi-layer approach. First, we decompose optimal well placement and control task of high dimension into a number of optimization problems of lower dimension: selection of optimal well pattern, local well placement optimization, selection of well control. That allows significantly decrease a number of simulation runs. Second, we use chain of simulators and dynamic models (from analytic models to fine-scale hydrodynamic model). The optimal solution for well placement obtained on simple model is used as input (baseline) solution for more complicated models. Thus we reduce number of complicated model runs. The proposed approach was implemented in experimental software that automatically optimize horizontal well placement and well control using Eclipse dynamic model. We use this software to optimize FDP of a JSC "Gazprom neft" greenfield. The optimization resulted in significant increase of the field NPV and increase of expected recovery factor: 14% and 1.7% respectively. We estimate that optimization techniques contribution is 9% of NPV and 0.4% of RF.

Simple zonation and a mathematical transformation based on principal component analysis are used in a distributed computing environment for the estimation of porosity and permeability from production and 4D-seismic data, in the form of zero offset amplitu