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ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
- Conference date: September 8-11, 2014
- Location: Catania, Sicily, Italy
- Published: 08 September 2014
121 - 136 of 136 results
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A Closer Look at Ensemble-based Optimization in Reservoir Management
Authors A. Størksen Stordal, S.P. Szklarz and O. LeeuwenburghSummaryWe consider life-cycle production optimization with the aid of the Ensemble Optimization (EnOpt) technique. Although the number of applications of EnOpt has increased, and the theoretical understanding, which is based on strong assumptions, has recently significantly improved, there is still ample room for further development of the underlying theory. Here we study the mathematics (or statistics) of EnOpt and show that it is a version of an already well-defined natural evolution strategy known as Gaussian Mutation. With increased focus on ensemble-based methods in reservoir history matching over the last decade, a natural description of uncertainty arises from the use of multiple realizations. Thus it is a logical step to incorporate this ensemble-based uncertainty description in life-cycle production optimization through defining the expected objective function value as the mean over all geological realizations. We show that the frequently advocated strategy of applying a different control parameter to each reservoir realization, as a means to incorporate geological uncertainty in optimization, delivers an unbiased estimate. However, it is more variance prone than the deterministic strategy of applying the entire ensemble of control parameters to each realization of reservoir models.
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A Mixed-integer Nonlinear Optimization Approach for Well Placement and Geometry
Authors C. Lizon, C. D’Ambrosio, L. Liberti, M. Le Ravalec and D. SinoquetSummaryOptimizing well configuration within oil fields usually consists in maximizing profits from oil production in a long-term horizon. Such profits are typically predicted using CPU-time demanding fluid flow simulations. The variables of the optimization problem considered in this work are the number of wells, their locations and types, as well as the number and trajectories of the branches drilled from the given producers.
We propose a methodology that reduces the complexity and the underlying simulation cost of this optimization problem. First, we introduce various physical constraints related to the distance between wells and oil bearing areas in order to select a suitable region for drilling.
A direct search method is then coupled with surrogate models approximating the objective function to obtain a good estimation of the optimal number, location and type of wells while limiting the simulations’ number.
Given the solution determined in the previous step, we analyze the responses provided by the fluid flow simulator (e.g., oil saturation distribution) and apply a mixed-combinatorial method to define the geometry of the rectilinear well branches. This makes it possible to improve the current solution.
The potential of the second step of the proposed methodology is evaluated with a synthetic two-dimensional reservoir model.
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Automated Field Development Planning for Unconventional Shale Gas
Authors P. Tilke, W. Zhou, S. Krishnamurthy, G. Grove, J. Spath, R.K.M. Thambynayagam, Y. Wang and M. BhanushaliSummaryWe present a framework that automatically generates an optimal well placement plan (WPP) based on a reservoir model of a shale gas field. The proposed WPP comprises wells, surface locations such as pads, well completion locations, and the drilling schedule. A suite of high-speed computational components allows generating this WPP in minutes. Different development strategies can be rapidly investigated.
The WPP is optimized using a constrained downhill-simplex approach. During a trial, WPPs proposed by the optimizer in previous trials were extrapolated to propose a new WPP. The proposed WPP must satisfy a wide range of geometric, operational, contractual, and legal constraints on the surface as well as in the overburden and reservoir. When a feasible WPP is discovered during a trial, the production forecast is computed using a high-speed semianalytic reservoir simulator. The framework supports a variety of objective functions, including recovery, net present value, return on investment, and profitability index. Optimization in the presence of subsurface uncertainty considers an ensemble of reservoir models. A proposed WPP will then have an uncertainty in the forecast value. For a specified aversion to risk, a conservative or aggressive WPP can then be optimized.
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Production Optimisation under Uncertainty in Fractured Reservoirs
Authors V. Demyanov, K. Gopa, D. Arnold and M. Ahmed ElfeelSummaryUncertainty in the distribution of fractures has a high impact on the fluid flow in oil reservoirs. The challenge is to propagate the uncertainty in the fracture distribution patterns into the reservoir flow response. Optimisation reservoir production under this geological uncertainty would result in to more robust operational decisions to maximise recovery and minimise production costs.
Commonly the uncertainty in fracture distribution is described by multiple discrete fracture network realisations (DFN) that represent a range of geologically plausible scenarios. The range of fracture distribution scenarios is captured by spatially varying properties such as facture density distribution, orientation, length etc. Fracture characteristics depend on both geomechanical factors and rock properties, which, therefore, have a high impact on the flow response. The corresponding flow response is also subject to upscaling errors introduced by the choice of the upscaling approach. Therefore, production optimisation (well placements, perforation etc.) becomes a computationally challenging task to perform over a range of possible realisations, modelling choices and upscaling methods required to account for the associated uncertainties.
We propose an approach that performs well placement optimisation over a selected sub-set of the reservoir realisations, which would represent the range of uncertainties introduced by geological and upscaling factors. The sub-set of the DFN scenarios is obtained through clustering the exhaustive set of flow response realisations in a flow metric space using a multi-dimensional scaling. The obtained clusters define a limited set of flow scenarios that can be represented by a much smaller number of selected realisations, which still adequately characterise the spread of uncertainty associated with the exhaustive set.
Optimisation over a limited set of selected realisations corresponding to the range of the flow response scenarios provides a set of well configurations that maximise oil recovery and minimise the costs (produced water and the number of wells). Optimisation over multiple geological scenarios with respect to the geological uncertainty identifies the most robust development decisions than the one based on the optimisation over a single scenario. Use of multi-objective optimisations provides a greater potential variability of possible solutions, which increases the confidence in the uncertainty prediction.
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Gradient-based Multiobjective Optimization with Applications to Waterflooding Optimization
Authors X. Liu and A.C. ReynoldsSummaryThe theory of multiobjective optimization indicates that the Pareto-optimal front lies on the boundary of the subset Z of where Z is the image of the feasible region of the design space. While the weighted sum method represents a classic approach for solving multiobjective optimization problems, it cannot find any point which lies on the “convex” parts of the Pareto front. We introduce a multiobjective optimization algorithm which is designed to find points on the boundary of Z and formulate this algorithm so that boundary points are found by maximizing an augmented Lagrangian function. Both procedures utilize gradients computed with an adjoint method. We compare the performance of the boundary-location algorithm with the weighted sum algorithm for waterflooding optimization problems where the design variables are the well controls (pressure or rates) at injectors and producers on the time intervals which represent the control steps. We consider two problems: (i) maximize both the life-cyle net-present-value (NPV) and the short-term NPV (or cumulative oil production) and (ii) in the case of geological uncertainty in the reservoir model, maximize the expected value of NPV and minimize the variance of NPV over the ensemble of geological realizations.
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Well-posedness of the Single-cell Transport Problem for Two-phase Flow with Polymer
Authors X. Raynaud, K.A. Lie, H.M. Nilsen and A.F. RasmussenSummaryA sequential splitting of the pressure and transport equations applied to a compressible two-phase flow with polymer leads to a considerable speed-up of the simulation, see [ 1 ]. To avoid excessive limitation on the size of the time step, the transport equations are solved implicitly. By using an iterative transport solver, in which the transport equations are solved cell-by-cell from upstream we can further decrease the computation time significantly. Such approach requires a robust single-cell transport solver. The single-cell problem consists of computing the saturation and the polymer concentration in a cell, given the total flux, the saturation, and the polymer concentration in the neighbouring cells. We derive a splitting and a discretization of the mass-conservation equations for which the single-cell problem is always well defined - for any time step size. We are now able to handle the compressible case, which requires a careful choice of the pressure equation and the segregation case, which requires to use a mixed upwind/downwind evaluation of the polymer concentration in the computation of the numerical flux.
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Effect of Time Stepping Strategy on Adjoint-based Production Optimization
Authors O. Volkov and D.V. VoskovSummaryThe adjoint gradient method is well recognized for its efficiency in large-scale production optimization. When implemented in a nonlinear programming (NLP) algorithm, adjoint gradients of the objective function and nonlinear constraints enable the construction of a convex approximation of the original optimization problem using just one forward and one backward simulation. Here we focus on the performance of the adjoint gradients with respect to the time step strategy applied in the underlying forward and backward simulations.
First, we demonstrate that the NPV objective is sensitive to the details of mass transfer in the forward reservoir simulation. Using simple examples with uniform time steps, we show that the adjoint gradients and optimal solutions for bottom-hole pressure (BHP) controls are less consistent with respect to time step refinement compared to the gradients and optimal solutions using rate controls. Next, we investigate an adaptive time step strategy within the simulator which generates a time step refinement immediately after the control update. We consider adjoint gradients of NPV with respect to injection BHP controls. We observe that time step refinement after control update improves the quality of adjoint gradients. Although the increase in the number of time steps does increase the number of objective function evaluations required to achieve a prescribed Karush-Kuhn-Tucker condition tolerance, the resulting optimal NPV is higher.
The instantaneous update of the BHP controls results in a sharp increase in the injection rates. The presence of high instantaneous rates influences the outcome of reservoir simulation when well rate constraints are present. We consider a strategy where constraints are applied directly during the forward simulations against the strategy with nonlinear constraints applied in the optimization process. We demonstrate on practical examples the influence of time step size on both strategies. In the case of optimization with constrained simulation, we observe that the response to the time step refinement is similar to an unconstrained production optimization. However, in the case of constrained optimization, the advantage of small time step refinement may be counterbalanced by excessive constraint violations after control updates.
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Robust Ensemble-based Multi-objective Optimization
Authors R.M. Fonseca, A.S. Stordal, O. Leeuwenburgh, P.M.J. Van Den Hof and J.D. JansenSummaryWe consider robust ensemble-based multi-objective optimization using a hierarchical switching algorithm for combined long-term and short term water flooding optimization. We apply a modified formulation of the ensemble gradient which results in improved performance compared to earlier formulations. We also apply multi-dimensional scaling to visualize projections of the high-dimensional search space, to aid in understanding the complex nature of the objective function surface and the performance of the optimization algorithm. This provides insights into the quality of the gradient, and confirms the presence of ridges in the objective function surface which can be exploited for multi-objective optimization. We used a 18553-gridblock reservoir model of a channelized reservoir with 4 producers and 8 injectors. The controls were the flow rates in the injectors, and the long-term and short-term objective functions were undiscounted net present value (NPV) and highly discounted (25%) NPV respectively. We achieved an increase of 15.2% in the secondary objective for a decrease of 0.5% in the primary objective, averaged over 100 geological realizations. The total number of reservoir simulations was around 20000, which indicates the potential to use the ensemble optimization method for robust multi-objective optimization of medium-sized reservoir models.
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A Computational Model of Coupled Multiphase Flow and Geomechanics to Study Fault Slip and Induced Seismicity
More LessSummaryAbstract.
Coupling between fluid flow and mechanical deformation in porous media plays a critical role in oil recovery. Production and injection of fluids in oil and gas fields have also been associated with surface subsidence and earthquakes along pre-existing faults. One of the key unresolved issues in geomechanical modeling of oil reservoirs is the ability to describe the mechanical and hydraulic behavior of faults, and the influence of the full stress tensor and change in pressure on fault slip. Here, we present a new computational approach to model coupled multiphase flow and geomechanics of faulted reservoirs. We represent faults as surfaces embedded in a three-dimensional medium by using zero-thickness interface elements to accurately model fault slip under dynamically evolving fluid pressure and fault strength. We employ a rigorous formulation of nonlinear multiphase geomechanics based on the increment in mass of fluid phases, instead of the more common, but less accurate, scheme based on the change in porosity. Our nonlinear formulation is required to properly model oil reservoirs where high compressibility or strong capillarity effects are present. To account for the effect of surface stresses along fluid-fluid interfaces, we use the ‘equivalent pore pressure’ in the definition of multiphase effective stress. We develop a numerical simulation tool by coupling a multiphase flow simulator with a mechanics simulator, using the unconditionally stable fixed-stress scheme for the sequential solution of two-way coupling between flow and geomechanics. We validate our modeling approach using several synthetic, but realistic, test cases that illustrate the ability of the model to capture ground deformation, and the onset and evolution of induced seismicity from fluid injection and production.
Research significance
- Seismicity induced by fluid injection and withdrawal has emerged as a cornerstone of the scientific discussion around subsurface technologies that tap into water and energy resources.
- We present a new computational approach to model coupled multiphase flow and geomechanics of faulted reservoirs, where faults are represented as surfaces capable of simulating runaway slip. Our framework allows us to investigate fault slip and earthquake induced in underground reservoirs due to coupled processes of fluid flow and mechanical deformation.
- We are currently applying our computational model for the study of ground deformations and for the post mortem analysis of natural or induced earthquakes.
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A Unified Framework for Fully-implicit and Sequential-Implicit Schemes for Coupled Poroelasticity
Authors N. Castelletto, J.A. White and H.A. TchelepiSummaryA comparison between fully-implicit and sequential-implicit methods for coupled poroelasticity is presented. By formulating the two approaches within a unified framework, we show that an accurate approximation for the Schur complement of the block structured linear system with respect to the displacement stiffness matrix is key for a successful implementation of both solution strategies. We analyze the performance and robustness of the different approaches using analytical solutions from the literature.
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Applications of Global-local Enrichment Functions to Coupled Flow and Geomechanics
Authors H. Florez and J. MoneagudoSummaryOne possible way to mitigate the computational burden associated to reservoir compaction and subsidence computations is to avoid propagating its mesh in a tensor-product fashion towards the surroundings. Typically structured meshes are preferred in the pay-zone in order to couple with cell-centered finite differences reservoir simulators in a straightforward manner. One is supposed to have almost exactly the same mesh for flow and mechanics in the pay-zone but in the non-pay-zone area other approaches are possible. We propose a two levels procedure, which involves the solution of local boundary value problems using boundary conditions from a global problem, defined on a coarser mesh. The technique combines global-local finite element method concepts with the partition of unity framework, thus the local solutions can be used to enrich the global solution. The method is suitable for parallel computing since the local problems are completely disconnected. In order to project the reservoir pressures in a different global mesh, we utilize the approach presented in ARMA paper 13–476. We then proceed to compute a global solution on a coarser mesh, which provides Dirichlet boundary conditions for the local mesh honoring the original reservoir mesh. The approach effectiveness in terms of computational cost is numerically investigated in this paper. The examples involve coupling a continuous Galerkin FEM for both slightly compressible single-phase flow and mechanics. Applications to unconventional synthetic plays are presented.
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Streamline-based Reservoir Geomechanics Coupling Strategies for Full Field Simulations
Authors B. Koohmareh Hosseini and R.J. ChalaturnykSummaryGeomechanics is a recent added physics into reservoir simulators that considers the interaction between reservoir fluid and rock, which is quite important in accurate recovery prediction of stress-sensitive reservoirs. However, inclusion of geomechanics into fluid flow simulation workflows has been computationally crucial and known as a bottleneck in both fully coupled and sequentially coupled scenarios. Therefore conventionally the geomechanical simulation of reservoirs is either neglected or is investigated only in the vicinity of injection/production well that is subjected to more pressure changes. To tackle this problem, and integrate geomechanics in field scale, streamline-based class of hydromechanical couplings were used. This paper presents and implements different coupled sequentially implicit and semifully implicit geomechanics-streamlines simulation techniques for simulation of large reservoirs with elastic geomechanical constitutive equations. The main idea behind inclusion of geomechanics in streamline simulation lies in the streamline time-stepping, which is different from conventional flow simulation time-steps: convective time steps, user induced time steps, and saturation forward sub-interval time steps. On the other hand, since porosity, and permeability change dynamically due to geomechanical rock-fluid interactions, the pressure field needs to be updated by selection of proper time steps. This work also provides a basis for selection of the coupling strategy to have a numerically and physically stable coupling strategy for both of compressible and incompressible scenarios. The techniques were tested on a highly heterogeneous two-dimensional plain-stress model, and a three-dimensional full-field case.
Sensitivities on the number of grid-cells were performed and provided a good foundation to assess the power of each single coupling technique for each particular application and reservoir type. The finding of this paper can be used for optimization techniques where inclusion of geomechanics is essential as well.
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How Much is an Oil Price Forecast Worth in Reservoir Management?
Authors T. Wen, D. Echeverria Ciaurri, M.R. Thiele, Y. Ye and K. AzizSummaryReservoir management has lately received significant attention in the oil industry because of the sizable potential increment in profit associated with optimized strategies, together with the increased reliability of new reservoir flow simulation techniques. Long-term (more than five years) management is especially challenging partially because of the difficulties brought by the uncertainty associated with forecasting oil production and price.
In this work, we first propose a risk measure of a given production strategy with respect to uncertainty in the oil price. This measure is interpreted as the value of information associated with an uncertain oil price. Decision makers can leverage value of information of oil price, for example, to qualify potential risks associated with the lack of knowledge of the market, to compare an exploitation strategy with the optimal strategy in the utopian situation where future oil price is known, and to evaluate possible capital investments for a better forecast of oil price. Then, we present a numerical approach using reservoir flow simulation to estimate efficiently this risk measure. The computational cost of this numerical method does not increase with the number of possible oil price scenarios considered, and this is a desirable feature when simulation is time-demanding. To the best of our knowledge, value of information of oil price has not been addressed using complex reservoir flow simulation.
The approach is validated on a synthetic case and two real field waterflooding scenarios: a relatively small field with eight wells, and a larger field with 174 wells. In both cases, we analyze 10,000 oil price scenarios, quantify the risk of waterflooding production strategies obtained through optimization, and estimate the monetary value associated of oil price forecasts with different degrees of market information and knowledge.
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Proxy Comparison for Sorting Models and Assessing Uncertainty on Oil Recovery Profiles
More LessSummaryTo study the impact of subsurface uncertainties on oil recovery, it is common to build a large set of models which cover these uncertainties. Despite increase of computational capabilities, as models become more complex, it is not possible to perform full physic flow simulation for all the generated models. This is why stochastic reservoir model sets are often decimated to assess the impact of static uncertainties on dynamic reservoir performance.
This contribution will focus on the use of proxy to perform this data set reduction. A lot of different proxies have been developed, from the simplest to the more complicated so it is difficult to choose the good one according to a particular goal.
We present different criteria to compare the proxy quality and their helps to assess uncertainties on oil recovery. A first criterion will be based on the relation which may exists between the model distances computed on the proxy responses and those compute on flow responses. Another criterion is the speed factor and simplification provide by the proxy compared to the full physic simulator. These two criteria are very simple and can be applied in an early time to avoid deploying time consuming proxies which won’t provide accurate information.
The last criterion presented here, is the confidence intervals which can be computed around probabilistic reservoir production forecasts computed on a small representative subset of model. Even if this criterion can be used only when the entire dataset has been simulated, it provides some quantification about a possible bias created by a proxy and the remaining uncertainties on oil recovery.
We present here a comparison study between widely different proxy responses applied on a real dataset of that methodology. This will give us some keys to choose a proxy which is a good compromise between accuracy and easy to handle methodology.
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Handling Geological Uncertainty in Oil Field Development with Multi-objective Optimization Technique
Authors Y. Chang, Z. Bouzarkouna and D. DevegowdaSummaryOptimal well placement targeting sweet spots within the reservoir is critical for oil field development. However, geological uncertainty can potentially impact the robustness of the well planning solutions and may negatively impact field development strategies. Traditional workflows may seek the optimal well locations either on one geological model or in an average manner over a set of selected geological realizations by optimizing a chosen objective function such as Net Present Value (NPV). These approaches however tend to be somewhat deficient for realistic field case studies. Firstly, traditional workflows avoid an explicit treatment of well planning variance due to geological uncertainty. Secondly, traditional optimization normally cannot meet the requirement of optimizing two or more conflicting objective functions simultaneously.
In this paper, we propose a workflow that handles geological uncertainty in a novel manner. The workflow is based on a multi-objective optimization approach using the Non-Dominated Sorting Genetic Algorithm (NSGA-II). The mean NPV is maximized while the standard deviation is minimized simultaneously for all well placement scenarios over all geological realizations. The power and utility of the proposed workflow is demonstrated on a reservoir case study. The results indicate that the proposed approach leads to improved decision making capabilities by providing a suite of well planning solutions that can be incorporated in decision making. Moreover, this workflow demonstrates a novel treatment of geological uncertainty. It takes into account the risk attitude of decision-makers and broadens field development strategies intelligently.
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Uncertainty Analysis for Reserves Estimation - An Efficient Workflow Applied to a Channelized Reservoir
Authors D.B. Busby, T.C. Chugunova and P.V. CorpelSummaryQuantifying uncertainty on reserves estimation requires considering structural, geological and dynamic uncertainties. We address the problem of uncertainty characterization of a channelized reservoir model and we discuss an approach to propagate both static and dynamic uncertainties for estimating reserves distribution integrating all available static data.
The approach is based on a kriging response surface method where specific parameterizations and parameter transformations are proposed to sample structural uncertainty while combining sampling of static and dynamic uncertainties such as architectural elements limits, channels geometry and proportions, rocktypes and associated petrophysical properties, fault transmissibility, vertical anisotropy, permeability. The method is applied to a real green field characterized by complex multi-level heterogeneities. Even for this very complex and high dimensional problem we obtain a good approximation of the reference reserves and in place distributions obtained from a full Monte Carlo method: the response surface can correctly propagate all the most relevant uncertainties, using only a reasonable number of model runs (typically hundreds).
We show that in the considered case study, the proposed approach outperforms our in-house workflow to estimate reserves distribution based on proprietary software. The method should allow reservoir engineers to perform a more efficient reserves distribution evaluation and also dynamic data integration at least when the small scale heterogeneities have a limited impact on the reserves.
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