Geological Realizations Research Articles

An efficient optimization process for hydrocarbon production in presence of geological uncertainty using a clustering method: A case study on Brugge field

We present the main steps of a production optimization process in presence of geological uncertainty. The geological model is the main source of uncertainty in hydrocarbon reservoir simulation which can reduce viability of the simulation results to be utilized in a production optimization process. Optimization of the expected net present value (NPV) based on evaluations of all probable geological realizations require prohibitive computation time. In this paper, we use a clustering method named Kernel K-means Method (KKM) to select a representative subset of geological models. The suggested method has been examined on the benchmark model of Brugge field. The clustering method selected 9 out of 40 realizations tuned in a previous history matching study. The statistics derived from NPV calculations in the selected realizations demonstrate a good match with those of all 40 realizations.A Reduced Order Modelling (ROM) coupled with a physically based optimization method named Guided Pattern Search (GPS) has been extended to take geological uncertainties into account. Four different optimization processes based on a full order or a reduced order simulation coupled with a GPS or a conventional pattern search (PS) algorithm have been carried out using the selected realizations. The best NPV results were obtained by execution of GPS on a full order simulation model. ROM led to reduction of the simulation time by a factor of eight which would make the optimization process tractable but caused some inaccuracy in the NPV evaluations. The combination of GPS and ROM resulted in an acceptable trade-off between NPV maximization and run time reduction.

Assisted History Matching of Channelized Models by Use of Pluri-Principal-Component Analysis

SummaryAssisted history matching (AHM) of a channelized reservoir is still a very-challenging task because it is very difficult to gradually deform the discrete facies in an automated fashion, while preserving geological realism. In this paper, a pluri-principal-component-analysis (PCA) method, which supports PCA with a pluri-Gaussian model, is proposed to reconstruct geological and reservoir models with multiple facies. PCA extracts the major geological features from a large collection of training channelized models and generates gridblock-based properties and real-valued (i.e., noninteger-valued) facies. The real-valued facies are mapped to discrete facies indicators according to rock-type rules (RTRs) that determine the fraction of each facies and neighboring connections between different facies. Pluri-PCA preserves the main (or principal) features of both geological and geostatistical characteristics of the prior models. A new method is also proposed to automatically build the RTRs with an ensemble of training realizations. An AHM work flow is developed by integrating pluri-PCA with a derivative-free optimization algorithm. This work flow is validated on a synthetic model with four facies types and a real-field channelized model with three facies types, and it is applied to update both the facies model and the reservoir model by conditioning to production data and/or hard data. The models generated by pluri-PCA preserve the major geological/geostatistical descriptions of the original training models. This has great potential for practical applications in large-scale history matching and uncertainty quantification.

Integration of Cumulative-Distribution-Function Mapping With Principal-Component Analysis for the History Matching of Channelized Reservoirs

SummaryAlthough principal-component analysis (PCA) has been widely applied to effectively reduce the number of parameters characterizing a reservoir, its disadvantages are well-recognized by researchers. First, PCA may distort the probability-distribution function (PDF) of the original model, especially for non-Gaussian properties such as facies indicator or permeability field of a fluvial reservoir. Second, it smears the boundaries between different facies. Therefore, the models reconstructed by traditional PCA are generally unacceptable.In this paper, a work flow is proposed to integrate cumulative-distribution-function (CDF) mapping with PCA (CDF/PCA) for assisted history matching on a two-facies channelized reservoir. The CDF/PCA is developed to reconstruct reservoir models by use of only a few hundred principal components. It inherits the advantage of PCA to capture the main features or trends of spatial correlations among properties, and more importantly, it can properly correct the smoothing effect of PCA. Integer variables such as facies indicators are regenerated by truncating their corresponding PCA results with thresholds that honor the fraction of each facies at first, and then real variables such as permeability and porosity are regenerated by mapping their corresponding PCA results to new values according to the CDF curves of different properties in different facies. Therefore, the models reconstructed by CDF/PCA preserve both geological (facies fraction) and geostatistical (non-Gaussian distribution with multipeaks) characteristics of their original or prior models.The CDF/PCA method is first applied to a real-field case with three facies to quantify the quality of the models reconstructed. Compared with the traditional PCA results, the integration of CDF-based mapping with PCA can significantly improve the quality of the reconstructed reservoir models. Results for the real-field case also reveal some limitations of the proposed CDF/PCA, especially when it is applied to reservoirs with three or more facies. Then, the CDF/PCA together with an effectively parallelized derivative-free optimization method is applied to history matching of a synthetic case with two facies. The geological facies, reservoir properties, and uncertainty characteristics of production forecasts of models reconstructed with CDF/PCA are well-consistent with those of the original models. Our results also demonstrate that the CDF/PCA is applicable for conditioning to both hard data and production data with minimal compromise of geological realism.

Geological uncertainty and effects of depositional sequence on improved oil recovery processes

Several emerging improved oil recovery (IOR) techniques have been proposed in the past decades with promising results. However, a systematic study of reservoir heterogeneity on these advanced processes has not yet been presented. This paper provides one of the first comparative evaluations of the effects of reservoir heterogeneity on various IOR processes from the conventional methods (waterflooding, CO2 flooding) to the emerging recovery technologies (Low-Salinity Waterflooding and CO2 Low-Salinity WAG) for wider and more successful implementation of these projects. Since weakness exists in the current simple and unrealistic models, detailed geostatistic models are employed to provide a more realistic and unbiased evaluation of reservoir heterogeneity. A new modeling approach that involves the integration of geological software, a reservoir simulator and a robust optimizer in a closed loop for generating multiple geologically driven realizations and uncertainty assessment of different recovery processes is introduced. Then a series of numerical simulations is conducted to investigate the influences of FU and CU sequences on oil recovery. Finally, the uncertainty range of reservoir heterogeneity is thoroughly evaluated using a large number of geological realizations with significant differences on porosity and permeability distributions. The effect of the K v /K h (aspect) ratio is also addressed in this study. The simulation results indicate that the depositional sequence has a dominant effect on oil recovery in all recovery processes. The CU distribution demonstrates superior performance over the FU distribution.

A test of analog-based tools for quantitative prediction of large-scale fluvial architecture

Outcrop analogs are routinely used to constrain models of subsurface fluvial sedimentary architecture built through stochastic modeling or interwell sand-body correlations. Correlability models are analog-based quantitative templates for guiding the well-to-well correlation of sand bodies, whereas indicator variograms used as input to reservoir models can be parameterized from data collected from analogs, using existing empirical relationships. This study tests the value and limitations of adopting analog-informed correlability models and indicator variogram models and assesses the effect and significance of analog choice in subsurface workflows for characterizing fluvial reservoirs. A 3.2-km (2-mi)-long architectural panel based on a virtual outcrop from the Cretaceous Blackhawk Formation (Wasatch Plateau, Utah) has been used to test the methodologies. Vertical dummy wells have been constructed across the panel, and the intervening fluvial architecture has been predicted using correlability models and sequential indicator simulations. The correlability and indicator variogram models employed to predict the outcrop architecture have been compiled using information drawn from an architectural database. These models relate to (1) analogs that partially match with the Blackhawk Formation in terms of depositional setting and (2) empirical relationships relating statistics on depositional element geometries and spatial relations to net-to-gross ratio, based on data from multiple fluvial systems of a variety of forms. The forecasting methods are assessed by quantifying the mismatch between predicted architecture and outcrop observations in terms of the correlability of channel complexes and static connectivity of channel deposits. Results highlight the effectiveness of correlability models as a check for the geologic realism of correlation panels and the value of analog-informed indicator variograms as a valid alternative to variogram model parameterization through geostatistical analysis of well data. This work has application in the definition of best-practice use of analogs in subsurface workflows; it provides insight into the typical degree of realism of analog-based predictions of reservoir architecture, as well as the effect of analog choice, and draws attention to associated pitfalls.

Linking outcrop analogue with flow simulation to reduce uncertainty in sub-surface carbon capture and storage: an example from the Sherwood Sandstone Group of the Wessex Basin, UK

Abstract Modelling the behaviour of carbon dioxide (CO 2 ) injected into sub-surface reservoirs as part of carbon capture and storage (CCS) strategies is often performed using models that incorporate very limited geological detail, particularly at the subseismic (metre to decametre) scale. Those modelling studies that incorporate varying degrees of geological realism show the inherent risks and uncertainties that can result from neglecting heterogeneity and reservoir–caprock topography along the migration path of an injected CO 2 plume. A key problem is that detailed geological data are often not available for the relatively deep saline aquifers that are an important target for CCS. Deep saline aquifers fall between the relatively data-rich environments of shallow freshwater aquifers and hydrocarbon reservoirs and it is in these settings that outcrop analogues may play an important part in reducing the risks and uncertainties associated with CCS. This study uses an example from the Sherwood Sandstone Group (Otter Sandstone Formation) of the Wessex Basin to show how an outcrop study can impart a much greater understanding of heterogeneity in critical reservoir–caprock zones. Here the transition from the Sherwood Sandstone Group (fluvial sandstone reservoir) to the Mercia Mudstone Group (playa lacustrine mudstone seal) is not simple, but includes a major change in fluvial style that introduces considerable heterogeneity at the top of the reservoir. The study shows how laser-scanned outcrop can be used to rapidly construct static geological models that are taken through to flow simulations. In combination, the use of appropriate outcrop analogues and flow modelling can reduce the risks and uncertainties associated with CCS.

Ensemble-Based Multiobjective Optimization of On/Off Control Devices Under Geological Uncertainty

Summary We consider robust ensemble-based (EnOpt) multiobjective production optimization of on/off inflow-control devices (ICDs) for a sector model inspired by a real-field case. The use of on/off valves as optimization variables leads to a discrete control problem. We propose a reparameterization of such discrete controls in terms of switching times (i.e., we optimize the time at which a particular valve is either open or closed). This transforms the discrete control problem into a continuous control problem that can be efficiently handled with the EnOpt method. In addition, this leads to a significant reduction in the number of controls that is expected to be beneficial for gradient quality when using approximate gradients. We consider an ensemble of sector models where the uncertainty is described by different permeability, porosity, net/gross ratios, and initial water-saturation fields. The controls are the ICD settings over time in the three horizontal injection wells, with approximately 15 ICDs per well. Different optimized strategies resulting from different initial strategies were compared. We achieved a mean 4.2% increase in expected net present value (NPV) at a 10% discount rate compared with a traditional pressure-maintenance strategy. Next, we performed a sequential biobjective optimization and achieved an increase of 9.2% in the secondary objective (25% discounted NPV to emphasize short-term production gains) for a minimal decrease of 1% in the primary objective (0% discounted NPV to emphasize long-term recovery gains), as averaged over the 100 geological realizations. The work flow was repeated for alternative numbers of ICDs, showing that having fewer control options lowers the expected value for this particular case. The results demonstrate that ensemble-based optimization work flows are able to produce improved robust recovery strategies for realistic field-sector models against acceptable computational cost.

Closed-Loop Field Development Under Uncertainty by Use of Optimization With Sample Validation

Summary In this work, we develop and apply a general methodology for optimal closed-loop field development (CLFD) under geological uncertainty. CLFD involves three major steps: optimizing the field-development plan on the basis of current geological knowledge; drilling new wells, and collecting hard data and production data; and updating multiple geological models on the basis of all the available data. In the optimization step, the number, type, locations, and controls for new wells (and future controls for existing wells) are optimized with a hybrid particle swarm optimization-mesh adaptive direct search algorithm. The objective here is to maximize expected (over multiple realizations) net present value (NPV) of the overall project. History matching is accomplished with an adjoint-gradient-based “randomized maximum likelihood” procedure. Because the CLFD history-matching component is fast relative to the optimization component, we generate a relatively large number of history-matched models. Optimization is then performed with a set of “representative” realizations selected from the full set of history-matched models. We introduce a systematic optimization with sample validation (OSV) procedure, in which the number of realizations used for optimization is increased if an appropriate validation criterion is not satisfied. The CLFD methodology is applied to 2D and 3D example cases. Results show that the use of CLFD increases the NPV for the “true” (synthetic) model by 10 to 70% relative to that achieved by optimizing over a large number of prior realizations. We also compare the results for CLFD with OSV to results that use a fixed number of geological realizations. These comparisons show that the use of too few realizations in the CLFD optimization step can result in lower true-model NPVs, whereas OSV provides a systematic approach for determining the proper number of realizations.

Geological realism in hydrogeological and geophysical inverse modeling: A review

Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data. The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data. The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g., using model compression); (2) the physical forward problem (e.g., using proxy models); and (3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today's computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios.

Reservoir uncertainty tolerant, proactive control of intelligent wells

Intelligent wells (I-wells) provide layer-by-layer production and injection control. This flow control flexibility relies on the real-time operation of multiple, downhole interval control valves (ICVs) installed across the well completion intervals. Proactive control of I-wells, with its ambition of creating an optimal, operational strategy of ICVs over the full well lifetime, is a high-dimensional optimization problem with a computationally demanding and uncertain objective function based on one or more simulated reservoir model(s). This paper illustrates how a stochastic search algorithm based on the simultaneous perturbation stochastic approximation (SPSA) coupled with a utility function approach to define an objective function to account for the uncertainty in the reservoir’s description can efficiently solve the proactive, I-well control problem. The utility function accounts for both the expectation and variance of the net present value (NPV) by modifying the objective function to consider multiple reservoir model realizations. Simultaneous optimization of full ensemble of model realizations is prohibitively expensive. By contrast, choosing a small ensemble of model realizations is computationally less demanding, but the small ensemble has to be itself selected. We introduce the use of k-means clustering for selecting a representative ensemble of model realizations that performs in an equivalent manner to all available realizations. A distance measure, tailored to the proactive optimization application, is used to define the similarity/dissimilarity of the different realizations which is then employed to perform the clustering. Moreover, we show that this robust proactive optimization process can either focus on the specific objective of increasing the mean or of reducing the variance (this is achieved via adjustable weights in the utility function). The relative importance of these conflicting objectives has to be taken into account during the model realization selection process to ensure the near-global success of the obtained control scenario. The proposed robust optimization framework has been tested on a representative test case (PUNQ-S3). This is a small field developed with an intelligent producer in which the uncertainty in the model has been quantified by several geological realizations. Our results demonstrate the computational efficiency of employing an ensemble of systematically selected realizations rather than the traditional methods that rely on either a single model realization or a randomly selected ensemble of realizations. Our results show the success of the developed framework in identifying control scenarios that correspond to an acceptable improvement in the expected added value at a controlled risk level while substantially reducing the computation time compared to using full ensemble of model realizations.

Influence of conceptual model uncertainty on contaminant transport forecasting in braided river aquifers

Hydrogeologist are commonly confronted to field data scarcity. An interesting way to compensate this data paucity, is to use analog data. Then the questions of prediction accuracy and uncertainty assessment when using analog data shall be raised. These questions are investigated in the current paper in the case of contaminant transport forecasting in braided river aquifers. In using analog data from the literature, multiple unconditional geological realizations are produced following different geological conceptual models (Multi-Gaussian, Object-based, Pseudo-Genetic). These petrophysical realizations are tested in a contaminant transport problem based on the MADE-II tracer experiment dataset. The simulations show that reasonable contaminant transport predictions can be achieved using analog data. The initial concentration conditions and location regarding the conductivity heterogeneity field have a stronger influence on the plume behavior than the resulting equivalent permeability. The results also underline the necessity to include a wide variety of geological conceptual models and not to restrain parameter space exploration within each concept as long as no field data allows for conceptual model or parameter value falsification.

Opening New Opportunities With Fast Reservoir-Performance Evaluation Under Uncertainty: Brugge Field Case Study

SummaryDecision making under uncertainty can be quite challenging, especially when complex numerical simulations are considered in the work flow and the decision has to be made relatively fast (e.g., in hours). This is the case when one needs to rank a given field portfolio within a limited budget and with acquisition constraints. If the ranking measure associated with each field is properly and rapidly evaluated, new prospect opportunities, which may lead to a favorable strategic position, can be readily identified.In this paper, we propose an efficient methodology for computing a “production-potential” measure that can be used to rank greenfield portfolios in the presence of geological uncertainty, quantifying both uncertainty and risk propagation. Next, we briefly describe the basics of the method proposed. First, uncertainty in sedimentary variability and flow behavior has to be characterized by a number of representative geological realizations. Sampling techniques are used to significantly reduce the number of realizations while preserving accuracy in the description and uncertainty propagation. Thereafter, multiple and varied field-development plans, based on primary/secondary-recovery mechanisms, are automatically generated while accounting for key parameters related to the number, drilling locations, and drilling sequence of wells. In these plans the reservoir is clustered by areas with similar production/injection potential, and the well locations and drilling schedules are obtained accordingly. The well controls are determined through estimations of the field-recovery factor. By means of experimental-design techniques a relatively small number of field-development plans are selected to capture the most significant production profiles. Each of these development plans is simulated for the realizations sampled previously, and the production-potential measure [e.g., average net present value (NPV) over all sampled realizations] is computed for all the plans. The highest of these measures (i.e., the best development plan) can be used for ranking the greenfield in the portfolio. Response-surface procedures are considered to perform additional analysis computations within iterative optimization procedures. It is important to note that other statistics related to the exploitation potential (e.g., standard deviation of the NPV) can also be used to complement the ranking, thereby mitigating the decision makers’ risk tolerance. The methodology has been tested on the Brugge Field benchmark, which presents 104 realizations of multiple geological parameters. The benchmark has been modified to simulate a greenfield scenario. The ranking measure is the (discounted) NPV averaged over the 104 realizations. The proposed work flow yields a ranking measure of USD 5.43 billion, and the computational cost is approximately 1,900 simulations (performed in a parallel-computing environment). This NPV is somewhat higher than those found for the Brugge benchmark (with similar modified settings) by other researchers. To validate the results, we performed more-exhaustive checking by use of approximately 17,000 simulations, and the ranking measure found was USD 5.51 billion.The new work flow presented allows one to efficiently and in a sufficiently accurate manner support decision making in greenfield-portfolio evaluation. Fast reservoir-performance-evaluation engines open new prospect opportunities that, with traditional decision-making techniques, may be frequently lost.

Multi-objective optimization for rapid and robust optimal oilfield development under geological uncertainty

Optimal well placement is critical to oil and gas field development. Typical workflows involve procedures to place a new well or a group of new wells in a reservoir in order to maximize some pre-defined reservoir performance metric. However, there are two main drawbacks with these traditional optimization approaches: First, the impact of geological uncertainty is often neglected or there may be no framework to include geological uncertainty. Second, traditional optimization techniques normally cannot meet the requirement of optimizing two or more conflicting objectives simultaneously—this may be useful when maximizing oil recovery while also minimizing water production. Consequently, in recent years, multiple objective optimization to obtain robust solutions that minimize the decision risk under geological uncertainty becomes a topic of renewed interest. Therefore, in this work, we develop a new work flow for well placement optimization while considering geological uncertainty in reservoir models. In general, when considering geological uncertainty, the primary goal is to maximize the mean net present value (NPV) over all realizations. However, restricting the search to simply maximizing the mean NPV may be inappropriate or inadequate for decision-making. A more reasonable choice is to maximize the mean NPV while minimizing the spread of the optimal NPV’s obtained for each realization. Therefore, in this work, we apply multi-objective optimization techniques to maximize the mean and minimize the variance of NPV values over all geological realizations to provide robust well placement solutions for decision-makers to select according to their risk attitude towards field development plans.

A Theoretical look at Ensemble-Based Optimization in Reservoir Management

Ensemble-based optimization has recently received great attention as a potentially powerful technique for life-cycle production optimization, which is a crucial element of reservoir management. Recent publications have increased both the number of applications and the theoretical understanding of the algorithm. However, there is still ample room for further development since most of the theory is based on strong assumptions. Here, the mathematics (or statistics) of Ensemble Optimization is studied, and it is shown that the algorithm is a special case of an already well-defined natural evolution strategy known as Gaussian Mutation. A natural description of uncertainty in reservoir management arises from the use of an ensemble of history-matched geological realizations. A logical step is therefore to incorporate this uncertainty description in robust life-cycle production optimization through the expected objective function value. The expected value is approximated with the mean over all geological realizations. It is shown that the frequently advocated strategy of applying a different control sample to each reservoir realization delivers an unbiased estimate of the gradient of the expected objective function. However, this procedure is more variance prone than the deterministic strategy of applying the entire ensemble of perturbed control samples to each reservoir model realization. In order to reduce the variance of the gradient estimate, an importance sampling algorithm is proposed and tested on a toy problem with increasing dimensionality.

Ensemble level upscaling for compositional flow simulation

Uncertainty quantification is typically accomplished by simulating multiple geological realizations, which can be very expensive computationally if the flow process is complicated and the models are highly resolved. Upscaling procedures can be applied to reduce computational demands, though it is essential that the resulting coarse-model predictions correspond to reference fine-scale solutions. In this work, we develop an ensemble level upscaling (EnLU) procedure for compositional systems, which enables the efficient generation of multiple coarse models for use in uncertainty quantification. We apply a newly developed global compositional upscaling method to provide coarse-scale parameters and functions for selected realizations. This global upscaling entails transmissibility and relative permeability upscaling, along with the computation of a-factors to capture component fluxes. Additional features include near-well upscaling for all coarse parameters and functions, and iteration on the a-factors, which is shown to improve accuracy. In the EnLU framework, this global upscaling is applied for only a few selected realizations. For 90 % or more of the realizations, upscaled functions are assigned statistically based on quickly computed flow and permeability attributes. A sequential Gaussian co-simulation procedure is incorporated to provide coarse models that honor the spatial correlation structure of the upscaled properties. The resulting EnLU procedure is applied for multiple realizations of two-dimensional models, for both Gaussian and channelized permeability fields. Results demonstrate that EnLU provides P10, P50, and P90 results for phase and component production rates that are in close agreement with reference fine-scale results. Less accuracy is observed in realization-by-realization comparisons, though the models are still much more accurate than those generated using standard coarsening procedures.

Integrating PCA and Streamline Information for History Matching Channelized Reservoirs

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 170636, “Integration of Principal-Component Analysis and Streamline Information for the History Matching of Channelized Reservoirs,” by C. Chen, SPE, Shell International Exploration and Production; G. Gao, SPE, Shell Global Solutions US; J. Honorio, Massachusetts Institute of Technology; P. Gelderblom, SPE, Shell Global Solutions International; E. Jimenez, Qatar Shell GTL; and T. Jaakkola, Massachusetts Institute of Technology, prepared for the 2014 SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October. The paper has not been peer reviewed. Although principal-component analysis (PCA) has been applied widely to reduce the number of parameters characterizing a reservoir, its disadvantages are well-recognized. A work flow was proposed to integrate cumulative-distribution-function-based PCA (CDF-PCA) and streamline information for assisted history matching on a two-facies channelized reservoir. The CDF-PCA was developed to reconstruct reservoir models by use of only a few hundred principal components. It inherits the advantage of PCA to capture the main features or trends of spatial correlations among properties, and, more importantly, it can properly correct the smoothing effect of PCA. Introduction Both object-based and multipointstatistics-based models generate relatively more geologically realistic channel bodies compared with conventional two-point geostatistics-based techniques. However, conditioning such models to production data and correctly sampling the posterior probability distribution are challenging problems. One of the major challenges is that the number of para meters to be tuned during history matching is too large to be handled effectively by available history- matching work flows, especially when the adjoint gradient is unavailable. Another challenge is that the models obtained after history matching generally violate or distort the geological and geostatistical characteristics of the original or prior models. One of the authors’ major objectives was to reconstruct channelized geological and reservoir models with much fewer uncertain parameters so that the models can be conditioned to production data through automatic/assisted history matching with use of model-based derivative-free optimization algorithms. The geological and reservoir models obtained by history matching have to capture major flow dynamics and are also constrained by the histogram of lithology distribution and the correlations between reservoir properties of the original model. The following four important questions must be addressed when regenerating geological realizations using new parameters: Are new parameters able to regenerate both static models and dynamic models? Are the models regenerated by new parameters still geologically realistic and relevant? In other words, do the new geological and reservoir models satisfy geologists’ requirements? Are the realizations generated from sampling the probability distribution of these new uncertain parameters equivalent to (but not biased from) the realizations generated from sampling the prior probability distribution? Is it feasible to history match production data by tuning these new parameters?

Bridging multipoint statistics and truncated Gaussian fields for improved estimation of channelized reservoirs with ensemble methods

In this paper, we present a new parameterization of channelized reservoirs with two facies types, which is coupled with the ensemble Kalman filter (EnKF) and the iterative adaptive Gaussian mixture filter (IAGM) for history matching (HM) of production data. The main objectives are to match the past data within the model and measurement uncertainties and to preserve the geological realism in order to predict the future behavior of the reservoir. The parameterization bridges the method of Gaussian truncation with multipoint statistics from a training image. To generate an ensemble of channelized reservoirs, a multi-point geostatistical tool (SNESIM) is used in combination with a training image. The parameterization is performed in a Gaussian space by drawing from a conditional Gaussian distribution with truncation rules estimated from the ensemble, ensuring that the updates are always facies realizations. The EnKF is a HM method that updates the ensemble based only on the first two statistical moments, which is not enough to characterize the posterior when channelized structures are present. Therefore, we propose using the iterative version of AGM in combination with SNESIM in the resampling step to better handle nonlinearities and preserve the channelized structure of the ensemble members. The results presented show that the IAGM procedure is able to reduce the uncertainty in the updated ensemble with realistic geological structure, in addition to having good predictability and preservation of channels. We performed a comparison with IAGM applied directly to the permeability field.

Reservoir Geological Uncertainty Reduction: an Optimization-Based Method Using Multiple Static Measures

Uncertainty in reservoir geological properties has a major impact in reservoir design and operations decision-making. To quantify the production uncertainty and to make optimal decisions in reservoir development, flow simulation is widely used. However, reservoir flow simulation is a computationally intensive task due to complex geological heterogeneities and numerical thermal modeling. Normally only a small number of realizations are chosen from a large superset for flow simulation. In this paper, a mixed-integer linear optimization-based geological realization reduction method is proposed to select geological realizations. The method minimizes the probability distance between the discrete distribution represented by the superset of realizations and the reduced discrete distribution represented by the selected realizations. The proposed method was compared with the traditional ranking technique and the distance-based kernel clustering method. Results show that the proposed method can effectively select realizations and assign probabilities such that the extreme and expected reservoir performances are recovered better than any of the single static measure-based ranking methods or the kernel clustering method.

Well Placement Optimization with Geological Uncertainty Reduction

Well placement optimization aims to determine optimal well locations so that the economic benefit from oil production can be maximized. Geological uncertainty has a significant impact on the optimal well placement plan and therefore has to be considered in the well placement optimization problem. A geological realization reduction framework for well placement under geological uncertainty is proposed in this work. The objective is to optimally select a small subset of realizations and incorporate them into the well placement optimization problem, so as to reduce the computational efforts. A reservoir case study demonstrates that the selected smaller subset of realizations is a very good representation of a larger superset of realizations and can significantly decrease the computational time associated with the well placement optimization problem.

Models for guiding and ranking well-to-well correlations of channel bodies in fluvial reservoirs

A probabilistic method has been devised to assess the geologic realism of subsurface well-to-well correlations that entail the lateral tracing of geologic bodies across well arrays with constant spacing. Models of geo-body correlability (based on the ratio between correlatable and penetrated geo-bodies) are obtained from total probabilities of penetration and correlation, which are themselves dependent on the distribution of lateral extent of the geo-body type. Employing outcrop-analog data to constrain the width distribution of the geo-bodies, it is possible to generate a model that describes realistic well-to-well correlation patterns for given types of depositional systems. This type of correlability model can be applied for checking the quality of correlation-based subsurface interpretations by assessing their geologic realism as compared with one or more suitable outcrop analogs. The approach is illustrated by generating total-probability curves that refer to fluvial channel complexes and that are categorized on the basis of outcrop-analog classifications (e.g., braided system, system with 20% net-to-gross), employing information from a large fluvial geo-body database, Fluvial Architecture Knowledge Transfer System (FAKTS), which stores information relating to fluvial architecture. From these total-probability functions, values can be drawn to adapt the correlability models to any well-array spacing. The method has been specifically applied to rank three published alternative interpretations of a stratigraphic interval of the Travis Peak Formation (Texas), previously interpreted as a braided fluvial depositional system, in terms of realism of correlation patterns as compared to (1) all analogs recorded in FAKTS and considered suitable for large-scale architectural characterization, and (2) a subset of them including only systems interpreted as braided.