Use of Well Test Data in Stochastic Reservoir Modelling

Constructing subsurface models that accurately reproduce geological heterogeneity and their associated uncertainty is critical to many geoscience and engineering applications. For hydrocarbon reservoir modeling and forecasting, for example, spatial variability must be consistent with geological processes, geophysical measurements, and time records of fluid production measurements. Generating such subsurface models can be time-consuming; conditioning them to different types of measurements is even more computationally intensive and technically challenging. Using too many free variables can cause overfitting of the data, thereby decreasing the predictive ability of the model; high dimensionality also slows convergence during history matching of fluid production measurements. To contend with these problems, we introduce here a new machine learning approach, referred to as the stochastic pix2pix method, which parameterizes high-dimensional, stochastic reservoir models into low-dimensional Gaussian random variables in latent space. Many of the world’s significant hydrocarbon fields originate from fluvial or turbidite deposits, with sedimentary processes and spatial distribution of rock facies significantly influencing their flow behavior. Rule- or object-based methods are commonly used to model geostatistically these types of reservoirs. Here, we introduce a new and efficient machine learning-based reservoir modeling workflow capable of generating 2D fluvial reservoir models that account for the available field data and the geometries of different facies. By constraining subsurface model realizations to available geophysical and petrophysical interpretations, multiphysics inversion can be greatly accelerated, thereby requiring only production history matching. Although our models are 2D, an extension to 3D can be readily implemented through zone-by-zone (i.e., reservoir unit) modeling and conditioning. The proposed method and workflow also partially solve the common problem of machine learning methods, wherein mapping low- to high-resolution images often yield reduced spatial variability. The proposed method is an extension of conditional generative adversarial networks, in which we incorporate a novel penalty term into the loss function in order to generate various realizations honoring the same conditional data, such as structural interpretation from seismic data, and borehole measurements at key well locations. We “train” the generative model on geologically realistic, multivariate spatial models generated with a rule-based fluvial reservoir simulator. Each high-resolution training image includes five lithofacies with distinct petrophysical property trends. To evaluate the performance of the proposed method, visual inspection, indicator variograms and multiple point density function are applied to gauge how well the realizations reproduce existing patterns in the true model. A new metric, the mean categorical error, is proposed to quantify how well the realizations match the conditioning data. The proposed method correctly reproduces patterns even when the conditioning data are significantly different from those in the training set. Likewise, the method can perform continuous model modifications, meaning that the machine learning procedure effectively reproduces the migration rule of a meandering (fluvial) system.

The Incorporated Research Institutions for Seismology (IRIS) Seismographs in Schools (SIS) program has supported teachers in the use of educational seismometers and real-time seismic data in the classroom for the past 20 years. To better understand how the seismographs and seismic data are being used in the classroom, we sent a survey to 770 past or current program participants. The survey asked about their seismometer, seismic data use, software use, the impact of seismic data on their classroom, and what additional seismology-related resources or instruction they provide to their students. Four highly-engaged teachers were then recruited from this larger pool for a case study. The purpose of this study was to better understand these highly-engaged teachers, their experiences with seismic instrumentation, software and data in the classroom, how and to what degree seismic data has impacted their curriculum and instruction, and their perceptions of the impact of the SIS program on their students’ understanding of Earth Science concepts. The case study results show that each of the highly-engaged teachers values data driven instruction, instrument science, and the integration of seismic data into the classroom more than just during their earthquake units. They have made it part of everyday class activities by having students be aware of data coming in, noting earthquakes in the news, and helping students learn more about analyzing data for advanced investigations. While there were differences in their implementations, in all cases a critical feature of their engagement with students was use of a variety of seismology-related resources which connected the seismic data to the rest of the curriculum. Thus, the use of seismic data was just one component of their seismology-related teaching. This study also highlights the value of a local sensor, as all four highly-engaged teachers stressed that students as stewards of the seismometer linked them to the science in an engaging and dynamic way. Thus, while the highly-engaged teachers had a primary responsibility to promote learning, their focus on student engagement is also helping to create young citizen scientists.

In current practice history matching is often performed on upscaled reservoir models without updating the original geological model. Taking into account new production data in an existing model is often problematic because of the lack of appropriate techniques. This problem becomes crucial when using geostatistical models. In such a case, the integration of new static and dynamic constraints requires the modification of an initial realization without destroying the initial history match and the overall geostatistical properties. This paper presents a new methodology based on advanced history matching techniques for updating dynamically 3D stochastic reservoir models to account for new production data. The proposed approach is based on the gradual deformation method. It allows local or global smooth transformations of the model while conserving the overall statistical characteristics. History matching is performed by coupling this method with an optimization process which integrates geostatistical modeling, upscaling, and fluid flow simulation in the same loop. This approach provides great flexibility in history matching various types of production data. In addition, inversion parameters can be selected throughout the entire modeling loop, from the facies spatial distribution, to petrochemical parameters and fluid flow parameters. Finally, local transformations may be performed to account for new wells or to update the reservoir model with new dynamic information. A successful application to a 3D stochastic reservoir model inspired from a real field is presented. The first step was to perform a history match using the production history available from an initial group of production wells. Then, new dynamic information is acquired from infill wells and over one year of additional production data. The heterogeneity distribution is locally modified by gradual deformation to update the model with this new information. The benefit of the proposed approach for improving the model characterization and reducing uncertainty on production forecasts is demonstrated.

Seismic data incorporation in reservoir simulation models history matching (HM) studies has been continuously growing. 4D seismic data, in contrast with well production data, can provide a very good scenario of fluids arrangement along reservoir. In this work we describe how 3D and 4D seismic data gathered in acquisitions performed in Campos Basin was incorporated in Marlim Sul deep water field geological model reconstruction and in assisted HM (AHM). It is taken advantage of both 3D and 4D seismic data in several stages of the study, for instance, in the construction of a new porosity – most influential in impedance – model by using a methodology based on the inversion of synthetic seismic (calculated by petro-elastic model) in porosity through an optimization process that aims to reduce the difference between observed and synthetic impedance, and when defining influential parameters based on fluids displacement registered by seismic signal, by using a technique based on the creation of transmissibility multipliers parameters regions that considers the fluids displacement shown in 4D signal. Another relevant point is the use of information from reservoir and 3D seismic data when weighting the 4D data in the objective function. Combining the above mentioned techniques with the knowledge of the field – supported by the 3D seismic data – which allowed, for instance, identification of faults – where fault transmissibility multipliers were used as parameters in the HM process – a fairly good agreement on the observed well and seismic production data was achieved. HM studies using AHM tools have been shown a much more time-efficient technique when compared to manual HM. The incorporation of 4D seismic data can considerably improve the HM quality by improving the reservoir description, once it increases the ability of describing fluids arrangement and pressure distribution. The techniques successfully applied in the Marlim Sul field HM support these conclusions.

High resolution sequence stratigraphical methods have been used in the detailed geological modeling of an element of the Ness formation of a North Sea field. This updated geological description has been used as input to the stochastic geological model MOHERES. 14 realizations of facies architecture and petrophysical properties have been generated. The stochastically generated realizations have been scaled up to a refined element of an existing deterministic, history matched reservoir simulation model for the full Upper Brent reservoir. The upscaled versions of the realizations have been connected to the full field model, and reservoir simulations have been performed to compare twelve years of production history with simulated results for well production, RFT- and PLT-data. Six of the realizations gave good to very good results when compared to measured production data. These realizations were used for simulation of the future production performance to the year 2010, making it possible to estimate its uncertainty.

Time-lapse seismic data has been widely used for the detailed reservoir characterization, and data assimilation algorithms are commonly used for petroleum reservoir history matching of production data. However, hardly any seismic data has been integrated into the reservoir inverse modeling workflow, due to the large data size, finer gridding, and especially the scarcity in time of the seismic data. Popular ensemble-based reservoir inverse modeling methods such as ensemble Kalman filter (EnKF) also face the problems of high computational cost due to the storage of the intermediate variables, restarting the reservoir simulating process and the inconsistency of the full-step and step-wise simulations. The intrinsic sequential data assimilations characteristics of the EnKF set obstacles to assimilate 4D seismic data. The alternative method can be the ensemble smoother (ES), which is an ensemble based method for data assimilation. The ES is based on a Bayesian updating scheme of the reservoir model to match the production history and improve the production forecast. To improve the algorithm convergence, a multiple data assimilation (MDA) method was proposed by Emerick and Reynolds (2012a). The algorithm we used is called ensemble smoother with multiple data assimilation (ESMDA), we modified the ESMDA to integrate the geophysical data, and created the new workflow to history match both the production and geophysical data. The available production data is well measurements, including oil production rate, well water cut and bottom-hole pressure, as well as time-lapse geophysical data, including P-wave impedance. In this paper, we first formulated the mathematical descriptions of ESMDA, we then down-scaled the seismic data, and modified the data assimilation algorithms, illustrated the history matching workflow for both production and geophysical data, finally, we showed how it works with a case study on a water flooding operation in a synthetic reservoir. In comparison, we also showed the history matching only on the production data, which yields an inferior results than the one matches both production and seismic data.

Significant uncertainty exists in the detailed 3-D distribution of lithofacies, porosity, and permeability in every reservoir. Understanding and modeling the heterogeneous 3-D distribution of these rock properties is critical for improved oil recovery and reservoir management. Geostatistical techniques are being increasingly used to generate alternative heterogeneous 3-D reservoir models that are consistent with the available data. Although a large number of stochastic reservoir models or realizations may be available, a small number of realizations are considered in practice. Due to computer limitations, it is only possible to visualize and perform fine-scale full-field flow simulation on a limited number of realizations. Techniques are reviewed in this paper for ranking a suite of geostatistical realizations so that low-side, expected, and high-side realizations may be reliably chosen. Detailed analysis/flow simulation may then be performed on these realizations that somehow bound the uncertainty in the reservoir. Reservoir management is improved when expected and bounding cases are considered rather than using a limited number of "random" realizations. This paper reviews a number of methods for ranking geostatistical reservoir models. These methods may be classified into three categories. The first category includes statistical methods such as simple statistics, 3-D measures of connectivity, and connectivity to specific well locations. Methods in the second class are based on approximations to flow simulation, e.g., random walk-type results. The third category is for flow-simulation based methods for a simpler process than that being considered for improved oil recovery, e.g., tracer simulation and flow simulation with coarsened models. The applicability of a number of ranking methods is illustrated with a small example. There is no unique ranking index when there are multiple flow response variables and no ranking measure is perfect. Nevertheless, the value of ranking realizations will be quantified by examining the expected loss knowing an economic loss function and the true distribution of uncertainty. Introduction The primary objective of the application of geostatistical tools for reservoir modeling is to create realistic numerical geological models or realizations of the 3-D spatial distribution of lithofacies, porosity. and permeability. An often disturbing fact of geological reservoir modeling is that there are alternative realizations that honor all of the available data equally well and yet yield different reservoir performance predictions. In fact, it is often advertised that "a different realization can be obtained by simply changing a random number seed". A fundamental principle of geostatistics is that of data integration, i.e., all known data should be honored "by construction" and not left to chance. Of course, this is not always possible; it is difficult to constrain detailed 3-D geological realizations to seismic and historical production data. We are restricting ourselves to plausible realizations. There are times when certain realizations would be rejected on the basis of familiarity with the reservoir or data not used in the geostatistical modeling such as production-related historical observations. We are not considering the rejects; only those realizations that meet all basic requirements of reasonableness are considered. Exact prediction / decision making would require exhaustive knowledge of the spatial distribution of porosity and permeability. At any specific instant in time, there is such a single true distribution of petrophysical properties. This true distribution was created by the complex interaction of many different chemical, physical. and biological processes over geological time and would be accessible only through exhaustive sampling. In all practical situations, the unique true distribution will remain unknown. This paper addresses the uncertainty due to incomplete information. We do not consider uncertainty due tothe volume support or scale difference between core measurements and geological modeling cells,the limited flexibility of our geostatistical modeling techniques to reproduce complex nonlinear features, ornumerical approximations in the subsequent flow simulator. P. 105

In recent years, stochastic modeling technique has become a hot topic in reservoir characterization. Wherease, what should be made clear, if the technique is used in constructing geological models in early evaluationphase, is what problems in oil-gas development study can be solved by this technique. In this paper, focusing on the early evaluation phase of reservoir, the application cases from two reservoirs are used to discuss what practical problems can be solved by sectional reservoir models, which were built up by means of this technique.

There exist several methods for history matching of reservoir facies distribution. When using these methods, the facies mean size is usually supposed to be prior information known without uncertainty. However, in reality, it is often difficult to acquire an accurate estimation of the facies mean size due to limited measurement data. Thus, it is more reasonable to treat the facies mean size as an uncertain model parameter for updating. In this work, we propose a methodology to jointly update the mean size and spatial distribution of facies in reservoir history matching. In the parameterization step, we utilize a Gaussian random field and a level set algorithm to parameterize each facies. The range of the Gaussian field controls the facies mean size of the generated facies distribution realizations. To accomplish jointly updating the mean size and spatial distribution of facies, the Gaussian random field is further parameterized by the Karhunen–Loeve (KL) expansion. We choose the range of the Gaussian field and the independent Gaussian random variables in the KL expansion as model parameters. After model parameterization, we use the Levenberg–Marquardt ensemble randomized maximum likelihood filter (LM_EnRML) to perform history matching. Three synthetic cases are set up to test the performance of the proposed method. Numerical results show that for estimating the facies field, the mean size and spatial distribution of facies can be jointly updated to match the reference distribution using the proposed method.

We present an approach for modeling facies bodies in which a highly constrained stochastic object model is used to integrate detailed seismic interpretation of the reservoir’s sedimentological architecture directly in a three-dimensional reservoir model. The approach fills the gap between the use of seismic data in a true deterministic sense, in which the facies body top and base are resolved and mapped directly, and stochastic methods in which the relationship between seismic attributes and facies is defined by conditional probabilities. The lateral geometry of the facies bodies is controlled by seismic interpretations on horizon slices or by direct body extraction, whereas facies body thickness and cross-sectional shape are defined by a mixture of seismic data, well data, and user defined object shapes. The stochastic terms in the model are used to incorporate local geometric variability, which is used to increase the geological realism of the facies bodies and allow for correct, flexible well conditioning. The result is a set of three-dimensional facies bodies that are constrained to the seismic interpretations and well data. Each body is defined as a parametric object that includes information such as location of the body axis, depositional direction, axis-to-margin normals, and external body geometry. The parametric information is useful for defining geologically realistic intrabody petrophysical trends and for controlling connectivity between stacked facies bodies.

A new methodology for stochastic reservoir modelling constrained to well and historical data has been developed and successfully applied to synthetic case studies. Multiple well historical data and prior geostatistical information can be integrated using a Bayesian inversion technique and an efficient optimization algorithm based on the gradient method. This inversion procedure allows direct selection of particular constrained model realizations within a confidence domain of the parameter space. The gradient method, implemented in an industrial numerical reservoir simulator within the fully implicit scheme, provides the sensitivities of production results with respect to the model parameters. These parameters can be, for example, the petrophysical properties over given reservoir zones or the well productivity indexes. Recently, a user-defined parameterization technique of a heterogeneous permeability distribution was introduced in order to locally modify the mean value of an initial stochastic distribution. An efficient quadratically convergent optimization algorithm is combined with the Bayesian formalism to directly obtain a constrained model from an initial realization. Greater efficiency of this procedure is reached by using the gradient results. A priori information on the parameters is introduced through Gaussian or lognormal probability density functions. A maximum likelihood model is obtained after history matching, as well as a posteriori information on the parameters with reduced uncertainties. After history matching, new model realizations can be selected, inside a confidence domain defined by an iso-probability criterion, in order to quantify production forecast uncertainties. An optimization procedure is used to obtain particular model realizations, which correspond to extreme values of a given production forecasting criterion. A successful application on a synthetic case study is described at the end of this paper. The petrophysical properties and the activity coefficient of an analytical aquifer are simultaneously constrained to match the historical data recorded for 7 wells. A parameterization technique is used in order to constrain the mean of a stochastic distribution of petrophysical properties. Introduction Our aim is to constrain geostatistical models to both well data and historical data. The proposed method is based on the Bayesian inversion technique, whose formalism is well-suited for integrating prior knowledge on the geological model and the dynamic data. Moreover, this formalism positions the inverse problem in a stochastic context, allowing uncertainty quantification on production forecasts. The main difficulty encountered in constraining geostatistical models is the cost in terms of CPU time spent to obtain a constrained realization and the amount of realizations needed to quantify uncertainties on production forecasts. The dimension of the inverse problem corresponds, theoretically, to the number of grid blocks multiplied by the number of petrophysical properties to be identified. A reduction of the dimension of the inverse problem is therefore necessary to preserve the feasibility of such methods. A parameterization of the distribution of the petrophysical properties can be used in order to reach this goal. The principle of the proposed method is to define the distribution of petrophysical properties as a function of parameters in a reduced space and to constrain these parameters to the production data. This paper proposes a parameterization technique, called pilot point method, which consists in constraining the initial model to several master points, located on a coarse grid. Each master point locally constrains the mean of an initial model realization. The gradient method can be used to improve the efficiency of the inversion procedure. The sensitivities of the simulations results with respect to the master point values can be used by an optimization algorithm. P. 155^

This paper presents an integrated methodology (using versatile history matching software) for constraining 3D stochastic reservoir models to well data and production history and its application to a real case (a tight-gas reservoir in the Southern North Sea). The approach is to formulate the history matching problem as a minimization problem where the objective function to be minimized is the squared difference of the real production data values and the corresponding simulated data. To resolve this inverse problem, we use gradient based optimization techniques to update the entire simulation workflow, thanks to advanced parametrization techniques. The set of model parameters characterizes the stochastic geological model (including the diagenetic modeling) and the fluid flow simulator, which allows the facies distributions (and their associated petrophysical properties), diagenetic overprint and well properties (such as skin) to be modified until an acceptable match is obtained. The parametrization technique is coupled to constrained optimization algorithms to ensure that model parameters remain within realistic bounds of the geological settings and ensures that the geologically derived stochastic properties of the initial reservoir are preserved throughout the history matching process. This application shows how the combination of a versatile history matching tool with efficient parametrization techniques can improve the quality and efficiency of a geologically driven history matching process. The speed of this process will be valuable when analyzing a set of history matched models allowing a better assessment to be made of the risk and uncertainty associated with predictions of future performance.

The oil and gas industry has been revolutionized within the last decade, with horizontal drilling and hydraulic fracturing enabling the extraction of huge amounts of shale gas in areas previously considered impossible and the recovering of hydrocarbons in harsh environments like the arctic or in previously unimaginable depths like the off-shore exploration in the South China sea and Gulf of Mexico. With the development of 4D seismic, engineers and scientists have been enabled to map the evolution of fluid fronts within the reservoir and determine the displacement caused by the injected fluids. This in turn has led to enhanced production strategies, cost reduction and increased profits. Conventional approaches to incorporate seismic data into the history matching process have been to invert these data for constraints that are subsequently employed in the history matching process. This approach makes the incorporation computationally expensive and requires a lot of manual processing for obtaining the correct interpretation due to the potential artifacts that are generated by the generally ill-conditioned inversion problems. I have presented here a novel approach via including the time-lapse cross-well seismic survey data directly into the history matching process. The generated time-lapse seismic data are obtained from the full wave 3D viscoelastic acoustic wave equation. Furthermore an extensive analysis has been performed showing the robustness of the method and enhanced forecastability of the critical reservoir parameters, reducing uncertainties and exhibiting the benefits of a full wave 3D seismic approach. Finally, the improved performance has been statistically confirmed. The improvements illustrate the significant improvements in forecasting that are obtained via readily available seismic data without the need for inversion. This further optimizes oil production in addition to increasing return-on-investment on oil & gas field development projects, especially in offshore environments.

Sequential assimilation of 4D seismic data for reservoir description using the ensemble Kalman filter

3D stochastic reservoir modelling is an emerging new technology for the oil and gas industry and is increasingly used by oil and gas companies as a tool to support major business decisions in field development planning, and the acquisition and management of petroleum assets. However, the potential benefit that 3D stochastic reservoir modelling can offer is still overlooked by many asset teams. Conventional methods are often still applied for field development planning and reserve estimation, where over-simplified geological models are used and reservoir uncertainties are substantially under-estimated. This is one reason why the oil and gas industry does not have a good track record in estimating reserves and field development planning. 3D stochastic reservoir modelling methods that incorporate the structural-stratigraphic framework, facies and petrophyscial properties can ensure that the reservoir models fully describe reservoir heterogeneity. This in turn lays a sound foundation for field development planning. The 3D stochastic reservoir modelling methods also quantify and reduce uncertainties in various aspects of the reservoir. This allows a field development plan to be more robust yet flexible enough to take the advantage of upside reserve potential and to be economically sound if the downside case occurs. Based on quantification of uncertainties, optimal well positions and well paths can be designed to maximise oil and gas recovery.