Characterization Of Reservoir Properties Research Articles

Characterization of reservoir properties and pore structure based on micro-resistivity imaging logging: Porosity spectrum, permeability spectrum, and equivalent capillary pressure curve

According to the capillary theory, an equivalent capillary model of micro-resistivity imaging logging was built. On this basis, the theoretical models of porosity spectrum (ϕi), permeability spectrum (Ki) and equivalent capillary pressure curve (pci) were established to reflect the reservoir heterogeneity. To promote the application of the theoretical models, the Archie's equation was introduced to establish a general model for quantitatively characterizing ϕi, Ki, and pci. Compared with the existing models, it is shown that: (1) the existing porosity spectrum model is the same as the general equation of ϕi; (2) the Ki model can display the permeability spectrum as compared with Purcell's permeability model; (3) the pci model is constructed on a theoretical basis and avoids the limitations of existing models that are built only based on the component of porosity spectrum, as compared with the empirical model of capillary pressure curve. The application in the Permian Maokou Formation of Well TSX in the Central Sichuan paleo-uplift shows that the ϕi, Ki, and pci models can be effectively applied to the identification of reservoir types, calculation of reservoir properties and pore structure parameters, and evaluation of reservoir heterogeneity.

Reservoir properties and genesis of tight sandstones—A case study from the Gaotaizi oil layer in the Qijia area, Songliao basin

The primary focus of oil and gas exploration for tight sandstone reservoirs is on a quantitative characterization of reservoir properties. This paper uses the tight sandstone reservoir developed in the Gaotaizi oil layer in the Qijia area of the Songliao Basin as an example. The petrology, physical properties, pore–throat characteristics, and the genesis of the densification of the oil-bearing sandstones are elucidated using casting thin-sections, scanning electron microscopy, 3D computerized tomography (CT), and petrophysical experimental techniques. The results show that the Gaotaizi oil layer is mainly composed of clastic rocks and contains small amounts of shell limestone. The clastic rocks are mainly lithic feldspar sandstone and feldspar lithic sandstone, while residual intergranular pores, intergranular dissolved pores, intragranular dissolved pores, intragranular pores and intercrystalline pores constitute the different pore types. Mercury intrusion and 3D computerized tomography analysis showed that micro-nano pores account for 53% of the total pores present. The pore–throat coordination number is distributed between 1 and 4, with an average of 1.8. The pores and throats in the Gaotaizi reservoir have poor connectivity. The porosity distribution of the Gaotaizi oil layer is 1.4%–22.5%, with an average of 9.5%, while the permeability distribution ranges from 0.01 to 27.10 mD, with an average of 0.41 mD. It is an ultra-low porosity and ultra-low permeability tight reservoir. The Gaotaizi oil layer is divided into three types of reservoirs through a systematic study of its pore developmental characteristics. Diagenetic processes like compaction and cementation result in a reduction in porosity and permeability. Compaction, calcite and siliceous cementation, and illite packing are primarily responsible for reservoir densification.

Machine learning-assisted upscaling analysis of reservoir rock core properties based on micro-computed tomography imagery

Optimum solutions for geologic modeling and reservoir simulation in industries such as oil and gas recovery and carbon capture and storage require accurate characterization of reservoir properties, which are often heterogeneous. In this study, high-quality micro-computed tomography (CT) images (1.475-μm/pixel resolution) of a sandstone core acquired from the Bell Creek oil field, USA, were used to provide nondestructive analysis of pore- and core-scale heterogeneity across measurement scales of 94–566 μm. In addition to characterizing the as-received sample, the core sample was flooded with brine to evaluate the capacity of the core sample to receive injected fluids. The micro-CT images were systematically segmented into pore spaces and grains via machine learning (ML) steps including image preprocessing, label creation using a traditional ML method based on limited manual image annotation, and finally U-Net segmentation. The segmented image stacks were reconstructed into digital cubes of various scales of voxel lengths. The 3D porosity values were calculated for all the digital cubes, and the fractal dimensions of the cubes were estimated using a box-counting method. The results showed that smaller cubes had greater heterogeneity and that the porosity values could be accurately estimated by fractal dimension and voxel lengths using ML models. For the core sample with brine flooding, the ratio of pores filled by brine to the total pore space was related to the porosity and could also be accurately estimated by porosity, fractal dimension, and voxel lengths using ML models. The results of this study demonstrate that the concept of fractal dimension can be a useful vector to perform upscaling analysis of sandstone rock heterogeneity from the pore to core scale and that fractal dimensions can be used to estimate porosity values and pore space-filling capacity across those scales.

Quantitative evaluation of tight oil reservoirs in the Chang 8 Member of the Yanchang Formation in southern Ordos Basin

The precise and quantitative characterization of reservoir properties is the key to efficient development of tight oil reservoirs. In this paper, taking the Chang 8 Member of the Yanchang Formation in the Shuimogou area in the southern Ordos Basin as an example, the sedimentary facies types, microscopic pore structures, diagenesis, influencing factors of physical properties, and hydrocarbon enrichment law of tight oil reservoirs are systematically studied. The research results show that the Chang 8 Member in the study area is a typical delta front subfacies deposit, including distributary channel and inter-distributary bay microfacies. The constructive diagenesis of the Chang 8 Member include dissolution, metasomatism and rupture; while the destructive diagenesis include mechanical compaction and cementation. The Chang 8 reservoir has entered the middle diagenetic stage A. The factors affecting the physical properties of tight oil reservoirs include deposition, compaction, cementation and dissolution. The secondary pores formed by dissolution account for 10–40% of the total surface porosity, with an average value of 24%. Local structures and sediments have significant control over hydrocarbon accumulation. The westward dipping tectonic setting of the northern Shaanxi Slope provides the basic conditions for the migration of oil and gas to the eastern updip areas. The changes of lithology and physical properties in the updip direction of the structure form the blocking conditions for the continued migration of oil and gas, which is conducive to the accumulation of oil and gas. In addition, the main oil reservoirs are mainly distributed along the distributary channel of the delta front, and most of the distributary channel sandstone is more than 20 m thick. The areas of thick sand body with multiple layers in the lateral direction is the main part of oil and gas accumulation. However, the reservoirs formed on the flanks of underwater distributary channels are generally thin and poorly sorted, which is not conducive to the accumulation of hydrocarbons.

An evaluation method for types of low-production coalbed methane reservoirs and its application

At present, the macro-parameters such as critical desorption pressure, comprehensive diffusion coefficient, and permeability are commonly used to characterize the properties of a reservoir, and the productivity of coalbed methane (CBM) wells can be predicted through numerical simulation or established mathematical models, and the types of low-producing CBM reservoirs can be classified. However, low production from CBM wells is often caused by the weakness of one (or more) of desorption, diffusion, and seepage in CBM reservoirs, and the evaluation of a single link and macro-parametric characterization of reservoir properties cannot really ascertain the cause of the low production from a given CBM well.In the present work, the influences of pores and fracture structure, fluid flow dynamics and resistance on the desorption, diffusion, and seepage of CBM were considered from the perspective of system theory, and the evaluative parameter index system of low-productivity reservoirs was established. This avoids the one-sidedness of the evaluative results arising when only considering macro-parameters. New methods of obtaining the evaluative parameters pertaining to desorption, diffusion, and seepage are proposed: the methods include isothermal adsorption experiments, the use of logging curves, drainage data, mercury injection, and a classical mathematical model. These methods combined the data from experiments with in-situ data, and ensure the accuracy and practicability of the resulting evaluative parameters. On this basis, types of low-production reservoirs were classified using an analytic hierarchy process with multi-parameter superposition.The evaluative results pertaining to Shizhuang North block in the Qinshui Basin, Shanxi Province, China show that there are six types of low-yield reservoirs among the evaluative wells tested. Among them, diffusion is the main factor governing the low yield of CBM wells, followed by desorption and seepage. Herein, the reservoir constraint on CBM production is comprehensively evaluated, identifying the main controlling link affecting the low productivity of CBM wells, and laying a theoretical foundation for targeted transformation measures.

About Identifiability of Oil and Water Relative Permeability Curves and Reservoir Heterogeneity through Integrated Well Test Study

Relative permeabilities (RP) play an important role in reservoir engineering. RP functions together with the permeability anisotropy coefficient predetermine waterflooding efficiency and oil/water ratio in production forecast. Traditionally multiphase flow parameters are estimated from core analysis data. But such measurements suffer from small representative elementary volume (REV) and limited characterization of reservoir properties. Therefore using core data in 3D reservoir modelling could lead to distorted description of actual flow conditions. Despite those functions (RP) could be history matched with assimilated production data, such a procedure would require long history of waterflooding. So the authors’ idea is to apply integrated well test study to estimate the displacement efficiency and/or relative permeability functions at downhole conditions. Well testing is traditionally applied in reservoir engineering for single-phase reservoir parameters estimation. Our approach is extended to multi-phase flow and is based on data collection at well bottomholes and subsequent data assimilation in flow model.In this paper we summarize both features of mathematical problem statement and identifiability of multiphase parameters through inverse problem solution, but also discuss 10+ -year experience in interpretation of two-phase well testing using our technologies. To estimate multiphase parameters, we have to jointly consider complex data of well logging and dynamic data of well testing. Both data sets are used in the inverse problem quality criteria, where the least squares method has been applied. Forward problem corresponds to a 3D multiphase fluid flow model in porous media. The latter consists of continuity equation with multiphase Darcy equation instead of moment balances. For data assimilation modern methods of optimal control theory were successfully applied. For all synthetic test cases real reservoir parameters were accurately recovered through the use of forward simulation data.In order to estimate reservoir heterogeneity, we applied a single-phase model to get the ratio of vertical to horizontal permeability. Data of well self-interference testing were used for vertical permeability estimation. Depending on the depth of reservoir pressure perturbation, reservoir properties could be properly inferred from observations. Two other options of 3D interference testing using vertical and horizontal wells are also presented.In other words, all the problems considered are identifiable, and the level of their correctness is completely predetermined by the amount and quality of observed data. And transition to digital (intelligent) oil-and-gas production and closed-loop reservoir management [1] provides a possibility to remove discussed restrictions and all inverse problems considered should be accounted as fully identifiable.

Integration of NMR and Conventional Logs for Vuggy Facies Classification in the Arbuckle Formation: A Machine Learning Approach

Summary Diagenetic effects in carbonate rocks can enhance or occlude depositional pore space. Reliable identification of porosity-enhancing diagenetic features (e.g., vugs and fractures) is essential for petrophysical characterization of reservoir properties (e.g., porosity and permeability), construction of geological and reservoir models, reserve estimation, and production forecasting. Challenges remain in characterizing these diagenetic features from well logs as they are often mixed with variations in mineral and fluid concentrations. Herein, we explore a data-driven approach that is based on a comprehensive well log data set from the Arbuckle Formation in Kansas to classify vuggy facies in carbonate rocks. The available well log data include conventional logs (gamma ray (GRTC), resistivity (RT), neutron/density porosity (NPHI/RHOB), photoelectric factor (PE), and acoustic slowness) and nuclear magnetic resonance (NMR) transverse relaxation time (T2) logs. We parameterized the measured T2 distribution using a multimodal lognormal Gaussian density function and combined the resulting Gaussian parameters with conventional logs as inputs into three supervised machine learning (ML) algorithms; namely, support vector machine (SVM), random forest (RF), and artificial neural network (ANN). The facies labeling data used in this study were based on visual examination of vug sizes from core samples, which include five classes; namely, nonvuggy, pinpoint-size, centimeter-size, fist-size, and super-vuggy. In total, 80% of the data set was used as the training set, and a fivefold cross validation was used for hyperparameter tuning. We conducted a detailed comparison of the above three ML algorithms on the basis of different combinations of features. The highest classification accuracy achieved on the holdout testing set is 84% using SVM on a combination of conventional logs and selected NMR Gaussian parameters as inputs. In general, inclusion of conventional log data improves the prediction accuracy compared with using NMR data alone. Feature selection improves the performance for SVM and ANN but is not recommended for RF.

Handling Spatial Heterogeneity in Reservoir Parameters Using Proper Orthogonal Decomposition Based Ensemble Kalman Filter for Model-Based Feedback Control of Hydraulic Fracturing

Accurate characterization of reservoir properties is of central importance to achieve a desired fracture geometry during a hydraulic fracturing process. However, the estimation of spatially varying geological properties in hydraulic fracturing is inherently ill-posed due to a limited number of measurements. In this work, parametrization is performed to reduce the dimensionality of spatially varying Young’s modulus profiles via proper orthogonal decomposition (POD), and a data assimilation technique called ensemble Kalman filter (EnKF) is used to estimate the parameter values in the reduced low-dimensional subspace. Through a series of simulation results, it is demonstrated that the POD-based EnKF technique provides a process model with updated spatially varying geological parameters, which is able to make an accurate prediction of the fracture propagation dynamics in hydraulic fracturing. Next, we use the updated high-fidelity process model in a model predictive control framework to construct a closed-loo...

Applying full-azimuth depth imaging in the local angle domain to delineate hard-to-recover hydrocarbon reserves

Hard-to-recover hydrocarbon reservoirs lie at great depths, in complex geological conditions. They are characterized by complex structures, low fluid permeability and a low oil and gas recovery ratio. In Russia today, about 60% of the potential oil and gas fields are located in this type of reservoir. These include hydrocarbon deposits in the Paleozoic basement (pre-Jurassic basement) of Western Siberia, subsalt carbonate sediments under salt dome tectonics, and carbonate and terrigenous deposits in the Volga region and Eastern Siberia. The exploration of these reservoirs benefits from a new, full-azimuth angle domain approach to seismic processing and imaging. This new technology can provide a more detailed depth image of the entire structural-tectonic reservoir skeleton, and a more accurate forecast of the main rock properties of the reservoirs. Conventional seismic depth imaging tools, such as ray-based or beam-based Kirchhoff migrations, applied to rich azimuth seismic data, normally generate multi-azimuth offset-domain common image gathers (CIGs). These are further used for anisotropic velocity model determination and for the characterization of reservoir properties, such as fracture systems. In these types of migrations, the input data is first binned into specific surface offset/ azimuth geometrical groups, such as offset vector tiles (OVT), azimuthal sectors or planner spirals, depending on the acquisition pattern. Each set of binned data is then independently migrated, with the final CIGs being simply a collection of individual images. However, in many cases, particularly when studying hydrocarbon reservoirs below complex geological areas and along steep inclined layers, the offset/azimuth CIGs do not provide the required information (in terms of accuracy and resolution, for example) to achieve the above mentioned goals. Unlike subsurface imaged events along the angle domain CIGs, which indicate ‘true’ local reflectivities, the reflection image events along the offset domain CIGs can be only considered a rough approximation of the ‘true’ reflectivities. Obviously, the accuracy and reliability of the offset domain CIGs are strongly compromised when imaging below complex geological areas with complex wave phenomena. One of the main drawbacks of offset domain imaging, especially in complex geological areas, is its inability to deal with the actual multi-pathing waves which are naturally handled within angle domain imaging.

Analysis of Effective Porosity and Effective Permeability in Shale-Gas Reservoirs With Consideration of Gas Adsorption and Stress Effects

Summary Nanoscale porosity and permeability play important roles in the characterization of shale-gas reservoirs and predicting shale-gas-production behavior. The gas adsorption and stress effects are two crucial parameters that should be considered in shale rocks. Although stress-dependent porosity and permeability models have been introduced and applied to calculate effective porosity and permeability, the adsorption effect specified as pore volume (PV) occupied by adsorbate is not properly accounted. Generally, gas adsorption results in significant reduction of nanoscale porosity and permeability in shale-gas reservoirs because the PV is occupied by layers of adsorbed-gas molecules. In this paper, correlations of effective porosity and permeability with the consideration of combining effects of gas adsorption and stress are developed for shale. For the adsorption effect, methane-adsorption capacity of shale rocks is measured on five shale-core samples in the laboratory by use of the gravimetric method. Methane-adsorption capacity is evaluated through performing regression analysis on Gibbs adsorption data from experimental measurements by use of the modified Dubinin-Astakhov (D-A) equation (Sakurovs et al. 2007) under the supercritical condition, from which the density of adsorbate is found. In addition, the Gibbs adsorption data are converted to absolute adsorption data to determine the volume of adsorbate. Furthermore, the stress-dependent porosity and permeability are calculated by use of McKee correlations (McKee et al. 1988) with the experimentally measured constant pore compressibility by use of the nonadsorptive-gas-expansion method. The developed correlations illustrating the changes in porosity and permeability with pore pressure in shale are similar to those produced by the Shi and Durucan model (2005), which represents the decline of porosity and permeability with the increase of pore pressure in the coalbed. The tendency of porosity and permeability change is the inverse of the common stress-dependent regulation that porosity and permeability increase with the increase of pore pressure. Here, the gas-adsorption effect has a larger influence on PV than stress effect does, which is because more gas is attempting to adsorb on the surface of the matrix as pore pressure increases. Furthermore, the developed correlations are added into a numerical-simulation model at field scale, which successfully matches production data from a horizontal well with multistage hydraulic fractures in the Barnett Shale reservoir. The simulation results note that without considering the effect of PV occupied by adsorbed gas, characterization of reservoir properties and prediction of gas production by history matching cannot be performed reliably. The purpose of this study is to introduce a model to calculate the volume of the adsorbed phase through the adsorption isotherm and propose correlations of effective porosity and permeability in shale rocks, including the consideration of the effects of both gas adsorption and stress. In addition, practical application of the developed correlations to reservoir-simulation work might achieve an appropriate evaluation of effective porosity and permeability and provide an accurate estimation of gas production in shale-gas reservoirs.

Characterization and estimation of reservoir properties in a carbonate reservoir in Southern Iran by fractal methods

Reservoir heterogeneity has a major effect on the characterization of reservoir properties and consequently reservoir forecast. In reality, heterogeneity is observed in a wide range of scales from microns to kilometers. A reasonable approach to study this multi-scale variations is through fractals. Fractal statistics provide a simple way of relating variations on larger scales to those on smaller scales and vice versa. Simple statistical fractal models (fBm and fGn) can be useful to understand the model construction and help the reservoir structure characterization. In this paper, the fractal methods (fGn and fBm) have been applied to characterize and to estimate of reservoir properties. Three methods, namely box-counting, variogram, and R/S analysis, were carried out on log and core data for porosity and permeability data to estimate fractal dimension; a high fractal dimension estimated in this study reveals a high heterogeneity in the reservoir. Moreover, sampling from simulated fractal data at non-existing data depths enables us to generate appropriate realizations of reservoir permeability with suitable accuracy at a proper computational time.

Origin of Micropores In Late Jurassic (Oxfordian) Micrites of the Eastern Paris Basin, France

Abstract: Porous micritic facies, either primary chalks or resulting from secondary destructive micritization, can constitute important hydrocarbon or water reservoirs. Characterization of reservoir properties and the understanding of factors which controlled the distribution of porosity are of primary interest to evaluate the prospective reserves. Middle and late Oxfordian limestones of the eastern Paris Basin show several horizons with porosities higher than 20%. The porosity is mainly microporous and located either within secondary micritized grains or in the micritic matrix. Using SEM, cathodoluminescence, as well as confocal microscopy, stable oxygen and carbon isotope ratios, and petrophysical measurements, a scenario for the evolution of the micropores is proposed. Lime mudstones to packstones constitute the majority of the high-porosity facies (HPFs). Inner lagoonal deposits are more micritized and thus more porous than grainstones, and facies rich in leiolitic oncoids and echinoid clasts are less impacted by micritization. Micritization was responsible for an increase of the intragranular porosity in most grain types. During both eogenesis and shallow burial, mineralogical stabilization dissolved aragonitic particles and allowed precipitation of calcite rhombs. This process was probably enhanced below surfaces of subaerial exposure. During burial, Ostwald ripening allowed the growth of larger micrite crystals at the expense of smaller ones during early Berriasian and late Aptian recharges of deep aquifers when the northern margin of the basin was exposed. Overgrowths on micrite crystals were more important in intervals strongly affected by chemical compaction, which favored oversaturation of waters with respect to calcite. In low-porosity horizons (LPFs), the dense micritic texture of oncoids and the monocrystalline architecture of echinoid clasts prevented an intense micritization, while the strong chemical compaction enhanced poronecrosis. Telogenetic fracturing created new fluid pathways that favored inputs of meteoric fluid in porous micrite and allowed the continuation of Ostwald ripening during Cenozoic times. As a whole, mesogenetic inputs of waters undersaturated with respect to calcite in deep aquifers during exposure of basin margins are a more efficient process than early subaerial exposure for enhancing aggrading neomorphism and appearance of microporous micrites. Initial mineralogical heterogeneities also impact the intensity of chemical compaction and thus the stratigraphical distribution of microporous limestones.

Application of complementary methods for more robust characterization of sandstone cores

This paper is based on detailed mineralogical, structural, petrophysical, and geochemical studies of sandstone core samples, using routine core analysis methods. These include X-ray computer tomography (CT) scanning, magnetic resonance imaging (MRI), particle size analysis, point counting based on petrographic thin sections, environmental scanning microscopy (ESEM), X-ray diffraction (XRD), and X-ray fluorescence (XRF). In this study, we demonstrate the feasibility of combing these complementary methods in the characterization of reservoir properties of sandstone cores. Four types of sandstones (Slick Rock Aeolian, Fife, Locharbriggs, and Berea sandstones) that differ in grain size, porosity, and mineralogy have been characterized. The results of the different methods used were found to be consistent with each other, but the combination of a variety of methods has allowed a fuller characterization of the rock samples than each method used on its own, bringing out subtle variations in petrographic characteristics that add significant value towards a better description of reservoir properties. For example, it becomes apparent that some types of rocks like Berea sandstones thought to be homogeneous are in fact heterogeneous. The recognition that rock heterogeneity at the sub-centimeter scale may have a significant effect on hydrocarbon recovery requires that field-scale reservoir models take account of these small-scale effects in order to lay claim to reasonable accuracy in production forecasts.

Determination of reservoir properties from the integration of CSEM, seismic, and well-log data

Peter Harris, Rock Solid Images, and Lucy MacGregor, Offshore Hydrocarbons Mapping, discuss the advantages in reservoir interpretation of integrating data from controlled source electromagnetic (CSEM) and seismic data, illustrated by an example from the Nuggets-1 gas reservoir in the UK Northern North Sea. The problem of remote characterization of reservoir properties is of significant economic importance to the hydrocarbon industry. For example, in exploration the ability to determine the gas saturation in an identified prospect would avoid the costly drilling of un-economic low saturation accumulations. During development and production, a detailed knowledge of the reservoir properties and geometry, and changes in these parameters through time, can aid optimization of well placement and enhance overall recovery rates. A range of geophysical techniques can be applied to this problem. Seismic data are commonly used to develop geological models of structure and stratigraphy. Amplitude variation with offset (AVO) and inversion for acoustic and elastic impedance may also be used to constrain reservoir properties such as elastic moduli and density. These can in turn be related to mineralogy, porosity, and fluid properties through rock physics relationships (for example, Mavko et al., 1998). However seismic data alone in many situations cannot give a complete picture of the reservoir. Ambiguities exist, for example, in AVO responses which may be caused either by fluid or lithological variations, and cannot be separated on the basis of the seismic data alone. The controlled source electromagnetic (CSEM) method is becoming widely used in the offshore hydrocarbon industry, and has been applied successfully in a variety of settings (see for example, Srnka et al., 2006; MacGregor et al., 2006; Moser et al., 2006). The CSEM method uses a high powered horizontal electric dipole to transmit a low frequency electromagnetic signal through the seafloor to an array of multi-com-ponent electromagnetic receivers. Variations in the received signal as the source is towed through the array of receivers are interpreted to provide the bulk electrical resistivity of the seafloor, through a combination of forward modelling, geophysical inversion, and imaging. The bulk resistivity of a porous rock is to a large degree controlled by the properties and distribution of fluids within it. Typical brine saturated sediments have a resistivity in the range 1-5 .m. Replacing the seawater with resistive hydrocarbon can result in an increase in the bulk resistivity of the formation by 1-2 orders of magnitude. CSEM sounding exploits this dramatic change in physical properties to distinguish water bearing formations from those containing hydrocarbons. However, as for seismic data, potential ambiguities exist in the interpretation of CSEM data. For example, tight limestones, volcanics, or salt bodies may also have high resistivity, and could give a CSEM response similar to that of a hydrocarbon reservoir. In addition, because of the diffusive nature of electromagnetic fields in the earth, the structural resolution is generally lower than that given by seismic data. Since the CSEM and seismic data are controlled by very different physical processes, it is clear that a careful combination of seismic and CSEM data, exploiting the strengths of each, can supply information which is not available or is unreliable from either type of data alone, thus reducing ambiguity and risk. A number of approaches to the integration of disparate data types have been proposed (e.g. Musil et al., 2003; Gallardo & Meju., 2004; Hoverston et al., 2006). Here we illustrate the advantages of an integrated interpretation using CSEM and seismic data collected on the Nuggets-1 gas reservoir.

Accurate, Efficient Quantification of Uncertainty for Flow in Heterogeneous Reservoirs Using the KLME Approach

Summary Accurate modeling of flow in oil/gas reservoirs requires a detailed description of reservoir properties such as permeability and porosity. However, such reservoirs are inherently heterogeneous and exhibit a high degree of spatial variability in medium properties. Significant spatial heterogeneity and a limited number of measurements lead to uncertainty in characterization of reservoir properties and thus to uncertainty in predicting flow in the reservoirs. As a result, the equations that govern flow in such reservoirs are treated as stochastic partial differential equations. The current industrial practice is to tackle the problem of uncertainty quantification by Monte Carlo simulations (MCS). This entails generating a large number of equally likely random realizations of the reservoir fields with parameter statistics derived from sampling, solving deterministic flow equations for each realization, and post-processing the results over all realizations to obtain sample moments of the solution. This approach has the advantages of applying to a broad range of both linear and nonlinear flow problems, but it has a number of potential drawbacks. To properly resolve high-frequency space-time fluctuations in random parameters, it is necessary to employ fine numerical grids in space-time. Therefore, the computational effort for each realization is usually large, especially for large-scale reservoirs. As a result, a detailed assessment of the uncertainty associated with flow-performance predictions is rarely performed. In this work, we develop an accurate yet efficient approach for solving flow problems in heterogeneous reservoirs. We do so by obtaining higher-order solutions of the prediction and the associated uncertainty of reservoir flow quantities using the moment-equation approach based on Karhunen-Loéve decomposition (KLME). The KLME approach is developed on the basis of the Karhunen-Loéve (KL) decomposition, polynomial expansion, and perturbation methods. We conduct MCS and compare these results against different orders of approximations from the KLME method. The 3D computational examples demonstrate that this KLME method is computationally more efficient than both Monte Carlo simulations and the conventional moment-equation method. The KLME approach allows us to evaluate higher-order terms that are needed for highly heterogeneous reservoirs. In addition, like the Monte Carlo method, the KLME approach can be implemented with existing simulators in a straightforward manner, and they are inherently parallel. The efficiency of the KLME method makes it possible to simulate fluid flow in large-scale heterogeneous reservoirs.