Conventional Reservoir Modeling Research Articles

A comparative analysis of gas mixing during the underground hydrogen storage in a conventional and fractured reservoir

Climate change and political tensions are reducing the time for the energy transition. Large-scale underground hydrogen storage (UHS) can be crucial in future energy systems for decarbonizing the world's economy as well as ensuring energy security. There are challenges, however, that prevent it from being used on large scale as an energy carrier. The high cost of hydrogen cushion gas is one of them. It is not economical that a portion of hydrogen remains in a reservoir as a cushion gas during UHS until the end of a storage operation. Consequently, inert gases such as nitrogen can be used as cushion gas. Hydrogen's heating value gets reduced, however, due to gas mixing. Since gas mixing behavior differs in reservoirs with different mechanisms, hydrogen heating value was employed to examine the gas mixing behavior during UHS in conventional and fractured reservoir models (dual-porosity) for the first time in this study. The mixing behavior of hydrogen gas with replaced cushion gas will first be examined in the absence and presence of diffusion using a conventional gas reservoir model. Then some reservoir and operational parameters will be investigated in order to determine how they affect the gas mixing behavior, including reservoir porosity, permeability, rock compressibility, and cushion gas type. Next, a basic UHS scenario with dual-porosity will be examined to determine how hydrogen gas and cushion gas mix in the presence and absence of diffusion and the effects of specific parameters on gas mixing behavior in the fractured reservoir (NFR) model, including matrix-fracture transmissibility and cushion gas type. According to the results, in the conventional reservoir model, considering diffusion during early hydrogen production results in a decrease in hydrogen heating value. While in the second stage of hydrogen production, diffusion increases the hydrogen heating value, resulting from the sweeping effect. Dual-porosity models illustrate the opposite behavior. As well, porosity reduction resulted in higher hydrogen heating values during early production but reversed during late production. Unlike the effect of rock compressibility on heating value of hydrogen, a lower hydrogen heating value was obtained during hydrogen production as the reservoir permeability increased. Also, carbon dioxide cushion gas showed reversed effect on gas mixing during UHS in the conventional compared to the NFR case.

AI, Data Analytics Enable Approach to History Matching in Geologically Complex Field

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 202460, “History Matching of Production Performance for Highly Faulted, Multilayered, Clastic Oil Reservoirs Using Artificial Intelligence and Data Analytics: A Novel Approach,” by Nis Ilyani Mohmad and Dipak Mandal, SPE, Petronas, and Hadi Amat, Petroliam Nasional, et al., prepared for the 2020 SPE Asia Pacific Oil and Gas Conference and Exhibition, originally scheduled to be held in Perth, Australia, 20-22 October. The paper has not been peer reviewed. History matching is a critical step for dynamic reservoir modeling to establish a reliable, predictive model. Numerous approaches have emerged over decades to accomplish a robust history-matched reservoir model. As geological and completion complexity of oil and gas fields increase, building a fully representative predictive reservoir model can be arduous to almost impossible. The complete paper outlines an approach to history matching that uses artificial intelligence (AI) with an artificial neural network (ANN) and data-driven analytics. The new approach has been used to mitigate history-matching challenges in a mature, highly geologically complex field offshore Malaysia. Overview The complete paper describes a step-by-step methodology for building a reservoir model and a history-matching process using ANN. The paper discusses data preparation and quality assurance and control (QA/QC), spatiotemporal database formulation, reservoir model design, ANN architecture design, model training, and history-matching strategy. A case study of implementation in an offshore Malaysian field is presented, wherein good-to-fair history-matching quality was obtained for all production parameters. Field A is a highly geologically complex, 25×75-km oil sandstone reservoir with more than 200 major and minor faults and more than 30 reservoir layers. It has been producing for more than 25 years. The challenges of history matching this field lie not only in its geologically complex structure and corresponding subsurface uncertainties, but also in a production strategy that has involved commingled dual-string production with several integrity issues that exacerbate the field’s complexities. To date, Field A has no fieldwide history-matched reservoir model because the complexity of history matching has precluded using conventional numerical simulation methods. This challenge has been mitigated by implementing an AI-based reservoir model and data analytics. The new approach is estimated to be more time- and cost-efficient than the conventional method. The complete paper compares the AI-based and conventional numerical reservoir modeling approaches and highlights the advantages, limitations, and areas of improvement of the new methodology. The authors present their case for AI-based reservoir modeling as a complement or alternative to conventional numerical modeling to create time-efficient reservoir models while reducing risk in field-development plans.

Integration of sub- meter scale lithological heterogeneity in reservoir models for an improved quantification of CO2 trapping capacities

Sub-meter scale lithological heterogeneity in the form of sedimentary structures such as cross, planar and massive beddings is known to enhance carbon mineral trapping. However, this understanding is largely qualitative. Quantitative estimates of trapping capacities at this scale are limited by the availability of high-resolution field data. Additionally, such heterogeneity is typically not accounted for in conventional reservoir models due to computational restriction posed by the grid size resolution. As a result, the impact of sub-meter scale lithological heterogeneity on carbon trapping capacities is typically not accounted for in dynamic flow and reactive transport simulations at the reservoir scale. The present study aims to quantify the impact of intraformational baffles on carbon mineralization for a range of rock types. A series of 2-D multiphase reactive transport simulations were set-up to model the geochemical processes occurring at the interface of a baffle and a reservoir rock for a period of 1000 years. The study shows that the presence of baffles with certain rock properties within the reservoir rock can enhance or reduce carbon mineral trapping capacity relative to homogeneous reservoir rocks depending on clay and carbonate mineral content in baffles. Further, a new workflow is developed to build a 2D high-resolution reservoir model of the Paaratte Formation, Otway Basin while overcoming the technical challenges associated with sub-meter scale discretization of geological models.

Digital core analysis: Characterizing reservoir quality through thin sandstone layers in heterolithic rocks

Conventional reservoir models of heterolithic reservoirs do not include millimetre-to-centimetre sandstone layers due to the resolution limitations of widely used well logs and core plug data, resulting in underestimation of hydrocarbon reserves. Continuity and the reservoir quality of the thin sandstone layers in heterolithic reservoir are critical factors for hydrocarbon reserves. We use multi-scale Digital Core Analysis techniques to estimate the reservoir properties (porosity and permeability) and characterize the connectivity of millimetre-to-centimetre sandstone layers in heterolithic rocks. We show that a reservoir heterolithic core plug contained continuous sandstone layers with permeability and porosity that are similar to a reference reservoir sandstone. A non-reservoir heterolithic core plug has thin sandstone with discontinuous layers with permeability and porosity that are significantly lower compared to the reference reservoir sandstone. We show that Digital Core Analysis can characterize reservoir properties at the millimetre-to-centimetre scale that contributes to a multi-scale reservoir model for improved hydrocarbon reserves estimates in heterolithic reservoirs.

Modeling of gas flow in fractured shale

Abstract In this paper equations and methodologies for the simple modeling of gas flow in fractured shale are developed. Transmissibility following hydraulic fracturing is related to the geo-mechanical properties of the shale. Methods for the application of these models using commercial conventional reservoir models to predict well productivity are developed. This provides a valuable tool in estimating the productivity and economic value of a potential shale gas play where only geological, petrophysical and geo-mechanical and limited or analogue production data is available.

Novel Forward Model Quantifies Uncertainty of Fracture Networks

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191395, “Uncertainty Quantification of the Fracture Network With a Novel Fractured-Reservoir Forward Model,” by Zhi Chai, SPE, Hewei Tang, SPE, Youwei He, and John Killough, SPE, Texas A&M University, and Yuhe Wang, Texas A&M University at Qatar, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed. A major portion of the uncertainty found in shale reservoirs is the result of the distribution and properties of the fracture network. However, explicit fracture models are rarely used in uncertainty quantification because of their high computational cost. This paper presents a work flow to match the history of reservoirs featuring complex fracture networks with a novel forward model. The efficiency of the model allows fractures to be characterized explicitly, and the corresponding uncertainty about the distribution and properties of fractures can be evaluated. Introduction For low-permeability unconventional shale reservoirs, the fracture network greatly determines the performance of the wells. Because of the large uncertainty of the fracture distribution, especially for natural fractures, the production behavior might differ dramatically. A possible way to characterize fractures is by use of core data, well-logging data, or seismic data. However, these data are either sparse in nature, and thus cannot be used to determine the exact location of fractures, or low in accuracy because of limited quality. An alternative approach is to use production data and characterize the fractures through history matching. Various approaches have been proposed for automatic history matching. Most of these were evaluated with conventional reservoir models through upscaling (partially the result of the cost of generating explicit fracture models and performing simulations). For fractured reservoir models, especially when explicit fracture models are used, nonlinearity is even more significant and challenges the applicability of the existing methods. In this work, the authors use the improved compartmental embedded discrete fracture model (cEDFM), combining the level-set approach and the ensemble Kalman filter (EnKF) for history matching. The cEDFM has a much better accuracy compared with the original embedded discrete fracture model (EDFM) in handling flux across the direction of fractures, which is a common case for interwell flow. The Forward Model EDFM. The concept of EDFM was first proposed in a work in which the transmissibility between fracture and the matrix is calculated in a manner similar to that used to calculate the well index. By assuming a linear relationship between the pressure in the matrix and the distance to the fracture, an analytical expression of the transmissibility can be obtained. Because the matrix grid does not need to conform to the geometry of the fractures, and the fracture is discretized by the boundary of the matrix gridblocks, this approach is flexible and compatible with traditional orthogonal or cornerpoint grid systems. In original EDFM implementation, three types of non-neighbor connections (NNCs) are considered: Between the fracture and the matrix grid it intersects Between two intersecting fracture grids Between two neighboring fracture grids from the same fracture

Evaluating seepage radius of tight oil reservoir using digital core modeling approach

The main development method of tight oil was depletion development. It is determined that the seepage radius of tight reservoir is crucial to the layout and prediction development of tight oil development. Since the pore throat level of tight reservoirs was frequently nanoscale, the reservoir pressure propagation velocity was even faster than conventional medium high permeability. The fracture system in the tight oil reservoir, which is the main flow channel of oil flow to the direction of wellbore, is more sensitive to the sharp change in reservoir pressure. Hence, the stress-sensitive absolute permeability of the reservoir near the wellbore will fluctuate significantly during the depletion development phase, rather than a constant value. At present, the numerical simulation and graph method, which are commonly utilized in the regression and prediction of the depletion-developing seepage radius. Both do not consider the stress sensitivity phenomenon which caused by nanoscale pores of tight oil and the change of the permeability in the model. As a result, the prediction is not accurate and the model needs to be modified. Meanwhile, the percolation parameters at the scale of the tight oil permeability cannot be accurately obtained in using conventional experimental methods owing to the limitations of the accuracy of the experimental instruments. In this paper, the test of fluid permeability under overburden was carried out to verify the stress sensitivity of the tight core. The microscopic mechanism of nanoscale pore-throat stress sensitivity in tight reservoirs was analyzed from the perspective of tight reservoir mineral composition and nanopore characteristics by using Quantitative Evaluation of Minerals by Scanning Electron Microscopy (Qemscan) and MAPS micro-image splicing technology. Nanoscale pore network model was established with nano-CT scanning and the digital core seepage simulation of tight core was figured out. The accuracy of the digital core seepage simulation method was verified in comparison with the indoor over pressure liquid permeability test. The conventional reservoir model was modified by using the digital core seepage simulation result, and the new model has a high degree of confidence in predicting the tight oil seepage radius.

A robust numerical method for modeling multiple wells in city-scale geothermal field based on simplified one-dimensional well model

An efficient numerical model, which can simulate the coupled fluid flow and heat transfer processes in geothermal fields, is essentially required to evaluate the fate of geothermal wells and the temperature and pressure evolutions of geothermal reservoirs in response to the long-term well operations. Due to the scale disparity between wells and geothermal reservoirs (∼dm vs. ∼km), very fine mesh is required to accurately represent the highly-dynamic zones near geothermal wells, and thus the conventional geothermal reservoir model including geothermal wells is usually time consuming. To improve the computational efficiency without losing accuracy, a simplified one-dimensional geothermal well model considering heat convection and conduction along well axis and heat transfer between geothermal fluid and rocks in the radial direction is proposed and incorporated into the geothermal reservoir model. Both a bench-mark example and a case study of Beijing city geothermal field are presented to demonstrate the reasonability and efficiency of the proposed reservoir modeling method. The computational time are significantly reduced because of avoiding mesh refinement near geothermal wells. The multiple wells effects, interactions between different reservoirs, and the role of faults in reservoir performance are also discussed based on the case study of Beijing city geothermal field.

An experimental study of alternative hot water alternating gas injection in a fractured model

Alternative injection of gas as slugs with water slugs, or alternative water gas injection, is the conventional technique for improving the recovery factor due to its high potential for mobilizing the residual oil in place in the reservoirs and to control gas mobility. The water alternating gas methodology is a combination of two oil recovery procedures: gas injection and waterflooding. The principal parameters that must be evaluated in water alternating gas injection in laboratory scale are reservoir heterogeneity, rock type, and fluid properties. In the current investigation, a feasibility study has been performed to analyze the five various scenarios of enhanced oil recovery techniques and compare them experimentally. The laboratory experiments are done for one of the Iranian reservoirs which have been subjected to waterflooding for several years, and the amount of recovery factor for water flooding is about 42%. The results of this study illustrate that water alternating gas injection and hot water alternating gas injection exert a profound impact on the amount of recovery factor. Moreover, the primary purpose of this study is to assess the application of alternative hot water and hot carbon dioxide gas injections in the conventional and fractured reservoir model.

Analysis of oil and gas flow characteristics in the reservoir with the elastic outer boundary

In the light of the idealization of the outer boundary conditions (infinite, constant pressure and closed) of the conventional homogeneous reservoir model, the paper introduces the elastic outer boundary conditions and establishes the percolation model of homogeneous reservoir. By combining Laplace transforms with the Similarity Construction Method, the solutions of the percolation model of homogeneous reservoir can be obtained in Laplace space. The solutions are inverted into real space with the Stehfest numerical inversion method. In addition, the characteristic curves are drawn, and the impacts of the variation of the main parameters on the curves are analyzed. The results show that the conventional three kinds of outer boundary conditions are actually three special cases of elastic outer boundary. The pressure curve under the elastic outer boundary is between the pressure curve of the constant pressure outer boundary and the closed outer boundary, and the curves above exhibit affine similarities. In this paper, the elastic outer boundary condition is introduced not only to enlarge the range of data interpretation, but also to reflect the real situation of the outer boundary of oil and gas reservoir (Strict closed and constant pressure boundaries rarely exist in real reservoirs). The similarity construction theory greatly simplifies the complicated process of solving the model, which will have a profound influence on the development of the well test analysis software in the future.

The integration of elastic wave properties and machine learning for the distribution of petrophysical properties in reservoir modeling

Conventional reservoir modeling employs variograms to predict the spatial distribution of petrophysical properties. This study aims to improve property distribution by incorporating elastic wave properties. In this study, elastic wave properties obtained from seismic inversion are used as input for an artificial neural network to predict neutron porosity in between well locations. The method employed in this study is supervised learning based on available well logs. This method converts every seismic trace into a pseudo-well log, hence reducing the uncertainty between well locations. By incorporating the seismic response, the reliance on geostatistical methods such as variograms for the distribution of petrophysical properties is reduced drastically. The results of the artificial neural network show good correlation with the neutron porosity log which gives confidence for spatial prediction in areas where well logs are not available.

Facies-independent reservoir characterization of the micropore-dominated Word field (Edwards Formation), Lavaca County, Texas

Micropore-dominated carbonate reservoirs remain challenging for accurate hydrocarbon evaluation and production as conventional reservoir models using depositional textures and petrophysical properties to distribute porosity and permeability cannot be applied. Nevertheless, understanding the distribution of pore systems and predicting the fluid flow behavior of microporous reservoirs is fundamental as micropores constitute a significant percentage of the total porosity and storage capacity. We present the results from an integrated study on the producing micropore-dominated Word Field characterized by a facies independent, diagenetically controlled pore system that approaches 100% microporosity. Four cored wells through the Albian Edwards Formation were described and correlated using stacking patterns and vertical facies trends; pore type characterization was done through thin section petrography, routine core analyses, SEM and MICP data. This study is an example of a permeable reservoir in which intergrain pores are cemented during burial diagenesis and micropores, being more resistant to cementation, remain open to depths greater than 4000 m (13,000 ft). A unique relationship exists between porosity, permeability, median pore-throat size and microcrystalline textures, independent of facies and fabrics. Cumulative gas production data show there is a correlation between the total porosity and the structural position of the wells – wells high on the structure have the highest production. We demonstrate that an equally well-connected micropore network exists in mud-dominated rocks via the matrix, and via grain-to-grain contacts in grain-dominated rocks. The here described intragrain micropore network through grain-to-grain contacts in cemented grainstones is a new carbonate flow path that will likely become more important as more unconventional carbonate reservoirs are explored.

A stochastic inversion workflow for monitoring the distribution of CO2 injected into deep saline aquifers

We present a two-step stochastic inversion approach for monitoring the distribution of CO2 injected into deep saline aquifers for the typical scenario of one single injection well and a database comprising a common suite of well logs as well as time-lapse vertical seismic profiling (VSP) data. In the first step, we compute several sets of stochastic models of the elastic properties using conventional sequential Gaussian co-simulations (SGCS) representing the considered reservoir before CO2 injection. All realizations within a set of models are then iteratively combined using a modified gradual deformation algorithm aiming at reducing the mismatch between the observed and simulated VSP data. In the second step, these optimal static models then serve as input for a history matching approach using the same modified gradual deformation algorithm for minimizing the mismatch between the observed and simulated VSP data following the injection of CO2. At each gradual deformation step, the injection and migration of CO2 is simulated and the corresponding seismic traces are computed and compared with the observed ones. The proposed stochastic inversion approach has been tested for a realistic, and arguably particularly challenging, synthetic case study mimicking the geological environment of a potential CO2 injection site in the Cambrian-Ordivician sedimentary sequence of the St. Lawrence platform in Southern Quebec. The results demonstrate that the proposed two-step reservoir characterization approach is capable of adequately resolving and monitoring the distribution of the injected CO2. This finds its expression in optimized models of P- and S-wave velocities, density, and porosity, which, compared to conventional stochastic reservoir models, exhibit a significantly improved structural similarity with regard to the corresponding reference models. The proposed approach is therefore expected to allow for an optimal injection forecast by using a quantitative assimilation of all available data from the appraisal stage of a CO2 injection site.

Probabilistic analysis of CO2 storage mechanisms in a CO2-EOR field using polynomial chaos expansion

Oil fields are already used for storing carbon via CO2-enhanced-oil-recovery (CO2-EOR). Such storage is an outcome of CO2-EOR, albeit not necessarily by design. A next step would be intentional storage via post-EOR CO2 injection. Trapping mechanisms in such post-EOR operations would include the same mechanisms as in CO2-EOR, including and especially hydrostratigraphic trapping and oil/aqueous dissolution. Forecasting the nature of trapping and the ultimate CO2 distribution in a reservoir is hindered by uncertainty in reservoir properties. The purpose of this study is to develop and apply reduced order models (ROMs) integrated with Monte Carlo simulations to quantify oil solubility trapping (oil phase), aqueous solubility trapping (aqueous phase), and hydrodynamic trapping (CO2 in supercritical phase). The case study site for this analysis is the SACROC unit in western Texas. A Polynomial Chaos Expansion (PCE) technique was used to develop the ROMs. The sources of uncertainty considered are porosity and permeability. Model results of interest include dissolved mass of CO2 in oil phase, mass of CO2 in supercritical phase, dissolved mass of CO2 in aqueous phase, and oil saturation in the rock formation. Reduced order models are developed for all cells in five selected layers of the model, which are adjacent to injection wells, at three specific time points of interest, including the end of a simulated CO2-EOR period, the end of a post-EOR continuous CO2 injection period, and the end of a post-injection monitoring period. Results of regression fit and validation analysis yield high R2 values and low NRMSE values, indicating that the ROMs derived from PCE are capable of meaningful predictions (compared to conventional reservoir models) and effectively represent relationships between model parameters (inputs) and model results (outputs) of interest. Results of 1000 Monte Carlo simulations indicate a dominantly upward transport of CO2 during injection, driven by buoyancy, and a dominantly downward transport of dissolved CO2 after injection stops, caused by increases in both oil and brine density. At the end of the 100-year simulation of the SACROC case study, the results forecast that the storage layers of interest store between 54% and 61% of total trapped CO2 in the entire domain in the oil phase, between 21% and 24% in the supercritical phase, and between 11% and 15% in the aqueous phase. These layers are forecasted to store between 89% and 98% of total trapped CO2 in the field by the end of simulation.

A Model for Wettability Alteration in Fractured Reservoirs

Summary We present a mathematical model for wettability alteration (WA) in fractured reservoirs. Flow in the reservoir is modeled by looking at a single fracture surrounded by matrix on both sides. Water is injected into the formation with a chemical component that enters the matrix and adsorbs onto the rock surface. These changes of the mineral surface are assumed to alter the wettability toward a more water-wet state, which leads to enhanced recovery by spontaneous imbibition. This can be viewed as a representation of “smart water” injection in which the ionic composition of injection brine affects recovery. The WA is described by shifting curves for relative permeability and capillary pressure from curves representing preferentially oil-wet (POW) conditions toward curves representing more-water-wet conditions. The numerical code was successfully compared with ECLIPSE for the specific case in which a fixed wetting state is assumed. Also, the relevance of the WA model was illustrated by modeling a spontaneous-imbibition experiment in which only a modification of the brine composition led to a change in oil recovery. The model can predict sensitivity to matrix properties such as wettability, permeability, and fracture spacing and to external parameters such as schedule of brine compositions and injection rate. Our model illustrates that one cannot use conventional reservoir modeling to capture accurately the behavior we observe. The rate of recovery and the level of recovery have a strong dependency on the component chemistry and its distribution. A significant feature of gradual WA by injecting a component is that the rate of fluid transfer is maintained between matrix and fracture. The resulting recovery profile after water breakthrough can behave close to linear as opposed to the square-root-of-time profile that is observed when the wetting state is fixed (Rangel-German and Kovscek 2002). The water will typically break through early as dictated by the initial POW state, but a higher final recovery will be obtained because higher saturations can imbibe. Improved understanding of the coupling between WA controlled by water/rock chemistry and fracture/matrix flow is highly relevant for gaining more insight into recovery from naturally fractured reservoirs.

Stratigraphic rule-based reservoir modeling

Abstract Stratigraphic rule-based modeling methods approximate sedimentary dynamics to generate numerical descriptions of reservoir architecture and the spatial distribution of petrophysical properties. A few intuitive rules included in a reservoir model construction workflow are shown to render realistic reservoir heterogeneity, continuity, and spatial organization to petrophysical property distributions that are difficult to obtain using conventional reservoir modeling methods. These rules may be inferred from mature reservoirs, surface and subsurface datasets, and process-based models. Examples include confinement, meander, compensation, and healing rules. By incorporating stratigraphic rules that relate to the underlying geological processes in temporal sequence, rule-based modeling methods offer more realistic representation of inferred reservoir heterogeneity beyond conventional geostatistical reservoir modeling approaches. These include variogram-based, multiple point-based and object-based approaches that rely on a limited set of spatial statistics to describe the products of geological processes. Moreover, since these methods operate within a geostatistical framework, uncertainty can be explored by varying geologically meaningful parameters over multiple scenarios and realizations whilst maintaining consistency with input data constraints and applied to reservoir modeling studies within standard workflows. Rule-based modeling methods enable a variety of applications, including use: directly as reservoir models, as a source of reservoir model input statistics such as variograms and training images, and as a numerical analog laboratory to explore relationships between data, model choices and forecasts. Challenges remain, such as reliability of emergent features, alignment to grid framework, and feasibility for broad application. Despite challenges, rule-based methods can offer uplift when the natural facies continuity patterns and their corresponding petrophysical properties are critical to support decisions in reservoir modeling projects.

Modeling and Simulation of Natural Gas Production from Unconventional Shale Reservoirs

Modeling and simulation of unconventional reservoirs are much more complicated than the conventional reservoir modeling, because of their complex flow characteristics. Mechanisms, which control the flow in the reservoir, are still under the investigation of researchers. However, it is important to investigate applications of mechanisms which are present to our knowledge. This paper presents the theory and applications of flow mechanisms in unconventional reservoir modeling. It is a well-known fact that most of the reservoir flow problems are non-linear due to pressure dependency of particular parameters. It is also widely accepted that fully numerical solutions are costly both computational and time wise. Therefore, the presented model in this paper follows semi-analytical solution methods. Gas adsorption in unconventional reservoirs is the major pressure dependent mechanism; in addition existence of natural fractures is also taken considerable attention. This paper aims to investigate combined effect of existence of natural fractures gas adsorption, and gas slippage effect while keeping the computational effort in acceptable range. Unlike the existing literature (Langmuir is widely used), BET multi-layer isotherm employed in this paper for gas adsorption modeling. A modified dual porosity modeling is used for natural fracture and gas slippage effect modeling. For model verification purposes a history matched is performed with real field data from Marcellus shale. The proposed model in this paper shows a good agreement with the field data. It is observed that BET isotherm models early time production performance more accurately than Langmuir isotherm. It is also concluded that gas adsorption significantly improves the production performances of unconventional reservoirs, with natural fractures. In addition, gas slippage has a slight effect in long term production.

Aquifer-scale flow equations as generalized linear reservoir models for strip and circular aquifers: Links between the Darcian and the aquifer scale

[1] An analytical treatment of aquifer flow is presented to establish a link between runoff models and aquifer properties. Recently developed one-dimensional analytical solutions for transient flows in homogeneous aquifers produce expressions for the flux between the aquifer and the surface water, and the difference between the average hydraulic head in the aquifer and the surface water. It is shown that the ratio between these large-scale variables (i.e., the aquifer-scale hydraulic conductivity) can assume one of three asymptotic values. A non-Darcian aquifer-scale flow equation is derived for the average head in the aquifer minus the surface water level. This first-order ordinary differential equation has nonconstant coefficients based in part on the aquifer-scale conductivity. The aquifer-scale equation is a generalization of linear reservoir models: when the aquifer-scale conductivity is stationary, its solution has an exponential term (like a linear reservoir) with a reservoir coefficient that depends on external factors, and a constant term. The solution applies to a wider range of problems than conventional linear reservoir models. The aquifer's characteristic time (derived from the solution) shows that dense drainage networks can make aquifers behave like linear reservoirs most of the time, while large systems never will. When the asymptotic values are used before the time period for which they become valid (i.e., shortly after a perturbation in the surface water level or recharge/extraction), the predicted fluxes can be very inaccurate, and possibly have the wrong sign. In such cases, the full analytical solutions should be used.

Fluid flow in relay zones revisited: Towards an improved representation of small-scale structural heterogeneities in flow models

Soft-linked relay zones may act as conduits for fluid flow across otherwise sealing fault zones; yet, relay zones are commonly also associated with a structurally complex linking damage zone, which in sandstone reservoirs may include low-permeable deformation bands. Incorporating such mm- to cm-scale baffles in flow models is important in order to understand the total effect of relay zones on cross-fault flow. Given the small-scale nature of deformation bands, well below the resolution of conventional reservoir models, their implementation requires implicit representation and upscaling. By applying a deterministically constrained stochastic approach using truncated Gaussian simulation (TGS), we generate reservoir models which closely reproduce observed structural geometries and spatial distribution patterns. Flow simulations of the stochastically generated models, where deformation band permeability is the main variable tested, are compared with the deterministic approach of a previous study of the same relay zone. Our comparison shows that contrasting flow behaviour in the stochastic and deterministic models is amplified as the ratio between host rock and deformation band permeabilities increases. Increasing this ratio causes increased fluid flow complexity in the relay zone and enhances differences in sweep efficiency between the stochastic and deterministic models. Reservoir performance on several model realizations show that time to water breakthroughs in the stochastic models can be 18% shorter whereas their total productions can be 23% lower. The results of the present study indicate that the TGS approach is well suited to capture the details of fluid flow in the presence of small-scale reservoir heterogeneity with intermediate to high permeability contrast relative to host rock (here, 3 to 5 magnitude orders). This has implications not only for the modelling of relay zones, but also for the modelling of other reservoir settings where small-scale (structural) heterogeneity is present.

Non-Gaussian gas hydrate grade simulation at the Mallik site, Mackenzie Delta, Canada

For the past decades, gas hydrate reservoirs have beneficiated from an increasing attention in the academic and industrial worlds. As a result, there is a growing need to develop specific and comprehensive gas hydrate reservoir characterization methods. This study explores the use of a stochastic Bayesian algorithm to integrate well-logs and 3D acoustic impedance in order to estimate gas hydrate grades (product of saturation and total porosity) over a representative volume of the Mallik gas hydrate field, located in the Mackenzie Delta, Northwest Territories of Canada. First, collocated log data from boreholes Mallik 5L-38 and 2L-38 are used to estimate the statistical relationship between acoustic impedance and gas hydrate grades. Second, conventional stochastic Bayesian simulation is applied to generate multiple gas hydrate grade 3D fields integrating log data and lateral variability of 3D acoustic impedance. These equiprobable scenarios permit to quantify the uncertainty over the estimation, and identify zones where this uncertainty is greater. Contrary to conventional stochastic reservoir modeling workflows, the proposed method allows integrating non Gaussian and non linear distributions. This permits to handle bimodal distributions without using complex stochastic transforms. The results present gas hydrate grade values that are in accordance with well-log data. The relatively low standard deviation calculated at each pixel using all realizations suggests that gas hydrate grades is well explained by acoustic impedance and log data.