Dual Porosity System Research Articles

Mimicking some features of a root-soil system by dual porosity media

We report an experimental study of evaporation from a non-homogeneous dual porous system consisting of a finer pore size material at the centre surrounded by coarser particles in a glass beaker. This configuration can be considered to mimic, to a first order, the coupling between the plant roots and soil water. Similar to how roots extract water from the soils, here also water moves, driven by the capillary pressure gradient, from larger to the smaller voids. We explore two different configurations (a) when the small pore sizes span the entire porous column along the gravitational direction and (b) when they are limited to a thin annular region at the porous medium top surface. We measured the mass loss from the system, surface temperature using a thermal camera, and the ambient conditions. We compared the results with two standard systems – (a) a homogeneous porous medium and (b) a texturally layered configuration of finer particles at the top and coarser at the bottom. Compared to the homogeneous case, the duration of stage 1 (high evaporation rate regime) of evaporation and thus the characteristic evaporative length increased significantly in the case of root-mimics; this outcome shows the ability of the root-mimics in sustaining the surface water content induced by the strong capillary pressure gradient in such a dual porosity system. Finally, we track the evaporation sites using the fluorescein dye particles method and assess its effect (if any) on the overall evaporation characteristics.

Regeneration of capillary water in unsaturated zones

Abstract In porous media subject to drying conditions such as arid regions and excavation zones (deep gas injection or nuclear waste disposal), capillarity is involved in weathering processes because it modifies the geochemical and poromechanical balances within the porous network. Heterogeneous porous media like sedimentary rocks can host significant volumes of tensile capillary water in large pore bodies, and the negative pressure within is controlled by capillary forces exerted at nanometric pore throats. We have developed experiments using synthetic bimodal pore systems conducive to capillary tension. In microtubes, salts precipitated in an evaporating solution to build a dual-porosity system. A large volume (o200 µm) became trapped behind nanometric pores, where high capillary tension was applied. We investigated the gas-water interactions there, especially how gas nucleated in the trapped liquid and how it subsequently changed size. After gas nucleation, the decreasing of gas volume that we observed has been attributed to two complementary geochemical effects. On the one hand, the water’s tensile state increases gas solubility, as predicted by thermodynamics: capillarity is a “gas-in” process. On the other hand, while the total volume of the gas-water assemblage remains constant, the water’s molar volume increases by capillary forces. Consequently, capillary forces exerted at the nano-throats can (re)induce a superheated monophasic liquid state from a biphasic liquid-gas assemblage even after gas nucleation. Tensions required for gas shrinkage have been estimated at 7 ± 3 MPa and 53 ± 15 MPa. This regeneration process offers opportunities for water to regularly return to a capillary state, making the capillary lifetime less limited than expected. This shows that pore heterogeneity in rocks submitted to drying processes results in tension for water in pores that is long-lived. As a consequence, capillarity may significantly impact the long-term geochemical budget through its effects on gas and solid solubility and/or poromechanics (compaction, tensile stress, fracturing, etc.), so that it may play an important role in the weathering of drying porous materials.

Mathematical Theory of Processes of Concrete Corrosion

Forecasting the processes of degradation of structures that determine their safe operation (especially in aggressive environments) is a task of national importance, given the significant volumes of structures whose service life is exhausted. The main directions of improving the mathematical theory of concrete corrosion are formulated in the article. For corrosion of chemical type they include: the account of phase transformations, dual porosity system and the use of experimental data on distribution of aggressive components along the depth of a layer of concrete of the operated structures as initial data for forecasting of processes of degradation. The function of the binding rate of the aggressive component under this approach is theoretically justified. The development of general provisions of the principles of building of mathematical models, methods of predicting the processes of degradation of structures makes it possible to combine research in this area and present them as a mathematical theory of corrosion processes of concrete.

Capillarity-driven supersolubility in dual-porosity systems

Capillary phenomena are widespread in unsaturated media such as soils, building stone, deep depleted aquifers and still gas storage/sequestration reservoirs. Processes linked to capillarity depend on pore size and environmental conditions such as relative humidity. When capillary forces are high, water’s internal pressure can reach negative values representative of a tensile state. In those conditions, the capillary tensile water provokes compaction in moist granular materials. In geochemical terms, thermodynamics predict a significant effect on the solvent properties of tensile water. However, very little experimental work has validated thermodynamics models or shown the porosity arrangements that make capillarity a significant player to control the geochemical balance and poromechanics of porous media. In this study, we designed an experimental setup in glass microtubes (o 200 µm) conducive to capillary tension. In the tubes, salts (halite and sodium sulfate) precipitated from an evaporating solution to build a strongly contrasted dual-porosity system. Large pore bodies (o 200 µm) coexisted with nanometric pores that induced capillary tension in the whole volume. We observed mineral–liquid interactions (mass gain/loss, crystal shaping), especially how salt solubility changed as a function of capillary conditions. The water’s tensile state increased salt solubility, changing the reactions’ equilibrium constants at constant composition as predicted by thermodynamics. In addition, mineral grains showed clear evidence of poromechanical tensile stress, driving salts to move towards the interior of the tube or to crack. The results showed the potential significance of capillarity in heterogeneous porous media including nanopores. They should be considered in relation to how porous structures change, in the contexts of increasing droughts due to climate changes and increasing excavation work in deep sedimentary basins.

Analytical dual-porosity gas model for reserve evaluation of naturally fractured gas reservoirs using a density-based approach

The development of naturally fractured gas reservoirs often requires the deployment of rigorous techniques for production data analysis incorporating dual-porosity gas behavior. It has been a prominent problem to linearize and analytically solve the governing equations for dual-porosity gas systems. This study applies a pseudo-pressure-based interporosity flow equation to derive a density-based rate-transient analysis method to accurately predict the gas production rate and estimate the amount of original gas in place (Gi) for the systems. The methodology also predicts the gas production rate by transforming the response of its liquid counterpart via a decoupling of the pressure-dependent effects using dimensionless depletion-driven parameters.For the first time, the density-based flowing material balance method is derived for the dual-porosity gas reservoir. More than that, an innovative fracture productivity equation that was missing for the dual-porosity system is derived as well. This study provided detailed derivations for the model and relationship used in past density-based dual-porosity rate-transient analysis. The dual-porosity productivity equation and the relationship between average matrix pseudopressure and average fracture pseudopressure are rigorously derived. The rescaling relationship between the dual-porosity liquid solution and the dual-porosity gas solution is also demonstrated in detail. An appropriate interporosity flow equation for gas is used. Based on that, the results show that the density-based approach is able to successfully capture the dual-porosity behavior of gas for constant bottomhole pressure condition.

Reservoir micro structure of Da'anzhai Member of Jurassic and its petroleum significance in Central Sichuan Basin, SW China

Abstract Based on the qualitative study of microscopic reservoir features using core analysis, cast and fluorescence thin sections inspection, scanning electron microscope (SEM) and field emission scanning electron microscope (FESEM) and quantitative examination of pore size and geometry using mercury injection, nano-CT and nitrogen adsorption, reservoir rock of Da'anzhai Member were divided into 9 types, while storage spaces were divided into 4 types and 14 sub-types. The study shows that sparry coquina is the most promising reservoir type. Pores that smaller than 1 μm in diameter contribute 91.27% of storage space volume. Most of them exhibit slot-like geometry with good connectivity. By building up storage space models, it was revealed that micron scale storage spaces mainly composed of fractures and nanometer scale pores and fractures form multi-scale dual porosity system. Low resource abundance, small single well controlled reserve, and low production are related to the nano-scale pore space in Da'anzhai Memer, whereas the dual-porosity system composed of pores and fractures makes for long-term oil yield. Due to the existence of abundant slot-like pore space and fractures, economic tight oil production was achieved without stimulations.

Production Optimization in Waterfloods: A New Approach to Interwell-Connectivity Modeling

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 182450, “Production Optimization in Waterfloods With a New Approach to Interwell-Connectivity Modeling,” by Xiang Zhai, Tailai Wen, and Sebastien Matringe, Quantum Reservoir Impact, prepared for the 2016 SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, 25–27 October. The paper has not been peer reviewed. In the complete paper, the authors present a novel methodology to model interwell connectivity in mature waterfloods and achieve an improved reservoir-energy distribution and sweep pattern to maximize production performance by adjusting injection and production strategy on the well-control level. The method involves a reduced-physics-based fast numerical tracer test on each well, which yields interwell connection strength or well-allocation factors (WAFs), and then a data-driven efficiency model on each interwell connection calibrated automatically from the injection and production history of the reservoir. Introduction The approach combines and balances the advantages of both simulation and data-driven techniques. The approach models interwell connections based on a relatively mature waterflood history and performs fast forecast and waterflood optimization on the basis of the interwell-connection analysis. Injector/producer connections are identified by computing WAFs with a numerical tracer method. Then, a data-driven empirical efficiency model is adopted that de-fines the profile of the oil cut of each interwell connection, and reservoir-production history is used to calibrate the model. Therefore, each interwell connection is quantified with two critical parameters: WAF and connection efficiency. The reservoir model is simplified into a connection-based network model that can be used to predict oil and water production without use of rigorous time-dependent numerical simulation. A production-optimization algorithm is then implemented. The optimization objective is to minimize water production while maintaining oil-production rate, subject to a range of practical constraints. The production optimization is integrated into a numerical-simulation model, and a blind test is run for 6 months. A significant decrease in water production is observed. Methodology Waterflood Surveillance. WAF. In the process of waterflooding, water is injected into injectors to displace remaining oil. In this water/oil communication system, incompressibility is assumed in fluid dynamics and reservoir rock. This assumption is equivalent to assuming that pressure communication between any two points in the reservoir is essentially instantaneous. The WAF quantifies the strength of connection between two wells of different types. WAF is often computed by tracing streamlines and counting the number of streamlines between wells. However, the streamline-based method is incompatible with a dual-porosity system, and in general has poor performance in unstructured grids. The authors adopt a stationary numerical tracer method to compute WAF. The equations used in this process are presented in the complete paper.

A Novel Approach To Detect Interacting Behavior Between Hydraulic Fracture and Natural Fracture by Use of Semianalytical Pressure-Transient Model

Summary The detection of interacting behavior between the hydraulic fracture (HF) and the natural fracture (NF) is of significance to accurately and efficiently characterize an underground complex-fracture system induced by hydraulic-fracturing technology. This work develops a semianalytical pressure-transient model in the Laplace domain to detect interacting behavior between HF and NF depending on pressure-transient characteristics. Our results have shown that no matter what the flow state (compressible or incompressible flow) within a hydraulically induced fracture system, we can easily detect interacting behavior between HF and NF depending on whether the “dip” shape occurs at the formation radial-flow regime. Referring to sensitivity analysis, distance between NF and well, horizontal distance between NF and HF, and NF length are the three most sensitive factors to detect fracture-interacting behavior. Depending on interference analysis, although the pressure-transient characteristics of a pseudosteady-state dual-porosity model can interfere with our proposed methodology, the difference between our model and a pseudosteady-state dual-porosity system lies in whether the value of the horizontal line of dimensionless pressure derivative is equal to 0.5 at the formation radial-flow regime. Our work obtains some innovative insights into detecting fracture-interacting behavior, and the valuable results can provide significant guidance for refracturing operations and fracture detection in an underground fracture system.

A comparison of discrete versus continuous adjoint states to invert groundwater flow in heterogeneous dual porosity systems

Abstract Dual porosity models become increasingly used for simulating groundwater flow at the large scale in fractured porous media. In this context, model inversions with the aim of retrieving the system heterogeneity are frequently faced with huge parameterizations for which descent methods of inversion with the assistance of adjoint state calculations are well suited. We compare the performance of discrete and continuous forms of adjoint states associated with the flow equations in a dual porosity system. The discrete form inherits from previous works by some of the authors, as the continuous form is completely new and here fully differentiated for handling all types of model parameters. Adjoint states assist descent methods by calculating the gradient components of the objective function, these being a key to good convergence of inverse solutions. Our comparison on the basis of synthetic exercises show that both discrete and continuous adjoint states can provide very similar solutions close to reference. For highly heterogeneous systems, the calculation grid of the continuous form cannot be too coarse, otherwise the method may show lack of convergence. This notwithstanding, the continuous adjoint state is the most versatile form as its non-intrusive character allows for plugging an inversion toolbox quasi-independent from the code employed for solving the forward problem.

A fully coupled hydro-mechanical model for the modeling of coalbed methane recovery

Most coal seams hold important quantities of methane which is recognized as a valuable energy resource. Coal reservoir is considered not conventional because methane is held adsorbed on the coal surface. Coal is naturally fractured, it is a dual-porosity system made of matrix blocks and cleats (i.e fractures). In general, cleats are initially water saturated with the hydrostatic pressure maintaining the gas adsorbed in the coal matrix. Production of coalbed methane (CBM) first requires the mobilization of water in the cleats to reduce the reservoir pressure. Changes of coal properties during methane production are a critical issue in coalbed methane recovery. Indeed, any change of the cleat network will likely translate into modifications of the reservoir permeability.This work consists in the formulation of a consistent hydro-mechanical model for the CBM production modeling. Due to the particular structure of coal, the model is based on a dual-continuum approach to enrich the macroscale with microscale considerations. Shape factors are employed to take into account the geometry of the matrix blocks in the mass exchange between matrix and fractures. The hydro-mechanical model is fully coupled. For example, it captures the sorption-induced volumetric strain or the dependence of permeability on fracture aperture, which evolves with the stress state. The model is implemented in the finite element code Lagamine and is used for the modeling of one production well. A synthetic reservoir and then a real production case are considered. To date, attention has focused on a series of parametric analyses that can highlight the influence of the production scenario or key parameters related to the reservoir.

Unconventional multi-fractured analytical solution using dual porosity model

Five-region linear flow system proved to be a useful model to reproduce the flow behavior for multi-fractured horizontal wells in shale reservoirs. In earlier developments, the model was assumed single-porosity throughout all five regions. However, assumption of single porosity system for stimulated region may promote errors in pressure transient analysis. So by adopting the existing mathematical models for naturally fractured reservoirs (dual-porosity system), one can apply the dual-porosity nature of flow in the stimulated reservoir volume (SRV). In this study the analytical solution for single-porosity model is reproduced and compared with numerical solution. Then the five-region model of previous studies is modified by implementing the dual porosity behavior in Laplace domain and compared to single-porosity solution using the same reservoir properties. Furthermore, a series of type-curves is constructed in this study using dimensionless properties, such as matrix-fracture capacity ratio and storativity ratio, hydraulic fracture conductivity, and hydraulic fracture half-length. Theses curves could provide valuable information to characterize the multi-fractured complex systems.

Evolution of Heterogeneous Mixed Siliciclastic/Carbonate Aquifers Containing Metastable Sediments

Mixed carbonate and siliciclastic marine sediments commonly become freshwater aquifers in eastern coastal regions of the United States and many other global locations. As these deposits age, the carbonate fraction of the sediment is commonly removed by dissolution and the aquifer can become a solely siliciclastic system or contain zones or beds of pure quartz sand. During aquifer evolution, the sediment grain size characteristics, hydraulic conductivity, and porosity change. An investigation of these changes using mixed carbonate/siliciclastic sediment samples collected from a modern barrier island beach in southern Florida showed that the average mean grain diameter decreased with removal of the carbonate fraction, but the average hydraulic conductivity and porosity increased slightly, but not to statistical significance. This counterintuitive result occurs because of the change in the pore types from a combined shelter and intergranular pore system producing a dual porosity system in the mixed sediments to a single intergranular pore system in the siliciclastic sediment fraction. Within the mixed carbonate/siliciclastic sediment, in the pure carbonate fraction, large shell fractions form grain-supported large pores, which become filled with sand-sized quartz as the shell fragments decrease in size or as the sediment becomes compacted. The hydraulic conductivity increases because the shell fragments that were oriented perpendicular to flow caused an increase in the length of the flow path, or a larger scale tortuosity, compared with the flow through pure quartz sand.

A new estimation of equivalent matrix block sizes in fractured media with two-phase flow applications in dual porosity models

Single and multiphase flows in fractured porous media at the scale of natural reservoirs are often handled by resorting to homogenized models that avoid the heavy computations associated with a complete discretization of both fractures and matrix blocks. For example, the two overlapping continua (fractures and matrix) of a dual porosity system are coupled by way of fluid flux exchanges that deeply condition flow at the large scale. This characteristic is a key to realistic flow simulations, especially for multiphase flow as capillary forces and contrasts of fluid mobility compete in the extraction of a fluid from a capacitive matrix then conveyed through the fractures. The exchange rate between fractures and matrix is conditioned by the so-called mean matrix block size which can be viewed as the size of a single matrix block neighboring a single fracture within a mesh of a dual porosity model.We propose a new evaluation of this matrix block size based on the analysis of discrete fracture networks. The fundaments rely upon establishing at the scale of a fractured block the equivalence between the actual fracture network and a Warren and Root network only made of three regularly spaced fracture families parallel to the facets of the fractured block. The resulting matrix block sizes are then compared via geometrical considerations and two-phase flow simulations to the few other available methods. It is shown that the new method is stable in the sense it provides accurate sizes irrespective of the type of fracture network investigated. The method also results in two-phase flow simulations from dual porosity models very close to that from references calculated in finely discretized networks. Finally, calculations of matrix block sizes by this new technique reveal very rapid, which opens the way to cumbersome applications such as preconditioning a dual porosity approach applied to regional fractured reservoirs.

Practical simulation of multi-porosity reservoirs through existing reservoir simulator

Complex heterogeneous reservoir exhibits special characteristics, such as multiple storage types, wide range of storage sizes, complicated storage combinations, and various flow behaviors. Multi-continuum model is needed to rigorously simulate this type of reservoir. However most reservoir simulators use dual porous media model, and the theory of the models is mainly focused on matrix-fracture system. Therefore when porous media is more complex than matrix-fracture system, such software cannot be utilized to simulate these reservoirs directly. Some studies have been proposed to solve the problem, but most of them are either at the theoretical level or cannot been used widely in the simulation softwares. The goal of this paper is not to develop new numerical simulation software, but to obtain appropriate ways to improve performance of current simulation software for complex reservoir.Our approach is theoretically based on multi-continuum seepage theory. By comparing the microscopic seepage model and multi-continuum seepage model, we find that the conventional theory becomes improper because of the absence of an important restriction to the interporosity flow. In the conventional way, an N-multiple flow model always can be established based on N types of continuous media. In fact, one more restrictive condition needs to be added to make it valid: all the crossflow between any two types of continuum can be simplified into a source or sink terms in the seepage model. Consequently, the multiplicity of the seepage model is always less or equal to the number of the continuum types. In addition, because different type of dual-medium has different crossflow, it is required to construct their crossflow models respectively and derive corresponding calculation formula.Several steps developed in this paper are as follows on the basis of multi-continuum theory and the restrictions appended: First, reservoir storage is categorized into continuous and non-continuous media according to storage scale characteristics, distribution and intensity. In general, small cavities, small fractures, and pores in the rock are continuous while large-scale fractures, big cavities or caves are non-continuous. The whole reservoir is therefore classified into continuum region and dis-continuum region. Second, in the continuum region, multi-media model and its multiplicity are determined by using the new theory proposed in this paper. Third, calculation formulae are constructed for each type of crossflow. This research takes fractured vuggy reservoirs as an example. A new calculation for the flux transfer is derived for such fracture-vug dual-porosity system. Forth, in the discrete region, flow in a filled non-continuous medium is described by Darcy's law and free flow in large unfilled cavities or caves follows Navier-Stokes equation and an approximate approach to using Darcy flow simulation is provided. Lastly, this paper introduces the methods how to simplify multi-media into two media and how to simulate the complex reservoir by using the existing simulators.The proposed method is applied to a naturally fractured carbonate reservoir with cavities in the Tarim Basin in China. The simulation results illustrate the production mechanisms of reservoir development using water flooding, including water injection and shut-in, stairs-shaped line of water cut with time, high production with low water cut for long time.

Integration of Pressure-Transient Data in Modeling Tengiz Field, Kazakhstan—A New Way To Characterize Fractured Reservoirs

Summary A systematic work-flow to integrate pressure-transient data collected from single-well buildup tests in numerical reservoir-simulation models for a fracture/matrix system is presented. The results of its application in a sector model in the southeast region of Tengiz field in Kazakhstan are also discussed. The procedure starts with a selected numerical-simulation model, either a discrete fracture/matrix (DFM) model or a dual-porosity dual-permeability (DPDK) model, and follows with the analysis of a numerically generated buildup test to calculate the fracture spacing and shape factor of the model. Then, following the correlations between pressure-transient-analysis results and the average or representative values of the model-input parameters near the well, which contain the previously obtained fracture spacing and shape factor, the numerical-model parameters are adjusted in each iteration to match the pressure-transient behavior observed in the buildup test including the interporosity flow between matrix and fracture and the radial flow in the total system. Before field application, the numerical-simulation results from both DFM and DPDK models were validated against analytical pressure-transient solutions for a dual-porosity system. The gridding and time-steps were calibrated to reproduce the analytical transient behavior. Finally, the new work-flow was applied to a sector model of Tengiz field in the southeast region focusing on two wells. Following the developed work-flow, a DFM model was constructed, and its fracture and matrix properties were adjusted to honor buildup-test data at both wells and the transient data collected during a pulse test conducted between them. The study results show that the key factors of a DFM model on buildup transient response are the fracture permeability, fracture aperture, and matrix permeability in the well-drainage area, and the dominant parameters on pulse-test response are the fracture permeability and matrix porosity in the influence area between the two wells. Using the correlations quantitatively for each simulation step could reduce the total number of iterations needed to converge to the numerical solution. The modified model also generated flow distribution along the wellbore, consistent with production-logging data at one well. The resulting sector map of pressure change during buildup test indicates the area with well-connected fracture network. Dynamic transient data contain rich information about reservoirs, and the effective integration of dynamic and static data would have a big impact on reservoir management by potentially minimizing the number of wells to be drilled, maximizing the production, and optimizing recovery. The novelty of this study is the quantitative use of the correlations between pressure-transient-analysis results and the representative values of the input parameters in a numerical model to reduce the number of simulation iterations. Its application in Tengiz is also one of the rare examples in which single-well and multiple-well transient data, production logging, and image-log data are all available.

Integration of static and dynamic reservoir data to optimize the generation of subsurface fracture map

This paper presents a new three-dimensional fully coupled poroelastic numerical model to simulate pressure transient response of naturally fractured reservoirs. One of the main applications of the new approach is to improve the reservoir characterization by decreasing the uncertainties associated with subsurface fracture map and to understand the interaction between fracture and matrix. The model is based on a hybrid methodology to simulate fluid flow by combining a single continuum and discrete fracture network approaches. To decrease the uncertainty associated with subsurface fracture map, a different realizations of the discrete fracture systems are generated based on image logs, seismic, geological features and the tectonic history of the studied reservoir. An iterative loops have been used between the reservoir static model and dynamic well-test data to optimize the generation of subsurface fracture maps. At each loop, a new discrete fracture system is used and the simulated pressure transient data are compared with the available field data. The process is repeated till the matching between the simulated and the measured pressure transient data is achieved using the most appropriate fracture realization. The numerical model is validated against an analytical pressure transient solution for dual-porosity system, and then applied to a real case taken from fractured basement reservoir in offshore Southern Vietnam. The developed hybrid methodology used to simulate fluid flow and rock deformation to improve the characterization of the fractured basement by simulating the pressure transient testing. The results predicted by the presented model are in a good agreement with field data; also the model was able to predict the fractures network distribution and fractures inherent properties around the tested well.

Pore volume compressibilities of sandstones and carbonates from Helium porosimetry measurements

For decades, several efforts have been put in place to understand the interaction between rock and fluids, and on the physical laws that describe the fluid behavior in a porous media. Petrophysical modeling is used in drilling, completion, compaction evaluation of the reservoir rocks and wellbore production to avoid unexpected interventions and optimize the hydrocarbon production throughout the life of the well. Pore volume compressibility is one of the main parameters to characterize the behavior of the reservoir rock as it quantifies the incremental pore volume variations due to external or internal pressures. This parameter is needed for reserve estimation, production forecasting, wellbore stability evaluation and seismic monitoring issues. In this work, uniaxial compression tests were carried out using helium gas porosimetry, which measured the variation of the pore volume for each applied load. The pore volume compressibility calculation was possible through a power-law fitting between pore volumes and confining pressure. That procedure was applied to six sandstone, six limestone and one dolomite samples at nine different confining pressures ranging from 400–2000 psi. Porosity was calculated for each pressure stage and the interdependency of the pore compressibility and porosity was evaluated, assuming that grain volume remains unaltered and using the pore volume measurements. Optical microscopy and Mercury Intrusion Porosimetry (MIP) aided to understand the pore space of some of the rocks and to quantify microporosity fraction, which impacts on a dual porosity system. This work also shows that the amount of microporosity influences how the pore volume changes as the external pressure increases. For rocks with small microporosity, the power-law behavior is likely to describe the relationship between the pore volume and the confining pressure practically perfect (R2~1), but as microporosity increases, the accuracy of this relationship decreases.

Dual-porosity poroviscoelasticity and quantitative hydromechanical characterization of the brain tissue with experimental hydrocephalus data

Hydromechanical brain models often involve constitutive relations which must account for soft tissue deformation and creep, together with the interstitial fluid movement and exchange through capillaries. The interaction of rather unknown mechanisms which produce, absorb, and circulate the cerebrospinal fluid within the central nervous system can further add to their complexity. Once proper models for these phenomena or processes are selected, estimation of the associated parameters could be even more challenging.This paper presents the results of a consistent, coupled poroviscoelastic modeling and characterization of the brain tissue as a dual-porosity system. The model draws from Biot׳s theory of poroviscoelasticity, and adopts the generalized Kelvin׳s rheological description of the viscoelastic tissue behavior. While the interstitial space serves as the primary porosity through which the bulk flow of the interstitial fluid occurs, a secondary porosity network comprising the capillaries and venous system allows for its partial absorption into the blood. The correspondence principle is used in deriving a time-dependent analytical solution to the proposed model. It allows for identical poroelastic formulation of the original poroviscoelastic problem in the Laplace transform space.Hydrocephalus generally refers to a class of medical conditions which share the ventricles enlargement as a common feature. A set of published data from induced hydrocephalus and follow-up perfusion of cats׳ brains is used for quantitative characterization of the proposed model. A selected portion of these data including the ventricular volume and rate of fluid absorption from the perfused brain, together with the forward model solution, is utilized via an inverse problem technique to find proper estimations of the model parameters. Results show significant improvement in model predictions of the experimental data.The convoluted and coupled solution results are presented through the time-dependent plots of the ventricular volume undergoing the perfusion experiment. The plots demonstrate the intricate interplay of viscous and poroelastic diffusive time scales, and their competition in reaching the steady state response of the system.

Effect of Matrix-Wellbore Flow and Porosity on Pressure Transient Response in Shale Formation Modeling by Dual Porosity and Dual Permeability System

A mathematical dual porosity and dual permeability numerical model based on perpendicular bisection (PEBI) grid is developed to describe gas flow behaviors in shale-gas reservoirs by incorporating slippage corrected permeability and adsorbed gas effect. Parametric studies are conducted for a horizontal well with multiple infinite conductivity hydraulic fractures in shale-gas reservoir to investigate effect of matrix-wellbore flow, natural fracture porosity, and matrix porosity. We find that the ratio of fracture permeability to matrix permeability approximately decides the bottom hole pressure (BHP) error caused by omitting the flow between matrix and wellbore and that the effect of matrix porosity on BHP is related to adsorption gas content. When adsorbed gas accounts for large proportion of the total gas storage in shale formation, matrix porosity only has a very small effect on BHP. Otherwise, it has obvious influence. This paper can help us understand the complex pressure transient response due to existence of the adsorbed gas and help petroleum engineers to interpret the field data better.

Deformation transition of intact coal induced by gas injection

Gas migration in coal bed is a multiple-physical process, of which not only includes gas desorption/diffusion through coal matrix and gas Darcy flow through the cleat system, but also results in deformation of solid coal. Especially for enhanced coal bed methane (ECBM) and CO2 capture and sequestration (CCS), gas injection is mainly controlled by the gas diffusivity in the coal matrix and coal permeability. Although the relevant coal permeability models have been frequently developed, how the dual-porosity system of coal affects gas adsorption/diffusion is still poorly understood. In this paper, a series of experiments were carried out in order to investigate deformation evolution of intact coal subjected to hydrostatic pressure of different gases (including pure H2, N2 and CO2) under isotherm injection. In the testing process, the coal strain and injected gas pressure were measured simultaneously. The results show that the pressure of non-adsorptive helium remained unchanged throughout the isothermal injection process, in which the volumetric strain of the coal shrinked firstly and maintained unchanged at lower isobaric pressure. With the injected pressure increasing, the coal volume underwent a transition from shrinking to recovery (still less than initial volume of the coal). In contrast, N2 injection caused the coal to shrink firstly and then recover with decreasing gas pressure. The recovery volume was larger than the initial volume due to adsorption-induced swelling. For the case of CO2 injection, although the stronger adsorption effect could result in swelling of the solid coal, the presence of higher gas pressure appears to contribute the swelling coal to shrink. These results indicate that the evolution of coal deformation is time dependent throughout the migration of injected gas. From the mechanical characteristics of poroelastical materials, distribution of pore pressure within the coal is to vary with the gas injection, during which the pore pressure in the cleats will rapidly increase, in contrast, the pore pressure in the matrix will hysteretically elevate. Such a difference on changes of pore pressure between the cleats and the matrix will contribute to the shrinkage of the matrix as a result of initially greater effective stress. Besides, both gas-adsorption-induced swelling and decreasing effective stress also control the coal deformation transition. This work gives us an insight into investigation on influence of effective stress on coal-gas interaction.