Triple Porosity Research Articles

A hydraulic-mechanical coupled triple porosity fractal model considering action mechanisms and gas transport mechanisms in carbon-hydrogen reservoirs

The shale formation, a common carbon-hydrogen reservoir, has numerous nanoscale pores that facilitate multiple gas transport mechanisms, including viscous flow, slip flow, Knudsen diffusion, and surface diffusion. Additionally, various action mechanisms involving effective stress, real gas effect, gas adsorption and desorption, and fracture-pore characteristics significantly influence gas transport. In this study, we conceptualize shale as a triple porosity medium comprising organic matrix, inorganic matrix, and microfractures. For each system, its hydraulic-mechanical coupled model with action mechanisms and gas transport mechanisms is derived based on fractal theory. After validating the model with Barnett and Marcellus data, the evolution of apparent permeability and gas pressure is studied, as well as the influences of pore fractal features, the real gas effect, and the number of hydraulic fractures on gas extraction. Simulation results indicate that, in comparison to organic matrix, inorganic pore fractal features exert a more noticeable effect on cumulative production. The real gas effect is critical in gas transport and reservoir reserve estimation; disregarding this effect results in a 17.4% underestimation of cumulative gas production by the 1600th day. Fracture interference attenuates the improvement in cumulative production gains from increased hydraulic fracture numbers.

Potential method in the coupled theory of thermoelastic triple-porosity nanomaterials

In this paper, the coupled linear theory of thermoelasticity for nanomaterials with triple porosity is considered in which the combination of Darcy’s law and the volume fraction concept for three levels of pores (macro-, meso- and micropores) is provided. The 3D basic boundary value problems (BVPs) of steady vibrations of this theory are formulated and these BVPs are investigated using the potential method (boundary integral equation method) and the theory of singular integral equations. Namely, the formula of integral representation of regular vectors is obtained. The surface (single-layer and double-layer) and volume potentials are introduced and their basic properties are given. Some useful singular integral operators are defined for which Noether’s theorems are valid. The symbolic determinants and indexes of these operators are calculated. The BVPs of steady vibrations are reduced to the equivalent singular integral equations. Finally, with the help of the potential method, we prove the existence theorems for classical solutions of the aforementioned BVPs.

Enhancing Reservoir Zonation through Triple Porosity System: A Case Study

Summary The Asmari-Jahrom reservoirs, located in southwest Iran, are recognized as one of the major fractured reservoirs in the world. Understanding the role of fractures in enhancing hydrocarbon flow and permeability is of utmost importance. In this study, petrophysical conventional logs [neutron porosity (NPHI), density (RHOB), sonic (DT), and gamma ray (GR)] and advanced image logs [formation microresistivity imaging (FMI)] were used to investigate the reservoir properties. The novelty of this study lies in the implementation of triple porosity on reservoir quality and identification of flow units in Asmari-Jahrom reservoirs using petrophysical and borehole image logs. By quantifying fracture and vuggy porosity and correlating them with velocity deviation log and fracture parameters [fracture aperture (VAH) and fracture density (VDC)], it was demonstrated that fracture porosity is directly related to VAH. High peaks were observed in fracture parameters, particularly in VAH diagrams where the velocity deviation log was negative and low. Total porosity from density logs was found to match secondary porosity from petrophysical logs, validating FMI results. However, FMI log resolution was higher, enabling clearer identification of fracture porosity peaks. The velocity deviation log indicated that the predominant type of porosity in the reservoir was matrix (primary) porosity. However, fracture and vuggy porosity were also observed in certain zones. Based on indirect evidence such as drilling mud loss, porosity type (matrix, fracture, and vuggy), porosity amount, and oil saturation, 18 zones were identified to determine quality zones with appropriate reservoir quality. Asmari-Jahrum reservoirs were found to possess high storage and flow capacity. The presence of multiple fracture types, especially longitudinal fractures, contributed to the development of secondary porosity and enhanced flow unit quality. Despite their complexity, these fractured carbonate reservoirs were analyzed comprehensively through integrated petrophysical and FMI log interpretation, enabling optimized reservoir performance and facilitating hydrocarbon production.

Granular activated carbon sound absorption predictions made using measured material parameters

Granular activated carbon (GAC) is hierarchical porosity material that yields better in low frequency sound absorption performance compared with many traditional porous materials due to the sorption effect created by nanometer-scale pores within the particles. In 2017, a triple porosity model accounting for the sorption effect in the micropores was proposed by Venegas et al. In the proposed model, some of input parameters (i.e., mesopore size and micropore effective diffusion coefficient) were fitted by matching the model to measured the surface impedance of a GAC stack; however, some fitted values are questionable from an inorganic material perspective. In the present work, the GAC material parameters, such as micro- and meso-pore sizes, were estimated from a standard isotherm measurement. The measurement results showed a standard Langmuir type isotherm behavior at different temperatures: i.e., 273.15 and 293.15 K. Thus, if the isotherms can be described with the Langmuir model, then the Langmuir constant and heat of adsorption can be estimated based on the isotherms. Finally, these parameters were used as the input to the GAC model and the absorption coefficient was calculated. The calculated result was also compared with the absorption coefficient measured following the E1050 standard.

A mixed finite element/finite volume formulation for granular bentonite mixtures

A mixed finite element/finite volume formulation is presented for characterising the macroscopic behaviour of granular bentonite mixtures. The formulation enables fitting the hydro-mechanical behaviour of a mixture parting from a double porosity numerical model. The granular bentonite mixture is abstracted as a finite set of homogeneous units made with bentonite grains (where microstructure and macrostructure coexist) embedded in megapores. The separate mass balances of macrostructural and microstructural water are solved for each unit using the finite volume method. The water mass balance in the megaporosity is calculated for the entire domain using the finite element method. To solve the equilibrium equation, a displacement-based finite element method is applied after defining a global stiffness matrix that integrates the effect of megaporosity. After implementing these approaches in a double porosity numerical model, satisfactory modelling results were obtained in agreement with the experimental tests. The results of the proposed model effectively fit those of a triple porosity bentonite unit model that uses a contact model for displacement compatibility of the units. This contributes to the qualification of the presented model’s ability to produce compatible strains of the units using the proposed global stiffness.

Fracture and vug effects on wormhole pattern during acidizing of triple porosity carbonate rocks

Carbonate reservoir acidization is performed to mitigate formation damage and create desirable and highly permeable pathways for the movement of oil and gas. The most significant characteristic of carbonate reservoirs is the presence of fractures and vugs within their structure, which contribute to their triple porosity. The presence of fractures and vugs complicates the flow equations in the medium, which can significantly impact the success or failure of the acidizing. Therefore, understanding their role in the behavior of fractured carbonate reservoirs is a challenging and important issue. Comprehensive studies investigating the simultaneous effect of fractures and vugs on the acidizing in these types of reservoirs have not been reported. Therefore, this study provides a detailed and more precise examination of the acidization process within a triple porosity carbonate media. To simulate the acidizing, a two-scale continuum model was coupled with the pseudo-fracture method in a triple porosity carbonate media. The flow within the matrix and the vug were modeled using Darcy's law, while the flow within the fracture was modeled using the cubic law (free flow). This modeling approach accurately simulated the overall flow of the acidizing fluid. Generally, increasing the length and decreasing the width of a single horizontal fracture improves the acidizing, whereas a vertical one causes a delay at average injection rate. The presence of cross-fractures enhances acidization at all injection rates, and when a horizontal fracture is present at the system's outlet, it also significantly reduces the PVbt. Conversely, the presence of multiple vertical ones within the reservoir delays the acid reaction time, Increasing the number and size of vug improves the acidizing. When fractures and vugs coexist within the rock, it is the type and location of these fractures that control the wormhole propagation pattern and the extent of variations in porosity inside the vug.

Fundamental solution in the coupled theory of thermoelastic nanoporous materials with triple porosity

AbstractIn this paper, the linear coupled theory of thermoelasticity for nanoporous materials with a triple porosity structure based on Darcy's law and the volume fraction concept is considered. The fundamental solution of the system of steady vibration equations is constructed by means of elementary functions. Finally, some basic properties of this solution are established.

Effects of fluid flow in triple porosity medium on fracture width and its propagation during lost circulation control

During oil and gas well construction, lost circulation is one of the major challenges, and to migrate the problem, lost circulation materials (LCMs) should be used to resist fracture reopening with the hypothesis of fracture tip isolation. A triple porosity medium Darcy flowing model was developed to capture pressure distribution along the fracture surface, coupled with a dislocation-based fracture mechanics model to calculate fracture width and assess its propagation. In the model, mud cake on wellbore and fracture surface was considered as the third type of pore medium. The rest dual pore medium models incorporate the fluid flow through LCMs within fracture and the fluid leakoff from fracture into matrix. Sensitivity analyses of the key parameters, such as triple pore medium permeability, viscosity, wellbore pressure, plugging location are implemented, and the results emphasize that fracturing resistance effect of LCMs was controlled not only by the fluid flow within fractures, but also by the flow through mud cake on wellbore into matrix. To inhibit fracture reopening, in high permeability formations, both reduction of mud cake permeability and LCMs permeability were required while in lower permeability formations, fluid flow within fractures dominates and should be minimized. Besides, tip isolation can be achieved by extending sealing fracture length. However, high wellbore pressure or long operation time will result in elevated distances and unallowable fluid loss. Then, wellbore pressure must be reduced to cure the lost circulation. More viscosity of the fluid and total integrity plugging of LCMs are another major factor extending the time for pressure transfer to fracture tip, resisting unexpected fracture propagation. The method proposed in this study clarifies that tip isolation can be realized by fracture plugging and reduction of fluid filtration from the wellbore to matrix. Moreover, operational insights on LCMs design can also be derived.

On the coupled linear theory of thermoelasticity for nanomaterials which triple porosity

In this paper, the linear mathematical model of thermoelastic nanomaterials with triple porosity is proposed in which the coupled phenomenon of Darcy’s law and the concept of the volume fractions of three levels of pores (macro-, meso- and micropores) is considered. Then, the 3D internal and external basic boundary value problems (BVPs) of steady vibrations of this model are formulated. The radiation conditions are established and Green’s identities are obtained in the considered theory. Finally, the uniqueness theorems for classical solutions of the above mentioned BVPs are proved.

External problems of steady vibrations in the theory of elastic materials with a triple porosity structure

AbstractIn this paper, the linear theory of elasticity for materials with a triple porosity (macro, meso and micro levels of porosities) structure based on the volume fraction concept is considered. The external boundary value problems (BVPs) of steady vibrations of this theory are investigated. Namely, the uniqueness theorem for classical solutions of these BVPs is established. Then, the basic properties of the surface (single‐layer and double‐layer) potentials are given. Finally, on the basis of the properties of potentials, the existence theorems for classical solutions of the above mentioned BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

Multimodal Evolution of Coal Permeability due to Interior Deformations within a Triple Porosity System

Summary Measurements of coal permeability are normally analyzed without considering the interaction among microfracture and pore size distributions within the sample (control volume). Without this inclusion, nearly all permeability predictions are monomodal as reported in the literature. However, experimental observations are multimodal for most cases. In this study, we hypothesize that these discrepancies or mismatches between measurements and analytical predictions are due to the exclusion of the interaction among microfracture and pore size distributions within the sample (control volume). We report a first experimental study of triple-porosity interactions on a prismatic sample containing millimeter-scale fractures (Ⅰ) and micron- (Ⅱ) through nanometer-scale (Ⅲ) pores. Migration speeds of sorbing (e.g., CH4) gases are conditioned by the strain field, which is in turn conditioned by effective stresses and swelling strains. These distinct pore populations exhibit characteristic times for a time-staged equilibration of the strain field as multiple plateaus. This time-staged evolution of strain in turn delimits the evolving fracture permeability into a series of stages. The relatively high permeability of fractures and micropores defines a brief intermediate equilibrium permeability, after which the nanopore system controls the final permeability evolution. Our results indicate that the multimodal evolution of coal fracture permeability can be explained by the time-staged evolution of strain due to multiporosity interactions and could be defined by a time-staged equilibration of the strain fields as multiple plateaus.

Simple modelling of fast hydration processes in bentonite pellet fills

A novel hydro-mechanical formulation is presented to simulate the fast wetting of bentonite pellet fills. The model is based on a triple porosity concept, but its formulation uses a double porosity structure for simplicity. It is assumed that the fast wetting process results in a liquid pressure in the inter-pellet voids equal to the boundary liquid pressure. This enables the system of equations to be solved to have the same structure than that used to analyse the behaviour of the bentonite blocks with numerical tools based on double porosity approaches. Thus, it is relatively simple to extend such tools to incorporate the triple porosity conceptual model that is presented in this paper. To assess the scope of the proposed formulation, a set of tests in which the inter-pellet void space is rapidly flooded and a test in which the inter-pellet void space is circulated with progressively more humid air are simulated. The results obtained for pellets fills of both FEBEX and MX-80 bentonites are very satisfactory, despite the simplicity of the formulation presented.

FILTRATION EQUATIONS FOR PORE AND CAPILLARY SYSTEM TAKING INTO ACCOUNT PRESSURE DIFFUSION

Biological media are characterized by a complex system of pores and capillaries, the interaction between which leads to features in the transport of biological fluids. At low flow velocities, the mutual influence of convection and diffusion becomes important, as well as the influence of pressure gradient on diffusion. To take into account the complex structure of porous space, models of fractured porous media, models of media with double and triple porosity, are known in the literature. In this paper, we propose a model of a medium with double porosity in which, in addition to diffusion and filtration, barodiffusion is taken into account. Definitive relations follow from thermodynamics of irreversible processes. We consider particular versions of the equations: for a medium with predominant convection in both pore systems; for media with predominantly diffusion transport mechanism, typical for nanoporous materials; and for a medium in which convection prevails in one pore system and diffusion in the second.

Role of pressure and pore microstructure on seismic attenuation and dispersion of fluid-saturated rocks: laboratory experiments and theoretical modelling

SUMMARY Understanding the effects of pressure and rock microstructure on seismic elastic properties of fully saturated rocks is of considerable importance in a range of geophysical applications, especially at seismic frequency range. A recently proposed theoretical model of squirt attenuation and dispersion can be used to interpret the stress and frequency dependence of elastic properties on the basis of a triple porosity structure. The poroelastic model requires the knowledge of a variety of pore microstructure parameters, in particular, the compliant pores with a discrete distribution of aspect ratio. We performed laboratory measurements of (compressional and shear wave) velocity dispersion and attenuation, associated with the pressure-related closure of compliant pores on three dry and wet sandstones, to verify the effects of squirt flow arising from compressibility heterogeneities in the rock microstructure on the pressure dependence of dynamic elastic moduli and attenuation. Ultrasonic velocities experimentally measured on dry rocks were applied to extract pressure-dependent pore aspect distribution of compliant pores and the effective porosity of three types of pores with distinct aspect ratios, via fitting of the poroelastic model to the pressure dependence of elastic compressibilities. Under the assumption of frequency-independent dry elastic properties, inferred velocities and the associated attenuation of the saturated rocks from the forced oscillation experiments, which are still scarcely investigated, are in fairly good agreement with the predictions of the squirt model of three porosity types at seismic frequencies. The Gassmann's relation was found, nevertheless, underpredicts the ultrasonic saturated velocity measurements. The results validate applicability of the recently developed squirt model to account for dispersion and attenuation of phase velocities at varying effective pressures.

Advanced Concepts in Naturally Fractured Reservoirs with Analysis of Field Data

Dual porosity reservoir is mainly defined as fractured reservoir. The Two porosities are included for fracture and matrix, Flow in the fractures, oil storage in the matrix. Dual Permeability reservoir are those pay zones with flow in both the fracture and matrix systems. Single porosity means matrix, dual porosity means both matrix and fractures and triple porosity means matrix, fractures and vugs. The description of displacement mechanisms in fractured reservoirs can be construed as: oil expansion, gravity forces, capillary forces, balance of gravity and capillary forces, diffusion and convection. Fractures are usually found in limestone and dolomites due to solution, re-crystallization. Two categories of fractures are available such as: Open Fractures and Closed Fractures which depend mainly on circulation water and precipitation. Fractures which are closed at surface conditions may be open in reservoir conditions. Fractures related to folding axis are such as: longitudinal fractures, along the folding axis and transverse fractures, perpendicular to the folding axis and diagonal fractures, in relation with the folding axis. There are some pivotal issues and expressions in fractured reservoirs that in this paper, an approach to the advanced concepts in Naturally Fractured Reservoirs has been studied.

A new macro-scale volume averaged transport model for diffusive dominated non-Darcian flow problem in multi-scaled naturally fractured reservoirs

Diffusive transport in porous media is a complex process in multi-scaled fractured media modeling. This paper presents a diffusive transport model for non-Dacian flow in a naturally fractured reservoir with triple porosity and permeability. To address the non-Darcian flow behavior associated with fluid transport in fractured porous media, the Darcy/Forcheimer equation was used. A point-diffusive equation was obtained from mass conservation and the Darcy–Forcheimer momentum equation; this is used together with interface conditions to incorporate the microscopic properties of the domain. Subsequently, the resulting equation was spatially smoothed to obtain an effective macroscopic average model. The macroscopic model obtained, unlike the existing models, has a cross-diffusive term for mass transport by induced fluxes and a mass transfer term accounting for mass transfer between the matrix and the surrounding fractures via the interface. The numerical simulation displayed a horizontal-linear flow behavior in the fractured network instead of a radial flow in the matrix. The results further suggest that despite the fractures aiding in fluid transport, they enhance fluid production in the reservoir compared to the matrix.

Improved triple porosity model for calculating porosity exponent of fractured-vuggy reservoirs based on Maxwell-Garnett mixing rule and anisotropic conductivity analysis

Porosity exponent (m) is a key parameter for calculating reservoir oil and gas saturation and evaluating reservoir effectiveness; the development of matrix pores, vug pores, and fractures makes the m response regularity of fractured-vuggy reservoirs unclear, which makes the accurate calculation of saturation difficult. By applying Maxwell-Garnett mixing rule to vuggy reservoirs and conductivity tensor analysis to fractured reservoirs, an improved Triple Porosity Model considering fracture dip angle is established. The newly improved Triple Porosity Model clarifies the response regularity of m to the matrix pores, vug pores, fracture pores, and fracture angles. Based on the improved Triple Porosity Model, the response regularity chart of m is further established. The findings show that: (1) m increases with the increase of fracture dip angle (θ) and the development of vugs; (2) m increases with the development of high-angle fractures and decreases with the development of low-angle fractures; (3) in fractured reservoirs, the fracture dip angle of 33° is the critical dip angle that determines the relationship between m and matrix porosity exponent (mb); (4) an increase in matrix porosity will weaken the influence of vugs, fractures, and fracture dip angle on m, which will eventually make m converge to mb. The field application of fractured-vuggy reservoirs shows that the water saturation calculated by the improved Triple Porosity Model is better in agreement with the core analysis results.

Identification of watered-out zones in carbonate reservoirs using resistivity curve reconstruction based on reservoir classification

The KT–II layer in the Zananor Oilfield, Caspian Basin, Kazakhstan, contains carbonate reservoirs of various types. The complex pore structure of the reservoirs have made it difficult to identify watered-out zones with traditional logging interpretation methods. This study classifies the reservoirs on the basis of core analysis and establishes an identification model for watered-out layers in the field to effectively improve the interpretation accuracy. Thin section analysis shows that there are three types of pores in the reservoirs, i.e., the matrix pore, fracture and dissolution vug. A triple porosity model is used to calculate the porosities of the reservoirs and the results are combined with core analysis to classify the reservoirs into the fractured, matrix pore, fracture-pore as well as composite types. A classification standard is also proposed. There are differences in resistivity logging responses from the reservoirs of different types before and after watering-out. The pre–watering-out resistivities are reconstructed using generalized neural network for different types of reservoirs. The watered-out layers can be effectively identified according to the difference in resistivity curves before and after watering-out. The results show that the watered-out layers identified with the method are consistent with measured data, thus serving as a reference for the evaluation of watered-out layers in the study area.

Semi-Supervised Learning–Based Petrophysical Facies Division and “Sweet Spot” Identification of Low-Permeability Sandstone Reservoir

The identification of the “sweet spot” of low-permeability sandstone reservoirs is a basic research topic in the exploration and development of oil and gas fields. Lithology identification, reservoir classification based on the pore structure and physical properties, and petrophysical facies classification are common methods for low-permeability reservoir classification, but their classification effect needs to be improved. The low-permeability reservoir is characterized by low rock physical properties, small porosity and permeability distribution range, and strong heterogeneity between layers. The seepage capacity and productivity of the reservoir vary considerably. Moreover, the logging response characteristics and resistivity value are similar for low-permeability reservoirs. In addition to physical properties and oil bearing, they are also affected by factors such as complex lithology, pore structure, and other factors, making it difficult for division of reservoir petrophysical facies and “sweet spot” identification. In this study, the logging values between low-porosity and -permeability reservoirs in the Paleozoic Es3 reservoir in the M field of the Bohai Sea, and between natural gamma rays and triple porosity reservoirs are similar. Resistivity is strongly influenced by physical properties, oil content, pore structure, and clay content, and the productivity difference is obvious. In order to improve the identification accuracy of “sweet spot,” a semi-supervised learning model for petrophysical facies division is proposed. The influence of lithology and physical properties on resistivity was removed by using an artificial neural network to predict resistivity R0 saturated with pure water. Based on the logging data, the automatic clustering MRGC algorithm was used to optimize the sensitive parameters and divide the logging facies to establish the unsupervised clustering model. Then using the divided results of mercury injection data, core cast thin layers, and logging faces, the characteristics of diagenetic types, pore structure, and logging response were integrated to identify rock petrophysical facies and establish a supervised identification model. A semi-supervised learning model based on the combination of “unsupervised supervised” was extended to the whole region training prediction for “sweet spot” identification, and the prediction results of the model were in good agreement with the actual results.

Waves in the theory of elasticity for triple porosity materials

Waves in the theory of elasticity for triple porosity materials