Dual-permeability Media Research Articles

Effect of Wettability and Permeability on Pore-Scale of CH4–Water Two-Phase Displacement Behavior in the Phase Field Model

Hydraulic measures such as hydraulic slotting and hydraulic fracturing are commonly used in coal seam pressure relief and permeability enhancement. Two-phase flow patterns of CH4–water in pore-sized coal seams after hydraulic measures are critical to improve gas extraction efficiency. The phase field module in COMSOL Multiphysics™ 5.4 and the classical ordered porous media model were used in this paper. The characteristics of CH4–water two-phase immiscible displacement in coal seams under different capillary numbers (Ca) and viscosity ratios (M) were simulated and quantitatively analyzed. By changing the contact angle of the porous media, the flow patterns of CH4–water two-phase in coal with different wettability were simulated. Results show that wettability significantly affects the displacement efficiency of CH4. Additionally, by constructing a dual-permeability model to simulate the varying local permeability of the coal, the flow patterns of different Ca and M in dual-permeability media were further investigated. It is found that CH4 preferentially invades high-permeability regions, and the displacement efficiency in low-permeability regions increases with higher Ca and M, providing a reference for gas extraction from coal seams after hydraulic measures.

Lattice Boltzmann method for solute transport in dual-permeability media

Dual-permeability models are currently under active investigation for predicting the flow and transport of pollutant concentration in porous media. The basic idea of these models is usually to separate the medium into two distinct flow regions with separate hydraulic and solute movement properties. Most of the dual-permeability approaches presented to date assume the reaction terms to be independent of space. For local reaction processes in soils, however, the depth effects are important and should be incorporated into the dual-permeability models. To reveal the transport phenomenon in such case, the best way is to obtain an exact solution with a suitable analytical approach, but it may be hard or even impossible for this general scenario. As such, this paper seeks an alternative method, and propose a lattice Boltzmann method for solute transport in dual-permeability media. The Chapman–Enskog analysis shows that the present model can recover the governing equations correctly. The capability and accuracy of this model is first verified by two problems: the non-reactive mass transfer in dual-permeability porous media, and the solute transport in a depth-dependent soil. With this model, we further studied the contaminant transport in dual-permeability soil with depth-dependent reaction rates. The numerical results show that when the exchange coefficient is relatively smaller, there are usually two peaks for the breakthrough curves (BTCs), whereas it degenerates to a single peak as the exchange coefficient increases. In addition, we note that the distributions of the concentration in different domains are nearly the same for a larger exchange coefficient. As for the pore water velocity, it is found that when the difference in the pore water velocity in the two domains is significant, the BTC exhibits a bimodal distribution. However, there is only one peak for the BTCs when the above difference is insignificant. Further, as compared with the constant-reaction rate cases, we observe that the BTCs obtained for the media with depth-dependent rates lie in the intermediate zone defined by the above two extremes. Finally, we adopt the current approach to simulate the solute transport in an Andisol and observe that the difference between the numerical and experimental results is insignificant, indicating our approach is capable in modeling solute transport in porous media.

INVESTIGATION OF THE EFFECT OF THE DISCONTINUITY DIRECTION ON FLUID FLOW IN POROUS ROCK MASSES ON A LARGE-SCALE USING HYBRID FVM-DFN AND STREAMLINE SIMULATION

Understanding the fluid behaviour in rock masses is of great importance in various rock mass-related engineering projects, such as seepage in tunnels, geothermal reservoirs, and hazardous waste disposal. Different approaches have been implemented to study the flow pattern in fractured porous rock masses. Laboratory experiments can provide good information regarding this issue, but high expenses aside, they are time-consuming and suffer the lack of ability to study field scale mediums. Numerical methods are beneficial in simulating such mediums with the Discrete Fracture Network (DFN) method in terms of costs and time as they offer sufficient flexibility and creativity. In this paper, a Matlab code was extended to study the flow regime in a Dual Permeability Media (DPM) with two point sources in the right and left side of the model as an injector and a producer well, respectively. A high permeability discontinuity with different angles was embedded in a very low-permeability limestone matrix. Pressure equations were solved implicitly with a two-point flux approximation scheme of the Finite Volume Method (FVM). Streamlines were traced in the medium and used to analyse the model’s hydraulic behaviour with the aid of Time Of Flight (TOF) for each point. The results show that the FVM-DFN hybrid method can be used as a fast method for fluid flow in DPM with the aid of streamline simulation to study the fluid flow in a large model with discontinuity.

A new model approach for reactive solute transport in dual-permeability media with depth-dependent reaction coefficients

In this study, we developed a one-dimensional mobile-mobile model (MM) for contaminant transport in subsurface with depth-dependent reaction coefficients. Two local systems at micro-scale level are involved in this model: a micro-pore system and a less permeable pore system. The breakthrough curves (BTCs) obtained from the MM with depth-dependent coefficients were thoroughly analyzed, where the case with constant coefficients was used as the reference system. The effects of different parameters on BTCs were studied, and a parameter analysis was also performed to illustrate the effects of adsorption coefficient and degradation coefficient on BTCs. Results show that the BTC patterns for the depth-dependent reactions, in which the reaction rate decreases with increasing depth, vary between the two extreme cases with constant-rate reactions in the topsoil and observation depth. The mass transfer coefficient (α) plays a significant role in defining the BTC pattern. The double peak changes to a single peak when the value of α is large enough. In addition, the velocity of the main flow determines the shape of the BTCs while the velocity of the SVD defines the pattern of the dual peaks in BTCs which also tends to be represented by a single peak as the velocity decreases. Finally, we tested the applicability of the proposed model (MM-FD) in the leaching experiments of both field herbicide and conservative tracer in an agricultural area of northeastern Greece, and compared its performance with that of the advection-dispersion equation (ADE) model by Gao et al. (2013), both of which have depth-dependent coefficients. The results showed that the proposed mobile-mobile model with depth-dependent reaction coefficients was able to satisfactorily capture the evolution of metolachlor concentration both at upper and lower depths.

Unified pipe network method for simulation of water flow in fractured porous rock

Rock masses are often conceptualized as dual-permeability media containing fractures or fracture networks with high permeability and porous matrix that is less permeable. In order to overcome the difficulties in simulating fluid flow in a highly discontinuous dual-permeability medium, an effective unified pipe network method is developed, which discretizes the dual-permeability rock mass into a virtual pipe network system. It includes fracture pipe networks and matrix pipe networks. They are constructed separately based on equivalent flow models in a representative area or volume by taking the advantage of the orthogonality of the mesh partition. Numerical examples of fluid flow in 2-D and 3-D domain including porous media and fractured porous media are presented to demonstrate the accuracy, robustness, and effectiveness of the proposed unified pipe network method. Results show that the developed method has good performance even with highly distorted mesh. Water recharge into the fractured rock mass with complex fracture network is studied. It has been found in this case that the effect of aperture change on the water recharge rate is more significant in the early stage compared to the fracture density change.

Modeling Transport in Dual-Permeability Media with Unequal Dispersivity and Velocity

Porous media such as fractured rock and aggregated soils consist of two pore domains with distinct transport properties. A numerical code was developed to simulate solute concentrations in the two domains using a partitioned solution procedure to efficiently model transport in dual-permeability media. Furthermore, an approximate analytical solution was obtained that allows for different advective and dispersive terms in both flow domains, for a first-type or a third-type inlet condition. Solutions were obtained for local concentrations in both domains as well as effluent concentration and the concentration per medium volume. The problem was solved by decoupling the transport equations using diagonalization. This involves an error for the dispersivity matrix that is related to the difference in dispersivity of both domains. The correctness of the solution was assessed by comparison with numerical results. For low Damköhler numbers the solution was accurate even for a dispersivity ratio of 10. The need for a dual-dispersivity instead of a single-dispersivity model was illustrated with sample breakthrough curves and the solution was applied to optimize experimental breakthrough curves for an Andisol with a distinct intraaggregate and interaggregate porosity.

Pore-scale modeling of non-isothermal two phase flow in 2D porous media: Influences of viscosity, capillarity, wettability and heterogeneity

This paper addresses simulation of non-isothermal water-oil displacements in porous media at pore-scale. The simulation approach was done by coupling Cahn–Hilliard phase field and heat equations using COMSOL Multiphysics™. Finite element method with interfacial adaptive mesh refinement was employed to solve the equation system. The approach was first applied to a non-isothermal Poiseuille flow through channel, for verification. The model was further developed to study flow instabilities in displacements through uniform and dual permeability media. Simulations were performed for the uniform medium with different viscosity ratios (M) and capillary numbers (Ca), ranging three orders of magnitude. A stability phase diagram for log–logCa–M was constructed and showed a good agreement with those obtained by micro-model experiments. Hot water injection in pore scale revealed that active water fingers have a major role in propagating heat to the immobile oil. Fluid displacements in a dual-permeability medium at different Ca and M showed that lowering M exacerbates the water channeling effect in high permeability layer and lowering Ca may result in higher water sweep efficiency due to capillary dominant flow. This work demonstrated the feasibility of polymer gel treatment in dual-permeability medium to increase the resistant of the high permeability layer, hence divert water to the matrix, e.g., un-swept areas.

Colloid transport in dual-permeability media

It has been widely reported that colloids can travel faster and over longer distances in natural structured porous media than in uniform structureless media used in laboratory studies. The presence of preferential pathways for colloids in the subsurface environment is of concern because of the increased risks for disease caused by microorganisms and colloid-associated contaminants. This study presents a model for colloid transport in dual-permeability media that includes reversible and irreversible retention of colloids and first-order exchange between the aqueous phases of the two regions. The model may also be used to describe transport of other reactive solutes in dual-permeability media. Analytical solutions for colloid concentrations in aqueous and solid phases were obtained using Laplace transformation and matrix decomposition. The solutions proved convenient to assess the effect of model parameters on the colloid distribution. The analytical model was used to describe effluent concentrations for a bromide tracer and 3.2- or 1-μm-colloids that were observed after transport through a composite 10-cm long porous medium made up of a cylindrical lens or core of sand and a surrounding matrix with sand of a different grain size. The tracer data were described very well and realistic estimates were obtained for the pore-water velocity in the two flow domains. An accurate description was also achieved for most colloid breakthrough curves. Dispersivity and retention parameters were typically greater for the larger 3.2-μm-colloids while both reversible and irreversible retention rates tended to be higher for the finer sands than the coarser sand. The relatively small sample size and the complex flow pattern in the composite medium made it difficult to reach definitive conclusions regarding transport parameters for colloid transport.

A study on transient fluid flow of horizontal wells in dual-permeability media

To adopt horizontal wells in dual media reservoirs, a good understanding of the related fluid flows is necessary. Most of the recent studies focus on dual porosity media instead of dual permeability media. In this article, through both integral transformation and sink-source superposition, a new Laplace-domain solution is obtained for the slightly-compressible fluid flow in the 3-D dual-permeability media in which the horizontal well is operating in a constant rate of production. Major asymptotic characteristics of diagnosis curves of dimensionless downhole pressure are analyzed by the limited analysis. Effects of parameters of dual-permeability media including mobility ratio κ, storativity ratio ω and inter-porosity flow parameter κ on the downhole pressure are studied by using the Laplace numerical inversion. The new solution obtained in this article includes and improves the previous results and then can be used as a basis for either pressure transient analysis or formation behavior evaluation for the typical reservoir with horizontal wells.

Eulerian spatial moments for solute transport in three-dimensional heterogeneous, dual-permeability media

A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field.

Modeling depth-variant and domain-specific sorption and biodegradation in dual-permeability media

A dual-permeability model (S_1D_DUAL) was developed to simulate the transport of land-applied pesticides in macroporous media. In this model, one flow domain was represented by the bulk matrix and the other by the preferential flow domain (PFD) where water and chemicals move at faster rates. The model assumed the validity of Darcian flow and the advective–dispersive solute transport in each of the two domains with inter-domain transfer of water and solutes due to pressure and concentration gradients. It was conceptualized that sorption and biodegradation rates vary with soil depth as well as in each of the two flow domains. In addition to equilibrium sorption, kinetic sorption was simulated in the PFD. Simulations were conducted to evaluate the combined effects of preferential flow, depth- and domain-variant sorption, and degradation on leaching of two pesticides: one with strong sorption potential (trifluralin) and the other with weak sorption potential (atrazine). Simulation results for a test case showed that water flux in the PFD was three times more than in the matrix for selected storm events. When equilibrium sorption was considered, the simulated profile of trifluralin in each domain was similar; however, the atrazine profile was deeper in the PFD than in the bulk matrix under episodic storm events. With an assumption of negligible sorption in the PFD, both the atrazine and the trifluralin profiles moved twice deeper into the PFD. The simulated concentrations of the chemicals were several orders higher in the PFD than in the matrix, even at deeper depths. The volume fraction of the macropores and the sorption and biodegradation properties of the chemicals could also affect the amount of pesticides leaving the root zone. For an intense storm event, slow sorption reaction rates in the PFD produced higher breakthrough concentrations of atrazine at the bottom of the simulated soil profile, thus posing the risk for breakthrough of chemicals from the root zone.