Nonlinear Seepage Research Articles

Threshold pressure gradient for helium seepage in coal and its application to equivalent seepage channel characterization

Seepage is the main gas migration form in coal seam. The experiments in this study show that there exist threshold pressure gradient and low-velocity nonlinear seepage phenomenon when non-adsorbable helium flows in coal briquette. To further explain that from microscopic view, we establish a capillary seepage model and use a new experimental method to characterize the equivalent seepage channel size distribution (ESCSD) of coal under different effective stress conditions (3–48 MPa). The experimental results prove that the ESCSD of coal obeys fractal distribution. The fractal dimensions in this study are in the range of 2.30–3.36, and decrease significantly with the increase of effective stress. Under the condition of effective stress <48 MPa, the seepage channels with size >1 μm in the experimental coal sample always control most seepage discharge (>90%). Based on the theoretically simplified seepage model and the measured threshold pressure gradient for seepage, the relationship between the critical seepage channel size (dcr) of helium in coal and the pressure gradient (∂P/∂L) is obtained, that is, dcr=α∂P/∂L and α is in the range of 0.0024–0.0033 Pa. Note that the critical condition here represents the transition not from flow to no flow but from seepage to diffusion.

Effect of non-Darcy seepage on productivity of tight gas reservoir

In the process of gas reservoir development, with the production of formation fluid, the effective overburden pressure on the rock skeleton of the reservoir increases, and the rock is deformed under compression, which changes the physical properties of the rock (porosity, permeability, etc.), especially the influence on permeability. Stress sensitivity and threshold pressure gradient are important factors for non-linear seepage in tight gas reservoirs. This paper establishes an empirical prediction model through experimental tests and uses numerical simulation to analyze the effects on productivity. The experimental results show that the relationship between stress sensitivity and permeability is exponential, and there is a strong hysteresis effect. The starting pressure gradient of gas presents a power function relationship with water saturation and permeability respectively, and an empirical relationship is established to predict the starting pressure gradient by comprehensively considering the influence of permeability and water saturation. The single well productivity simulation shows that: The effect of starting pressure gradient on gas well development is greater than stress sensitivity. When starting pressure gradient or stress sensitivity is taken into account, the formation average pressure increases relative to each other and the stable production period decreases obviously.

Experimental study on permeability evolution and nonlinear seepage characteristics of fractured rock in coupled thermo-hydraulic-mechanical environment:a case study of the sedimentary rock in Xishan area

An understanding of how the fracture permeability evolves in a coupled thermo-hydraulic-mechanical (THM) environment at real-time ultrahigh temperature has a great significance for many underground excavations. This paper designs a testing apparatus to take the effects of THM processes into account by coupling high temperatures and high triaxial stress. Correspondingly, the permeability evolution of fractured rock in the coupled THM environment under real-time ultrahigh temperature (20–650 °C) and triaxial stress (confining pressure of 5–25 MPa)/seepage pressure (0.5–6 MPa) conditions is studied. Then, using the X-ray micro-computed tomography technique, the evolution of the fracture aperture in the fractured rock subjected to various conditions is analyzed. The results indicate that for the coupled THM environment, the variations of the volumetric flow rate, nonlinear seepage parameters, and the fracture aperture of the fractured rock with the temperature and the triaxial stress are not straightforward, and the inflexion points of the curves happen at a confining pressure of 15 MPa and a temperature of 300 and 500 °C. Second, in the temperature range of 20–300 °C, in all the triaxial stress states, the volumetric flow rate and the fracture aperture decline slightly with an increase in the temperature due to the recoverable elastic compression on the propping asperities. However, in the temperature range of 300–650 °C (at a confining pressure equal to or lower than 15 MPa), the parameters rise slightly with an increase in the temperature due to the relatively large axial and lateral deformation of the semicylinders. Third, in temperature ranges of 500–650 °C (at a confining pressure equal to or lower than 15 MPa) and 300–650 °C (at a confining pressure higher than 15 MPa), the parameters rise sharply owing to the lateral fracturing of the semicylinders, so the variational trends are irregular. The findings of the current work can provide theoretical guidance on the assessment of the stability and compactness of high-temperature underground excavations.

Seepage Flow Properties of a Columnar Jointed Rock Mass in a True Triaxial Experiment

A columnar jointed rock mass is a type of rock mass with strong geometric anisotropy and high interface permeability. Its seepage characteristics pose new challenges to the construction and maintenance of the Baihetan Hydropower Station on the Jinsha River. The research object in this study is the columnar jointed rock mass (basalt) in the dam area of Baihetan Hydropower Station. Similar-material model samples of the columnar jointed rock mass with different column dip angles ( α = 0 ° ~90°) were prepared following a similar principle. A true triaxial seepage–stress coupling test was conducted to evaluate the seepage characteristics of similar-material samples with different dip angles under intermediate principal stress and minimum principal stress. The experimental results showed that the columnar jointed rock mass exhibited apparent seepage anisotropy. The relationship curve between the volume flow rate Q and the pressure gradient − d P / d L of the samples with different dip angles showed evident nonlinear seepage under intermediate principal stress, which could be well expressed using the Forchheimer equation. It shows the characteristics of a typical linear Darcy flow under minimum principal stress. The law of variations in the permeability of the samples with different dip angles under intermediate principal stress can be well expressed using the one-dimensional quadratic function equation k = a + b σ 2 + c σ 2 2 , and the law of variations in the permeability of the samples with different dip angles under minimum principal stress can be well expressed using the logarithmic function k = a + b ln σ 3 . The permeabilities of the columnar jointed rock mass with dip angles of 0°, 15°, 30°, and 60° were most sensitive to changes in stress, and the seepage characteristics increased in complexity after changes in stress.

Experimental Research of the Influence of Microfracture Morphology on Permeability of Shale Rock

Hydraulic fracturing is currently one of the main technical methods of shale gas exploitation. The permeability variation of shale gas reservoir after fracturing is inevitable, while the influence of fracture length and fracture width on permeability and seepage characteristics of shale rock is a mystery. Besides, the stress sensitivity characteristics of shale rock, derived from different initial permeability, with the same permeability after fracturing are also ambiguous. To this end, a series of seepage characteristic experiments related to different fracture parameters are carried out with the black shale of the Longmaxi Formation in Sichuan gas field as the research target. The results show that the fracture length and fracture width have a good exponential relationship with the corresponding permeability of the reformed shale rock, and the contribution of the fracture width to shale permeability is much greater than that of the fracture length. In addition, the nonlinear seepage characteristics of shale rock are gradually significant with the reduction of fracture length and fracture width. Taking the primitive effective stress (10 MPa) as a critical point, the permeability of shale with large initial permeability decreased by 26.4%, which is about twice as much as that of shale rock with small initial permeability (14.9%) in the selected pressure loading stage, owing to the difference of fracture width inside the shale rock. The permeability of the shale rock with a large initial permeability is restored by 14.7%, while the shale rock with a small initial permeability is only recovered to 5.2% in the pressure unloading stage, which is attributed to the closure of fractures, especially the loss of fracture width. This research can provide some new insights for the production prediction of shale gas reservoir after fracturing.

Experimental study and production model of multiscale stress sensitivity in tight oil reservoirs

ABSTRACT Stress sensitivity is an inevitable issue in the depletion exploitation of tight oil reservoirs, especially in the reformed multiscale region. Through a series of improved laboratory experiments, the stress sensitivity characteristics of multiscale media were thoroughly evaluated based on the primitive effective stress. Furthermore, based on the nonlinear seepage theory and equivalent seepage resistance method, a corresponding multiscale production prediction model of vertical wells in tight oil reservoirs with stress sensitivity established. The results showed that the decline in permeability of main fracture rock (12.86%) was more than twice that of the microfracture rock (5.25%), which was approximately four times that of the matrix rock (3.32%) in the selected pressure range. In addition, there was a fine power function relationship between permeability variation and effective stress in multiscale representative media. Compared with the actual daily production and cumulative production of the coring well, the production curve fitting of the proposed multiscale model was 91.25%, which was reliable to guide the development scheme design in the target block of tight oil reservoirs.

Numerical Simulation on Mesoscale Mechanism of Seepage in Coal Fractures by Fluid-Sloid Coupling Method

Trying to reveal the mechanism of gas seepage in coal is of significance to both safe mining and methane exploitation. A series of FEM numerical models were built up and studied so as to explore the mesoscale mechanism of seepage in coal fractures. The proposed mesoscale FEM model is a cube with micron fractures along three orthogonal directions. The distribution of velocity and pressure under fluid-solid coupling was obtained, and furthermore, the seepage flow flux and an equivalent permeability of the whole model were calculated. The influences of fracture width, outlet velocity, and in situ stress level on seepage were investigated. The numerical results show that nonlinear Darcy seepage occurs during low velocity zone. The permeability is increased linearly with the increasing of facture width and outlet velocity. A certain change of lateral coefficient of in situ stress also affects seepage. The permeability is increased sharply once deviating the isotropic spherical stress state, but it is no longer changed obviously after the lateral coefficient has been increased or decreased more than 20%. The mesoscale seepage mechanism in coal fractures has been preliminarily revealed by considering fluid-solid coupling effect, and the key factors influencing fluid seepage in coal fractures were demonstrated. The proposed methods and results will be helpful to the further study of seepage behaviour in coal with more complex structures.

Study on the microscopic pore structures of the four different kinds of lithological reservoirs in the basin of Western China

In the basin of western China, four different kinds of lithological reservoirs are developed, including low-permeability sandstone, sedimentary tuff, shale and volcanic rock. There is generally a large difference in the micropore structure characteristics and distribution laws due to different reservoirs. The reserving capacity as well as the porous flowability, mechanism and laws are determined by the micropore structure characteristics and distribution laws of hydrocarbon reservoirs. Low-temperature nitrogen adsorption and desorption technology, high-pressure mercury injection experiment and nuclear magnetic resonance (NMR) testing technology are applied to study the micropore size, quantity, structure and distribution laws of four different kinds of lithological reservoirs as well as their similarities and differences of corresponding relation with macroporosity–permeability physical parameters. This paper also studies the movable fluid and nonlinear seepage flow characteristics of four different kinds of lithological reservoirs.

Does Rheology of Bingham Fluid Influence Upscaling of Flow through Tight Porous Media?

Non-Newtonian fluids may cause nonlinear seepage even for a single-phase flow. Through digital rock technologies, the upscaling of this non-Darcy flow can be studied; however, the requirements for scanning resolution and sample size need to be clarified very carefully. This work focuses on Bingham fluid flow in tight porous media by a pore-scale simulation on CT-scanned microstructures of tight sandstones. A bi-viscous model is used to depict the Bingham fluid. The results show that when the Bingham fluid flows through a rock sample, the flowrate increases at a parabolic rate when the pressure gradient is small and then increases linearly with the pressure gradient. As a result, an effective permeability and a start-up pressure gradient can be used to characterize this flow behavior. By conducting flow simulations at varying sample sizes, we obtain the representative element volume (REV) for effective permeability and start-up pressure gradient. It is found that the REV size for the effective permeability is almost the same as that for the absolute permeability of Newtonian fluid. The interesting result is that the REV size for the start-up pressure gradient is much smaller than that for the effective permeability. The results imply that the sample size, which is large enough to reach the REV size for Newtonian fluids, can be used to investigate the Bingham fluids flow through porous media as well.

Experimental Study on Seepage Anisotropy of a Hexagonal Columnar Jointed Rock Mass

Many columnar jointed rock masses (basalt) are present at the Baihetan hydropower dam site, and their seepage characteristics have a significant impact on the project’s safety and stability. In this study, model samples consisting of material similar to the columnar jointed rock mass with different inclination angles (0°–90°) were prepared and laboratory triaxial seepage tests were performed to study the seepage characteristics of the columnar jointed rock mass under maximum axial principal stress. The experimental results showed that the similar material model samples of columnar jointed rock mass showed obvious seepage anisotropy. The nonlinear seepage characteristics were well described by the Forchheimer and Izbash equations, and the fitting coefficients of the two equations were in good correspondence. The curves describing the relationship between the inherent permeability and the stress of the samples with different dip angles were U-shaped and L-shaped, and a one-variable cubic equation well described the relationship. The 45° angle specimen had the highest sensitivity to the maximum principal stress, and its final permeability increased by 144.25% compared with the initial permeability. The research results can provide theoretical support for the stability evaluation of the Baihetan hydropower station.

Determination of nonlinear seepage slope for dislocation interface by in situ tests

Seepage failure test means the foundation soil instability caused by underground water perturbation, which is one of the most common methods to evaluate a site seepage resistance, but it is time consuming. High water pressure is always applied to shorten the test time. However, significant error is generated as calculating the seepage failure slope (SPS), the gradient, due to the nonlinear characteristics as the pressure increases. The Darcy law and the permeability coefficient are no longer applicable. Here, an analytical method for confined aquifer is proposed to investigate the nonlinear permeability coefficient and SPS. The in situ tests were conducted on the dislocation interfaces at the reservoir banks of the Baihetan hydropower station to verify the proposed method. The test results indicate that the SPS calculated values by nonlinear equation is much smaller than that by linear equation, which means that the conventional linear calculation results will overestimate the resistance of the site seepage failure. Moreover, the results calculated by steady and nonsteady nonlinear equations are very close, while the storativity is between 1 × 10−3 and 1 × 10−5, which is the ordinary storativity of most aquifers in this region. Hence, in general, the steady nonlinear equation can be used to calculate the site SPS to simplify the calculation.

Discrepancy between Forward and Reverse Seepage Characteristics in a Single Rough Fracture

Under the uniform seepage boundary condition, the forward and reverse seepage flow rates will vary widely. In response to this phenomenon, this paper studies the mechanism of the difference in seepage characteristics between the forward and reverse directions from the fracture profile’s roughness, Darcy and non‐Darcy seepage, and distribution of eddy currents. First of all, wavelet transform was used to decompose and reconstruct the single rough fracture for 8 times, and then 9 fracture models with various roughness degrees were constructed. Then, Finite Volume Method was used to simulate the seepage in the original and approximate models of the Reynolds number varying from 0.001 to 1000. The results show that the nonlinear seepage is necessary for the difference between the forward and reverse seepage characteristics of the single rough fracture. The mechanism of the discrepancy between forward and reverse nonlinear seepages is the diverse shapes and distribution of the eddy current generated by the forward and reverse seepage. The secondary roughness provides space for the existence and development of the eddy current. The secondary roughness is the geometric basis of the discrepancy between the forward and reverse seepage characteristics.

The non-Darcy characteristics of fault water inrush in karst tunnel based on flow state conversion theory

The fault water inrush is a key factor which leads to tunnel construction in karst regions. Based on the fluid mechanics principles, the paper addresses a numer?ical coupled model for karst fault tunnel with COMSOL Multiphysics software. Besides, the Darcy law equation, Brinkman equation, and Navier-Stokes equation are inserted to stimulate the steady flow of aquifer, the non-linear seepage of fault and the free flow in tunnel excavating area in software, respectively. Then, the pres?sure and flow velocity in three flow fields are analyzed under different permeability ratios in numerical model. It is shown that the fault permeability is the key factor affecting water inrush, and that the pressure and flow velocity change visibly in adjacent domains between two flow fields.

Analysis free surface of nonlinear seepage using the MQRBF method

In order to solve the characteristics of low accuracy and slow efficiency in traditional numerical solution the free surface problem, the multiquardatic radial base function collocation method(MQ RBF) is used to analyze the constant seepage and unsteady seepage of the homogeneous earth dam. Computation of transient problem of free surface of earth dam by the linear derivation of Richards equation. The results show that the calculation accuracy of the MQRBF is higher than that of the traditional numerical method. The solution process does not involve numerical integral calculation and grid reorganization, which greatly reduces the calculation amount. Compared with the Trefftz method, it has the advantage of solving boundary values and internal values at the same time. It is not limited by the solution of the Laplace equation, and its application is wider and simpler.

Study on the Influence of Nonlinear Seepage and Grouting Reinforcement on Surrounding Rock in Subsea Tunnel

He, X.; Zhou, X.; Xu, Y.; Ma, W., and Wu, T., 2020. Study on the influence of nonlinear seepage and grouting reinforcement on surrounding rock in subsea tunnel. In: Liu, X. and Zhao, L. (eds.), Today's Modern Coastal Society: Technical and Sociological Aspects of Coastal Research. Journal of Coastal Research, Special Issue No. 111, pp. 162–167. Coconut Creek (Florida), ISSN 0749-0208.Seepage is an important problem of tunneling engineering, which shows nonlinear characteristics in the low permeability media. Particularly in the seabed environment, Darcy's law is not accurate when considering the design of grouted subsea tunnels. Therefore, in this article, an analytical model considering nonlinear seepage and grouting reinforcement is established. Under a series of conditions, the analytical solutions of seepage fields and stress fields are derived and verified by numerical calculation. Then the influence of nonlinear seepage and grouting reinforcement on the pore pressure and effective stress of surrounding rock is investigated, and tunnel drainage is also discussed. The results indicate that tunnel excavation under nonlinear seepage is safer than that under linear Darcy's seepage, and grouting is a significant support that can not only improve the bearing capacity of surrounding rock, but also effectively reduce tunnel drainage.

Investigation on Nonlinear Flow Behavior through Rock Rough Fractures Based on Experiments and Proposed 3-Dimensional Numerical Simulation

Rock fractures as the main flow channels, their morphological features, and spatial characteristics deeply influence the seepage behavior. Reservoir sandstones as a case study, four splitting groups of fractures with different roughness were scanned to get the geometric features, and then the seepage experiments were taken to analyze the relationship of the pressure gradient ∇ P and flow rate Q , and the critical Reynolds number( Re c ) and wall friction factor ( f ) were determined to explain the translation of linear seepage to nonlinear seepage condition. Based on the scanning cloud data of different rough fractures, the fractures were reconstructed and introduced into the COMSOL Multiphysics software; a 3-dimensional seepage model for rough fractures was calibrated and simulated the seepage process and corresponding pressure distribution, and explained the asymmetry of flow velocity. And also, the seepage characteristics were researched considering aperture variation of different sample fractures; the results indicated that increasing aperture for same fracture decreased the relative roughness, the fitting coefficients by Forchheimer formula based on the data ∇ P ~ Q decreased, and the figures about the coefficients and corresponding aperture described nonlinear condition of the above rough fractures. In addition, the expression of wall friction factor was derived, and relationship of f , Re , and relative roughness indicated that f increased with increasing fracture roughness considering the same aperture, resulting in nonlinear flow more easily, otherwise is not, showing that f could be used to describe the seepage condition and corresponding turning point. Finally, it can be seen from the numerical results that the nonlinearity of fluid flow is mainly caused by the formation of eddies at fracture intersections and the critical pressure gradient decreases with increasing angle. And also, analysis about the coefficient B in the Forchheimer law corresponding to fracture intersections considering the intersecting angle and surface roughness is proposed to reveal the flow nonlinearity. The above investigations give the theoretical support to understand and reveal the seepage mechanism of the rock rough fractures.

Prediction of water inflow into a tunnel based on three-district zoning of faults

Water inflow into a tunnel subject to fault zones and fault effective zones is interpreted in this study using a three-district zoning method. An improved Brinkman model is proposed to investigate the seepage law of the geological defects of a fault. A coupled calculation model of typical Darcy seepage and Brinkman rapid seepage is constructed to establish a mathematical model of nonlinear seepage flow based on three-district zoning and the corresponding numerical implementation. In addition, the influence of the angle between the fault dip and tunneling directions on the water inrush in a tunnel is also studied. The variation characteristics of the pore pressure and velocity fields under various construction stages are analyzed, as is the seepage velocity of pore water at the tunnel heading. Moreover, the effects of the fault dip direction on the seepage field and water inflow are discussed. The following results were obtained. (1) Before excavation to the fault effective zone, the pore pressure at the same depth remained essentially unchanged in front of the tunnel heading. After excavation to the fault effective zone, the pore pressure at the same depth increases linearly with distance in front of the tunnel heading. (2) The seepage velocity changed gently before excavation to the fault effective zone but showed wavy fluctuating after excavation to the fault effective zone. The velocity reached its maximum value in the fault zone before decreasing rapidly and remaining close to zero in the general surrounding rock zones. (3) As the excavation length increased, the water inflow increased gradually, reaching its maximum value in the fault zone. (4) In the fault zone, the seepage velocity decreased with an increase in the fault dip. The water inflow reached maximum and minimum values at angles of 90° and 150°, respectively.

Experimental investigation on low-velocity seepage characteristics and influencing factors in a shale oil reservoir

The seepage behavior in shale oil reservoir is very complicated. In this study, the characteristics and influencing factors of low-velocity seepage in brittle shale oil reservoirs were investigated by high precision experimental methods. The velocity used in this study was as low as 10−4 ml/min, and at least eight different flow rates were measured for each experiment. During the operation, the pressure difference between the inlet and outlet was controlled within 0.35 MPa to eliminate the influence of stress sensitivity. The effects of core permeability, fluid viscosity, pore pressure, and propped artificial fracture on the seepage behavior were analyzed. The results show that the seepage flow rate and pressure gradient in shale core samples presents a convex relationship, which is entirely different from the results of a concave relationship in tight sandstone oil reservoirs. The slippage effect and boundary layer effect in the flow channels were investigated to explain the convex flow regime theoretically. The convex shape flow regime is caused by the heterogeneous of shale core samples associated with the completed developed micro-fractures in this area. The seepage flow divides into two stages: the non-linear stage when the applied pressure gradient is lower than 2 MPa/m and the linear stage when it is higher than 2 MPa/m. The non-linear seepage characteristics become more obvious with a higher viscosity crude oil. With the increase of pore pressure, micro-fractures in shale core samples gradually close, leading to the reduction of flowing channel and the significant decrease of apparent permeability. The seepage characteristics are similar to those of tight sandstone oil, and the flow rate and pressure gradient curve presents a concave shape. With a propped artificial fracture, the seepage flow behavior follows Darcy's law. This work provides a feasible and reliable method and valuable experiment data for the study of low-velocity seepage in shale reservoirs.

Method for Calculating Non-Darcy Flow Permeability in Tight Oil Reservoir

Capillary force and boundary layer effect are the main causes of non-Darcy flow in tight oil reservoir. This paper proposes a non-Darcy flow dynamics characterization method for low-speed water flooding in tight oil reservoirs. It applies constant-speed mercury injection and casting thin section experiments to quantitatively characterize the micro-pore throat structure parameters, and uses the visual experimental device to measure the boundary layer thickness and fit the expression of the relationship between boundary layer thickness and displacement pressure gradient and fluid viscosity. The results show that the ratio of boundary layer thickness to microtubule radius changes exponentially with the pressure gradient and fluid viscosity and that the boundary layer thickness decreases gradually with the increase of pressure gradient. Given the capillary force and boundary layer thickness, the flow rate of single capillary is calculated. On this basis, the equation of nonlinear seepage dynamic characteristics per unit area of core is derived by taking into account the throat distribution frequency and throat size characteristics. The new seepage flow model can reflect the nonlinear seepage flow law of tight oil reservoir and provide reference for parameter formulation during water flooding development of tight oil reservoir.

Analysis of Nonlinear Seepage Characteristics of High Water Cut Preferential Channel

After long-term water injection, some preferential seepage channels would form which are several times or even hundreds of times larger than the original channels in the reservoir. The inefficient and ineffective circulating water injection caused by the preferential channel restricts the efficient development of the oilfield. In this paper, based on the seepage law of the preferential channel, the seepage model for the preferential channel is established. The pressure gradient, seepage velocity and average formation pressure under the nonlinear seepage flow are calculated. The nonlinear seepage characteristics in the preferential channel are analyzed. After comparing with the Darcy linear flow, it is considered that the existence of the preferential channel has a great influence on the production, and the influence of the nonlinear flow in the preferential channel should be considered in the calculation of the development index.