Nonlinear Flow Characteristics Research Articles

Combined effects of the roughness, aperture, and fractal features on the equivalent permeability and nonlinear flow behavior of rock fracture networks

The hydraulic properties of a fractured rock mass are largely controlled by connected fracture networks. A thorough understanding of the physical flow processes in fracture networks is essential for assessing the transport capacity of the rock mass. However, the fracture surface roughness morphology, fracture distribution characteristics, and fluid flow regimes strongly influence the flow capacity of a fracture network. To this end, the rough topographic characteristics of fracture surfaces were quantified using fractal theory, and then the effective permeability model and nonlinear seepage effect assessment model of the rough fracture network for different flow regimes were developed based on the possible occurrence of laminar and turbulent flows in a single fracture. Finally, the influences of the geometric parameters of the fracture network on the effective permeability and nonlinear flow characteristics were analyzed. The results show that the prediction results of the proposed models are in good agreement with the field test data and can effectively reveal the seepage influence mechanisms under different flow regimes. Additionally, the results show that the effective permeability is closely related to the fractal dimension, relative roughness, aperture scale, distribution characteristics, and hydraulic gradient of the fractures. The nonlinear behavior of fluid flow significantly reduces the effective permeability of the rock mass. The proposed models can provide a reference for evaluating the transport capacity of rock masses under different fracture distributions and flow regimes.

The Nonlinear Flow Characteristics within Two-Dimensional and Three-Dimensional Counterflow Models within Symmetrical Structures

In this paper, we investigate the nonlinear characteristics of the flow in a two-dimensional and a three-dimensional counterflow model with symmetrical structures. Through numerical simulations, we obtain the velocity fields of the fluid flow in these models for different Re. The numerical results are analyzed to understand the nonlinear characteristics and differences between the two-dimensional and three-dimensional models. The findings indicate that, when Re varies, both the two-dimensional and three-dimensional models exhibit solution bifurcations and nonlinear phenomena such as symmetry breaking, self-sustained oscillations, and chaos. As Re increases, the two-dimensional counterflow model displays a unique solution, an asymmetric solution, and an oscillating solution. Specifically, when Re < 4320, both the laminar and turbulent models show a unique, symmetric, and steady-state velocity distribution. For 4652 < Re < 8639, the two-dimensional model solutions are not unique, presenting a pair of antisymmetric, asymmetric solutions that nevertheless remain steady-state. When Re > 8639, the solution becomes oscillatory and unsteady. The three-dimensional counterflow model exhibits a two-dimensional solution independent of the Z-axis. At Re = 4652, both the three-dimensional and two-dimensional models produce the same unique, symmetric, and steady-state velocity distribution with no three-dimensional flow (W = 0). At Re = 8639, the three-dimensional model solutions are not unique, showing a pair of antisymmetric, asymmetric solutions, while still being steady and time-independent. At Re = 87,627, the three-dimensional model solution becomes oscillatory and unsteady. By elucidating the flow characteristics and nonlinear features of both models, this study compares the differences between the two-dimensional and three-dimensional flows, thereby laying the groundwork for simplification of the problem and further theoretical research.

Identification for Nonlinear Flow Characteristics of Main Steam Regulating Valves in Power Plants by Mining Special Data Segments

Identification for Nonlinear Flow Characteristics of Main Steam Regulating Valves in Power Plants by Mining Special Data Segments

Research on Mathematical Model of Shale Oil Reservoir Flow

There are complex pore structures in shale reservoirs, and the nonlinear flow characteristics of shale reservoirs are complicated by stress sensitivity and boundary layer effects. In this research, a new flow mathematical model was established based on capillary model, stress sensitivity and boundary layer effect. The model was verified by the experimental results of Jilin shale oil reservoir, and the influencing factors of flow characteristics were analyzed. The results show that the new shale oil flow model has good fitting and high reliability with the experimental results. The boundary layer effect and stress sensitivity are the main factors affecting the seepage characteristics. With the increase in the pressure gradient, the influence of the boundary layer effect on the flow is gradually enhanced, and the influence of the stress sensitivity on the flow is gradually weakened. At the same time, this study developed a method for the evaluation of effective displacement distance of shale oil reservoir with CO2 injection through the limited injection-production well spacing method, and obtained the nonlinear flow curve of displacement distance with reservoir permeability under different injection and production pressure difference. This research deeply studies the flow characteristics of shale oil reservoir and provides a theoretical basis for the enhanced oil recovery of shale oil with CO2 injection.

Potential of redcurrant protein-enriched fractions as emulsifier in oil–water-emulsions

Berry protein, due to its functional properties, was extracted from redcurrant pomace seeds (RPS) in aqueous media to utilise side-streams and increase the sustainability of food production. Emulsions containing 1% redcurrant seed protein and 10% rapeseed oil were prepared by high pressure homogenisation. The emulsions’ structure, droplet surface charge, stability, rheological behaviour, and colour were characterised by microscopy, dynamic laser light scattering, storage tests and bulk rheology including large amplitude oscillatory shear rheology, respectively. Protein extracts of RPS proved to stabilise oil–water-interfaces by formation of a protein film having non-linear flow characteristics. While at low to medium shear, the emulsions showed pseudoplastic behaviour, limited molecular mobility at the interface induced softening at high shear. The shear stability of the interfacial protein layer decreased with increasing pH, i.e. with increasing molecular charge. Emulsions were prone to flocculation and subsequent creaming, either because of low surface charge at low pH or due to bridging by proteins and polymerised polyphenol complexes under neutral conditions. Although redcurrants only occupy a small market share in the berry sector, they are of high importance for specialised local producers and results presented here might evince possibilities for the utilisation of other pomace types.

Experimental study on the nonlinear flow characteristics of fractured granite after high-temperature cycling

To understand the influence of temperature on the flow characteristics of fractured granite, high-temperature cyclic thermal treatment and flow tests on the fractured rock sample with different joint roughness coefficients and intact rock samples were conducted. The larger confining pressure and larger joint roughness coefficient will increase the resistance of fluid flow and affect the flow characteristics of the fluid. With the temperature increasing, the aperture of the fractures, the number of micro-fractures, and micropores increase which forms a large number of new connected hydraulic channels in the matrix. Forchheimer's law and Izbash equation can well describe the nonlinear flow characteristics, and the fitting coefficients are greater than 0.99. As the increasing temperature, the slope of the curve between the volumetric flow rate and pressure gradient gradually decreases, and the coefficients in Forchheimer's law and the Izbash equation decrease. The transmissivity decrease with the increasing Reynolds number and the change range of that increase with the increasing temperature. When the temperature is at the lower level (T = 200 ~ 600 °C), the contribution of split fracture to the permeability is greater than that of the matrix. When the temperature continuously increases to 800 °C, the contribution of the matrix to the permeability gradually rises and then exceeds that of split fracture. The results indicate that 400 °C is the critical temperature, after which the flow characteristics of fractured granite after high-temperature cycling change more obviously.

Nonlinear flow and permeability anisotropy characteristics in hydraulic fracturing-induced rock fractures subjected to various normal compressive stresses

Well productivity after hydraulic fracturing is strongly affected by the flow behaviors in created fracture complexity. In this study, gas flow tests were conducted in splitting fractures (induced by Brazilian splitting) and hydraulic fractures (created by hydraulic fracturing) to study the nonlinear fluid flow behaviors in rough fractures. 3D fracture surfaces were first digitally reproduced with a scanner and then the fracture geometry parameters (roughness profile index R_{p}, the root mean square of the fracture profile wall slope Z_{2}), aperture distributions were computed for both fractures. The influence of the fracture geometry characteristics on the nonlinear flow behaviors were systematically analyzed. The permeability anisotropy was numerically examined in detail. The results show that R_{p}, Z_{2} and mean aperture of hydraulic fractures are relatively smaller, indicating that the fracture surfaces are smoother. The transmissivity of splitting fracture is relatively higher than that of hydraulic ones, and the ratio of splitting to hydraulic one varies from 2.51 at sigma_{c} = 1 MPa to 60.95 at sigma_{c} = 40 MPa. By contrast, splitting fractures have larger critical Reynolds number and lower critical pressure gradient, implying that nonlinearity is easier to occur in splitting fractures. The average Forchheimer coefficient for splitting fractures is 0.00577, which is 1.5 times larger than that (0.0041) for hydraulic ones. In addition, the fractures exhibit strong permeability anisotropy and this anisotropic effect is significantly dependent on the loading stress. In general, the permeability anisotropy in hydraulic fracture is more significant, showing that their permeability anisotropy ratios K are larger and more sensitive to the loading. The obtained results confirm that there exist some discrepancies in flow behaviors between splitting and hydraulic fractures and for more accurate evaluation in engineering practice, hydraulic fractures should be fully considered.

Effect of shear-induced contact area and aperture variations on nonlinear flow behaviors in fractal rock fractures

This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus. A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm, 3 mm, 5 mm, 7 mm and 10 mm under a normal stress of 0.5 MPa. Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions. The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface. The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots. As the shear displacement continues to increase, preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation; yet the area of single contacts increases. Based on the experimental results, an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension. • A visualization method is developed to determine the channelization of sheared fracture. • A model for predicting the Re c is proposed.

Study of nonlinear flow mechanisms and microfracture networks in low-permeability reservoirs

As efficient technologies boost oil yields and economic benefits, horizontal wells and hydraulic fracturing are widely used in low- permeability reservoirs. To better evaluate the reserve and improve recovery, it is essential to determine fluid flow patterns and transport mechanisms. Laboratory experiments, field operations, and analytical studies have identified nonlinear flow and microfracture networks during the fluid flow in a reservoir with fractured horizontal wells. However, the interactions between nonlinear flow and microfracture networks are still not fully understood. In this study, nonlinear flow experiments and triaxial compression tests were carried out to analyze nonlinear flow characteristics in the vicinity of microfracture networks. By analyzing the effects of microfracture networks on nonlinear flow, two-phase flow, rock stress sensitivity, and artificial fractures, we found that fluid capacity in capillaries with smaller dimensions decreased along with a drop in the pressure gradient, generating a nonlinear flow pattern. The area of nonlinear flow was diminished by the presence of microfractures, which improved flow efficiency and reservoir quality. Considering the size of fracture apertures, microfractures behave more like matrix pores than natural fractures. Also, microfractures significantly increase rock stress sensitivity and reduce the threshold permeability, which enhances fluid flow capacity. This study contributes to our understanding of flow behavior, predicting production and improving recovery in low-permeability reservoirs.

Integration of Profile Control and Thermal Recovery to Enhance Heavy Oil Recovery

The proven reserves of heavy oil in the Bohai oilfield exceed 600 million tons. Heavy oil is highly viscous, temperature sensitive, and suitable for thermal extraction, but due to the strong inhomogeneity of the reservoir, the recovery rate of pure thermal extraction development is low, and there is an urgent need to conduct research on profile control + thermal extraction to guide the actual production. In this paper, we propose an integrated technology of profile control and thermal recovery to enhance heavy oil recovery. The heavy oil exhibited strong temperature dependence and nonlinear flow characteristics. An inorganic gel was selected for profile control to assist thermal recovery. Thermal recovery experiments were conducted in the laboratory using cores saturated by crude oil with different viscosities to simulate the oil in areas swept by thermal fluid. The 4% to 6% inorganic gel can seal up to 99% on 2000 × 10−3 μm2 cores. As the thermal recovery temperature increased from 55 to 200 °C, the efficiency of oil recovery increased from 10.8% to 42.9% in experiments with three-layer heterogeneous cores; it increased by 8.9–13.2% when profile control was implemented using the inorganic gel with a concentration of 4%. The injection parameters for thermal recovery were optimized with a thermal fluid swept area of 3/10 times the injector–producer distance, including three slugs of crude oil with different viscosities. According to the experiments involving an inverted nine-point well pattern, the integrated technology of profile control and thermal recovery enhances oil recovery by 1.4% compared to of profile control or thermal recovery alone.

A New Method to Calculate the Relative Permeability of Oil and Water in Tight Oil Reservoirs by Considering the Nonlinear Flow

The theoretical research on the percolation mechanism and oil-water relative permeability of low-permeability oil reservoirs is the focus and hotspot of international researchers. Oil-water relative permeability is an important parameter that describes the characteristics of oil-water two-phase flow and is widely used in the dynamic analysis of development and numerical simulation technology in the reservoir. The traditional calculation method of oil-water relative permeability (i.e., the JBN method) is based on the Darcy flow law. When the velocity and the displacement pressure gradient do not follow the linear flow law, there are some errors in the results of oil-water relative permeability calculated by the JBN method. In this paper, the traditional JBN method is improved, and we establish a new processing method of experimental data for oil-water relative permeability considering the effects of nonlinear flow, capillary pressure, and gravity in tight oil reservoirs. The experiments on the flow characteristics of single-phase oil and oil-water relative permeability under nonsteady-state conditions were carried out. The flow velocity and displacement pressure gradient show nonlinear characteristics when single-phase oil is passed through a tight core. At the same time, when the air permeability decreases from 1.92 × 10 − 3 μ m 2 to 0.1 × 10 − 3 μ m 2 , the nonlinear characteristics are becoming more and more obvious. Compared with the traditional JBN method, when the nonlinear flow characteristics are considered, the oil phase relative permeability increases, and the water phase relative permeability is slightly lower. If nonlinear flow characteristics are considered, when the water saturation increases from 0.605 to 0.699, the difference of oil phase relative permeability calculated by the JBN method and this method is gradually decreasing and, with the increase of water saturation, decreases from 0.0029 to 0.0001. In addition, the effects of capillary pressure, gravity, and the nonlinear flow coefficient on the oil-water relative permeability in tight oil reservoirs are studied. The capillary pressure also has a great influence on the relative permeability of the oil phase, and the relative permeability of the oil phase increases with the increase in capillary pressure. In the development process of the low-permeability reservoir, the seepage characteristics of each flow area are different, and the oil-water relative permeability is also different. Therefore, the research results play an important role in guiding the understanding of seepage characteristics of low permeability of tight oil reservoirs.

Flow Characteristics through Granular Soil Influenced by Saline Water Intrusion: A Laboratory Investigation

The coastal geoenvironment initiates saline water intrusion into the freshwater aquifers, producing a geohydraulic problem. Such intrusion not only contaminates the fresh groundwater resources, making them unsuitable for human use, but also alters the hydraulic conductivity of the aquifer materials, which affects the coastal groundwater flow, influencing the water resources planning and management. Past investigations reveal that the groundwater flow can be linear or nonlinear depending upon the hydraulic gradient. Thus, the coefficients of nonlinear hydraulic conductivities are affected by saltwater intrusion. The present study focuses on an in-depth laboratory investigation into the influence of saltwater submergence on the nonlinear flow characteristics through granular soil. The fine sand samples have been submerged under saline water of specified concentrations for a specific duration, and the alteration in their nonlinear geohydraulic properties has been studied. It is observed that the flow characteristics through fine sand are significantly affected by the period of submergence and saline concentration. Appropriate analyses of the test results are performed to interpret the experimental data, and relevant conclusions are drawn therefrom. The novelty of this study is an in-depth analysis of nonlinear flow characterization affected by saline water intrusion. Doi: 10.28991/CEJ-2022-08-05-02 Full Text: PDF

Investigation of Nonlinear Flow in Discrete Fracture Networks Using an Improved Hydro-Mechanical Coupling Model

Fractures commonly exist in rock masses; the coalescence of fractures provides fluid flow pathways in a fractured rock mass and greatly increases the flow capacity of fractured rock. This work aims to study the characteristics of nonlinear flow in fractures. A series of tests were conducted and indicated that the Forchheimer law performed well when describing the nonlinear relationship between hydraulic gradient and flow. The test results also indicate that higher water pressure may induce stronger nonlinearity. Additionally, the linear and nonlinear coefficients of the Forchheimer law increase with a decrease in the particle size of the filling material in fractures. On the basis of the laboratory results, the classical Forchheimer law was modified by considering the influence of stress on the variation of fracture aperture. A hydro-mechanical coupling model for fractured rock masses was built and programmed with a subroutine through ABAQUS. Furthermore, a random discrete fracture network was generated and simulated to prove that a high flow velocity will result in a nonlinear flow, not only in a single fracture, but also in a fracture network. The numerical results from fractured rock masses show that a ratio of the flow to the hydraulc gradient will change the flow from linear to weak nonlinearity and, finally, to strong nonlinearity with an increase in the hydraulic gradient. It also shows that the linear and nonlinear coefficients increase with an increase in the confining pressure and that they decrease with an increase in the aperture. Due to the complexity of fracture channels, a nonlinear flow is likely to occur in a fractured rock mass. Finally, the developed model was applied to simulate the flow behavior of underground engineering; the results show that the smaller the hydraulic aperture is, the higher the water pressure is required to be in order to change the flow regime from linear to nonlinear.

An improved rock typing method for tight sandstone based on new rock typing indexes and the weighted fuzzy kNN algorithm

Petrophysical rock typing is a very important problem in flow unit interpretation and reservoir characterization. Unlike the sandstone, the presence of numerous nanopores in tight sandstone can cause strong gas and liquid non-linear flow. And this makes the traditional rock typing indexes derived from Darcy'law unsuitable for tight sandstone. In this paper, new rock typing indexes, including the Darcy index (Fi), the gas non-Darcy index (Kc) and the liquid non-Darcy index (Sr), have been proposed to describe the non-linear flow characteristics in tight sandstone. In addition, the limit pore ranges for gas and liquid non-Darcy flow have been determined based on these indexes. Then the weighted fuzzy kNN algorithm, which can consider the weight differences between different rock typing indexes, is combined with three indexes to improve the accuracy of rock typing. In order to test the rock typing indexes and the weighted fuzzy kNN algorithm, the tight sandstone dataset in Upper Triassic Yanchang Formation, Ordos Basin, NW China has been constructed with RES (representative element surface) random pore network and experiment data. The results show that the new rock typing indexes and the weighted fuzzy kNN algorithm have better performance in typing tight sandstone than the traditional methods. Moreover, 30 mercury injection capillary pressure (MICP) curves measured on highly inhomogeneous tight sandstone samples from the research area have also been used to validate our method. All the results have proved that the proposed new rock typing indexes and weighted fuzzy kNN algorithm can type the tight sandstone very well, and they play a significant role in permeability prediction, reservoir modeling and simulation. • New rock typing indexes have been proposed to describe the non-Darcy flow characteristics in tight sandstone. • The limit pore ranges for gas and liquid non-Darcy flow have been determined based on the new indexes. • The weighted fuzzy kNN algorithm is combined with three indexes to improve the accuracy of rock typing. • The improved method has been proved to have better performance in typing tight sandstone than the traditional methods.

Influence of Liquid Hydrogen Diffusion on Nonlinear Mixed Convective Circulation around a Yawed Cylinder

A yawed cylinder is a cylinder inclined in the plane of a flowing liquid. The liquid flow past the yawed cylinder is important for practice, namely, for bubble suppression and control of the boundary layer transition in undersea applications. It should be noted that an inclined cylinder characterizes an asymmetrical behavior of fluid flow and heat transfer. Energy and mass transference characteristics of a steady nonlinear convective flow over the yawed cylinder by accounting for chemically reactive species and viscous dissipation are analyzed in this investigation. The differential equations defining the boundary layer parameters are then transformed into a dimensionless view, taking into account the non-similar transformation. It should be noted that the governing equations have been written using the conservation laws of mass, momentum, energy, and concentration. These considered equations allow the simulation of the analyzed phenomenon using numerical techniques. Further, quasilinearization and implicit finite difference approximation are used to work out the non-dimensional governing equations. A parametric investigation of all the pertinent characteristics accompanies this. A descriptive system of computation outcomes for the velocity, temperature, and concentration patterns, the drag coefficients, Nu and Sh, is demonstrated by graphs. Enhancing the magnitudes of the Eckert number raises the temperature pattern while energy transport strength is reduced. As the species concentration profile diminishes, the mass transfer characteristics are enhanced for raising magnitudes of the nonlinear chemical reaction parameter. Further, a velocity profile along the chordwise direction rises with enhancing magnitudes of nonlinear convection characteristics and yaw angle. Furthermore, the velocity pattern along the spanwise direction enhances with the growing magnitudes of yaw angle. For assisting buoyancy flow, the friction parameter at the border in the spanwise direction enhances with rising values of yaw angle.

A Laboratory Investigation on Flow Traits in Saturated Clay

The properties of flow through saturated soil are complicated. When the head is low, the flow is virtually linear, and Darcy's rule applies. The flow is nonlinear at the increasing head and is mathematically known as Forchheimer's flow. Several factors, including soil and fluid properties, influence the critical flow velocity for this transition and the corresponding Reynold's number. An experimental examination was carried out in this paper using a falling head permeameter and a locally accessible soft soil sample. The test findings were subjected to a careful analysis and interpretation to identify the linear and nonlinear flow characteristics, and key conclusions were obtained as a result.

Research on Non-Linear Flow Characteristics for the Expandable Packer Rubber in High Temperature and High Pressure Wells

Research on Non-Linear Flow Characteristics for the Expandable Packer Rubber in High Temperature and High Pressure Wells

Experimental investigation of nonlinear flow characteristics in cracked polypropylene fibre-reinforced concrete

Experimental investigation of nonlinear flow characteristics in cracked polypropylene fibre-reinforced concrete

Nonlinear gas flow characteristics of acidified and water-saturated sandstone

Nonlinear gas flow characteristics of acidified and water-saturated sandstone

Numerical calculation method of aperture function for rough rock fracture flow

Fracture is the main path of rock seepage and plays a decisive role in the permeability of rock masses. The method of solving Navier-Stokes (NS) equation directly to study the fracture seepage flow has high accuracy and can well reflect the nonlinear flow characteristics in the fracture, but there is also the problem of excessive calculation. In this paper, the fracture aperture spatial data is substituted into the local cubic law as an aperture function to form a numerical calculation method for seepage in rough rock fractures, namely, the aperture function method(AFM). After comparing with the experimental calculation results of fracture seepage, it is found that the AFM calculation results are in good agreement. Using the method of solving the NS equation, the seepage calculations were performed for two typical fracture models with multiple boundary conditions. After comparison and analysis, a) the nonlinear term in the rough fracture flow mainly originates from the local pressure drop (LPD), and the generation of the recirculation zone(RZ) is the main reason for the formation of the LPD. b)The AFM calculation results are compared with the NS method under low hydraulic gradient conditions and its error is not significant (i. e., 0.21%, 0.81%). AFM is an excellent numerical calculation method when the condition of neglecting the effect of nonlinear items in fracture flow is allowed. c) The main advantage of AFM is that it has a very high numerical calculation efficiency, which makes the method available for seepage calculations in large-scale rough fractures.