A calculation method for pipe-matrix water flow exchange based on karst fissure development

Abstract

Karst aquifers are composed of media such as bedrock fractures and karst conduits. Existing models usually assume that they conform to Darcy's law and use linear equations or non-linear equations with fixed power exponents to quantitatively describe the pipe-matrix exchange flow in karst conduits, and cannot reflect the non-linear exchange flow process between pipes and matrices under different karst wide fracture development conditions. Aiming at the above deficiencies, the present invention proposes a calculation method for pipe-matrix water flow exchange based on karst fracture development. By designing indoor experiments to simulate different degrees of fracture development, the regression analysis method is used to fit the experimental data to propose a non-linear exchange flow equation Q ex = α(H c ―H m ) n , where the non-linearity n varies according to different wide fracture developments, and its value range is 0.5 ≤ n ≤ 1. Based on the above equation, the CFP model is improved. The numerical simulation results of the designed indoor experiments are 11% and 12% higher than the original CFP model in terms of the coefficient of determination (R 2 ) and the Nash efficiency coefficient (NSE) respectively, and the root mean square error (RMSE) and percentage bias (PBIAS) are reduced by 45% and 44% respectively.

Description

Technical Field

[0001] The present invention relates to the technical field of water conservancy and hydropower engineering, and particularly relates to a calculation method for pipe-matrix water flow exchange based on karst fissure development. Background Technique

[0002] Due to corrosion, the karst aquifer forms a complex pipe-fissure dual-medium structure, which has the characteristics of coexistence of slow fissure flow and fast pipe flow, mutual conversion between laminar flow and turbulent flow, and alternating recharge between the fissure system and the pipe system. Therefore, the water volume exchange relationship between the karst pipe and the surrounding bedrock fissures makes the hydrological process characteristics of the karst pipe-fissure matrix dual-medium exchange flow very complex. Regarding the calculation of the water flow exchange volume of the karst pipe-matrix dual-medium, traditional models usually assume that a linear equation (Darcy's law) or a non-linear equation with a fixed power exponent is used to quantitatively describe the exchange flow, that is, the water volume exchange is proportional to the difference between the pipe head and the fissure matrix head or proportional to the square root. In areas with developed karst wide fissures, local turbulent flow sections can be formed, and the exchange flow has a non-linear flow state. Therefore, using a linear equation (Darcy's law) or a non-linear equation with a fixed power exponent to quantitatively describe the pipe-matrix dual-medium exchange flow in traditional models cannot fully reflect the water volume exchange relationship with the surrounding pipes under different karst wide fissure development conditions, resulting in inaccurate calculation of the exchange volume and difficulty in characterizing the karst aquifer pipe-matrix dual-medium exchange flow process. Aiming at the problem of how to characterize the hydrodynamic characteristics and exchange flow law of the karst pipe-matrix dual-medium exchange flow under different karst width fissure conditions, proposing a method for calculating the karst pipe-matrix exchange flow using a non-linear equation based on the developed karst wide fissure conditions is one of the most effective ways to solve this problem.

[0003] Previous studies have been carried out on the exchange flow of the pipe-matrix dual medium as linear Darcy flow and certain results have been achieved. Niu Zihao et al. in their research "Tracer Test Study on Water Flow Exchange between Fracture-Pipe Media under Different Recharge Conditions" aimed to explore the water flow exchange between fracture-pipe media under different recharge methods in a karst aquifer system. They conducted visual observations in the laboratory with the help of a high-precision camera and a colored tracer, and designed multiple groups of experiments to discuss the water flow exchange under three recharge methods: separate recharge to fractures, combined recharge, and separate simultaneous recharge of fractures and sinkholes. The results show that the influence of the sinkhole on the diffusion of fracture water decreases with the increase in the distance between the fracture and the sinkhole. Compared with the combined recharge situation, the sinkhole has a greater influence on the diffusion of fracture water in the case of separate recharge to fractures. When the recharge water volumes of the fracture and the sinkhole are the same in the case of separate simultaneous recharge, only unidirectional recharge from the fracture to the sinkhole is presented. This experiment studied the exchange flow under different recharge conditions based on the assumption of a linear equation (Darcy's law), ignoring the widespread phenomenon of pipe-fracture flow exchange in areas with developed karst wide fractures, resulting in a turbulent section and non-linear flow in the exchange flow, and unable to correctly reflect the water volume exchange relationship between the pipe and the surrounding bedrock fractures.

[0004] Shu Longcang et al. in their research "Hydrological Effects of the Heterogeneity of Pipe-Fracture Karst Aquifer Media" carried out indoor simulation experiments on the hydrological process through the SWMM model and studied the influence of the heterogeneity of pipe-fracture karst aquifer media on the system's hydrological process. The results show that the pipe size, the porosity of the aquifer medium, and the water volume exchange coefficient between groundwater and surface water have little influence on the water level and flow process at the system outlet, but the pipe size has a certain control effect on the highest groundwater level. The porosity of the aquifer medium has a certain influence on the growth and decline process of the groundwater level, and the water volume exchange coefficient between groundwater and surface water has an important influence on the change rate of the groundwater level and the maximum value it can reach. However, as a traditional model, the SWMM model quantitatively describes the exchange flow of the pipe-matrix dual medium by using a linear equation, defaulting that the exchange flow belongs to Darcy flow and lacking consideration of the non-linear flow state of the exchange flow in the case of developed karst wide fractures.

[0005] Chang Yong's "Analysis and Simulation of Karst Spring Hydrological Processes in the Fracture-Pipeline Dual Structure" proposed a new water tank-CFP combined model. The water tank was used to reflect the hydrological processes in the epikarst zone, and the CFP model was used to simulate the hydrological processes in the saturated zone. The simulation results also showed that the model could well simulate the dynamic change process of Spring S31 under different rainfall conditions. During heavy rainstorms, more than 33.6% of the rainfall was directly recharged into the pipeline in the form of concentrated recharge after being regulated by the epikarst zone. As a calculation module for calculating the exchange flow of the pipe-fracture matrix dual medium in the MODFLOW numerical simulation software, the CFP model can characterize the hydrodynamic property differences between the pipe-fracture dual media. However, based on the Darcy flow hypothesis, the CFP model calculates the water flow exchange volume between the fracture-pipeline media, ignoring the extensive pipe-fracture flow exchange phenomenon between the pipeline and the fracture matrix when karst wide fractures develop, resulting in a turbulent section where the exchange flow has a non-linear flow state, thus making the calculation of the exchange volume inaccurate.

[0006] Wang Xi et al.'s "Experimental Study on the Relationship between the Regulation Coefficient and Recharge Intensity of Fracture-Pipeline Media" aimed to explore the influencing mechanism of the regulation function of fracture-pipeline media. By establishing a physical model of fracture-pipeline media, the relationship between the regulation coefficient and recharge intensity of the model under different recharge methods was analyzed. The results showed that as the recharge intensity increased, the regulation coefficient gradually increased. In the case of single recharge to fractures, the regulation coefficient and recharge intensity showed an exponential increase trend. When recharging the sinkhole alone or jointly recharging fractures and sinkholes, the regulation coefficient and recharge intensity showed a linear increase trend. However, this experiment studied the relationship between the regulation coefficient and recharge intensity of fracture-pipeline media on the premise that the pipe-matrix dual medium exchange flow is a linear equation, without considering that local turbulent sections can form in areas with developed karst wide fractures, where the exchange flow has a non-linear flow state at this time.

[0007] Sun Chen et al.'s "Experimental Study and Numerical Simulation on the Spring Discharge Attenuation Process of Fracture-Pipeline Media" used a self-developed physical model of fracture-pipeline media to simulate the spring discharge attenuation process of karst fracture-pipeline media, and designed multiple groups of experiments to explore the influence of different factors on the spring discharge attenuation process. The experimental results showed that the attenuation process was divided into 3 sub-dynamics with the change of the water release medium, that is, the magnitude of the attenuation coefficient was mainly affected by the spring orifice size, recharge state, and initial water storage state of the water-bearing medium. The self-developed physical model mainly studied the influence of different factors on the spring discharge attenuation process, and quantitatively described the pipe-fracture matrix dual medium exchange flow by a linear equation. However, in the case of developed wide fractures, the exchange flow has a non-linear flow state, and its law is not applicable to be described by a linear equation.

[0008] Shu Longcang et al., "Hydrogeological Simulation Experiment of Spring Basin with Fracture-Pipeline Medium". In order to deeply understand the influencing factors and action mechanisms of the flow process in the karst spring basin, a physical model and a numerical model of the fracture-pipeline medium at the laboratory scale were established based on the hydrogeological conceptual model of the southwest karst spring basin. The recharge rainfall intensity, the diameter of the spring outlet, and the positions of the sinkhole and the production well were selected as the influencing factors, and the spring flow process was simulated. The experimental results show that three stages, namely, the increase, stable fluctuation, and attenuation of the spring flow, can be observed in a single precipitation experiment. Under the condition of the same spring outlet diameter, the influence of the recharge intensity on the attenuation coefficient of the spring flow is extremely small, and the attenuation coefficients corresponding to the spring outlet diameters of 3, 4, 5, 6, and 7 mm are 0.0036, 0.0067, 0.0115, and 0.0129, respectively. However, the dual-medium exchange flow between the pipeline and the fracture matrix in this physical model and numerical model is quantitatively described based on a linear equation, ignoring the extensive pipeline-fracture flow exchange phenomenon that exists between the pipeline and the fracture matrix when wide fractures develop, resulting in a turbulent section and non-linear flow state of the exchange flow, thus leading to inaccurate calculations.

[0009] In summary, the literature research shows that the experiments are all based on the assumption of a linear equation (Darcy's law) to study the dual-medium exchange flow between the pipeline and the fracture, ignoring that local turbulent sections can be formed in areas with developed karst wide fractures and the non-linear flow state of the exchange flow. Therefore, the experiments that quantitatively describe the exchange flow based on Darcy's law cannot accurately characterize the water volume exchange process between the pipeline and the surrounding bedrock fractures.

[0010] Some scholars found that Darcy's law is not applicable to the exchange flow during the study of the dual-medium exchange flow between the pipeline and the fracture matrix. Sun Huan et al., "Experimental Study on the Nonlinear Flow Characteristics of Pipeline-Fracture Water during the Fracture Process of Carbonate Rock", focused on the study of the microscopic seepage characteristics and fracture mechanisms of carbonate rock, carried out a visualization experiment on the flow of pipeline-fracture water during the rock fracture process, quantitatively analyzed the flow state evolution process of the transition from pipeline fluid to fracture fluid based on the experimental results at the rock block scale, and studied the influence of multi-level loads on the flow characteristics of pipeline-fracture water. The experimental results show that the flow state stability of carbonate rock is related to the fracture state. At the initial stage of the pipe wall damage, the pipeline flow is mainly laminar flow, and the local pipe wall splitting causes the time-domain flow state alternation of the pipeline fluid. The precursor characteristics of the transformation of the pipeline fluid to the fracture fluid are mainly manifested as the critical conversion point of the transitional flow state. This study considered the existence of non-Darcy flow in the dual-medium exchange flow between the pipeline and the fracture matrix, but did not carry out relevant research on the method for calculating the exchange flow, and did not consider the influence of the change in the permeability coefficient on the exchange flow when there are different degrees of wide fractures in the karst.

[0011] Liangjie Zhao, "Research on the Flow Exchange Mechanism of Karst Fracture-Pipe Dual Aquifer Media", designed a physical model for the hydrodynamic simulation of karst pipes and bedrock fracture media, proposed 6 groups of pipe-fracture combination modes, quantitatively studied the hydrodynamic characteristics of bedrock fractures and karst pipes and the flow exchange law between media under different flow states, and through multiple groups of experiments and regression analysis, it was concluded that the flow exchange volume is proportional to the square root of the head difference, and the power exponent of this nonlinear formula is a fixed value of 0.5. This physical model considered the existence of non-Darcy flow in the exchange flow of the pipe-fracture matrix dual media, and through fitting calculation, it was concluded that the flow exchange volume is proportional to the square root of the head difference between the pipe and the fracture matrix, and the power exponent of the nonlinear formula is a fixed value of 0.5.

[0012] However, in the case of different widths of karst fractures, the present invention found that as the fracture width increases, the flow velocity of the exchange flow gradually increases, and the flow regime gradually changes from laminar flow to turbulent flow. The power exponent (nonlinearity n) of the head difference between the corresponding pipe and the fracture matrix gradually decreases from 1 (when the exchange flow is completely in the laminar flow state). When the flow regime of the exchange flow is completely transformed into turbulent flow, based on the Forchheimer turbulent flow law, the power exponent (nonlinearity n) is 0.5 (when the exchange flow is completely in the turbulent flow state). This experiment did not study the exchange flow in the case of well-developed fractures forming wide fractures, that is, in the case of different widths of fractures, different permeability coefficients result in different values of the nonlinearity n of the exchange flow, and the nonlinear formula of the pipe-fracture matrix dual media exchange flow is also different. The value of n is determined by the hydrogeological conditions of the pipe-fracture system around the exchange flow area. The smaller the permeability coefficient, the closer the value is to 1; the larger the permeability coefficient, the closer the value is to 0.5. Therefore, the power exponent n in the exchange flow formula of the pipe-fracture matrix dual media should not be a fixed value of 0.5, but a variable value n (0.5 ≤ n ≤ 1).

[0013] In summary, the literature research shows that previous studies on the exchange flow of pipe-fracture matrix dual media found the existence of non-Darcy flow and improved the linear exchange flow formula into a nonlinear formula with a fixed power exponent of 0.5, but ignored that in the case of different widths of karst fractures, with the change of the permeability coefficient, the nonlinearity n value of the nonlinear formula will also change, rather than a fixed value of 0.5.

[0014] In summary, in the case where karst fissures are fully developed to form wide fissures, the existing research methods for the exchange flow of pipe-fissure matrix dual media are difficult to effectively and accurately calculate the water flow exchange. The methods are mainly divided into two categories. The first category is to use the "linear equation" method to quantitatively describe the exchange flow of pipe-fissure matrix dual media. This method does not consider the non-linear flow situation of the exchange flow, and both physical experiments and numerical simulations are carried out based on the condition that the exchange flow is a linear flow. The second category is that during the research process, it is found that there is a non-Darcy flow phenomenon in the exchange flow, and the linear formula is improved so that the power exponent of the water head difference between the pipe and the fissure matrix in the water flow exchange is a fixed value of 0.5. However, it is ignored that in the case of different widths of karst fissures, the value of the non-linearity n changes with the different widths of the fissures. Obviously, in the case of wide karst fissure development, there is an urgent need for a method that can accurately describe the hydrodynamic characteristics of the karst pipe-matrix dual media exchange flow and the law of the exchange flow. Summary of the Invention

[0015] Aiming at the problems in the prior art, the present invention provides a method for calculating the pipe-matrix water flow exchange based on karst fissure development, which can accurately describe the hydrodynamic characteristics of the karst pipe-matrix dual media exchange flow and the law of the exchange flow. The specific technical solutions are as follows:

[0016] A method for calculating the pipe-matrix water flow exchange based on karst fissure development includes the following steps:

[0017] Step S1, establishing a physical experiment model of karst pipe-fissure dual media, the physical experiment model includes:

[0018] A model box body, with an inlet pipe and an outlet pipe respectively arranged on two opposite sides of the model box body;

[0019] A water supply tank, which is fixed on a vertical electric sliding table module, can adjust the height of the water supply tank through the vertical electric sliding table module to control the water supply intensity, and can be fixed at a certain height to maintain a stable water head;

[0020] A water pump, which is connected to the water supply tank;

[0021] A pipe, which is communicated with the water supply tank and sequentially passes through the inlet pipe and the outlet pipe of the model box body; a number of first exchange holes are evenly arranged on the pipe;

[0022] Several quartz sand containers, and several of the quartz sand containers can be arranged in a model box if necessary, and are closely arranged on both sides and above the pipeline. By placing gaskets with different thicknesses between adjacent two quartz sand containers and pasting and fixing them, a fracture network with different permeability coefficients is simulated; the quartz sand containers are cuboids, and a number of second exchange holes are evenly arranged on all 6 faces; several rotary sprinklers, and several of the rotary sprinklers are evenly arranged above the model box, and the rotary sprinklers are communicated with a water supply tank through a plastic pipe network;

[0023] A data acquisition system, the data acquisition system includes 3m pressure sensors, flow meters, a data conversion module, and a host computer. Specifically, m pressure sensors are evenly arranged at the bottom of the pipeline, and m pressure sensors are evenly and symmetrically arranged at the bottom of the quartz sand containers on the left and right sides of the pipeline respectively, and the m pressure sensors on the left and right sides of the pipeline are symmetric with respect to the m pressure sensors at the bottom of the pipeline respectively; the flow meters are arranged at the inlet and outlet of the pipeline; the data conversion module is electrically connected to the pressure sensors, flow meters, and host computer respectively;

[0024] Step S2, set several experimental groups with different fracture widths; turn on the water pump to simulate single-point confluence recharge of a sinkhole, and the water supply intensity is constant within a single experiment; wherein changing the fracture width means changing the thickness of the gasket between adjacent two quartz sand containers;

[0025] Step S3, the data acquisition system collects the pressure value at the bottom of the pipeline, the pressure value at the bottom of the quartz sand container, and the flow values at the inlet and outlet of the pipeline, and calculates the head difference between the pipeline and the fracture matrix according to the collected pressure value at the bottom of the pipeline and the pressure value at the bottom of the quartz sand container, and obtains the exchange flow value between the pipeline and the fracture according to the flow values at the inlet and outlet of the pipeline; based on the obtained head difference between the pipeline and the fracture matrix and the exchange flow value between the pipeline and the fracture, use the regression analysis method for fitting, calculate the regression equation of the fitting curve under the conditions of each experimental group, and determine the non-linearity degree n of each experimental group i , where i represents the number of experimental groups; based on the different degrees of karst fracture development, different non-linearity degree values n are obtained i , so the exchange flow formula for each experimental group is as follows:

[0026]

[0027] Among them, Q exi represents the exchange flow calculated for the i-th experimental group; H ci represents the pipeline head calculated for the i-th experimental group; H mi represents the fracture head calculated for the i-th experimental group; α is the water volume exchange coefficient.

[0028] Preferably, the aperture of the first exchange hole on the pipeline in step S1 is 4.5 - 5.5 mm, the center distance is 9.5 mm - 10.5 mm, and the outer wall of the pipeline is wrapped with a steel wire filter screen with an aperture of 1.5 - 2.5 mm.

[0029] Preferably, the particle size of the quartz sand contained in the quartz sand container in step S1 is 2.8 - 3.2 mm.

[0030] Preferably, the size of the quartz sand container in step S1 is 4.5 - 5.5 cm × 4.5 - 5.5 cm × 4.5 - 5.5 cm, and a number of second exchange holes with an aperture of 0.8 - 1.2 mm are uniformly arranged on 6 faces; the inner wall of the quartz sand container includes a steel wire filter screen with an aperture of 0.8 - 1.2 mm.

[0031] Preferably, calculating the water head difference between the pipeline and the fracture matrix according to the pressure value at the bottom of the pipeline and the pressure value at the bottom of the quartz sand container collected in step S4 specifically includes the following:

[0032] Suppose that m pressure sensors at the bottom of the pipeline are on the same straight line, and the sequence of collected pressure values is P g =[P g1 , P g2 , P g3 , …, P gm ; m pressure sensors on the left side of the pipeline are on the same straight line, and the sequence of collected pressure values is P l =[P l1 , P l2 , P l3 , …, P lm , m pressure sensors on the right side of the pipeline are on the same straight line, and the sequence of collected pressure values is P r =[P r1 , P r2 , P r3 , …, P rm ; the flow rate data collected by the flow meter set at the inlet of the pipeline is Q 0 , assuming that flow meters are also respectively set before the outlet of the pipeline and after each pressure sensor, then the data collected by the flow meters are Q 1 , Q 2 , Q 3 …, Q m ;

[0033] The calculation formula for the pipeline water head is: The calculation formula for the fracture water head is: The exchange flow Q exi =Q 0 -Q m ;

[0034] In the i-th group of experiments, the exchange flow formula at the m pressure sensors at the bottom of the pipeline is as follows:

[0035]

[0036] Preferably, the calculation method of the water volume exchange coefficient α is as follows:

[0037]

[0038] Where K is the number of connected pipelines; K w is the pipeline wall permeability coefficient; d k is the diameter of the k-th pipeline; Δl k is the straight-line length between the two pipeline nodes of the connected pipelines k; r k is the radius of the k-th pipeline; τ k is the tortuosity of the k-th pipeline.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] Compared with previous methods that used linear equations (Darcy's law) or non-linear equations with fixed power exponents to calculate the water flow exchange in karst conduit-fissure matrix dual media, while ignoring the non-linear exchange flow between the conduit and the fissure matrix that changes with the fissure width when there are karst fissures of different widths, resulting in inaccurate calculation of the exchange volume and difficulty in characterizing the hydrodynamic characteristics of the exchange flow and the hydrological process of the exchange flow. The method for calculating the conduit-matrix water flow exchange based on karst fissure development proposed in the present invention has two advantages. On the one hand, it fully considers that the exchange flow has different flow states and follows the hydrological process of the conduit-fissure matrix exchange flow in the case of wide karst fissures. Compared with the traditional assumption based on Darcy's law, which defaults the exchange flow of the conduit-fissure matrix dual media to be linear Darcy flow, the present invention is based on physical experimental data (width of the fissure matrix, conduit outlet flow rate, rainfall recharge intensity, sinkhole recharge intensity, conduit water head and fissure water head), and uses the regression analysis method to fit the experimental data to obtain the non-linearity n of the conduit-matrix water flow exchange formula, thereby determining the specific non-linear exchange flow formula. This formula not only considers that when the fissure development is insufficient and there are no wide fissures, the exchange flow is linear Darcy flow, that is, the non-linearity n = 1. It also considers that in the case of wide fissure development, the flow state of the exchange flow is non-Darcy flow, that is, the non-linearity 0.5 ≤ n < 1. On the other hand, based on the exchange flow rate data results obtained from physical experiments under different widths of karst fissures, the regression analysis method is used to fit the exchange flow rate data to obtain the specific non-linear exchange flow formula, and it is determined that the power exponent (non-linearity n) of the water head difference between the conduit and the fissure matrix changes with the different widths of karst fissures. Therefore, the proposed non-linear exchange flow calculation method makes the calculation of the conduit-matrix water flow exchange more accurate, and plays an important role in karst water resource evaluation and karst water resource development. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to actual scale.

[0042] Figure 1 It is the flowchart of the method of the present invention;

[0043] Figure 2 It is the schematic diagram of the physical experiment model of karst conduit-fissure dual media;

[0044] Figure 3 It is the schematic diagram of the physical model;

[0045] Figure 4 It is the layout diagram of the pressure sensors;

[0046] Figure 5 It is a front view schematic diagram of an acrylic box;

[0047] Figure 6 It is a scatter plot and fitting curve of water flow exchange volume and water head difference for the standard control group and the wide crack experimental group;

[0048] Figure 7 It is the measured flow rate and simulation results: (a) 0.5 mm wide crack group; (b) 1.0 mm wide crack group; (c) 1.5 mm wide crack group. Specific implementation manners

[0049] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0050] It should be understood that when used in this specification and the appended claims, the terms "include" and "comprise" indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their combinations.

[0051] It should also be understood that the terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0052] It should be further understood that the term "and / or" used in the specification of the present invention and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0053] In view of the problem of how to characterize the hydrodynamic characteristics and the exchange flow law of the karst conduit-matrix dual medium exchange flow under the condition of wide fissure development in karst, the present invention proposes a method for calculating the karst conduit-matrix exchange flow using a non-linear formula based on the condition of wide fissure development in karst. By designing an indoor physical experiment model of conduit-fissure matrix, wherein, the water head difference and exchange volume data between the conduit and the fissure matrix are obtained through point-like experiments, and the non-linear exchange flow formula is obtained by fitting through regression analysis. The proposed non-linear exchange flow formula is verified through surface experiments, revealing the law of the conduit-fissure matrix dual medium exchange flow under the condition of different widths of fissure development in karst, finding the phenomenon of non-linear flow in the conduit-fissure matrix exchange flow, proposing a formula for non-linear conduit-fissure matrix exchange flow, and improving the CFP numerical model based on the proposed non-linear exchange flow formula, and verifying the accuracy of the improved CFP numerical model using the indoor physical experiment model. The present invention will be further described in conjunction with the accompanying drawings as follows:

[0054] As Figure 1 shown, this embodiment provides a method for calculating the water flow exchange between a conduit and a matrix based on karst fissure development, including the following steps:

[0055] Step S1, establish a physical experiment model of the karst conduit-fissure dual medium, and the principle of the physical experiment model is as Figure 2 shown.

[0056] As Figure 3 shown in the schematic diagram of the physical experiment model, the physical experiment model includes a model box body, a water supply tank, a water pump, a conduit, a plurality of quartz sand containers, a plurality of rotary nozzles, and a data acquisition system.

[0057] Inlet pipes and outlet pipes are respectively arranged on two opposite sides of the model box body. The water supply tank is fixed on the vertical electric sliding table module, and the height of the water supply tank can be adjusted through the vertical electric sliding table module to control the water supply intensity, and it can be fixed at a certain height to maintain the stability of the water head. The water pump is connected to the water supply tank, and the water supply tank is kept in an overflow state during the water supply by the water pump, and the water flows out through the overflow tank and can be circulated by the water pump. The pipeline is communicated with the water supply tank and sequentially passes through the inlet pipe and the outlet pipe of the model box body; a number of first exchange holes are uniformly arranged on the pipeline. A number of quartz sand containers can be arranged in the model box body when necessary, and are closely arranged on both sides and above the pipeline. By placing gaskets with different thicknesses between adjacent two quartz sand containers and pasting and fixing them, a fracture network with different permeability coefficients is simulated; the quartz sand containers are cuboids, and a number of second exchange holes are uniformly arranged on all 6 faces. A number of rotating nozzles are uniformly arranged above the model box body, and the rotating nozzles are communicated with the water supply tank through a plastic pipe network. The data acquisition system includes 3m pressure sensors, flow meters, a data conversion module and a host computer. Specifically, m pressure sensors are uniformly arranged at the bottom of the pipeline, m pressure sensors are uniformly and symmetrically arranged at the bottom of the quartz sand containers on the left and right sides of the pipeline respectively, and the m pressure sensors on the left and right sides of the pipeline are symmetric with respect to the m pressure sensors at the bottom of the pipeline respectively; the flow meters are arranged at the inlet pipe and the outlet pipe of the pipeline; the data conversion module is electrically connected to the pressure sensors, the flow meters and the host computer respectively.

[0058] In this embodiment, the fractured matrix filled in the quartz sand container is homogeneous quartz fine sand with a particle size of 3.0 mm. The first exchange holes of the pipeline are opened in a plum blossom shape, with a hole diameter of 5 mm and a center distance of 10 mm. The outer wall of the pipeline is wrapped with a steel wire filter screen with a hole diameter of 2 mm to prevent quartz sand from infiltrating into the pipe. The permeability of the filter screen and the pipeline opening is much greater than that of the quartz sand to ensure that the permeability coefficient of the pipeline wall will not be affected.

[0059] In this embodiment, the quartz sand container is an organic glass box, the size of the organic glass box is 5 cm × 5 cm × 5 cm, and 25 small holes with a diameter of 1 mm are uniformly arranged on 6 faces. The plan view of the organic glass box is as Figure 5 shown, and the inner wall is wrapped with a steel wire filter screen with a hole diameter of 1 mm to prevent quartz sand from infiltrating into the glass box. The permeability of the filter screen and the opening of the glass box is much greater than that of the quartz sand to ensure that the permeability coefficient of the quartz sand will not be affected.

[0060] 25 rotating nozzles are arranged, which are located 0.4 - 0.7 m above the model box body. Specifically, 0.5 m can be selected. This height can ensure that the precipitation on the aquifer is evenly distributed and will not deviate from the physical model. In the present invention, the intensity of the areal recharge rainfall is set to be constant during the simulated rainfall.

[0061] In this embodiment, m = 5, that is, 15 MIK-P300 diffused silicon pressure sensors are used, as Figure 4As shown, 5 pressure sensors are arranged at the bottom of the pipeline, and 5 pressure sensors are set on each of the left and right sides of the pipeline, forming a 3×5 pressure sensor matrix. The distribution of the pressure sensors and the flowmeter is as Figure 4 shown. The flowmeter uses a turbine flowmeter, and the data conversion module uses a 16-channel paperless recorder (MIK-R5000C), which can be converted into digital signals in real time and imported into the upper computer, and can directly draw real-time curves.

[0062] Step S2: Set several experimental groups with different fracture widths; turn on the water pump to simulate the single-point confluence recharge of the sinkhole, and keep the water supply intensity constant within a single experiment; where changing the fracture width means changing the thickness of the gasket between adjacent quartz sand containers.

[0063] The present invention sets up a standard control group experiment so that the exchange flow of the control group experiment is in the state of Darcy flow. Therefore, the filled fracture matrix is homogeneous quartz fine sand with a particle size of 3.0 mm. Measure the diameter of a single pipeline, the width of the fracture spacing, and the matrix diameter in the physical model, and use the Darcy experiment to measure the permeability coefficient of the fracture matrix. The permeability coefficient measured by the Darcy experiment is about 0.0028 m / d. When filling the quartz sand, compact it tightly so that the matrix part composed of quartz sand can be regarded as a homogeneous condition.

[0064] Set up four wide-fracture experimental groups, namely the standard control group, the 0.5-mm-width fracture group, the 1.0-mm-width fracture group, and the 1.5-mm-width fracture group. That is, place gaskets with thicknesses of 0.5 mm, 1.0 mm, and 1.5 mm between the plexiglass boxes and reinforce them. Among them, the standard control group does not set plexiglass boxes; the experimental groups with fractures of different widths are filled with 3.0-mm quartz sand same as the fracture matrix in the plexiglass boxes. The recharge source is the single-point confluence recharge of the sinkhole, and the water supply intensity is constant within a single experiment. And stop the water supply when the water head value of the pipeline is equal to the water head value of the bedrock fractures on the left and right sides, that is, stop the water supply when the values of the corresponding pressure sensors on both sides of the pipeline are the same. The entire hydrological process is divided into two stages: ① During the sinkhole recharge period, the pipeline recharges the fracture, and at this time the water head of the pipeline is higher than the water head of the fracture matrix. ② After the water supply stops, the fracture recharges the pipeline, and at this time the water head of the fracture matrix is higher than the water head of the pipeline.

[0065] Step S3: The data acquisition system collects the pressure at the bottom of the pipeline, the pressure at the bottom of the quartz sand container, and the flow values at the inlet and outlet of the pipeline, and calculates the water head difference between the pipeline and the fracture matrix according to the collected pressure values at the bottom of the pipeline and the bottom of the quartz sand container, and obtains the exchange flow value between the pipeline and the fracture according to the flow values at the inlet and outlet of the pipeline; based on the obtained water head difference between the pipeline and the fracture matrix and the exchange flow value between the pipeline and the fracture, use the regression analysis method for fitting, calculate the regression equation of the fitting curve under the conditions of each experimental group, and determine the non-linearity n of each experimental group i, where \(i\) represents the number of experimental groups; based on different karst fissure widths, different non-linearity values \(n\) are obtained i , and the exchange flow formulas for each experimental group are obtained as follows:

[0066]

[0067] Among them, \(Q\) exi represents the exchange flow rate calculated for the \(i\)-th experimental group; \(H\) ci represents the pipeline water head calculated for the \(i\)-th experimental group; \(H\) mi represents the fissure water head calculated for the \(i\)-th experimental group; \(\alpha\) is the water volume exchange coefficient.

[0068] The calculation formula for the water volume exchange coefficient \(\alpha\) is as follows:

[0069]

[0070] Among them, \(K\) is the number of connected pipelines; \(K\) w is the pipeline wall permeability coefficient. In the present invention, the pipeline wall permeability coefficient \(K\) w is obtained through the internal structure of the pipeline. To ensure that the \(K\) w coefficient does not affect the drainage process from the fissure system to the pipeline, this parameter is taken as a relatively large value of \(0.00833\ m / s\) to eliminate the influence of the exchange coefficient on the water volume exchange between the fissure system and the pipeline system, \(L / T\); \(d\) k is the diameter of the \(k\)-th pipeline, \(L\); \(\Delta l\) k is the straight-line length between two pipeline nodes of the connected pipelines \(k\), \(L\); \(r\) k is the radius of the \(k\)-th pipeline, \(L\); \(\tau\) k is the tortuosity of the \(k\)-th pipeline.

[0071] According to the pressure values collected at the bottom of the pipeline and the pressure values at the bottom of the quartz sand container, the water head difference between the pipeline and the fissure matrix is calculated, specifically including the following:

[0072] Suppose \(m\) pressure sensors at the bottom of the pipeline are on the same straight line, and the sequence of collected pressure values is \(P\) g =\([P\) g1 , \(P\) g2 , \(P\) g3 , …, \(P\) gm ; \(m\) pressure sensors on the left side of the pipeline are on the same straight line, and the sequence of collected pressure values is \(P\) l =\([P\) l1 , \(P\) l2 , \(P\) l3 , …, \(P\) lm , and \(m\) pressure sensors on the right side of the pipeline are on the same straight line, and the sequence of collected pressure values is \(P\) r =\([P\) r1 , \(P\) r2, P r3 , …, P rm ; The flow rate data collected by the flow meter set at the inlet of the pipeline is Q 0 , and the flow rate data collected by the flow meter set at the outlet of the pipeline is Q m+1 , assuming that flow meters are also respectively set before the outlet on the pipeline and after each pressure sensor, then the data collected by the flow meters are respectively Q 1 , Q 2 , Q 3 …, Q m-1 ;

[0073] The calculation formula for the pipeline water head is: The calculation formula for the fissure water head is: In the i-th group of experiments, the exchange flow formula at m pressure sensors at the bottom of the pipeline is:

[0074]

[0075] Calculate the regression equation of the fitting curve under the conditions of each experimental group, and determine the non-linearity n 1 = 1, n 2 = 0.797, n 3 = 0.711 and n 4 = 0.582, and the fitting results are as Figure 6 shown. It can be seen that the non-linearity n of the exchange flow formula with different fissure widths is different and is not a fixed value of 0.5.

[0076] This embodiment further includes step S4. In this embodiment, the water pump is turned on to simulate single rainfall surface recharge with a constant rainfall intensity, and the karst sinkhole confluence point recharge is not set, and the remaining experimental conditions are the same as those in step S2. This step is used to verify the calculation accuracy of the method provided in this embodiment.

[0077] In the surface experiment scenario, the recharge method for each group of experiments is single rainfall surface recharge with a constant rainfall intensity of 0.0025 mm / s, the karst sinkhole confluence point recharge is not set, and four groups of wide fissure experimental groups are set, namely the standard control group, the 0.5 mm width fissure group, the 1.0 mm width fissure group, and the 1.5 mm width fissure group, that is, gaskets with widths of 0.5 mm, 1.0 mm, and 1.5 mm are respectively placed between the plexiglass boxes and reinforced. Among them, the standard control group does not set plexiglass boxes; the experimental groups with different widths of fissure development are that the plexiglass boxes are filled with 3.0 mm quartz sand the same as the fissure matrix, and the remaining experimental conditions are the same as those in the point experiment.

[0078] Step S5, based on the experimental conditions of each group in step S4, run the numerical simulation software CFP to obtain the original CFP result data of each group; as Figure 7 shown.

[0079] Step S6: Modify the non - linearity value n in the source code of the computational exchange flow module of the numerical simulation software CFP i , and based on the experimental conditions in Step S5, run the numerical simulation software CFP to obtain the improved CFP result data for each group. The improved CFP result data for each group is as Figure 7 shown.

[0080] The modification steps are as follows: ① SUBROUTINE CFPBCF7BDCH, SUBROUTINE CFPLPF7 BDCH, and SUBROUTINE CFPHUF7BDCH are all for calculating the exchange volume between the pipeline unit and the constant - head unit. In the program, hdiff is the head difference. Add a real - number variable n and introduce a variable hh to control the positive and negative. Modify hdiff to DABS(hdiff)**n*hh. Determine whether the positive and negative change after the exchange volume is changed through IF(hdiff.GT.0). If they are inconsistent, change the positive and negative of hh to make it consistent with the original program. ② In the SUBROUTINE CON1FM head - calculation subroutine, SUBROUTINE F_X0 pipeline - flow equation iterative - calculation subroutine, and SUBROUTINE GWF2CFP1BD pipeline - equilibrium subroutine, B_MAT is the pipeline - node head and Hnew is the MODFLOW cell head. Introduce a variable hh to control the positive and negative. Modify B_MAT - Hnew to DABS(B_MAT - Hnew)**n*hh. Determine whether the positive and negative change after the exchange volume is changed through IF(hdiff.GT.0). If they are inconsistent, change the positive and negative of hh to make it consistent with the original program.

[0081] Step S7: Compare the original CFP result data for each group with the improved CFP result data for each group and calculate the improvement in accuracy.

[0082] Compare the experimental results of each group in the areal experiment, the original CFP results of each group, and the improved CFP simulation results of each group. And calculate the improved accuracy based on the coefficient of determination (R 2 ), Nash - Sutcliffe efficiency coefficient (NSE), root - mean - square error (RMSE), and percentage bias (PBIAS) formulas. The results are shown in Table 1.

[0083] Among them, the calculation formula for the coefficient of determination R 2 is as follows:

[0084]

[0085] Among them, J is the number of data - collection points, Q g (j) is the actual measured j - th observed flow rate, Q s(j) is the j-th simulated flow obtained by CFP simulation, which are the means of the observed flow and the simulated flow respectively. The coefficient of determination R 2 is generally used to reflect the regression fitting degree of the regression model. The closer it is to 1, the better the fitting degree.

[0086] The calculation formula of the Nash-Sutcliffe efficiency coefficient NSE is as follows:

[0087]

[0088] The Nash-Sutcliffe efficiency coefficient NSE is used to verify the quality of the simulation results of the hydrological model. The closer it is to 1, the better the fitting degree.

[0089] The calculation method of the root mean square error RMSE is as follows:

[0090]

[0091] The root mean square error RMSE is used to measure the deviation between the observed value and the true value. The smaller the value, the better.

[0092] The calculation method of the percentage bias PBIAS is as follows:

[0093]

[0094] The percentage bias PBIAS, also known as the relative error, reflects the deviation between the simulated cumulative value and the measured cumulative value.

[0095] In the experimental group of the uniform distribution mode, by comparing the evaluation indexes in the table, it can be seen that the simulation accuracy of the improved CFP model is higher than that of the original CFP model. Among them, the coefficient of determination and the Nash-Sutcliffe efficiency coefficient are increased by 0.11 and 0.12 on average, and the root mean square error and the percentage bias are reduced by 45% and 44% on average. By comparing the differences of the indexes of the two models, it shows that in the uniform distribution mode, as the fracture width increases, the average simulation accuracy improvement amplitude of the improved CFP model increases.

[0096] Table 1 Simulation accuracy before and after model improvement in each experimental group with a rainfall intensity of 0.0025 mm / s

[0097]

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered by the scope of the claims and the description of the present invention.

Claims

1. A method for calculating pipeline-matrix water flow exchange based on karst fissure development, characterized in that: The following steps are involved: Step S1, establishing a physical experimental model of karst pipe-crack dual medium, the physical experimental model includes: A model box, wherein a pipe inlet and a pipe outlet are respectively arranged on two opposite sides of the model box; A water supply tank, which is fixed on a vertical electric slide module, and the height of the water supply tank can be adjusted by the vertical electric slide module to control the water supply intensity, and can be fixed at a certain height to keep the water head stable; A water pump, wherein the water pump is connected to the water supply tank; A pipeline, the pipeline is connected to the water supply tank and passes through the pipe inlet and the pipe outlet of the model box in sequence; a plurality of first exchange holes are evenly arranged on the pipeline; A plurality of quartz sand containers are arranged in the model box and closely arranged on both sides and the top of the pipeline, and gaskets of different thicknesses are placed between two adjacent quartz sand containers and fixed by gluing to simulate fracture networks with different permeability coefficients; the quartz sand container is a rectangular parallelepiped, and a plurality of second exchange holes are evenly arranged on six faces; A plurality of rotating nozzles, wherein the plurality of rotating nozzles are evenly arranged above the model box body, and the rotating nozzles are connected to the water supply tank through a plastic pipe network; A data acquisition system, the data acquisition system includes 3m pressure sensors and flow meters, a data conversion module, and a host computer. Specifically, m pressure sensors are evenly arranged at the bottom of the pipeline, and m pressure sensors are evenly and symmetrically arranged at the bottom of the quartz sand containers on the left and right sides of the pipeline, and the m pressure sensors on the left and right sides of the pipeline are respectively symmetrical with the m pressure sensors at the bottom of the pipeline; the flow meter is arranged at the pipeline inlet and outlet; the data conversion module is electrically connected to the pressure sensor, the flow meter, and the host computer respectively; Step S2, setting up several experimental groups with different crack widths; turning on the water pump to simulate the point-like confluence recharge of a single sinkhole, and the water supply intensity is constant in a single experiment; wherein changing the crack width means changing the thickness of the gasket between two adjacent quartz sand containers; Step S3, the data acquisition system collects the pressure value at the bottom of the pipeline, the pressure value at the bottom of the quartz sand container, and the flow value at the pipeline inlet and outlet, and calculates the head difference between the pipeline and the fracture matrix according to the collected pressure value at the bottom of the pipeline and the pressure value at the bottom of the quartz sand container, and obtains the exchange flow value between the pipeline and the fracture according to the flow value at the pipeline inlet and outlet; based on the obtained head difference between the pipeline and the fracture matrix and the exchange flow value between the pipeline and the fracture, a regression analysis method is used for fitting, and the regression equation of the fitting curve under the conditions of each experimental group is calculated to determine the nonlinearity of each experimental group , where i represents the number of experimental groups; different nonlinear values ​​are obtained based on the different degrees of karst fissure development , so the exchange flow formula of each experimental group is as follows: ； in, represents the exchange flow calculated by the i-th experimental group; represents the pipe head calculated by the ith experimental group; represents the fracture water head calculated for the ith experimental group; is the water exchange coefficient.

2. A method for calculating pipeline-matrix water flow exchange based on karst fissure development according to claim 1, characterized in that: The first exchange hole on the pipeline in step S1 has a pore size of 4.5-5.5 mm, a center distance of 9.5 mm-10.5 mm, and the outer wall of the pipeline is wrapped with a steel wire filter with a pore size of 1.5-2.5 mm.

3. The method for calculating pipeline-matrix water flow exchange based on karst fissure development according to claim 1 is characterized in that: The particle size of the quartz sand contained in the quartz sand container in step S1 is 2.8-3.2 mm.

4. The method for calculating the pipe-matrix water flow exchange based on the development of karst fissures according to claim 1 is characterized in that: In step S1, the size of the quartz sand container is 4.5-5.5 cm×4.5-5.5 cm×4.5-5.5 cm, and a plurality of second exchange holes with a pore size of 0.8-1.2 mm are evenly arranged on 6 surfaces; the inner wall of the quartz sand container includes a steel wire filter with a pore size of 0.8-1.2 mm.

5. The method for calculating the pipe-matrix water flow exchange based on the development of karst fissures according to claim 1 is characterized in that: The step S3 calculates the water head difference between the pipeline and the fracture matrix according to the collected pressure value at the bottom of the pipeline and the pressure value at the bottom of the quartz sand container, and specifically includes the following: Assume that the m pressure sensors at the bottom of the pipeline are on the same straight line, and the pressure value sequence collected is ; The m pressure sensors on the left side of the pipeline are on the same straight line, and the pressure value sequence collected is , the m pressure sensors on the right side of the pipeline are on the same straight line, and the collected pressure value sequence is ; The flow data collected by the flow meter installed at the pipeline inlet is , assuming that a flow meter is provided before the outlet of the pipeline and after each pressure sensor, the data collected by the flow meter are ; The calculation formula for pipe head is: ; The calculation formula of fracture head is: ; Exchange flow in fractures ; In the i-th group of experiments, the exchange flow formula at the m pressure sensors at the bottom of the pipeline is: 。 6. A method for calculating pipeline-matrix water flow exchange based on karst fissure development according to claim 1 or 5, characterized in that: The water exchange coefficient The calculation method is as follows: ； in, is the number of connected pipes; is the pipe wall permeability coefficient; is the diameter of the kth pipe; is the length of the straight line connecting the two pipeline nodes between pipeline k; is the radius of the kth pipe; is the tortuosity of the kth pipe.

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