Pipeline-matrix water flow exchange calculation method based on karst fissure development

Abstract

A karst aquifer is composed of bedrock fissures, karst pipelines and other media, and an existing model generally assumes that a linear equation or a nonlinear equation with a fixed power exponent is adopted to quantitatively describe karst pipeline-matrix exchange flow according to the Darcy law. And a nonlinear exchange flow process existing in a pipeline-matrix under the development condition of different karst wide fractures cannot be reflected. In order to overcome the defects, the invention provides a karst fissure development-based pipeline-matrix water flow exchange calculation method. Different degrees of fracture development are simulated by designing indoor experiments, a nonlinear exchange flow equation Qex = alpha (Hc-Hm) n is proposed by fitting experimental data with a regression analysis method, the nonlinearity n changes according to different development of wide fractures, and the value range of the nonlinearity n is larger than or equal to 0.5 and smaller than or equal to 1. The CFP model is improved on the basis of the equation, compared with an original CFP model, the decisive coefficient (R2) and the Nash efficiency coefficient (NSE) of indoor experiment results designed through numerical simulation are improved by 11% and 12% respectively, and the root-mean-square error (RMSE) and the percentage deviation (PBIAS) are reduced by 45% and 44% respectively.

Description

Technical Field

[0001] The invention relates to the technical field of water conservancy and hydropower engineering, and in particular to a pipeline-matrix water flow exchange calculation method based on karst fissure development. Background Art

[0002] Karst aquifers have formed a complex conduit-fracture binary medium structure due to dissolution, which has the characteristics of coexistence of slow fracture flow and fast conduit flow, mutual conversion between laminar flow and turbulent flow, and alternating supply between fracture system and conduit system. Therefore, the water exchange relationship between karst conduits and surrounding bedrock fractures leads to very complex hydrological process characteristics of karst conduit-fracture matrix dual medium exchange flow. Regarding the calculation of water flow exchange in karst conduit-matrix dual medium, traditional models usually assume that linear equations (Darcy's law) or nonlinear equations with fixed power exponents are used to quantitatively describe the exchange flow, that is, the water exchange is proportional to the difference between the conduit head and the fracture matrix head or the square root of the relationship. In areas with wide karst fissures, local turbulent areas can be formed, and the exchange flow has nonlinear flow patterns. Therefore, the traditional model uses linear equations (Darcy's law) or nonlinear equations with fixed power exponents to quantitatively describe the pipe-matrix dual medium exchange flow, which cannot fully reflect the water exchange relationship between the surrounding pipes under different karst wide fissure development conditions, resulting in inaccurate calculation of the exchange volume and difficulty in characterizing the pipe-matrix dual medium exchange flow process in karst aquifers. Aiming at the problem of how to characterize the hydrodynamic characteristics and exchange flow laws of the karst pipe-matrix dual medium exchange flow under different karst width fissure conditions, a method of calculating the karst pipe-matrix exchange flow using nonlinear equations based on the development of karst wide fissures is proposed as one of the most effective methods to solve this problem.

[0003] Previous studies have been conducted based on the exchange flow of the dual medium of pipe-matrix as linear Darcy flow, and certain results have been achieved. Niu Zihao et al. "Tracer Experimental Study on Water Exchange between Fracture-Pipeline Media under Different Recharge Conditions" In order to explore the water exchange between fracture-pipeline media under different recharge modes in karst aquifers, high-precision cameras and colored tracers were used to visualize the observations in the laboratory, and multiple groups of experiments were designed to explore the water exchange under three recharge modes: single recharge of fractures, joint recharge, and separate and simultaneous recharge of fractures and sinkholes. The results show that the influence of sinkholes on the diffusion of fracture water decreases with the increase of the distance between the fracture and the sinkhole. Compared with the joint recharge, the sinkhole has a greater influence on the diffusion of fracture water in the case of single recharge of fractures. In the case of separate and simultaneous recharge, when the recharge water volume of the fracture and the sinkhole is the same, only one-way recharge of 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 existence of pipeline-fracture flow exchange in areas with wide karst fissures, forming turbulent sections that lead to nonlinear flow in the exchange flow, and cannot correctly reflect the water exchange relationship between the pipeline and the surrounding bedrock fissures.

[0004] Shu Longcang et al. conducted an indoor simulation experiment on the hydrological process through the SWMM model in "Hydrological Effects of Pipe-Fissure Karst Aquifer Heterogeneity" and studied the influence of pipeline-fracture karst aquifer heterogeneity on the hydrological process of the system. The results show that the pipeline size, the porosity of the aquifer and the water exchange coefficient between groundwater and surface water have little effect on the water level and flow process at the outlet of the system, but the pipeline size has a certain control effect on the highest groundwater level. The porosity of the aquifer has a certain influence on the growth and decline of the groundwater level, and the water exchange coefficient between groundwater and surface water has an important influence on the rate of change of the groundwater level and the maximum value it can reach. However, as a traditional model, the SWMM model quantitatively describes the pipeline-matrix dual medium exchange flow by using linear equations, and assumes that the exchange flow belongs to Darcy flow, which lacks consideration of the nonlinear flow state of the exchange flow under the development of wide karst fractures.

[0005] Chang Yong's "Analysis and Simulation of Hydrological Processes of Karst Springs with Fracture-Pipeline Binary Structure" proposed a new water tank-CFP combination model, using the water tank to reflect the hydrological process in the surface karst zone, and the CFP model to simulate the hydrological process in the saturated zone. The simulation results also show that the model can well simulate the dynamic change process of the S31 spring under different rainfall conditions. During heavy rains, more than 33.6% of the rainfall is directly replenished to the pipeline in a centralized manner after being stored in the surface karst zone. As a calculation module for calculating the dual medium exchange flow of pipeline-fracture matrix in MODFLOW numerical simulation software, the CFP model can characterize the difference in hydrodynamic properties between pipeline-fracture binary media, but the model calculates the water flow exchange volume of fracture-pipeline media based on the Darcy flow assumption, ignoring the widespread existence of pipeline-fracture flow exchange between pipelines and fracture matrix when wide karst fractures are developed, forming a turbulent section, resulting in nonlinear flow state of exchange flow, and thus inaccurate calculation of exchange volume.

[0006] Wang Xi et al. "Experimental study on the relationship between the regulation coefficient and recharge intensity of fracture-pipeline media" In order to explore the influencing mechanism of the regulation function of fracture-pipeline media, a physical model of fracture-pipeline media was established to analyze the relationship between the regulation coefficient and recharge intensity of the model under different recharge modes. The results show that with the increase of recharge intensity, the regulation coefficient gradually increases. In the case of single recharge of fractures, the regulation coefficient and recharge intensity show an exponential increase trend. When the sinkhole is recharged alone or the fracture and sinkhole are recharged together, the regulation coefficient and recharge intensity show a linear increase trend. However, this experiment is based on the premise that the pipeline-matrix dual medium exchange flow is a linear equation to study the relationship between the regulation coefficient and recharge intensity of fracture-pipeline media. It does not take into account that local turbulent sections can be formed in areas with developed wide karst fractures, and the exchange flow has a nonlinear flow state at this time.

[0007] Sun Chen et al.'s "Experimental Study and Numerical Simulation of the Flow Attenuation Process of Fracture-Pipeline Media Springs" used a self-developed fracture-pipeline media physical model to simulate the flow attenuation process of karst fracture-pipeline media springs, and designed multiple groups of experiments to explore the influence of different factors on the flow attenuation process of springs. The experimental results show that the attenuation process is divided into three sub-dynamics with the change of water-releasing media, that is, the magnitude of the attenuation coefficient is mainly affected by the size of the spring mouth, the recharge state, and the initial water storage state of the water-containing medium. This self-developed physical model mainly studies the influence of different factors on the flow attenuation process of springs, and quantitatively describes the dual medium exchange flow of pipeline-fracture matrix by linear equations. However, in the case of wide fracture development, the exchange flow has nonlinear flow states, and its law is not suitable for description by linear equations.

[0008] Shu Longcang et al. "Hydrogeological Simulation Experiment of Fracture-Pipeline Medium Spring Basin" In order to deeply understand the influencing factors and action mechanisms of the flow process in karst spring basins, the hydrogeological conceptual model of the southwestern karst spring basin was used as the prototype to establish a laboratory-scale fracture-pipeline medium physical model and numerical model. The recharge rainfall intensity, spring mouth diameter, and the location of the sinkhole and the mining well were selected as influencing factors to simulate the spring flow process. The experimental results show that a single precipitation experiment can observe three stages of spring flow increase, stable fluctuation and attenuation. Under the same spring mouth diameter conditions, the recharge intensity has little effect on the spring flow attenuation coefficient. The attenuation coefficients corresponding to spring mouth 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 of pipe-fracture matrix in the physical model and numerical model is quantitatively described based on linear equations, ignoring the fact that when wide fractures develop, there is extensive pipe-fracture flow exchange between the pipe and the fracture matrix, forming turbulent sections, resulting in nonlinear flow states in the exchange flow, and thus 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 pipe-fracture dual medium exchange flow, ignoring the fact that local turbulent sections can be formed in areas with developed wide karst fissures, and that the exchange flow has a nonlinear flow state. Therefore, the experiment based on Darcy's law to quantitatively describe the exchange flow cannot accurately characterize the water exchange process between the pipe and the surrounding bedrock fractures.

[0010] Some scholars found that Darcy's law is not applicable to exchange flow in the process of studying the dual medium exchange flow of pipe-fracture matrix. Sun Huan et al.'s "Experimental Study on Nonlinear Flow Characteristics of Pipe-Fissure Water during Carbonate Rock Fracture" focused on the study of microscopic seepage characteristics and fracture mechanism of carbonate rocks, carried out visualization experiments on pipe-fracture water flow during rock fracture, quantitatively analyzed the flow state evolution process of transition from pipe fluid to fracture fluid based on rock block scale experimental results, and studied the influence of multi-level loads on pipe-fracture water flow characteristics. The experimental results show that the flow stability of carbonate rocks is related to the fracture state. In the early stage of pipe wall damage, the pipe flow is mainly laminar. Local pipe wall splitting causes the time-domain flow state of pipe fluid to alternate. The precursor characteristics of the transition from pipe fluid to fracture fluid are mainly manifested as the critical transition point of transition flow state. This study considers the existence of non-Darcy flow in the dual medium exchange flow of pipe-fracture matrix, but no relevant research has been carried out on the method of calculating exchange flow, and the experiment does not consider the influence of changes in permeability coefficient on exchange flow when there are different degrees of wide cracks in karst.

[0011] Zhao Liangjie's "Research on the Mechanism of Water Exchange in Karst Fracture-Pipeline Dual Water-Containing Media" designed a physical model for hydrodynamic simulation of karst pipelines and bedrock fracture media, proposed 6 groups of pipeline fracture combination modes, quantitatively studied the hydrodynamic characteristics of bedrock fractures and karst pipelines under different water flow conditions, and the law of water exchange between media. Through multiple groups of experiments and regression analysis, it was concluded that the amount of water exchange is proportional to the square root of the head difference, and the power exponent of the nonlinear formula is a fixed value of 0.5. This physical model takes into account the existence of non-Darcy flow in the dual medium exchange flow of pipeline-fracture matrix, and after fitting calculation, it is concluded that the amount of water exchange is proportional to the square root of the head difference between the pipeline and the fracture matrix, and the power exponent of the nonlinear formula is a fixed value of 0.5.

[0012] However, when the karst fissures have different widths, the present invention finds that as the width of the fissure increases, the flow rate of the exchange flow gradually increases, and the flow state gradually changes from laminar flow to turbulent flow. The power exponent (nonlinearity n) of the head difference between the corresponding pipeline and the fracture matrix gradually decreases from 1 (when the exchange flow is completely in a laminar state). When the flow state of the exchange flow is completely transformed into turbulent flow, based on Forchheimer's turbulence law, the power exponent (nonlinearity n) is 0.5 (when the exchange flow is completely in a turbulent state). This experiment did not study the exchange flow when the fissures are fully developed to form wide fissures, that is, when the fissures have different widths, the exchange flow nonlinearity n values ​​caused by different permeability coefficients are different, and the nonlinear formulas of the dual medium exchange flow of the pipeline-fracture matrix are also different. The value of n is determined according to the hydrogeological conditions of the pipeline-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 medium 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 predecessors discovered the existence of nonlinear Darcy flow in the process of studying the dual medium exchange flow of pipe-fracture matrix, and improved the linear exchange flow formula into a nonlinear formula with a fixed power exponent of 0.5. However, they ignored the fact that when karst fissures have different widths, the nonlinearity n value of the nonlinear formula will change with the change of permeability, instead of a fixed value of 0.5.

[0014] In summary, when karst fissures are fully developed and wide fissures are formed, the existing research methods for the dual medium exchange flow of pipe-fracture matrix are difficult to effectively and accurately calculate the water exchange amount. The methods are mainly divided into two categories. The first category is to use the "linear equation" method to quantitatively describe the dual medium exchange flow of pipe-fracture matrix. This method does not consider the situation where the exchange flow has nonlinear flow. Both physical experiments and numerical simulations are based on the condition that the exchange flow is linear. The second category is that in the process of research, it is found that the exchange flow has non-Darcy flow phenomenon, and the linear formula is improved to the power exponent of the water exchange amount and the head difference between the pipe and the fracture matrix is ​​a fixed value of 0.5, but it is ignored that when the karst fissures have different widths, the value of the nonlinearity n varies with the width of the fissure. Obviously, when there are wide fissures in karst, there is an urgent need for a method that can accurately characterize the hydrodynamic characteristics and exchange flow laws of the dual medium exchange flow of karst pipe-matrix. Summary of the invention

[0015] In view of the problems in the prior art, the present invention provides a pipeline-matrix water flow exchange calculation method based on karst fissure development, which can accurately describe the hydrodynamic characteristics and exchange flow laws of the karst pipeline-matrix dual medium exchange flow. The specific technical solution is as follows:

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

[0017] Step S1, establishing a physical experimental model of karst pipe-crack dual medium, the physical experimental model includes:

[0018] A model box, wherein a pipe inlet and a pipe outlet are respectively arranged on two opposite sides of the model box;

[0019] 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;

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

[0021] 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;

[0022] A plurality of quartz sand containers, wherein the plurality 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, and gaskets of different thicknesses are placed between two adjacent quartz sand containers and are glued and fixed 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 the 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;

[0023] 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;

[0024] 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;

[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 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 n of each experimental group. i , where i represents the number of experimental groups; different nonlinear values ​​n are obtained based on the different degrees of karst fissure development i , so the exchange flow formula of each experimental group is as follows:

[0026]

[0027] Among them, Q exi represents the exchange flow calculated by the ith experimental group; H ci represents the pipe head calculated by the ith experimental group; H mi represents the fracture water head calculated for the ith experimental group; α is the water exchange coefficient.

[0028] Preferably, 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.

[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 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.

[0031] Preferably, in step S4, the head difference between the pipeline and the fracture matrix is ​​calculated based on 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:

[0032] 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 P g =[P g1 ,P g2 ,P g3 ,…,P gm ]; The m pressure sensors on the left side of the pipeline are on the same straight line, and the pressure value sequence collected is P l =[P l1 ,P l2 ,P l3 ,…,P lm ], the m pressure sensors on the right side of the pipeline are on the same straight line, and the pressure value sequence collected is P r =[P r1 ,P r2 ,P r3 ,…,P rm ]; The flow data collected by the flow meter installed at the pipe inlet is Q 0 , 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 Q 1 , Q 2 , Q 3 …, Q m ;

[0033] The calculation formula for pipe head is: The calculation formula of fracture head is: The exchange flow Q of the crack 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:

[0035]

[0036] Preferably, the water exchange coefficient α is calculated as follows:

[0037]

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

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] Compared with previous studies that used linear equations (Darcy's law) or nonlinear equations with fixed power exponents to calculate the water flow exchange volume of the karst conduit-fracture matrix dual medium, this paper ignores the nonlinear exchange flow between the conduit and the fracture matrix that changes with the width of the fracture when there are fractures of different widths in the karst, resulting in inaccurate calculation of the exchange volume and difficulty in characterizing the hydrodynamic characteristics and hydrological process of the exchange flow of the karst conduit-fracture matrix dual medium. The present invention proposes a method for calculating the pipe-matrix water flow exchange based on the development of karst fissures, which has two advantages. On the one hand, it fully considers that the exchange flow has different flow states, follows the hydrological process of the pipe-fracture matrix exchange flow in the presence of wide fissures in karst, and compared with the traditional assumption based on Darcy's law, the pipe-fracture matrix dual medium exchange flow is assumed to be a linear Darcy flow. Based on physical experimental data (fracture matrix width, pipe outlet flow, rainfall recharge intensity, sinkhole recharge intensity, pipe head and fracture head), the present invention uses a regression analysis method to fit the experimental data to obtain the nonlinearity n of the pipe-matrix water flow exchange formula, thereby determining a specific nonlinear exchange flow formula. The formula not only takes into account that when the fissures are not fully developed and there are no wide fissures, the exchange flow is a linear Darcy flow, that is, the nonlinearity n=1. It also takes into account that in the case of wide fissures, the exchange flow state is a non-Darcy flow state, that is, the nonlinearity is 0.5≤n<1; on the other hand, based on the exchange flow data results obtained from physical experiments under different widths of karst fissures, the exchange flow data are fitted by regression analysis to obtain a specific nonlinear exchange flow formula, and the power exponent (nonlinearity n) of the head difference between the pipeline and the fracture matrix is ​​determined to vary with the width of the karst fissure. Therefore, the proposed nonlinear exchange flow calculation method makes the calculation of the pipeline-matrix water flow exchange more accurate, which plays an important role in the evaluation and development of karst water resources. 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 is a brief introduction to the drawings required for the specific embodiments or the description of 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 according to the actual scale.

[0042] Figure 1 is a flow chart of the method of the present invention;

[0043] Figure 2 This is the principle diagram of the karst pipe-crack dual medium physical experiment model;

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

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

[0046] Figure 5 This is a schematic diagram of the front of the plexiglass box;

[0047] Figure 6 The scatter plot and fitting curve of water exchange volume and head difference of standard control group and wide crack experimental group;

[0048] Figure 7 Measured flow rate and simulation results: (a) 0.5 mm width crack group; (b) 1.0 mm width crack group; (c) 1.5 mm width crack group. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

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

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

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

[0054] like Figure 1 As shown, this embodiment provides a method for calculating pipeline-matrix water flow exchange based on karst fissure development, comprising the following steps:

[0055] Step S1, establish a physical experimental model of karst pipe-crack dual medium. The principle of the physical experimental model is as follows: Figure 2 shown.

[0056] like Figure 3 The schematic diagram of the physical experiment model shown in the figure includes a model box, a water supply tank, a water pump, a pipeline, several quartz sand containers, several rotating nozzles, and a data acquisition system.

[0057] The model box body is provided with an inlet and an outlet on opposite sides. The water supply tank is fixed on the vertical electric slide module. 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. The water pump is connected to the water supply tank. The water supply tank is kept in an overflow state during the water supply of the water pump. The water flows out through the overflow trough and can be circulated by the water pump. The pipeline is connected to the water supply tank and passes through the inlet and outlet of the model box body in sequence; a plurality of first exchange holes are evenly arranged on the pipeline. A plurality 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. Gaskets of different thicknesses are placed between two adjacent quartz sand containers and are glued and fixed to simulate the fracture network with different permeability coefficients; the quartz sand container is a rectangular parallelepiped, and a plurality of second exchange holes are evenly arranged on the six faces. A 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. 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 symmetrical with the m pressure sensors at the bottom of the pipeline; the flow meter is arranged at the inlet and outlet of the pipeline; the data conversion module is electrically connected to the pressure sensor, the flow meter, and the host computer respectively.

[0058] The fracture matrix filled in the quartz sand container of this embodiment is homogeneous quartz fine sand with a particle size of 3.0 mm. The first exchange hole of the pipeline adopts a plum blossom-shaped opening 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 with a pore size of 2 mm to prevent quartz sand from penetrating into the pipe. The permeability of the filter and the pipeline opening is much greater than the permeability of the quartz sand to ensure that the permeability coefficient of the pipeline wall is not affected.

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

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

[0061] In this embodiment, m=5, that is, 15 MIK-P300 diffused silicon pressure sensors are used. Figure 4As shown in the figure, 5 pressure sensors are arranged at the bottom of the pipeline, and 5 pressure sensors are arranged on the left and right sides of the pipeline respectively, forming a 3*5 pressure sensor matrix. The pressure sensors and flow meters are arranged as shown in the figure. Figure 4 The flow meter uses a turbine flow meter, 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 host computer, and can directly draw real-time curves.

[0062] 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.

[0063] The present invention sets a standard control group experiment so that the exchange flow of the control group experiment is under the Darcy flow state. Therefore, the filled fracture matrix is ​​homogeneous quartz fine sand with a particle size of 3.0 mm, and the single pipe diameter, the width of the fracture spacing, and the matrix diameter in the physical model are measured, and the fracture matrix permeability coefficient is determined using the Darcy experiment. The permeability coefficient is determined to be about 0.0028 m / d by the Darcy experiment. When filling the quartz sand, compaction and tightness treatment are performed so that the matrix part composed of the quartz sand can be regarded as a homogeneous condition.

[0064] Four groups of wide crack experimental groups were set up, namely the standard control group, 0.5mm width crack group, 1.0mm width crack group and 1.5mm width crack group, that is, 0.5mm, 1.0mm and 1.5mm gaskets were placed between the plexiglass boxes and reinforced. Among them, the standard control group did not set up plexiglass boxes; the experimental groups with different width cracks were plexiglass boxes filled with 3.0mm quartz sand, the same as the crack matrix. The recharge source was a single sinkhole point confluence recharge. The water supply intensity was constant in a single experiment, and the water supply was stopped when the pipeline head value was equal to the bedrock crack head value on the left and right sides, that is, the water supply was stopped when the pipeline and the corresponding pressure sensor values ​​on both sides were the same. The entire hydrological process was divided into two stages: ① During the sinkhole recharge, the pipeline recharged to the crack, and the pipeline head was higher than the crack matrix head. ② After the water supply stopped, the crack recharged to the pipeline, and the crack matrix head was higher than the pipeline head.

[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 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 n of each experimental group. i, where i represents the number of experimental groups; different nonlinear values ​​n are obtained based on the different widths of karst fissures. i , the exchange flow formula of each experimental group is as follows:

[0066]

[0067] Among them, Q exi represents the exchange flow calculated by the ith experimental group; H ci represents the pipe head calculated by the ith experimental group; H mi represents the fracture water head calculated for the ith experimental group; α is the water exchange coefficient.

[0068] The calculation formula of water exchange coefficient α is as follows:

[0069]

[0070] Where K is the number of connected pipes; K w is the pipe wall permeability coefficient. In the present invention, the pipe wall permeability coefficient K w Obtained through the internal structure of the pipeline, to ensure K w The coefficient does not affect the drainage process from the fracture system to the pipeline. This parameter takes a larger value of 0.00833m / s to eliminate the influence of the exchange coefficient on the water exchange between the fracture system and the pipeline system, L / T; d k is the diameter of the kth pipe, L; Δl k is the length of the straight line connecting the two pipeline nodes between pipeline k, L; r k is the radius of the kth pipe, L; τ k is the tortuosity of the kth pipe.

[0071] The water head difference between the pipeline and the fracture matrix is ​​calculated based on the collected pressure values ​​at the bottom of the pipeline and the pressure values ​​at the bottom of the quartz sand container, including the following:

[0072] 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 P g =[P g1 ,P g2 ,P g3 ,…,P gm ]; The m pressure sensors on the left side of the pipeline are on the same straight line, and the pressure value sequence collected is P l =[P l1 ,P l2 ,P l3 ,…,P lm ], the m pressure sensors on the right side of the pipeline are on the same straight line, and the pressure value sequence collected is P r =[P r1 ,P r2,P r3 ,…,P rm ]; The flow data collected by the flow meter installed at the pipe inlet is Q 0 The flow data collected by the flow meter installed at the outlet of the pipeline is Q m+1 , 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 Q 1 , Q 2 , Q 3 …, Q m-1 ;

[0073] The calculation formula for pipe head is: The calculation formula of fracture head is: In the i-th group of experiments, the exchange flow formula at the 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 nonlinearity n 1 =1, n 2 =0.797, n 3 = 0.711 and n 4 =0.582, the fitting results are as follows Figure 6 As shown. It can be seen that the nonlinearity n of the exchange flow formula for different crack widths is different and is not a fixed value of 0.5.

[0076] This embodiment also includes step S4, in which the water pump is turned on to simulate single rainfall surface recharge with constant rainfall intensity, and no sinkhole confluence point recharge is set, and the other experimental conditions are consistent with step S2. This step is used to verify the calculation accuracy of the method provided in this embodiment.

[0077] In the surface experimental scenario, the recharge method of each group of experiments was single rainfall surface recharge with a constant rainfall intensity of 0.0025 mm / s. No sinkhole confluence point recharge was set up. Four groups of wide crack experimental groups were set up, namely the standard control group, 0.5 mm width crack group, 1.0 mm width crack group, and 1.5 mm width crack group. That is, 0.5 mm, 1.0 mm, and 1.5 mm gaskets were placed between the plexiglass boxes and reinforced. Among them, the standard control group did not set up plexiglass boxes; the experimental groups with different width cracks were plexiglass boxes filled with 3.0 mm quartz sand, the same as the crack matrix, and the other experimental conditions were consistent with the point experiment.

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

[0079] Step S6, modifying the nonlinear value n in the source code of the calculation exchange flow module of the numerical simulation software CFP i Based on each set of experimental conditions in step S5, the numerical simulation software CFP is run to obtain each set of improved CFP result data. The results of each set of improved CFP result data are as follows: Figure 7 shown.

[0080] The modification steps are as follows: ①SUBROUTINE CFPBCF7BDCH, SUBROUTINE CFPLPF7 BDCH, 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, a real number variable n is added, and a variable hh for controlling the positive and negative is introduced. Modify hdiff to DABS(hdiff)**n*hh, and use IF(hdiff.GT.0) to determine whether the positive and negative change after the exchange volume is changed. If not, change the positive and negative of hh to make it consistent with the original program. ②In the SUBROUTINE CON1FM head calculation subroutine, SUBROUTINE F_X0 pipeline flow equation iterative calculation subroutine, and SUBROUTINE GWF2CFP1BD pipeline balancing subroutine, B_MAT is the pipeline node head, Hnew is the MODFLOW cell head, and the variable hh that controls the positive and negative is introduced. B_MAT-Hnew is modified to DABS(B_MAT-Hnew)**n*hh. IF(hdiff.GT.0) is used to determine whether the positive and negative signs change after the exchange amount is changed. If inconsistent, the positive and negative signs of hh are changed to make it consistent with the original program.

[0081] Step S7, comparing each group of original CFP result data with each group of improved CFP result data, and calculating the improved accuracy.

[0082] The experimental results of each group of surface experiments, the original CFP results of each group and the improved CFP simulation results of each group were compared. And based on the determination coefficient (R 2 ) formula, Nash efficiency coefficient (NSE) formula, root mean square error (RMSE) formula and percentage bias (PBIAS) calculation improved the accuracy, and the results are shown in Table 1.

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

[0084]

[0085] Among them, J is the number of collected data points, Q g (j) is the jth observed flow actually collected, Q s(j) is the jth simulated flow obtained by CFP simulation, are the means of observed flow and simulated flow respectively. 2 It is generally used to reflect the degree of regression fit of the regression model. The closer it is to 1, the better the fit.

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

[0087]

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

[0089] The root mean square error RMSE is calculated 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 percentage bias PBIAS is calculated as follows:

[0093]

[0094] The percentage deviation PBIAS is also called relative error, which reflects the deviation between the simulated cumulative value and the measured cumulative value.

[0095] In the uniform distribution model experimental group, the comparison of the evaluation indicators in the table shows that the simulation accuracy of the improved CFP model is higher than that of the original CFP model, among which the coefficient of determination and Nash efficiency coefficient increased by an average of 0.11 and 0.12, and the root mean square error and percentage deviation decreased by an average of 45% and 44%. By comparing the difference in various indicators of the two models, it is shown that in the uniform distribution mode, as the crack width increases, the average simulation accuracy of the improved CFP model increases.

[0096] Table 1 Simulation accuracy of each experimental group before and after model improvement with 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 it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for calculating the pipe-matrix water flow exchange based on the development of karst fissures. It is 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, wherein the plurality 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, and gaskets of different thicknesses are placed between two adjacent quartz sand containers and are glued and fixed 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 the 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 n of each experimental group. i , where i represents the number of experimental groups; different nonlinear values ​​n are obtained based on the different degrees of karst fissure development i , so the exchange flow formula of each experimental group is as follows: Q exi =α(H ci -H mi ) ni ; Among them, Q exi represents the exchange flow calculated by the i-th experimental group; H ci represents the pipe head calculated by the ith experimental group; H mi represents the fracture water head calculated for the ith experimental group; α is the water exchange coefficient.

2. A method for calculating pipe-matrix water flow exchange based on karst fissure development according to claim 1, It is 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. According to claim 1, a method for calculating the pipe-matrix water flow exchange based on the development of karst fissures, It 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. According to claim 1, a method for calculating the pipe-matrix water flow exchange based on the development of karst fissures, It 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. According to claim 1, a method for calculating the pipe-matrix water flow exchange based on the development of karst fissures, It is characterized in that The step S4 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 P g =[P g1 ,P g2 ,P g3 ,…,P gm ]; The m pressure sensors on the left side of the pipeline are on the same straight line, and the pressure value sequence collected is P l =[P l1 ,P l2 ,P l3 ,…,P lm ], the m pressure sensors on the right side of the pipeline are on the same straight line, and the pressure value sequence collected is P r =[P r1 ,P r2 ,P r3 ,…,P rm ]; The flow data collected by the flow meter installed at the pipe inlet is Q 0 , 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 Q 1 , Q 2 , Q 3 …, Q m ; The calculation formula for pipe head is: The calculation formula of fracture head is: The exchange flow Q of the crack exi =Q 0 -Q m ; 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 pipe-matrix water flow exchange based on karst fissure development according to claim 1 or 5, It is characterized in that The water exchange coefficient α is calculated as follows: Where K is the number of connected pipes; K w is the pipe wall permeability coefficient; d k is the diameter of the kth pipe; Δl k is the length of the straight line connecting the two pipeline nodes between pipeline k; r k is the radius of the kth pipe; τ k is the tortuosity of the kth pipe.

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