CN118428241B - Aquifer parameter estimation method considering pressure-bearing-non-pressure conversion and well loss - Google Patents
Aquifer parameter estimation method considering pressure-bearing-non-pressure conversion and well loss Download PDFInfo
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Abstract
The application relates to the technical field of hydraulic engineering, in particular to an aquifer parameter estimation method considering pressure-bearing and non-pressure conversion and well loss. Firstly, basic information of an aquifer is obtained; then, according to stratum distribution information and quasi-steady-state water level depths corresponding to different pumping stages, determining the pressure state change of the aquifer, adopting a pre-established ladder pumping water level degradation analysis model considering pressure-bearing-non-pressure conversion and well loss influence, and estimating the permeability coefficient, storage coefficient and corresponding well loss coefficient of the aquifer under the pressure-bearing condition by using a particle swarm optimization method; finally substituting the parameter values into an analytical model, and calculating a critical time point when pressure-bearing and non-pressure conversion occurs; comprehensively considering the influence of pressure-bearing and non-pressure conversion and well loss coefficient in the pumping process, and simultaneously realizing parameter estimation by adopting a particle swarm optimization method; the change process of the pressure state of the aquifer is characterized by calculating the critical time point, so that the deviation between the analysis result and the actual situation is reduced.
Description
Technical Field
The application relates to the technical field of hydraulic engineering, in particular to an aquifer parameter estimation method considering pressure-bearing and non-pressure conversion and well loss.
Background
The water resource is an important basis for human survival and development, and reasonable exploitation and utilization of the underground water resource has important significance for maintaining water circulation balance and ensuring sustainable utilization of the water resource. The aquifer parameters such as permeability coefficient, water supply degree and the like are important basic data for evaluating and protecting groundwater resources and preventing and controlling groundwater disasters, and the stepped-down pumping test is a common means for evaluating the aquifer parameters, and has guiding significance for developing and utilizing the groundwater resources and preventing and controlling groundwater disasters.
The water pumping test is the most commonly used method for estimating the hydrogeological parameters of the aquifer, and can provide important references for the underground water condition evaluation and engineering safety of the engineering construction area. Mathematical models interpret observed data by fitting the observed data to numerical data, and therefore, a suitable mathematical model is critical to interpreting pumping tests. Theis (Theis 1935) first proposed a deep analytical solution when conducting constant flow pumping tests in an equal-thickness confined aquifer. Later, to address more complex scenarios not covered by Theis (Theis 1935) in field pumping trials, a series of analytical solutions were derived, including constant head trials (Wen et al, 2011), fidaxyl flows (Wen et al, 2009, 2013), leakage effects (Wen et al, 2009 b; zhu and Wen 2020), wellbore storage (Wen et al, 2014), skin effects (Feng and Wen 2016), microbiological effects (Zhu et al, 2019), and the like.
In many on-site pumping tests, variable speed pumping tests are characterized in that the flow boundary conditions in the model are time dependent. The popularity of this test is mainly due to the increasing head of the pump over time and the head loss caused by friction between the water and the pipe (Sen and Altunkaynak2004; wen et al 2017). In the variable speed pumping test, the step-down pumping test enables the simultaneous estimation of aquifer parameters and well loss using a single well (Clark 1977; kawecki 1995), while in the step-down test, the initial pumping rate remains constant until the drop reaches a quasi-steady state. The pumping flow is then typically increased and maintained constant until the water level reaches another quasi-steady state. According to the relevant criteria, it is recommended that this process is repeated at least three times.
Previous studies on step-down tests have focused mainly on well loss estimation, including graphical methods (Rorabaugh 1953; sheahan1971; birsoy and Summers 1980), analytical methods (Mathias and Todman2010; chen et al 2022), numerical methods and optimization methods (Labadie and Helweg1975; sheahan1975; gupta1989; avci 1992) have been proposed for calculating well loss coefficients based on step-down water tests, especially in confined aquifers. However, none of these studies have considered the transient state of groundwater transitioning from a pressurized to a pressureless state, which is common in stepped-down pumping tests, mainly because the water level may drop below the top of the aquifer as the water volume increases at a particular stage of the test. Thus, the solution proposed in the previous study for finding well loss coefficients and hydrogeologic parameters will fail in the case of a pressure-to-no pressure transition.
In response to the challenges faced in testing pressure-bearing to pressureless conversion to estimate well loss and hydrogeologic parameters, it is desirable to develop a comprehensive model that accounts for this complex scenario, and which allows simultaneous estimation of multiple parameters, including but not limited to permeability coefficients, storage coefficients, well loss coefficients, and critical time for conversion.
In summary, transient switching from pressure-bearing to pressureless mode is a common phenomenon in stepped-down pumping tests, but lacks a method to interpret well loss coefficients and aquifer parameters under such conditions.
In the process of the stepped-down pumping test, the stepped-down pumping test usually experiences the transition from a pressure-bearing condition to a non-pressure condition due to the continuous increase of the pumping rate, but the existing shaft hydraulics model is difficult to accurately explain the phenomenon, so that the analysis result is deviated from the actual situation, and the situation needs to be further improved.
Disclosure of Invention
In order to solve the problem that the analysis result of the traditional well flow model deviates from the actual situation, the application provides an aquifer parameter estimation method considering pressure-bearing-non-pressure conversion and well loss, which adopts the following technical scheme:
In a first aspect, the present application provides a method for estimating aquifer parameters taking into account pressure-to-non-pressure conversion and well loss, comprising the steps of:
Acquiring an initial water head of an aquifer, the elevation of the top of the aquifer and the pumping flow of different pumping stages;
acquiring stratum distribution information and quasi-steady-state water level depths corresponding to different water pumping stages, determining the pressure state change of the aquifer, and determining whether the aquifer undergoes pressure-bearing-non-pressure conversion according to the pressure state change;
Under the condition that the aquifer is confirmed to undergo pressure-free conversion, estimating the permeability coefficient, the storage coefficient and the corresponding well loss coefficient under the pressure-bearing condition of the aquifer by adopting a particle swarm optimization method according to a pre-established ladder pumping water level deep-falling analysis model considering the pressure-free conversion and the well loss effect;
Substituting the initial water head of the aquifer, the elevation of the top of the aquifer, the pumping flow of different pumping stages, the permeability coefficient, the storage coefficient and the well loss coefficient corresponding to the pressure-bearing condition into the stepped pumping water level deep analysis model considering the pressure-bearing-non-pressure conversion and the well loss influence, and calculating the critical time point of the pressure-bearing-non-pressure conversion.
By adopting the technical scheme, the method firstly acquires basic information such as the initial water head of the aquifer, the elevation of the top of the aquifer, the pumping flow of different pumping stages and the like; then, according to stratum distribution information and quasi-steady-state water level depths corresponding to different water pumping stages, determining the pressure state change of the aquifer, and judging whether the aquifer undergoes pressure-bearing-non-pressure conversion; under the condition that the aquifer is confirmed to undergo pressure-free conversion, a pre-established ladder pumping water level deep analysis model which takes the pressure-free conversion and well loss into consideration is adopted, and a particle swarm optimization method is utilized to estimate the permeability coefficient, the storage coefficient and the corresponding well loss coefficient of the aquifer under the pressure-bearing condition; finally substituting the estimated parameter value into the analysis model, and calculating a critical time point when pressure-bearing and non-pressure conversion occurs; comprehensively considering the influence of pressure-bearing and non-pressure conversion and well loss coefficients in the pumping process, and establishing a water level deep-falling analysis model which is more in line with the actual situation; meanwhile, a particle swarm optimization method is adopted to realize the automation and optimization of the parameter estimation process; the change process of the pressure state of the aquifer is quantitatively described by calculating the critical time point, so that the deviation between the analysis result and the actual situation is reduced.
Optionally, the particle swarm optimization method is adopted to estimate the permeability coefficient, the storage coefficient and the well loss coefficient corresponding to the water-bearing layer under the pressure-bearing condition, and specifically comprises the following steps:
establishing an objective function ；
Wherein R is the minimum root mean square error in the particle swarm iteration process; n represents the calculated dip for fittingAnd observe the lowering of depthIs the number of data points; h represents a dataset of target parameters in the iteration;
Setting input parameters of a particle swarm optimization algorithm, wherein the input parameters comprise a particle number N, an inertia weight w, a maximum iteration number M, a parameter number D and an individual learning factor And social learning factors；
Determining a search range of a permeability coefficient K, a storage coefficient S and a well loss coefficient B;
And running a particle swarm optimization algorithm based on the input parameters and the search range to estimate and obtain values of the permeability coefficient K, the storage coefficient S and the well loss coefficient B.
By adopting the technical scheme, the method and the device have the advantages that the objective function is constructed, then the particle swarm optimization algorithm is selected as an optimization solver, the permeability coefficient, the storage coefficient and the well loss coefficient are used as optimization variables, and the optimal parameter value is obtained through iterative optimization solving, so that the advanced mathematical model and the optimization algorithm are effectively integrated, the description capability of the theoretical model can be fully exerted, the key parameters can be solved in a high-precision and high-efficiency mode, and a more reliable analysis result is obtained.
Optionally, substituting the initial water head of the aquifer, the elevation of the top of the aquifer, the pumping flow of different pumping stages, the permeability coefficient, the storage coefficient and the well loss coefficient corresponding to the pressure-bearing condition into the stepped pumping water level degradation analysis model considering pressure-bearing-non-pressure conversion and well loss influence, and calculating a critical time point of pressure-bearing-non-pressure conversion, wherein the critical time point comprises the following steps:
Determining a flow stage at which the bearing-pressureless conversion of the aquifer occurs according to the pressure state change;
Determining a comprehensive expression of the step pumping water level drop change considering the pressure-free conversion and the well loss according to the flow stage of the pressure-free conversion of the aquifer and the step pumping water level drop analysis model considering the pressure-free conversion and the well loss;
taking the difference between the initial water head of the aquifer and the elevation of the top of the aquifer as an allowable descent depth value;
Substituting the permeability coefficient, the storage coefficient, the well loss coefficient corresponding to the pressure-bearing condition and the allowable deep-down value into the comprehensive expression, and solving the corresponding time when the allowable deep-down value is obtained, namely the critical time of pressure-bearing and non-pressure conversion.
By adopting the technical scheme, the application judges the flow stage of pressure-bearing-non-pressure conversion according to pressure state change by observing the descending data, then determines the comprehensive expression of the step pumping water level descending change considering the pressure-non-pressure conversion and well loss effect, calculates the difference between the initial water head and the upper layer of the water-bearing layer top layer as the permissible descending depth value, substitutes the estimated permeability coefficient K, storage coefficient S, well loss coefficient B and permissible descending depth value into a theoretical descending depth model, and solves the time corresponding to the permissible descending depthNamely, the required critical conversion time point; the combination of qualitative analysis and quantitative calculation is realized, and the key time node of pressure-bearing-non-pressure conversion is accurately determined.
Optionally, the building process of the ladder pumping water level lowering analysis model considering the pressure-bearing-non-pressure conversion and well loss influence comprises the following steps:
Assuming that the confined aquifer and the pressureless aquifer extend isotropically and infinitely in the radial direction, acquiring potential functions of the confined aquifer and the pressureless aquifer by using a GIRINSKII potential function method;
assuming initial hydrostatic pressure balance, establishing a control equation, a hydrostatic pressure initial condition, an external boundary condition and a well wall boundary condition considering single complete well step deep pumping flow;
According to potential functions of the confined aquifer and the pressureless aquifer, the control equation, the initial condition, the outer boundary condition and the inner boundary condition, respectively obtaining basic analytic solutions of the falling depths of the confined and pressureless conditions caused by constant pumping flow;
According to the basic analytic solution, a step pumping water level drop analytic model considering pressure-bearing and non-pressure conversion and well loss influence is established by combining a well loss expression and a superposition principle, wherein the well loss coefficients of the well loss expression corresponding to the pressure-bearing and non-pressure conditions are different.
By adopting the technical scheme, the application assumes that the aquifer extends isotropically and infinitely in the radial direction, obtains potential functions under pressure bearing and non-pressure conditions by utilizing a GIRINSKII potential method, establishes a control equation, an initial condition and a boundary condition, obtains a basic analysis solution under constant pumping flow according to the conditions, establishes a control equation for describing seepage of the aquifer and the non-pressure aquifer by combining a well loss expression and a superposition principle, and introduces a well loss expression under different working conditions, so that the influence of pressure bearing-non-pressure conversion and well loss on the change of the descent depth can be accurately analyzed, the accuracy of estimating the parameters of the aquifer is improved, and theoretical support is provided for efficient development and utilization of groundwater resources.
Alternatively, assuming that the confined aquifer and the pressureless aquifer extend isotropically and infinitely in the radial direction, the GIRINSKII potential function method is used to obtain the potential functions of the confined aquifer and the pressureless aquifer,
The potential function of the confined aquifer is:；
the potential function of the pressureless aquifer is: ；
wherein K is a permeability coefficient, and M and h respectively represent the thicknesses of the confined aquifer and the pressureless aquifer; h represents the head of water in the confined aquifer.
Optionally, assuming an initial hydrostatic pressure balance, establishing a control equation, a hydrostatic pressure initial condition, an external boundary condition and a wellbore wall internal boundary condition considering single complete well step-down pumping flow, dividing the aquifer into a plurality of unit volumes along the radial direction, wherein each unit volume is represented by a cylinder with the thickness dr and the radius r, and obtaining
The control equation is:；
The initial conditions are: ；
The outer boundary conditions are: ；
wherein, Represents GIRINSKII potential in confined aquifers and pressureless aquifers, t represents pumping duration, and r represents radial distance from the center of the wellbore; a is the aquifer diffusivity and a = T/S, T and S are the aquifer 'S permeability and the aquifer' S storage coefficient, respectively,Is the initial potential expressed as。
Optionally, the boundary conditions in the wall of the well bore considering the single complete well step deep pumping flow are described as:
；
；
；
wherein, 、AndRespectively represents the constant flow rate of each pumping depth, wherein，AndThe time points at which the first and second dips end are indicated, respectively.
Optionally, the basic analysis solutions of the pressure bearing and pressureless condition descending depths caused by the constant pumping flow are respectively obtained according to the potential functions of the pressure bearing aquifer and the pressureless aquifer, the control equation, the initial condition, the outer boundary condition and the inner boundary condition, and specifically include the following steps:
Obtaining a general solution of the control equation, the initial condition and the outer boundary condition according to a Theis analytical model
；
Wherein, ; W (u) is a Theis well function expressed as an integral function;
based on the potential functions of the confined aquifer and the pressureless aquifer and the general solution, it is assumed that a confined-pressureless transition is caused by a constant pumping flow Q, then
The drop in confined aquifer is expressed as:；
The dip of the pressureless aquifer is expressed as: ；
wherein, Indicating the initial head of the confined aquifer.
Optionally, according to the basic analytic solution, in combination with a well loss expression and a superposition principle, a stepped pumped water level deep analytic model considering pressure-bearing-non-pressure conversion and well loss influence is established, and the method specifically comprises the following steps:
Acquiring a well loss coefficient B under a pressure-bearing condition and a well loss coefficient C under a non-pressure condition;
According to the superposition principle, the water head expression of the confined aquifer and the water head expression of the pressureless aquifer, a stepped water pumping water level lowering analysis model considering the effects of pressure bearing-pressureless conversion and well loss is obtained:
；
；
wherein, Represents the descent depth in the pumping well, B represents the well loss coefficient under the pressure-bearing condition, C represents the well loss coefficient under the non-pressure condition,Indicating the critical point in time at which the pressure-to-no-pressure transition occurs.
By adopting the technical scheme, the method and the device acquire the critical time point of pressure-free conversion by acquiring the well loss coefficient B under the pressure-bearing condition and the well loss coefficient C under the non-pressure condition and then determining the time node of the change of the pumping flow; according to the superposition principle, the final descent depth change expression is obtained by combining the parameters, the pressure-bearing and pressureless conversion and the well loss change under the pressure-bearing and pressureless conditions are considered, a theoretical model for comprehensively describing each influence factor of the step descent depth test is established, the actual descent depth change process can be more accurately simulated, and a reliable theoretical basis is provided for accurate estimation of aquifer parameters.
In summary, the present application includes at least one of the following beneficial technical effects:
Firstly, acquiring basic information of an aquifer; then, according to stratum distribution information and quasi-steady-state water level depths corresponding to different pumping stages, determining the pressure state change of the aquifer, adopting a pre-established ladder pumping water level degradation analysis model considering pressure-bearing-non-pressure conversion and well loss influence, and estimating the permeability coefficient, storage coefficient and corresponding well loss coefficient of the aquifer under the pressure-bearing condition by using a particle swarm optimization method; finally substituting the parameter values into an analytical model, and calculating a critical time point when pressure-bearing and non-pressure conversion occurs; comprehensively considering the influence of pressure-bearing and non-pressure conversion and well loss coefficient in the pumping process, and simultaneously realizing parameter estimation by adopting a particle swarm optimization method; the change process of the pressure state of the aquifer is characterized by calculating the critical time point, so that the deviation between the analysis result and the actual situation is reduced;
According to the application, an objective function is constructed, then a particle swarm optimization algorithm is selected as an optimization solver, a permeability coefficient, a storage coefficient and a well loss coefficient are used as optimization variables, and an optimal parameter value is obtained through iterative optimization solving, so that an advanced mathematical model and an optimization algorithm are effectively integrated, the descriptive capacity of a theoretical model can be fully exerted, key parameters can be solved in a high-precision and high-efficiency mode, and a more reliable analysis result is obtained;
The application judges the flow stage of pressure-bearing-pressureless conversion according to pressure state change by observing the descending data, then determines the comprehensive expression of the step pumping water level descending change considering the pressure-bearing-pressureless conversion and well loss effect, calculates the difference between the initial water head and the upper layer of the water-bearing layer top as the permissible descending value, substitutes the estimated permeability coefficient, storage coefficient, well loss coefficient and permissible descending value into the theoretical descending model, and solves the time corresponding to the permissible descending, namely the required critical conversion time point; the combination of qualitative analysis and quantitative calculation is realized, and the key time node of pressure-bearing-non-pressure conversion is accurately determined.
Drawings
FIG. 1 is a flow chart of an embodiment of the method for estimating aquifer parameters taking into account pressure-to-non-pressure conversion and well loss;
FIG. 2 is a schematic flow chart of a process for establishing a stepped pumped water level deep resolution model taking into consideration pressure-bearing-non-pressure conversion and well loss effects in the embodiment of the application;
FIG. 3 is a schematic diagram of a confined aquifer model with a complete well in a method for estimating aquifer parameters considering confined-to-non-confined transitions and well losses in accordance with an embodiment of the present application;
FIG. 4 is a core histogram of a pumping well in one embodiment of the method of estimating aquifer parameters in consideration of pressure-to-non-pressure conversion and well loss in accordance with an embodiment of the present application;
FIG. 5 is a graph of a fitting result of step-down in an aquifer parameter estimation method taking into account pressure-bearing-non-pressure conversion and well loss in an embodiment of the application;
FIG. 6 is a schematic flow chart of acquiring a critical time point tc in an aquifer parameter estimation method considering pressure-bearing-non-pressure conversion and well loss according to an embodiment of the present application;
FIG. 7 is a schematic flow chart of estimating the hydrogeological coefficients in the aquifer parameter estimation method considering the pressure-bearing-non-pressure conversion and well loss according to the embodiment of the application;
fig. 8 is an internal structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
The terminology used in the following embodiments of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in the specification of the present application and the appended claims, the singular forms "a," "an," "the," and "the" are intended to include the plural forms as well, unless the context clearly indicates to the contrary. It should also be understood that the term "and/or" as used in this disclosure is intended to encompass any or all possible combinations of one or more of the listed items.
The terms "first," "second," and the like, are used below for descriptive purposes only and are not to be construed as implying or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature, and in the description of embodiments of the application, unless otherwise indicated, the meaning of "a plurality" is two or more.
In order to solve the problem, the application provides an aquifer parameter estimation method considering pressure-bearing-non-pressure conversion and well loss, and the embodiment of the application is described in further detail below with reference to the accompanying drawings.
In a first aspect, the present application provides a method for estimating aquifer parameters taking into account pressure-to-non-pressure conversion and well loss, referring to fig. 1, the method comprising the steps of:
S11, acquiring an initial water head of the aquifer, the top elevation of the aquifer and the pumping flow of different pumping stages.
The initial water head of the aquifer refers to the water head value in the aquifer before the pumping test starts, and the water head value can be obtained through observation of the static water level of the well; the height of the top of the aquifer refers to the height of the top of the aquifer relative to a certain reference plane, and is obtained by geological drilling or geophysical prospecting methods; the pumping flow of different pumping stages refers to constant pumping flow corresponding to each pumping stage in the step pumping test. In the step-down test, the initial pumping rate is kept constant until the down-depth reaches a quasi-steady state, after which the pumping flow is typically increased and kept constant until the water level reaches another quasi-steady state, and this process is repeated at least three times, i.e., at least three pumping stages.
S12, stratum distribution information and quasi-steady-state water level depths corresponding to different water pumping stages are obtained, the pressure state change of the aquifer is determined, and whether the aquifer undergoes pressure-bearing-non-pressure conversion is determined according to the pressure state change.
The stratum distribution information mainly comprises the lithology, thickness, burial conditions and the like of the aquifer, and can be obtained by methods of drilling core observation, geophysical exploration and the like; the quasi-steady-state water level depth is obtained by observing the dynamic change of the water level in the well for a long time in each pumping stage when the water level is reduced to be stable and the difference between the steady water level value and the initial water level is obtained; the pressure state of the aquifer can be judged according to the relative position relation between the water level and the aquifer top plate, if the water level is above the aquifer top plate, the aquifer is in a pressure-bearing state, and if the water level is below the aquifer top plate, the aquifer is in a non-pressure state; the pressure-bearing-pressureless conversion means that the water-bearing layer is converted from an original pressure-bearing state to a pressureless state in the water pumping process.
Specifically, by observing and describing drill cores of the pumping well and the observation well, stratum distribution information such as lithology, thickness, burial depth and the like of the aquifer is obtained, and if necessary, the space distribution range of the aquifer can be further determined by combining a geophysical prospecting method (such as electrical prospecting); in the water pumping test process, after each water pumping stage lasts for a certain time, the water level is reduced to be stable, the stable water level value at the moment is recorded, and the difference between the water level value and the initial water level is the quasi-steady water level depth of the water pumping stage; comparing the quasi-steady-state water level depths of different pumping stages with the burial depths of the top plate of the aquifer, if the former is smaller than the latter, the aquifer is in a pressure-bearing state, and if the former is larger than the latter, the aquifer is in a non-pressure state; if the quasi-steady state water level depth is observed to exceed the burial depth of the aquifer roof in a certain pumping stage, the transition from pressure bearing to non-pressure is generated in the pumping stage.
And S13, under the condition that the aquifer is confirmed to undergo pressure-free conversion, estimating the permeability coefficient, the storage coefficient and the corresponding well loss coefficient under the pressure-bearing condition of the aquifer by adopting a particle swarm optimization method according to a pre-established ladder pumping water level deep analysis model considering the pressure-free conversion and the well loss influence.
The application pre-establishes a ladder pumping water level deep analysis model considering pressure-bearing-non-pressure conversion and well loss influence, the model not only considers the conversion from a pressure-bearing state to a non-pressure state, but also considers the head loss (namely well loss influence) caused by non-Darcy seepage near a well wall, the permeability coefficient represents the water guiding capacity of an aquifer, the storage coefficient represents the water storage capacity of the aquifer, the well loss coefficient represents the head loss degree caused by non-Darcy seepage near the well wall, and the parameters are important physical quantities for describing the hydraulic characteristics of the aquifer; the particle swarm optimization method is a heuristic intelligent search algorithm, and by simulating the feeding behavior of the bird swarm, an optimal solution is found in a solution space, so that the particle swarm optimization method has the characteristics of high search efficiency, strong robustness and the like.
Specifically, firstly, selecting a proper aquifer water flow mathematical model according to factors such as aquifer type, boundary condition, well type and the like, introducing a water level degradation analysis solution considering well damage influence on the basis, describing a pressure-non-pressure conversion process in a piecewise function form, and thus establishing a ladder pumping water level degradation analysis model considering the pressure-non-pressure conversion and the well damage influence; then, substituting the actually observed quasi-steady-state water level drop value into the analysis model as a known quantity to form an optimization problem about the permeability coefficient, the storage coefficient and the well loss coefficient, searching for an optimal parameter combination by adopting a particle swarm optimization algorithm with the minimum root mean square error of the observed value and the calculated value as an objective function and with the physical meaning and the empirical value of the parameter as constraint conditions; in the particle swarm optimization process, parameters such as particle number, maximum iteration number, learning factors and the like are reasonably set, the convergence speed and precision of an algorithm are controlled, and finally estimated values of the permeability coefficient, the storage coefficient and the well loss coefficient are obtained.
S14, substituting the initial water head of the aquifer, the elevation of the top of the aquifer, the pumping flow, the permeability coefficient, the storage coefficient and the well loss coefficient corresponding to the pressure-bearing condition in a stepped pumping water level deep analysis model considering the pressure-bearing-non-pressure conversion and the well loss influence, and calculating the critical time point of the pressure-bearing-non-pressure conversion.
The critical time point when the pressure-bearing-non-pressure conversion occurs is a time point corresponding to the conversion of the pressure-bearing state to the non-pressure state of the aquifer, the water level drop depth in the pumping well is regarded as equal to the difference between the embedded depth of the top plate of the aquifer and the embedded depth of the initial water level at the moment, the initial water head of the aquifer, the elevation of the top of the aquifer and the pumping flow of different pumping stages obtained in the step S11, the permeability coefficient, the storage coefficient and the well loss coefficient obtained in the step S13 are estimated, the permeability coefficient, the storage coefficient and the well loss coefficient are substituted into the stepped pumping water level drop depth analysis model which is established in the step S13 and is considered to be influenced by the pressure-non-pressure conversion and the well loss, and the time point which meets the pressure-non-pressure conversion condition is determined through a numerical solution method, namely the critical time point. By solving the critical time point, different calculation modes are adopted at different stages, and the reservoir change of the aquifer is estimated more accurately.
Specifically, in one embodiment, referring to fig. 2, the process of establishing the ladder pumping water level lowering analysis model taking into consideration the pressure-bearing-non-pressure conversion and well loss effects includes the following steps:
s21, assuming that the confined aquifer and the pressureless aquifer extend isotropically and infinitely in the radial direction, and acquiring potential functions of the confined aquifer and the pressureless aquifer by using a GIRINSKII potential method.
Wherein, the radial isotropy means that the permeability of the aquifer is uniform and consistent in space and the permeability coefficients are equal in radial direction; infinite extension means that the horizontal extent of the aquifer is much greater than the investigation region, and boundary effects can be ignored; the GIRINSKII potential method is a mathematical method for solving the water flow problem of the aquifer based on the variational principle and the potential functional minimization theory, and a differential equation for describing the water flow of the aquifer can be obtained by constructing the potential functional of the aquifer and solving the minimum value of the potential functional.
In particular, for a homogeneous isotropic and infinitely extending confined aquifer, its potential function can be expressed as the product of the aquifer roof elevation and the difference in hydrostatic head times the aquifer thickness; for a homogeneous isotropic and infinitely extending pressureless aquifer, its potential function can be expressed as the square of the difference between aquifer roof elevation and hydrostatic head divided by the permeability coefficient of 2 times. By utilizing GIRINSKII potential method and combining Darcy's law and continuity condition, differential equation describing water flow of confined aquifer and pressureless aquifer can be obtained, which lays foundation for subsequent derivation of analysis model of water level drop of ladder pumping.
S22, assuming initial hydrostatic pressure balance, establishing a control equation, a hydrostatic pressure initial condition, an outer boundary condition and a wellbore wall inner boundary condition considering single complete well step deep pumping flow.
The initial hydrostatic pressure balance means that the water pressure in the aquifer is in a balance state before pumping begins, and no water flow movement exists; the control equation is a partial differential equation describing the movement of aquifer water flow; the initial conditions give the initial water head distribution needed by solving the aquifer water flow control equation; the outer boundary condition describes the water head or flow condition on the outer boundary of the aquifer, and common water head boundary, constant flow boundary, no flow boundary and the like; the internal boundary conditions describe the head or flow conditions on the walls of the pumping well, considering single complete well step down pumping means that the pumping flow is kept constant during each pumping phase.
S23, obtaining basic analytic solutions under pressure bearing and non-pressure conditions caused by constant pumping flow according to potential functions, control equations, initial conditions, outer boundary conditions and inner boundary conditions of the pressure bearing aquifer and the non-pressure aquifer.
S24, according to basic analytic solution and by combining the well loss expression and the superposition principle, obtaining a descending depth change expression in the stepped descending depth pumping well considering pressure-non-pressure conversion and well loss, wherein the well loss coefficients of the well loss expressions corresponding to the pressure-non-pressure conditions are different.
Specifically, referring to FIG. 3, FIG. 3 depicts a confined aquifer with a complete well, assuming that the origin of the cylindrical coordinates is at the bottom-hole center, the aquifer is homogeneous, radially isotropic, and has a uniform infinite thickness in the radial direction. Before pumping, the underground water level is in a hydrostatic pressure balance state, and the flow and the quasi-steady state descending depth are increased in a step mode.
In step S21, using the GIRINSKII potential method,
The potential function of the confined aquifer is obtained as follows:（1）；
the potential function of the pressureless aquifer is obtained as follows: （2）；
wherein K is a permeability coefficient, and M and h respectively represent the thicknesses of the confined aquifer and the pressureless aquifer; h represents the head of water in the confined aquifer.
In step S22, the aquifer is divided into a plurality of unit volumes in the radial direction, each unit volume being represented by a cylinder of thickness dr and radius r, resulting in a lower control equation and initial and outer boundary conditions.
（3）；
（4）；
（5）；
Wherein, The voltages GIRINSKII in the confined and pressureless aquifers are represented uniformly in equations (1) and (2); t represents pumping duration; r represents the radial distance from the center of the wellbore; a is the aquifer diffusivity and a = T/S, T and S are the aquifer' S permeability and storage coefficient, respectively.Is the initial potential expressed as
(6)；
Assuming three pumping phases are experienced, the wellbore wall boundary conditions that consider stepped-down pumping flow may be described as
（7）；
（8）；
（9）；
Wherein, 、AndRespectively represents the constant flow rate of each pumping depth, wherein，AndThe time points at which the first and second dips end are indicated, respectively. The model described in equations (3) - (6) has the same mathematical structure as the Theis model (Theis 1935) except for the stepped pumping flow, so that the solution of equations (3) - (6) and the solution of constant pumping flow Q should be the Theis solution, namely
（10）
Wherein, ; W (u) is a Theis well function expressed as an integral function; from equations (1), (2), (6) and (10), it can be deduced that if pressure-to-pressureless conversion is caused by a constant pumping flow rate Q, the head in the pressure-and pressureless aquifers can be expressed as
（11）；
And
（12）；
Wherein the method comprises the steps ofIndicating the initial head of the confined aquifer. By using the expression and superposition principle of well loss, the solution of the stepped descent test model which considers well loss and undergoes pressure-bearing-pressureless conversion can be obtained.
To obtain the general expression, it is assumed that the time point of the pumping flow rate change is expressed as，，，...，WhereinAndRespectively a start point and an end point of pumping. In addition, it is assumed that critical time points of pressure-bearing-no-pressure conversionIn the (n+1) -th step, i.eWherein n=0, 1,2, 3..the term "is used to refer to the water head expression of the confined aquifer and the water head expression of the pressureless aquifer according to the superposition principle, the solution to obtain the time-dependent degradation in the pumping well can be expressed as
（13）；
（14）；
In equations (13) and (14),Representing the depth of the well before and after pressure-bearing-no-pressure conversion; b and C represent different well loss coefficients, since well losses under no pressure must be different from those under pressure.
It is noted that the well loss factor C in the absence of pressure constitutes a comprehensive indicator covering the effect of well loss, because as the water level in the vicinity of the well bore transitions from pressure-bearing conditions to non-pressure conditions, the water level changes dynamically and the well loss factor gradually decays from B to a lower value than C. Therefore, C is only a representative value, representing the well loss coefficient evolving in the process.
In one specific pumping test, pumping time was from 10 a.m.: 30 last to 2 pm the next day: 30. the pumping rates were subjected to three different pumping rates, including q1= 49.44m 2/d, q2= 88.68m 2/d and q3= 104.55m 2/d. Preliminary hydrogeological surveys were first conducted on the fourth formation to determine that the gravel layer was the primary aquifer. Thus, during drilling of a pumping well, drilling is stopped when core samples show that weathered conglomerates are encountered. The core bar graph of the pumping well is shown in fig. 3, and is composed of miscellaneous fill, silty clay, gravel sand, silty clay (residual soil) and conglomerate from the surface down. The initial water level depth of the confined aquifer is 2.80 meters, and the three quasi-steady water level depths in the well in the stepped-descent pumping test are 5.27 meters, 7.59 meters and 8.73 meters respectively. As can be seen from fig. 4, the top of the main aquifer (i.e., the gravel layer) is located between the quasi-steady state water level depths of the second stage and third stage pump, and therefore, there must be a pressure-no pressure transition during the third stage pump. The formation conditions revealed from adjacent boreholes outside the impact of the pumping test are similar to those shown in fig. 4, indicating that the pumping test can be characterized by the models represented by equations (3) through (5).
For the stepped-down pumping test undergoing pressure-to-no-pressure conversion, its analytical solution is characterized by the piecewise functions shown in equations (13) and (14), thus determining the critical time of the conversion [ ]) It is important.
The present application uses the observed dip data in the well during the first and second pumping stages in combination with Particle Swarm Optimization (PSO) algorithm to estimate the hydrogeologic coefficients, including permeability coefficient K, storage coefficient S and well loss coefficient B, as shown in FIG. 5, and the present application has been found experimentally to be unaffected by the pressure-to-non-pressure transition in the first and second pumping stages, and thus the method is viable.
Referring to fig. 6, a critical point in time for a pressure-to-no-pressure transition is obtainedThe method specifically comprises the following steps:
s61, estimating a permeability coefficient K, and storing the coefficient S and a well loss coefficient B.
Referring to fig. 7, the estimated permeability coefficient K, the storage coefficient S, the well loss coefficient B, specifically includes the following steps:
S71, establishing an objective function.
Specifically, the objective function is
（15）；
Wherein R is the minimum root mean square error in the particle swarm iteration process; n represents the calculated dip for fittingAnd observe the lowering of depthIs the number of data points; h represents the dataset of target parameters in the iteration.
S72, setting input parameters of a particle swarm optimization algorithm, wherein the input parameters comprise the number N of particles, inertia weight w, maximum iteration number M, the number D of parameters and individual learning factorsAnd social learning factors。
In the pumping test, the number of particles N, the inertia weight w, the maximum iteration number M, the parameter number D and the individual learning factorAnd social learning factorsAs shown in FIG. 4, the number of particles N is 40, the inertia weight w is 0.35, the maximum iteration number M is 20, the number of parameters D is 3, and the individual learning factorIs 0.1 and social learning factor1.
S73, determining a permeability coefficient K, and storing search ranges of the coefficient S and the well loss coefficient B.
And S74, running a particle swarm optimization algorithm based on the input parameters and the search range, and estimating to obtain the permeability coefficient K, and storing the values of the coefficient S and the well loss coefficient B.
S62, determining the flow stage of pressure-bearing-non-pressure conversion according to the pressure state change.
S63, determining a comprehensive expression of the step pumping water level drop change considering the pressure-free conversion and the well loss according to the flow stage of the pressure-free conversion of the aquifer and the step pumping water level drop analysis model considering the pressure-free conversion and the well loss.
S64, taking the difference between the initial water head of the aquifer and the elevation of the top of the aquifer as an allowable descent value.
Wherein the initial water head observed is the initial water head of the aquifer.
S65, substituting the estimated permeability coefficient K, the storage coefficient S, the well loss coefficient B and the allowable degradation value into the comprehensive expression, and solving the corresponding time when the allowable degradation value is obtainedThe critical time of pressure-bearing-non-pressure conversion is obtained.
Specifically, based on the recorded dip data, we determined that the transition occurred during the third pumping step, and therefore, the comprehensive expression of equation (13) is:
（16）；
wherein, Is the initial water head and is used for the water treatment,Is the elevation of the top of the aquifer.
The implementation principle of the embodiment of the application is as follows: firstly, basic information of an aquifer is obtained; then, according to stratum distribution information and quasi-steady-state water level depths corresponding to different pumping stages, determining the pressure state change of the aquifer, adopting a pre-established ladder pumping water level degradation analysis model considering pressure-bearing-non-pressure conversion and well loss influence, and estimating the permeability coefficient, storage coefficient and corresponding well loss coefficient of the aquifer under the pressure-bearing condition by using a particle swarm optimization method; finally substituting the parameter values into an analytical model, and calculating a critical time point when pressure-bearing and non-pressure conversion occurs; comprehensively considering the influence of pressure-bearing and non-pressure conversion and well loss coefficient in the pumping process, and simultaneously realizing parameter estimation by adopting a particle swarm optimization method; the change process of the pressure state of the aquifer is characterized by calculating the critical time point, so that the deviation between the analysis result and the actual situation is reduced.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic, and should not limit the implementation process of the embodiment of the present application.
In one embodiment, the present application provides an electronic device, which may be a server, and an internal structure thereof may be as shown in fig. 8. The electronic device includes a processor, a memory, and a network interface connected by a system bus. Wherein the processor of the electronic device is configured to provide computing and control capabilities. The memory of the electronic device includes a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The database of the electronic device is for storing data. The network interface of the electronic device is used for communicating with an external terminal through a network connection. The computer program when executed by the processor implements a method for estimating aquifer parameters taking into account pressure-to-non-pressure conversion and well loss.
It will be appreciated by those skilled in the art that the structure shown in fig. 8 is merely a block diagram of a portion of the structure associated with the present inventive arrangements and is not limiting of the electronic device to which the present inventive arrangements are applied, and that a particular electronic device may include more or fewer components than shown, or may combine certain components, or have a different arrangement of components.
In an embodiment, there is also provided an electronic device including a memory and a processor, the memory storing a computer program, the processor implementing the steps of the method embodiments described above when executing the computer program.
Those skilled in the art will appreciate that implementing all or part of the above-described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in embodiments provided herein may include at least one of non-volatile and volatile memory. The nonvolatile memory may include Read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, or the like. Volatile memory can include random access memory (RandomAccessMemory, RAM) or external cache memory. By way of illustration, and not limitation, RAM can take many forms, such as static random access memory (StaticRandomAccessMemory, SRAM) or dynamic random access memory (DynamicRandomAccessMemory, DRAM), among others.
The above embodiments are not intended to limit the scope of the present application, so: all equivalent changes in structure, shape and principle of the application should be covered in the scope of protection of the application.
Claims (9)
1. The aquifer parameter estimation method considering pressure-bearing-non-pressure conversion and well loss is characterized by comprising the following steps:
Acquiring an initial water head of an aquifer, the elevation of the top of the aquifer and the pumping flow of different pumping stages;
acquiring stratum distribution information and quasi-steady-state water level depths corresponding to different water pumping stages, determining the pressure state change of the aquifer, and determining whether the aquifer undergoes pressure-bearing-non-pressure conversion according to the pressure state change;
Under the condition that the aquifer is confirmed to undergo pressure-free conversion, estimating the permeability coefficient, the storage coefficient and the corresponding well loss coefficient under the pressure-bearing condition of the aquifer by adopting a particle swarm optimization method according to a pre-established ladder pumping water level deep-falling analysis model considering the pressure-free conversion and the well loss effect;
Substituting the initial water head of the aquifer, the elevation of the top of the aquifer, the pumping flow of different pumping stages, the permeability coefficient, the storage coefficient and the well loss coefficient corresponding to the pressure-bearing-non-pressure conversion and the well loss under the pressure-bearing condition into the stepped pumping water level degradation analysis model considering the pressure-bearing-non-pressure conversion and the well loss influence, and calculating the critical time point of pressure-bearing-non-pressure conversion.
2. The method for estimating aquifer parameters considering pressure-bearing-non-pressure conversion and well loss according to claim 1, wherein the method for estimating the permeability coefficient, storage coefficient and well loss coefficient corresponding to the bearing condition of the aquifer by adopting particle swarm optimization comprises the following steps:
establishing an objective function ；
Wherein R is the minimum root mean square error in the particle swarm iteration process; n represents the calculated dip for fittingAnd observe the lowering of depthIs the number of data points; h represents a dataset of target parameters in the iteration;
Setting input parameters of a particle swarm optimization algorithm, wherein the input parameters comprise a particle number N, an inertia weight w, a maximum iteration number M, a parameter number D and an individual learning factor And social learning factors；
Determining a search range of a permeability coefficient K, a storage coefficient S and a well loss coefficient B;
And running a particle swarm optimization algorithm based on the input parameters and the search range to estimate and obtain values of the permeability coefficient K, the storage coefficient S and the well loss coefficient B.
3. The aquifer parameter estimation method considering pressure-non-pressure conversion and well loss according to claim 1, wherein the method is characterized in that the initial water head of the aquifer, the elevation of the top of the aquifer, the pumping flow rate of different pumping stages, the permeability coefficient, the storage coefficient and the well loss coefficient corresponding to the pressure-bearing condition are substituted into the stepped pumping water level lowering analysis model considering pressure-non-pressure conversion and well loss influence, and the critical time point of pressure-non-pressure conversion is calculated, and specifically comprises the following steps:
Determining a flow stage at which the bearing-pressureless conversion of the aquifer occurs according to the pressure state change;
Determining a comprehensive expression of the step pumping water level drop change considering the pressure-free conversion and the well loss according to the flow stage of the pressure-free conversion of the aquifer and the step pumping water level drop analysis model considering the pressure-free conversion and the well loss;
taking the difference between the initial water head of the aquifer and the elevation of the top of the aquifer as an allowable descent depth value;
Substituting the permeability coefficient, the storage coefficient, the well loss coefficient corresponding to the pressure-bearing condition and the allowable deep-down value into the comprehensive expression, and solving the corresponding time when the allowable deep-down value is obtained, namely the critical time of pressure-bearing and non-pressure conversion.
4. The aquifer parameter estimation method considering pressure-non-pressure conversion and well loss according to claim 1, wherein the step pumping water level lowering analysis model establishing process considering pressure-non-pressure conversion and well loss comprises the following steps:
Assuming that the confined aquifer and the pressureless aquifer extend isotropically and infinitely in the radial direction, acquiring potential functions of the confined aquifer and the pressureless aquifer by using a GIRINSKII potential function method;
assuming initial hydrostatic pressure balance, establishing a control equation, a hydrostatic pressure initial condition, an external boundary condition and a well wall boundary condition considering single complete well step deep pumping flow;
According to potential functions of the confined aquifer and the pressureless aquifer, the control equation, the initial condition, the outer boundary condition and the inner boundary condition, respectively obtaining basic analytic solutions of the falling depths of the confined and pressureless conditions caused by constant pumping flow;
According to the basic analytic solution, a step pumping water level drop analytic model considering pressure-bearing and non-pressure conversion and well loss influence is established by combining a well loss expression and a superposition principle, wherein the well loss coefficients of the well loss expression corresponding to the pressure-bearing and non-pressure conditions are different.
5. The method for estimating aquifer parameters considering pressure-bearing-pressureless conversion and well loss as claimed in claim 4, wherein, assuming that the pressure-bearing aquifer and the pressureless aquifer are homogeneously isotropic and infinitely extended in radial direction, the potential functions of the pressure-bearing aquifer and the pressureless aquifer are obtained by GIRINSKII potential function method,
The potential function of the confined aquifer is:；
the potential function of the pressureless aquifer is: ；
wherein K is a permeability coefficient, and M and h respectively represent the thicknesses of the confined aquifer and the pressureless aquifer; h represents the head of water in the confined aquifer.
6. The method for estimating an aquifer parameter considering pressure-bearing-pressureless conversion and well loss according to claim 5, wherein the aquifer is divided into a plurality of unit volumes along the radial direction, each unit volume is represented by a cylinder with thickness dr and radius r, in the wellbore wall internal boundary condition considering single complete well step down pumping flow, by establishing a control equation, a hydrostatic pressure initial condition, an external boundary condition, and assuming initial hydrostatic pressure balance, and obtaining
The control equation is:；
The initial conditions are: ；
The outer boundary conditions are: ；
wherein, Represents GIRINSKII potential in confined aquifers and pressureless aquifers, t represents pumping duration, and r represents radial distance from the center of the shaft, namely radius of a cylinder taking a vertical line of the center of the shaft as an axis; a is the aquifer diffusivity and a = T/S, T and S are the aquifer 'S permeability and the aquifer' S storage coefficient, respectively,Is the initial potential expressed asWherein, the method comprises the steps of, wherein,Indicating the initial head of the confined aquifer.
7. The method for estimating aquifer parameters considering pressure-bearing-non-pressure conversion and well loss according to claim 6, wherein the wellbore wall internal boundary condition considering single complete well step deep pumping flow is described as:
；
；
；
wherein, 、AndRespectively represents the constant flow rate of each pumping depth, wherein，AndThe time points at which the first and second dips end are indicated, respectively.
8. The aquifer parameter estimation method considering pressure-non-pressure conversion and well loss according to claim 7, wherein the basic analysis solutions of the pressure-bearing and non-pressure condition drop depths caused by constant pumping flow are obtained according to the potential functions of the pressure-bearing aquifer and non-pressure aquifer, the control equation, the initial conditions, the outer boundary conditions and the inner boundary conditions, respectively, specifically comprising the following steps:
Obtaining a general solution of the control equation, the initial condition and the outer boundary condition according to a Theis analytical model
；
Wherein, ; W (u) is a Theis well function expressed as an integral function;
based on the potential functions of the confined aquifer and the pressureless aquifer and the general solution, it is assumed that a confined-pressureless transition is caused by a constant pumping flow Q, then
The drop in confined aquifer is expressed as:；
The dip of the pressureless aquifer is expressed as: ；
wherein, Indicating the initial head of the confined aquifer.
9. The aquifer parameter estimation method considering pressure-non-pressure conversion and well loss according to claim 8, wherein the step water level lowering analysis model considering pressure-non-pressure conversion and well loss is established by combining well loss expression and superposition principle according to the basic analysis solution, and specifically comprises the following steps:
Acquiring a well loss coefficient B under a pressure-bearing condition and a well loss coefficient C under a non-pressure condition;
According to the superposition principle, the water head expression of the confined aquifer and the water head expression of the pressureless aquifer, a stepped water pumping water level lowering analysis model considering the effects of pressure bearing-pressureless conversion and well loss is obtained:
；
；
wherein, Represents the descent depth in the pumping well, B represents the well loss coefficient under the pressure-bearing condition, C represents the well loss coefficient under the non-pressure condition,Indicating the critical point in time at which the pressure-to-no-pressure transition occurs,Indicating the radius of the pumping well,The i-th time point of the pumping flow rate change is represented, where i=0 is the starting point of pumping.
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