Inclined aquifer free surface elevation and parameter inversion calculation method with free surface positioned on air inlet value plane

Abstract

The invention discloses an inclined aquifer free surface elevation and parameter inversion calculation method with a free surface positioned on an air inlet value plane, and relates to the technical field of hydrogeology, and the method comprises the following steps: 1, building a parameter calculation inversion model; step 2, inputting an air inlet value surface elevation observation value to the calculation inversion model; 3, obtaining an inversion result, and continuing calculation; and 4, obtaining a forward modeling prediction result. According to the inclined aquifer free surface elevation and parameter inversion calculation method with the free surface positioned on the air inlet value plane, the free surface is positioned on the air inlet value plane, and a negative pressure saturation region above the underground water level is fully considered, so that the real physical states of aquifers with different thicknesses can be accurately described, and particularly, under the scene of a thin aquifer, the calculation accuracy is greatly improved. And the accuracy of describing the characteristics of the aquifer is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of hydrogeology, and specifically to a method for inverse calculation of the free surface elevation and parameters of an inclined aquifer with the free surface positioned at the intake value plane. Background Technique

[0002] Previous studies on the groundwater flow in inclined aquifers have shown that the Dupuit assumption and the Boussinesq equation completely ignore the capillary saturation zone, and it assumes that the free surface of the unconfined aquifer is located at the groundwater level. At the same time, this assumption means that the thickness of the capillary zone above the groundwater level is much smaller than the thickness of the saturated zone below the groundwater level, so it can be ignored. Although this approximation is usually acceptable for relatively thick aquifers (e.g., more than dozens of meters), problems may occur when the aquifer is relatively thin (e.g., less than one or two meters). The existence of the intake value plane (hereinafter referred to as the ha plane) means that there is a negative pressure saturation zone above the groundwater level, and its thickness may be comparable to the thickness of the positive pressure saturation zone below the groundwater level.

[0003] At the same time, due to the neglect of capillary action, when constructing a saturated flow model of an unconfined aquifer with the free surface located at the groundwater level, it has become a common practice to use the effective porosity as the specific yield. However, the specific yield is not equal to the effective porosity, and it is jointly affected by many factors such as lithology, medium saturation, pore size and connectivity, groundwater dynamics, and saturation.

[0004] Existing studies have shown that the classical saturated seepage theory, which locates the free surface at the water table (or the hanging zero-pressure plane), cannot give a reasonable explanation for the hydrodynamic processes contained in the surface water-groundwater interaction. The reason is that there is a physical paradox in the water table equation constructed by locating the free surface at the water table. According to the water table (or the hanging zero-pressure plane) equation based on the abrupt interface assumption and the water table (or the hanging zero-pressure plane) equation based on the modified specific yield, both will lead to the numerical positive and negative signs of the buried depth of the front of the hanging saturated zone calculated by the mathematical model being opposite to the buried depth of the hanging saturated zone specified by the physical model. In the general form of the water table equation, according to the definition of the specific yield located at the water table and considering capillary action, since the capillary saturated zone changes with the water table, the specific yield μ is always equal to 0. This shows that the water table or the hanging zero-pressure plane is only driven by the infiltration recharge intensity at the water table or the hanging zero-pressure plane and has nothing to do with the specific yield. Obviously, the general form of the water table equation is not self-consistent either.

[0005] Under the condition of satisfying the Dupuit assumption, the water table equation and the saturated seepage control equation are simplified to the Boussinesq equation. Therefore, the Boussinesq equation naturally inherits the limitations of the water table equation.

[0006] To overcome the limitations of the Boussinesq equation with the free surface located at the phreatic surface, the present invention constructs a Boussinesq equation with the free surface located at the air-entry value surface, and uses it to describe the groundwater dynamics of an inclined aquifer and perform the inversion of aquifer parameters. Summary of the Invention

[0007] To achieve the above object, the present invention is realized through the following technical solutions: A method for calculating the free surface elevation and inverting parameters of an inclined aquifer with the free surface located at the air-entry value plane, comprising the following steps:

[0008] Step 1: Establish a calculation model for the free surface elevation of the inclined aquifer;

[0009] Step 2: Establish an inversion model for parameter calculation;

[0010] Step 3: Input the observed value of the air-entry value surface elevation into the calculation and inversion model;

[0011] Step 4: Obtain the inversion result and continue the calculation;

[0012] Step 5: Obtain the forward prediction result;

[0013] Preferably, the calculation model for the free surface elevation of the inclined aquifer is composed of the following calculation equations:

[0014]

[0015] where μ ha is the specific yield at the h a plane, k x is the horizontal hydraulic conductivity of the aquifer, W is the infiltration recharge rate at the h a plane, z ha (x, t) is the elevation of the h a plane, and z is the elevation in the vertical direction;

[0016] The z ha (x, t) is obtained from the following calculation equation:

[0017] z ha = h ha (x,t)+h b (x);

[0018] where h ha is the thickness of the inclined aquifer from the bottom of the inclined aquifer to the h a plane;

[0019] The h b is the vertical distance of the inclined aquifer from the bottom of the inclined aquifer to the h a plane;

[0020] The said h b is obtained from the following calculation equation:

[0021] h b =(B - x)tanα;

[0022] Wherein, B is the coordinate of the intersection point of the bottom surface of the inclined aquifer and the reference plane.

[0023] Preferably, the said h ha at the initial conditions and boundary conditions, specifically is the following equation:

[0024] h ha (x, 0) = h0 0 < x < B;

[0025] h ha (0, t) = h1 t > 0;

[0026] h ha (B, t) = h2 t > 0;

[0027] Preferably, let s = h ha - h0;

[0028] Therefore h a the surface elevation is:

[0029] z ha = h ha + h b = s + h0 + h b ;

[0030] The said s is obtained from the following calculation formula:

[0031]

[0032] Wherein,

[0033]

[0034] Wherein, is the average thickness of the inclined aquifer.

[0035] Preferably, the said parameter calculation inversion model specifically includes the following formulas:

[0036]

[0037] Wherein, z cij and z tij are respectively the calculated value and the observed value of the intake value surface elevation at the jth moment and the ith observation point.

[0038] The present invention provides a method for calculating the free surface elevation and parameter inversion of an inclined aquifer with the free surface positioned at the intake value plane. It has the following beneficial effects:

[0039] 1. A method for inverting the elevation and parameters of the free surface of an inclined aquifer with the free surface positioned at the air entry value plane. By positioning the free surface at the air entry value plane, the negative pressure saturation zone above the groundwater level is fully considered, enabling the accurate characterization of the true physical state of aquifers with different thicknesses. Especially in the scenario of thin aquifers, the accuracy of describing the characteristics of the aquifer is greatly improved.

[0040] 2. The method for inverting the elevation and parameters of the free surface of an inclined aquifer with the free surface positioned at the air entry value plane can more accurately describe the groundwater dynamic process of the inclined aquifer, providing strong support for the in-depth study of the movement law of groundwater. In terms of inverting aquifer parameters, compared with the traditional limited equations, the new equation of this patent can obtain more accurate and reliable inversion results, helping to more efficiently determine the various parameters of the aquifer. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 FIG. is a schematic diagram of the initial conditions and boundary conditions of a method for inverting the elevation and parameters of the free surface of an inclined aquifer with the free surface positioned at the air entry value plane according to the present invention;

[0042] Figure 2 FIG. is a schematic diagram of the forward and inversion calculation processes according to the present invention;

[0043] In the figure: 1. Initial h a surface; 2. Instantaneous h a surface. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments. The embodiments of the present invention are given for the purpose of illustration and description, and are not exhaustive or limit the present invention to the disclosed form. Many modifications and variations are obvious to those of ordinary skill in the art. The embodiments are selected and described to better illustrate the principles and practical applications of the present invention, and enable those of ordinary skill in the art to understand the present invention and design various embodiments with various modifications suitable for specific purposes.

[0045] The present invention provides a technical solution: a method for inverting the elevation and parameters of the free surface of an inclined aquifer with the free surface positioned at the air entry value plane, including the following steps:

[0046] Step 1. Establish a calculation model for the elevation of the free surface of the inclined aquifer;

[0047] Step 2. Establish an inversion model for parameter calculation;

[0048] Step 3. Input the observed value of the elevation of the air entry value plane into the calculation inversion model;

[0049] Step 4: Obtain the inversion result and continue the calculation;

[0050] Step 5: Obtain the forward prediction result;

[0051] The calculation model for the elevation of the free surface of the inclined aquifer consists of the following calculation equations:

[0052]

[0053] Where, μ ha is the specific yield at the h a plane, k x is the horizontal hydraulic conductivity of the aquifer, W is the infiltration recharge rate at the h a plane, z ha (x, t) is the elevation of the h a plane, and z is the elevation in the vertical direction;

[0054] The z ha (x, t) is obtained from the following calculation equation:

[0055] z ha = h ha (x,t) + h b (x);

[0056] Where, h ha is the thickness of the inclined aquifer from the bottom of the inclined aquifer to the h a plane;

[0057] The h b is the vertical distance of the inclined aquifer from the bottom of the inclined aquifer to the h a plane;

[0058] The h b is obtained from the following calculation equation:

[0059] h b = (B - x)tanα;

[0060] Where, B is the coordinate of the intersection point of the bottom surface of the inclined aquifer and the reference plane.

[0061] The h ha at the initial condition and boundary condition is specifically the following equation:

[0062] h ha (x,0) = h0 0 < x < B;

[0063] h ha (0,t) = h1 t > 0;

[0064] h ha (B,t) = h2 t > 0;

[0065] Let s = h ha - h0;

[0066] Therefore, h a The surface elevation is:

[0067] z ha = h ha + h b = s + h0 + h b ;

[0068] The s is obtained from the following calculation formula:

[0069]

[0070] where,

[0071]

[0072] where, is the average thickness of the inclined aquifer.

[0073] Second embodiment, on the basis of the first embodiment,

[0074] The parameter calculation and inversion model specifically includes the following formulas:

[0075]

[0076] where, z cij and z tij are respectively the calculated value and the observed value of the intake value surface elevation at the j-th moment and the i-th observation point.

[0077] Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art and related fields without creative efforts shall fall within the protection scope of the present invention. The structures, devices, and operation methods not specifically described and explained in the present invention, unless otherwise specified and limited, are implemented according to the conventional means in the art.

Claims

1. A method for inverse calculation of the free surface elevation and parameters of an inclined aquifer with the free surface located in the intake value plane, characterized in that, It includes the following steps: Step 1, establish a calculation model for the elevation of the free surface of the inclined aquifer; Step 2, establish an inversion model for parameter calculation; Step 3, input the observed value of the elevation of the air intake value surface into the calculation inversion model; Step 4, obtain the inversion result and continue the calculation; Step 5, obtain the forward prediction result.

2. The free surface elevation and parameter inversion calculation method for an inclined aquifer with the free surface positioned in the intake value plane according to claim 1, characterized in that: The calculation model for the elevation of the free surface of the inclined aquifer consists of the following calculation equations: Among them, μ ha is the specific yield at the h a plane, k x is the horizontal hydraulic conductivity of the aquifer, and W is the infiltration recharge rate at the h a plane, z ha (x, t) is the elevation of the h a plane, and z is the elevation in the vertical direction; The said z ha (x, t) is obtained from the following calculation equation: z ha = h ha (x, t) + h b (x); where h ha is the thickness of the inclined aquifer floor to the h a plane of the inclined aquifer; The said h b is the vertical distance from the inclined aquifer floor to h a for the planar inclined aquifer; The said h b is obtained from the following calculation equation: h b = (B - x) tan α; Among them, B is the coordinate of the intersection point of the bottom surface of the inclined aquifer and the reference surface.

3. A method for inverse calculation of the free surface elevation and parameters of an inclined aquifer with the free surface positioned in the intake value plane according to claim 2, characterized in that: The said h ha Under the initial conditions and boundary conditions, specifically, the following equation: h ha (x,0) = h0 0 < x < B; h ha (0,t) = h1 for t > 0; h ha (B, t) = h2 t > 0.

4. A method for inverse calculation of the free surface elevation and parameters of an inclined aquifer with the free surface located in the intake value plane according to claim 3, characterized in that: Let s = h ha - h0; Therefore, h a The surface elevation is: z ha = h ha + h b = s + h0 + h b ; The said s is obtained from the following calculation formula: Among them, Among them, is the average thickness of the inclined aquifer.

5. A method for inverse calculation of the free surface elevation and parameters of an inclined aquifer with the free surface positioned in the intake value plane according to claim 4, characterized in that: The parameter calculation inversion model specifically includes the following formulas: where z cij and z tij are the calculated value and the observed value of the intake value surface elevation at the j-th moment and the i-th observation point, respectively.

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