First, establish a hydrogeological conceptual model.
On the basis of comprehensive and in-depth analysis of the groundwater system in Heihe River Basin, according to the purpose of the study, the components and interrelationships of the groundwater system are reasonably simplified and assumed, and the conceptual model of the groundwater system is reproduced in the form of words, block diagrams, plans and sections.
(1) Generalization of spatial structure and determination of boundary of groundwater system
1. schema represents the spatial structure of groundwater system.
According to the hydrogeologic map and hydrogeologic profile of Heihe River Basin, the main aquifers, aquicludes and weakly permeable layers are sorted and divided, their occurrence, distribution range and thickness are found out, and the permeability and water resistance of faults are determined. Various isolines of groundwater system are analyzed, including Quaternary basement buried depth isoline, groundwater head isoline, aquifer top and bottom elevation isoline, aquifer and aquifuge thickness isoline, etc.
2. Determine the boundary of groundwater system
The boundary of groundwater system includes natural boundary (fixed boundary) and hydraulic boundary (movable boundary). Natural boundaries include impermeable rock strata, impermeable faults or fault zones and large surface water bodies. Hydraulic boundary includes groundwater watershed and groundwater streamline.
In the study of numerical model simulation, the bottom boundary of the object is generally impermeable rock. The lateral boundary can be natural boundary, hydraulic boundary or infinite boundary (the boundary head or flow rate is not affected by input conditions). The simulated top boundary is generally impermeable boundary or overflow boundary for confined water system, and atmospheric boundary (evaporation and infiltration) is generally adopted for submersible system. The internal boundary of groundwater system includes zero flow boundary (impermeable rock mass) and flow boundary (seepage zone of rivers, lakes or reservoirs).
3. Hydrogeological parameters
Hydrogeological parameters are the soul of numerical model simulation research, which generally include permeability coefficient, hydraulic conductivity coefficient, water supply, water storage rate, water storage coefficient, porosity, vertical permeability coefficient and overflow coefficient of aquifer group, as well as precipitation infiltration coefficient, river leakage coefficient, well irrigation regression coefficient, field and channel leakage coefficient, phreatic water evaporation coefficient and land evaporation coefficient of vadose zone.
The methods to determine the recharge coefficient of precipitation infiltration, irrigation leakage coefficient and evaporation coefficient include hydrological analysis (precipitation, river runoff curve, groundwater head dynamic curve, etc. ), direct test (permeameter, tensiometer, isotope tracer, etc. ), calculation (chlorine mass balance method, unsaturated model method, etc. ), empirical formula method and ZFP zero flux surface measurement method.
(2) Generalization of groundwater flow system
The groundwater flow system is generalized, including the determination of the basic flow direction of groundwater, the composition of groundwater recharge elements, the discharge mode, the transformation relationship between groundwater and surface water, and the hydraulic relationship between aquifers in different horizons. The main basis is the isogram of groundwater head, hydrochemical information, isotope information, groundwater temperature information and water level dynamic curve.
According to the state and characteristics of groundwater flow, the specific properties of the groundwater flow system studied are determined, such as stable or unstable flow, one-dimensional flow, two-dimensional flow, quasi-three-dimensional flow or three-dimensional flow.
(3) Calculation of model input
Precipitation infiltration, surface water infiltration (river canal), lateral inflow of groundwater, irrigation infiltration, evaporation and transpiration, spring water discharge, basic flow discharge, lateral outflow of groundwater, exploitation, etc.
Second, establish a mathematical model.
According to the established hydrogeological conceptual model, the appropriate mathematical model is selected. Generally, it consists of partial differential equations describing the law of groundwater movement and definite solution conditions reflecting the boundary conditions and initial conditions of groundwater system.
The partial differential equation of three-dimensional unsteady flow in heterogeneous confined water is
Water Cycle and Evolution Model of Groundwater in Heihe River Basin
The partial differential equation of three-dimensional unsteady flow in heterogeneous diving has the following situations: the first boundary condition (Dirichlet boundary) is
Water Cycle and Evolution Model of Groundwater in Heihe River Basin
The second boundary condition (Newman boundary) is
Water Cycle and Evolution Model of Groundwater in Heihe River Basin
The initial condition is
Water Cycle and Evolution Model of Groundwater in Heihe River Basin
Third, the calculation program, model design and identification
(A) calculation program and model design
The calculation program is divided into one-dimensional flow, two-dimensional flow, quasi-three-dimensional flow or three-dimensional flow model, and the ability to deal with homogeneous, heterogeneous, isotropic or anisotropic and different input terms. At present, available softwares include MODFLOW, FEWFLOW, PM, GMS, GWVISTA, MODME, PM, etc. Most of them are finite difference method and finite element method. Model design, including grid division (regular division or irregular division, triangular division or rectangular division), time step selection (trial algorithm), model boundary setting, initial condition setting, data input (precipitation infiltration rate, field irrigation infiltration rate, evaporation rate, well location and mining or recharge intensity, temporal and spatial distribution of interaction between groundwater and surface water, temporal and spatial distribution of spring water, boundary water level or flow rate, observation well location and observation water level, etc. ).
(2) Model identification and testing
1. Model recognition
Model identification is also called inversion problem, that is, using the measured groundwater dynamic data and pumping test data, the hydrogeological parameters or source-sink terms and determination conditions are obtained in reverse. The purpose of model identification is to solve the problem of whether the selected partial differential equation is appropriate, determine the hydrogeological parameters, source-sink terms and definite solution conditions in the model, and establish a simulation model that can reproduce the actual function (head or concentration) of groundwater system. Model identification generally adopts trial and error method. It is to select a suitable time period, estimate a set of hydrogeological parameter input model according to hydrogeological conditions and empirical data, and use the input and output data of the selected time period to solve the model. Then the calculated results of the model are compared with the measured results. If the fitting result does not meet the accuracy requirements, adjust the parameters appropriately and repeat the above process until the accuracy requirements are met. You can also use the method of combining trial estimation-correction method with optimization method. First, rough adjustment is carried out by trial estimation-correction method, and then fine adjustment is carried out by optimization method, that is, a set of optimal parameter values are obtained by optimization method, so that the difference between the calculated head value and the observed value is minimum under given constraints.
The results of model identification have multiple solutions. The number of parameters to be identified should be less than the total data. In other words, there must be a known quantity. The more known quantities, the more accurate the parameters and the better the applicability of the model. It is precisely because of the multiple solutions of the model identification results that different people get different parameter combinations for the same problem, and even the same person gets different parameters at different times. Obviously, the parameters determined by the model are not necessarily the inherent parameters of the aquifer. Therefore, some people call the parameters of model identification "model parameters" to show the difference. Although the model parameters can't fully reflect the parameters of the actual system, the model parameters have a special function, which can make the mathematical model replace the actual groundwater system in behavior and function and become a "replica" of the groundwater system.
2. Model checking
In order to verify the reliability of the identified model, it is necessary to use the data input model of the same system at another time period for verification. If the calculated results are consistent with the actual data, it can be explained that the model can truly reflect the actual system. It should be pointed out that the two sets of data used in model identification and model verification must be relatively independent data in different time periods.
The purpose of model sensitivity analysis is to understand the influence of parameter change on calculation results and identify important parameters at the same time. Sensitivity analysis is usually performed before or after model identification.
Select a parameter (θ) for analysis, and then fix other parameters to change the numerical analysis and calculation results of θ. The calculated water head (g) is a function of θ, that is, g=f(θ). Its definition is as follows: in the vicinity of θ=θ0, the ratio of the change rate of the head variable g(θ) relative to the initial value g*(θ) to the change rate of the parameter θ relative to θ0 is called the sensitivity of the head to the parameter θ, which is expressed by the following formula:
Water Cycle and Evolution Model of Groundwater in Heihe River Basin
4. Generalization of hydrogeological conditions in Heihe River Basin simulation area
In the numerical model simulation area of groundwater quantity transformation research, Zhangye Basin and Jiuquan East Basin are selected, including all irrigation areas in Zhangye, Linze and Gao Tai, individual irrigation areas in Minle and Shandan, and Minghua District in Sunan County, covering an area of nearly 9000 km2.
The numerical simulation area is an intermountain fault basin with only lateral inflow and no lateral outflow, which is filled with extremely thick loose sediments, forming a natural place of groundwater, a continuous and unified Quaternary water-bearing rock series, and the surrounding mountains are natural geological boundaries. In Zhangye Basin, groundwater moves from southeast to northwest, flows into the mainstream of Heihe River and flows out of this area. In Jiuquan East Basin in the west, groundwater moves from southwest to northeast, and the line from Yumushan to Gaotai County is the natural catchment line of the two basins.
The main recharge sources of groundwater in the numerical simulation area are river water (including rain and flood), channel water diversion and vertical infiltration of field irrigation water, and the discharge methods are mainly spring overflow, evaporation and artificial mining.
According to the balance calculation results, the recharge in11.94×108m3 is 14.09× 108 m3, and the balance difference is -2. 15× 65438+.
The periphery of the numerical simulation area is the secondary flow boundary. The mountain boundary is distributed along the piedmont fault, and the inflow is mainly the lateral inflow of bedrock fissure water and gully undercurrent. The sections of eastern folk music, western Shandan and Minghua are the outward inflow of this area, which is obtained by section method. The buried fault of Xinba-Hongyazi in the south makes the groundwater flow discontinuous. As the boundary of this section, the generalized hydrogeological model is shown in Figure 5- 1.
Generalization of verb (Verb's abbreviation) Mathematical Model
The south of the numerical simulation area is phreatic water and the north is confined water, so the mathematical model of phreatic confined water should be adopted. But the degree of groundwater exploitation in each irrigation area is different. In some areas, groundwater has been connected with confined water, and the dynamic changes of confined water head and groundwater level are consistent. Therefore, the model is generalized as a two-dimensional heterogeneous and isotropic diving model. In view of the large regional area and small annual variation of groundwater level, which can be ignored compared with aquifer thickness, the product of permeability coefficient (K) and aquifer thickness (H) is approximately replaced by hydraulic conductivity coefficient (T).
The mathematical model and definite solution conditions are as follows:
Figure 5- 1 Overview of Hydrogeological Model in Heihe River Basin Simulation Area
Water Cycle and Evolution Model of Groundwater in Heihe River Basin
Where: t refers to the permeability coefficient of aquifer (m2/d);
μ —— the water supply of aquifer (dimensionless);
Wb—— sum of intensities of various replenishment projects (m3/km2 d);
Wp—— the sum of various excreta intensities (m3/km2 d);
Q—— flow rate per unit width of flow boundary (m3/km2 d);
γ2- flow boundary code;
N-the direction of the inner normal on the boundary.
Linear interpolation and Galerkin finite element method are used to solve the above equations, as shown in the program block diagram (Figure 5-2).
Figure 5-2 Solving Process of Numerical Model Simulation Program in Heihe River Basin
Sixth, the solution of the article
(1) initial conditions
Based on the unified water level measurement results of 1999 and the long-term observation data of groundwater dynamics, the 1 month contour map is drawn as the initial flow field. The calculation area is divided into 142 1 unit and 799 nodes by triangulation method. There are 624 internal nodes and 175 boundary points. There are 33 water level observation points, all of which are distributed at nodes (Figure 5-3). At the same time, try to arrange the nodes on the boundary of generalized irrigation area.
(2) Calculation period
Taking 1 early month 1999 to the end of February 65438+ the actual number of days in each natural month as the cycle length, the whole year is divided into 12 cycles.
(3) Hydrogeological parameters
According to the research results of Heihe investigation report, the parameters of numerical simulation area range from100 to 6500m2/d, and the μ value is 0. 1 ~ 0.25. Parameter zoning is based on irrigation area and divided according to different buried depths.
(4) Source and sink projects
Groundwater in the calculation area mainly depends on river infiltration, canal diversion, irrigation water, precipitation condensate and boundary water. It is consumed by evaporation and transpiration, spring overflow and artificial mining. The selection of relevant parameters is mainly based on the Heihe report and the research results of water conservancy departments in various counties. The recharge and discharge are calculated by water balance method.
Because of the large numerical simulation area, developed agriculture, dense main branches and canals, and many water intakes along the main river (Heihe River), the available hydrological and hydraulic data are limited, so the subdivision should not be too fine. The infiltration and artificial exploitation of river water (including rain and flood), canal water, irrigation water and pour point depressant water can be regarded as surface quantity, and the balance calculation results of different buried depths in each irrigation area can be used as the input model of unit surface quantity with positive recharge term. During the non-irrigation period (1~ March,/10 ~ 65438+2+February), the infiltration of canal water and irrigation water and the intensity of artificial exploitation are zero, and the annual infiltration is divided into irrigation periods (April ~ September).
Figure 5-3 Division Diagram of Numerical Calculation Area of Heihe River Basin
1999 River water infiltration accounted for 32% of Heihe River (Yingluoxia) runoff in that year, and the proportion of monthly runoff to annual runoff was allocated to 12. Precipitation and evaporation intensity are allocated to 12 periods according to the proportion of each month to the whole year. The annual precipitation in1~ March and 10 ~ 12 is 0, 30% in April-June and 70% in July-September. According to the different buried depths of groundwater, the evaporation is calculated, in which1~ March accounts for 13%, April-June accounts for 4 1%, July-September accounts for 35%, and10 ~1%.
The spring flood zones are all distributed in the fine soil plain, and the buried depth of groundwater is less than 3.5m The groundwater level of each spring ditch and Heihe river bed is higher than the river bed elevation, which is actually linear. However, because the subdivision unit is large, it cannot be accurately described, so the linear quantity is treated as a plane quantity. Assuming that the area where the groundwater level is lower than 3.5m is a spring overflow zone, the specific method is to subtract 3.5m from the ground elevation of all nodes, then the groundwater level in this area is negative. Divide the spring overflow of 1999 by the area of this area, and then divide it by the average head difference of 1.5m to get the spring overflow intensity under the condition of unit head difference, and introduce it into the model. Then, according to the change of water head in each period, the spring overflow in different periods is obtained.
The boundary of the numerical simulation area is permeable boundary or weakly permeable boundary, both of which give the single-width discharge, which is consistent throughout the year and is no longer divided by time period.
Seven, several models bear fruit.
According to the above recharge elements and their parameters, the groundwater level of the observation point is fitted, and the realization model of 1999 is determined.
There are 33 observation points in the area, which are concentrated in the fine soil plain belt of Zhangye, Linze and Gao Tai. In the process of parameter adjustment, the fitting point error decreases continuously, the initial flow field is consistent with the calculated flow field, and the water level deviation of each node should not be too large. Due to parameter adjustment, the numerical simulation area * * * has 60 parameter partitions, as shown in Figure 5-4 and Table 5-2. See Figure 5-5 and Figure 5-6 for the fitting results of observation points, and Figure 5-7 for the fitting of groundwater flow field.
Figure 5-4 Numerical Simulation Parameter Zoning Map of Heihe River Basin
Table 5-2 Relevant Hydrogeological Parameters Adopted by Heihe River Basin Model