CN102855390A - Finite difference method for calculating recharge quantity of signal well - Google Patents
Finite difference method for calculating recharge quantity of signal well Download PDFInfo
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- CN102855390A CN102855390A CN2012102809420A CN201210280942A CN102855390A CN 102855390 A CN102855390 A CN 102855390A CN 2012102809420 A CN2012102809420 A CN 2012102809420A CN 201210280942 A CN201210280942 A CN 201210280942A CN 102855390 A CN102855390 A CN 102855390A
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Abstract
The invention relates to a finite difference method for calculating the recharge quantity of signal well. The method includes subjecting a well filter tube to equivalent simplification process and performing finite difference division on computation space of the well filter tube; establishing node water balance finite difference relations for grids obtained through the division; performing hydrogeological parameter assignment on the stratum where a simplification well according to actual engineering, and distinguishing a simplification filter tube, fillers around the filter tube and an actual stratum through arrangement of a water level boundary, a fixed water level boundary or a waterproof boundary; establishing a water balance linear equation system according to a groundwater three-dimensional unsteady flow motion equation, solving the equation by using Gauss-Seide iteration; and calculating the recharge quantity through accumulation of water quantity difference flowing through adjacent grids on the periphery of the simplification filter tube. According to the method, aiming at the problems that the determination of the recharge quantity of signal well is depended on engineering analog and recharge tests after well forming and calculation and prediction in advance are difficult in the existing foundation pit projects, according to hydrogeological investigation results and recharge requirements, the finite difference method is adopted to predict the recharge quantity of signal well of recharge wells with different lengths and positions of filter tubes, and a low-cost, rapid and quantitative basis is provided for design and optimization of the whole recharge scheme.
Description
Technical field
The invention belongs to engineering hydrogeology, hydrographic water resource, underground water scientific domain, be specifically related to a kind of finite difference method that calculates the single well reinjection amount.
Background technology
In recent years, the artificial groundwater supply work of China has had large development, particularly in control land subsidence, enlarge the groundwater resource exploitation, utilize the aspect such as water-bearing zone energy storage to play obvious effect.So-called artificial groundwater supply namely by various artificial measureses, adds to available groundwater resource increase in the water-bearing zone to various surface water resources.The recharge of ground water comprises mainly directly and indirect two class methods that wherein the pipe well injection method is one of direct methods of a large amount of uses both at home and abroad.The work efficiency of inverted well and single well reinjection amount (unit interval flows into the water yield in water-bearing zone during inverted well work) are closely related, become one of problem of paying close attention in the engineering.
The single well reinjection amount can obtain by site test and theoretical calculating usually.Yet every procedure in the one-tenth well process of inverted well (punching, change slurry, lower pipe, fill out gravel, sealing, well-flushing) all has direct relation with the amount of recharging, this amount of recharging personal error that has caused site test (in test pit, the less situation of operating condition of test) to obtain is larger, can not be as typical value.Secondly, theoretical calculating owing to relate to the factors such as experimental formula, raise of stage amount, and a large amount of on-the-spot Returning tests show, the common amount of recharging (P) has the various ways such as linear pattern, parabolic type, power function type, logarithmic curve type with the relation of raise of stage amount (s), therefore breaks away from a large amount of site tests and also is difficult to directly by the theoretical calculative determination amount of recharging.In this case, set up numerical model according to the engineering actual conditions, obtaining the single well reinjection amount by numerical evaluation has become important supplementary means.
Summary of the invention
The object of the present invention is to provide a kind ofCalculate the finite difference method of single well reinjection amount.
The present invention proposesCalculate the finite difference method of single well reinjection amount, comprise the steps:
(1) well screen is simplified, so that finite difference simulator is more succinct;
(2) the well screen computer memory being carried out finite difference divides;
(3) step (2) is divided each grid that obtains and set up node hydrologic(al) budget finite difference relation;
(4) carry out the hydrogeological parameter assignment according to Practical Project to simplifying stratum, well place, and by known head boundary being set or deciding head boundary, water proof border and distinguish filler and actual formation around chimney filter, the chimney filter; Then set up the hydrologic(al) budget system of linear equations according to the underground water three dimensions stream equation of motion, and use Gauss-Seide iterative equation;
(5) simplify the poor single well reinjection amount of calculating of the water yield of the peripheral adjacent mesh of chimney filter by cumulative flowing through.
Concrete steps are as follows:
(1), pipe well structure is carried out equivalent-simplification
1. according to the girth equal principle, the well cross section is reduced to square by circle;
2. according to chimney filter percentage of open area equal principle, following simplification is carried out in chimney filter perforate and arrangement: the round hole mode is reduced to the square opening mode, and makes its perforated area equate that the spacing between each perforate is carried out calculative determination according to the percentage of open area equal principle;
(2), pipe well structure carried out grid divide, the density that grid is divided should be less than the square opening length of side on the chimney filter and the minimum value of spacing;
(3), the grid that obtains in step (2) carries out the meticulous simulation of well screen skeleton tubular construction: shaft bottom (sand sediment pipe bottom), chimney filter wall, chimney filter top all are defined as dead unit, the chimney filter position of opening is set to decide head boundary, and filtrate section and the stratum hydrogeological parameter that report provides according to geotechnical engineering investigation carries out assignment (infiltration coefficient, coefficient of storage etc.) around the chimney filter;
(4), divide finite difference equation and boundary condition and the starting condition equation that each the single grid obtain is set up hydrologic(al) budget in step (2), see formula 1;
In the formula:
,
,
Be respectively anisotropy principal direction infiltration coefficient (m/d);
For the point
Head value (m) constantly;
Be source sink term (1/d);
Be coefficient of storage (1/m);
Be time (d);
Be computational fields;
Be First Boundary Condition;
Be First Boundary Condition
On head value (m);
(5), adopt the difference approximation method that step (4) Chinese style 1 is carried out discretize to process, the three-dimensional flow node is seen shown in the formula (2) with node hydrologic(al) budget difference relation on every side:
（2）
In the formula:
The expression point
On
Head constantly;
,
Often get three kinds of situations: when
The time claim finite difference to show difference scheme, when
The time claim the finite difference central difference schemes, when
The time claim finite difference implicit difference scheme.Take central difference schemes in departure process, solution is unconditional stability, and discrete linear equation is carried out Gauss-Seide iteration convergence speedup speed;
(6), water yields that on the chimney filter all are decided to flow out in the peripheral adjacent mesh of head boundary add up, accumulated result is individual well single well reinjection amount.
Among the present invention, described simplification well refers to have the well of simplifying chimney filter by equivalent-simplification, simplifies chimney filter and be to refer in particular to those that substitute actual chimney filter in finite difference simulator and decide head boundary.
The present invention at first carries out equivalence to well screen, so that finite difference simulator is more succinct; Then the well screen computer memory is carried out finite difference and divide, and each grid that division obtains is set up node hydrologic(al) budget finite difference relation; Then carry out the hydrogeological parameter assignment according to Practical Project to simplifying stratum, well place, and by known head boundary being set or deciding head boundary, water proof border and distinguish and simplify filler and actual formation around chimney filter, the chimney filter; Then set up the hydrologic(al) budget system of linear equations according to the underground water three dimensions stream equation of motion, use Gauss-Seide iterative solution equation according to the Practical Project condition; Simplify the poor amount of recharging of calculating of the water yield of the peripheral adjacent mesh of chimney filter by cumulative flowing through at last.
Beneficial effect of the present invention is: Returning test is determined after mainly relying on engineering analogy and become well for single well reinjection amount in the base pit engineering in the past, calculate the prediction hard problem in advance, according to the Hydrogeologic Survey achievement with recharge requirement, adopt finite difference method to predict the single well reinjection amount of different chimney filter length and different chimney filters position inverted well, that the design and optimization that recharges scheme for integral body provides is low-cost, fast and the foundation of quantification.
Description of drawings
Fig. 1 is the chimney filter rough schematic view.Wherein: (a) be actual chimney filter structural representation, (b) be the chimney filter synoptic diagram after simplifying.
Fig. 2 is chimney filter perforate rough schematic view.Wherein: (a) be actual chimney filter perforate and arrangement, (b) be chimney filter perforate and arrangement after simplifying.
Fig. 3 simplifies the chimney filter Finite Difference Meshes to divide synoptic diagram.Wherein: (a) being horizontal section, (b) is vertical cross section.
S 1 To simplify chimney filter with inner region,
S 2 To simplify in addition filtrate fill area of chimney filter, S
3The water proof border that at the bottom of chimney filter top and chimney filter, arranges,
pBe to simplify the chimney filter region, the chimney filter wall passes through
pThe center in each little balanced territory, zone.
The implementation phase that being, simplifies Fig. 4 the well construction synoptic diagram.
S 1 To simplify chimney filter with inner region,
S 2 Filtrate fill area beyond the simplification chimney filter,
pBe to simplify the chimney filter region, the chimney filter wall passes through
pThe center in each little balanced territory, zone,
S 3 The water proof border that at the bottom of chimney filter top and chimney filter, arranges,
L 1 ,
L 2 ,
L 3 ,
L 4 Be respectively table water aquifer, water-resisting layer, confined aquifer, impermeable layer thickness.
Fig. 5 simplifies the well amount of recharging to calculate synoptic diagram.Wherein chosen a part of simplifying chimney filter,
S 1 To simplify chimney filter with inner region,
S 2 Filtrate fill area beyond the simplification chimney filter,
pBe to simplify the chimney filter region, the chimney filter wall passes through
pThe center in each little balanced territory, zone, 1,2,3 ... for
PThe zone each little balanced grid with
S 2 The limit that the zone is adjacent,
q 1 ,
q 2 ,
q 3 Be respectively the little balanced grid limit 1,2,3 of flowing through in a certain smile time period ... the water yield, direction is inflow
S 2 The zone.
Embodiment
Further specify by reference to the accompanying drawings the present invention below by embodiment.
Embodiment 1: followingly be positioned at the confined aquifer complete penetration of well as example explanation the inventive method (Fig. 4) take chimney filter, wherein chimney filter bag net outer rim radius is
R 2 , chimney filter length is all mutually with confined aquifer
L 3 For the purpose of simple and easy, suppose that the earth's surface absolute altitude is 0m, the stratum is made as altogether four layers, is respectively from top to bottom (m of unit):
Layer: water-resisting layer is thick
L 2 , head is
h
1, with the equivalence of real well chimney filter is chimney filter in the finite difference computation model, namely simplifies the chimney filter (see figure 1).Comprise chimney filter wall, chimney filter perforate and chimney filter bag net among the figure (a),
R 1,
R 2 Chimney filter radius and chimney filter outsourcing net outer rim radius on the actual chimney filter; Figure (b) is the square chimney filter after simplifying,
bBe the square chimney filter length of side, we think that this square chimney filter all is perforate, and are stable because flow velocity, the hydraulic pressure of penetrating shape stream that the chimney filter bag net outside forms all are close to, and are real radius
R 1 Chimney filter be reduced to radius and be
R 2 Circular open chimney filter, be radius
R 2 Circular open chimney filter be generalized as square open chimney filter, square is considered tube edge length and is calculated according to the following formula:
（1）
In the formula:
R 2 Be actual chimney filter bag net outer rim radius (m),
bFor simplifying the chimney filter length of side (m).
2, the zoning is divided into several unit (being Finite Difference Meshes), a computing node is arranged on each unit, carry out hydrologic(al) budget at node and calculate.In the surface level rectangular coordinate system, exist at first respectively
xAxle,
yEvenly divide on the direction of principal axis, then near planning to build well, carry out mesh refinement; Edge on vertically
zAxle is evenly divided and is seen Fig. 2, Fig. 3.
If 3 ground water movements are three dimensions stream and meet Darcy's law, confined aquifer is heterogeneous body, anisotropy, the water-bearing zone reaches wherein, and underground water is considered as elastic body, the elasticity reserves discharged (or storage) instantaneous finishing when head changed, and the hydrologic(al) budget in each little balanced territory that grid division obtains meets following formula:
In the formula:
,
,
Be respectively anisotropy principal direction infiltration coefficient (m/d);
For the point
Head value (m) constantly;
Be source sink term (1/d);
Be coefficient of storage (1/m);
Be time (d);
Be computational fields.Above equation adds that definite condition just consists of heterogeneous anisotropic pore media Groundwater Mathematical Model, and this mathematical model is parabolic type, has dissipation effect, and any disturbance in the flow field all can affect whole flow field.Adopt the difference approximation method that partial differential equation is carried out discretize and process, three-dimensional flow node and node hydrologic(al) budget difference relation on every side as shown in Equation (3):
In the formula:
The expression point (
i,
J, k) on
t n Head constantly;
,
θOften get three kinds of situations: when
θClaimed finite difference to show difference scheme at=0 o'clock, when
θClaimed the finite difference central difference schemes at=0.5 o'clock, when
θClaimed finite difference implicit difference scheme at=1 o'clock.Take central difference schemes in departure process, solution is unconditional stability, and discrete linear equation is carried out Gauss-Seide iteration convergence speedup speed.
4, the simulation equipressure is recharged, and needs two class boundary conditions in formula (1), and is a kind of for to decide head boundary, realizes by the node assignment; Another kind is the water proof border, by 0 flow border being set or dead unit is realized.
5, grid division is carried out the hydrogeological parameter assignment.Simplify the well construction synoptic diagram implementation phase that Fig. 4 being, give respectively different hydrogeological parameters to well casing, gravel, stratum,
S 1 The head assignment is decided hydraulic pressure reduced pressure head for recharging in (well screen is with inner region), chimney filter (among Fig. 2, Fig. 3
pRegional) with
S 1 The identical hydraulic pressure of deciding is set, represents recharge water with isqpressure type seepage flow in the stratum.Because well screen top and not perforate of bottom in the process of recharging, it is set to the water proof frontier district in Fig. 3, Fig. 4
S 3
6, choose certain one deck grid in simplifying the chimney filter length range, its cross-sectional Fig. 5 that meets personally is in a certain small time period
tIn, simplifying the chimney filter place
pExist on each limit that filler is adjacent outside the zone, each little grid and chimney filter to flow to and fill out gravel
S 2 The amount of recharging in zone
q(limit and the amount of recharging to grid among Fig. 5 are numbered) is the recharge amount of simplification well on this transverse section when the amount of recharging on each limit is added up in the transverse section
Q 1 , and then the amount of recharging on each section added up along simplifying the chimney filter length direction, namely obtain the recharge amount of inverted well within this small time period
Q 2 , the amount of recharging in each small time period in the time of recharging is added up namely obtain the amount of recharging of inverted well at last.
Wherein:
,
,
n 1 Be simplification chimney filter reticulate layer on chimney filter length,
n 2 For simplifying the chimney filter place at a certain xsect
pLittle grid on the zone with
S 2 The limit number that the zone is adjacent,
n 3 Number for the small time period in the time of recharging.
7, adopt finite difference to calculate the single well reinjection amount, adopt site test results correction calculation parameter, the model after the correction can be used for Guiding Practice.
Claims (1)
1. calculate the finite difference method of single well reinjection amount, it is characterized in that concrete steps are as follows:
(1), pipe well structure is carried out equivalent-simplification
1. according to the girth equal principle, the well cross section is reduced to square by circle;
2. according to chimney filter percentage of open area equal principle, following simplification is carried out in chimney filter perforate and arrangement: the round hole mode is reduced to the square opening mode, and makes its perforated area equate that the spacing between each perforate is carried out calculative determination according to the percentage of open area equal principle;
(2), pipe well structure carried out grid divide, the density of mesh generation should be less than the minimum value of the square opening length of side and spacing on the chimney filter;
(3), the grid that obtains in step (2) carries out the meticulous simulation of well screen skeleton tubular construction: shaft bottom or sand sediment pipe bottom, chimney filter wall, chimney filter top all are defined as dead unit, the chimney filter position of opening is set to decide head boundary, filtrate section and the stratum hydrogeological parameter that report provides according to geotechnical engineering investigation carries out assignment around the chimney filter, and described hydrogeological parameter is infiltration coefficient, coefficient of storage;
(4), divide finite difference equation and boundary condition and the starting condition equation that each the single grid obtain is set up hydrologic(al) budget in step (2), see formula 1;
In the formula:
,
,
Be respectively anisotropy principal direction infiltration coefficient (m/d);
For the point
Head value (m) constantly;
Be source sink term (1/d);
Be coefficient of storage (1/m);
Be time (d);
Be computational fields;
Be First Boundary Condition;
Be First Boundary Condition
On head value (m);
(5), adopt the difference approximation method that step (4) Chinese style 1 is carried out discretize to process, the three-dimensional flow node is seen shown in the formula (2) with node hydrologic(al) budget difference relation on every side:
In the formula:
The expression point
On
Head constantly;
,
Often get three kinds of situations: when
The time claim finite difference to show difference scheme, when
The time claim the finite difference central difference schemes, when
The time claim finite difference implicit difference scheme; Take central difference schemes in departure process, solution is unconditional stability, and discrete linear equation is carried out Gauss-Seide iteration convergence speedup speed;
(6), all water yields of deciding to flow out in the head boundary peripheral meshes on the chimney filter are added up, accumulated result is individual well single well reinjection amount.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103995976A (en) * | 2014-05-29 | 2014-08-20 | 西安建筑科技大学 | Prediction and diagnosis method for blocking of recharge wells based on permeability coefficient model |
| CN104865372A (en) * | 2015-06-12 | 2015-08-26 | 济南轨道交通集团有限公司 | Test method of indoor recirculation model test system for simulating confined water layer |
| CN109885894A (en) * | 2019-01-24 | 2019-06-14 | 江西理工大学 | A kind of rare earth ore bed seepage action of ground water model based on Trefftz multi-source point point collocation |
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|---|---|---|---|---|
| US20090294122A1 (en) * | 2006-05-24 | 2009-12-03 | Jens Henrik Hansen | Flow simulation in a well or pipe |
| CN101806224A (en) * | 2010-03-09 | 2010-08-18 | 煤炭科学研究总院重庆研究院 | Method for predicting extraction productivity of underground coal-seam gas |
| CN102063577A (en) * | 2011-01-13 | 2011-05-18 | 黄河勘测规划设计有限公司 | Method for calculating underground water seepage flow based on equipotential surface |
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2012
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20090294122A1 (en) * | 2006-05-24 | 2009-12-03 | Jens Henrik Hansen | Flow simulation in a well or pipe |
| CN101806224A (en) * | 2010-03-09 | 2010-08-18 | 煤炭科学研究总院重庆研究院 | Method for predicting extraction productivity of underground coal-seam gas |
| CN102063577A (en) * | 2011-01-13 | 2011-05-18 | 黄河勘测规划设计有限公司 | Method for calculating underground water seepage flow based on equipotential surface |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103995976A (en) * | 2014-05-29 | 2014-08-20 | 西安建筑科技大学 | Prediction and diagnosis method for blocking of recharge wells based on permeability coefficient model |
| CN103995976B (en) * | 2014-05-29 | 2017-02-15 | 西安建筑科技大学 | Prediction and diagnosis method for blocking of recharge wells based on permeability coefficient model |
| CN104865372A (en) * | 2015-06-12 | 2015-08-26 | 济南轨道交通集团有限公司 | Test method of indoor recirculation model test system for simulating confined water layer |
| CN109885894A (en) * | 2019-01-24 | 2019-06-14 | 江西理工大学 | A kind of rare earth ore bed seepage action of ground water model based on Trefftz multi-source point point collocation |
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