CN108319791B - Concentration calculation method of mineral leaching agent for ionic rare earth in-situ mineral leaching - Google Patents

Concentration calculation method of mineral leaching agent for ionic rare earth in-situ mineral leaching Download PDF

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CN108319791B
CN108319791B CN201810130892.5A CN201810130892A CN108319791B CN 108319791 B CN108319791 B CN 108319791B CN 201810130892 A CN201810130892 A CN 201810130892A CN 108319791 B CN108319791 B CN 108319791B
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龙平
王观石
彭陈亮
胡世丽
罗嗣海
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Jiangxi University of Science and Technology
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Abstract

The invention relates to a method for calculating the concentration of an ore leaching agent for in-situ ion rare earth leaching, which comprises 6 steps of: (1) determining an ion exchange model of the ore body; (2) calculating a selection coefficient of the ion exchange model; (3) calculating the average pore flow rate of the ore body; (4) calculating the concentrations of cation ions and liquid-phase rare earth ions of the mineral leaching agent by considering a convection-dispersion process; (5) calculating the concentrations of cations and liquid-phase rare earth ions of the liquid-phase mineral leaching agent by considering the ion exchange process; (6) and calculating the concentration of the mineral leaching agent. On the basis of testing the actual ore body solute transport parameters and grade, the method can calculate the concentration of the leaching agent of the ionic rare earth in-situ leaching ore by using the established calculation method, and provides a basis for determining the concentration of the leaching agent in-situ leaching ore. The invention reduces the dosage of the mineral leaching agent on the premise of ensuring the rare earth leaching rate, reduces the mining cost, avoids the pollution of the excessive mineral leaching agent to the environment and is beneficial to the protection of water resources.

Description

Concentration calculation method of mineral leaching agent for ionic rare earth in-situ mineral leaching
Technical Field
The invention belongs to the field of in-situ ore leaching, and relates to an ore leaching agent concentration calculation method for ionic rare earth in-situ ore leaching.
Background
Rare earth, especially heavy rare earth, is an important strategic resource, and southern ionic rare earth ore is a main source of the heavy rare earth. The in-situ leaching process has the advantages of no damage to vegetation, less excavation engineering amount and the like, and becomes a main process for mining the ionic rare earth ore which is widely popularized and applied in China. The process of the in-situ mineral leaching process comprises the steps of firstly arranging a liquid injection pore network and a liquid collection engineering on an ore block, using an ammonium sulfate solution as a mineral leaching agent, injecting the ammonium sulfate solution into the liquid injection pore network, enabling the ammonium sulfate solution to permeate in an ore body, enabling ammonium ions in the ammonium sulfate solution to perform ion exchange with rare earth ions adsorbed on rare earth ores, enabling the rare earth ions to enter the solution to form a mother solution, collecting the mother solution by the liquid collection engineering, and adopting an impurity removal precipitator to treat the mother solution to achieve the purpose of resource recovery.
The ion exchange between ammonium ions in the ammonium sulfate solution and rare earth ions adsorbed on the rare earth ore is one of the key processes for recovering rare earth by in-situ leaching. Research shows that the rare earth ion exchange of ammonium ions is a reversible ion exchange process, the concentration of ammonium sulfate solution has great influence on the ion exchange efficiency, and if the concentration of ammonium sulfate solution is lower, the ion exchange is insufficient, and the resource leaching rate is low; if the concentration of the ammonium sulfate solution is too high, on one hand, the mining cost is increased, on the other hand, the residual amount of ammonium sulfate in a mining area is increased, and after mining is finished, the residual ammonium sulfate flows into peripheral water under the action of rainfall and the like, so that the ammonia nitrogen of surface water and underground water exceeds the standard. Therefore, the reasonable determination of the concentration of the ammonium sulfate solution plays an important role in mining the ionic rare earth ore by the in-situ ore leaching process.
At present, the concentration of the ammonium sulfate solution is mainly determined in two ways: (1) designers determine the concentration of the ammonium sulfate solution according to the experience of early mining, and because of the complexity of geological conditions and different geological conditions of different mining areas, the concentration of the ammonium sulfate solution determined directly through experience is often out of a reasonable range; (2) the concentration of the ammonium sulfate solution is determined through an indoor column leaching test, and the test shows that the mechanical parameters of solute transfer in the ore leaching process have obvious scale effect, and the concentration of the ammonium sulfate solution in-situ ore leaching on the site is difficult to accurately determine through the indoor test.
Disclosure of Invention
The invention aims to provide a method for calculating the concentration of an ore leaching agent for in-situ ion type rare earth leaching, so that the using amount of the ore leaching agent is saved, and the environmental protection is facilitated.
The technical scheme of the invention is as follows: a method for calculating the concentration of an ore leaching agent for ionic rare earth in-situ ore leaching comprises the following steps:
the first step is as follows: an ion exchange model of the ore body is determined,
(1) performing a cup leaching test on the ionic rare earth ore sample, performing a cup leaching test on the rare earth ore sample with the concentration of the leaching agent of 1.0-20.0 g/L, and testing the concentration of rare earth ions in the corresponding leachate to obtain a relation curve between the concentration of the leaching agent and the concentration of the rare earth ions in the leachate;
(2) fitting a relation curve of the concentration of the mineral leaching agent and the concentration of rare earth ions in the leaching solution by adopting an ion exchange model, and selecting the ion exchange model with the minimum average relative error as an ion exchange model for describing the rare earth sample leached by the mineral leaching agent;
the second step is that: the selection coefficient of the ion exchange model is calculated,
fitting a relation curve of the concentration of the mineral leaching agent and the concentration of rare earth ions in the leaching solution by using the ion exchange model determined in the first step by taking the selection coefficient as an unknown number to obtain the selection coefficient of the ion exchange model of the mineral sample;
the third step: the ore body is tested for average pore flow rate,
testing the saturated permeability coefficient of the on-site ore body by adopting the existing method, wherein the Darcy flow rate of the ore body is numerically equal to the saturated permeability coefficient, sampling the on-site ore body, testing the porosity of the ore body by adopting the existing method, and determining the average pore flow rate of the on-site ore body according to the relation (1);
relation (1):
u＝v/n (1)，
in relation (1): u is the average pore flow rate, v is the darcy flow rate, and n is the porosity;
determining the hydrodynamic dispersion coefficients of ore bodies at different coordinates by using a relation (2):
the relationship of the formula (2),
D＝0.1z·|u| (2)，
in relation (2): d is a hydrodynamic dispersion coefficient, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, the vertical direction is positive, u is the average pore flow velocity, and | u | is an absolute value operation on u;
the fourth step: the concentration of the liquid-phase mineral leaching agent cation and the concentration of the liquid-phase rare earth ion are calculated by considering the convection-dispersion process,
when the mineral leaching agent is transported in an ore body, the cations of the liquid-phase mineral leaching agent and the rare earth ions adsorbed on the surface of the soil particles are subjected to ion exchange reaction in the transporting process to replace the rare earth ions adsorbed on the surface of the soil particles of the ore body, and the whole process has not only a convection-dispersion process of the cations of the mineral leaching agent and the rare earth ions, but also an ion exchange process of the cations of the mineral leaching agent and the rare earth ions; firstly, calculating the distribution of cations and rare earth ions of the mineral leaching agent in a convection-dispersion process, and then calculating the exchange capacity of the cations and the rare earth ions of the mineral leaching agent, wherein the cations and the rare earth ions of the mineral leaching agent in the convection-dispersion process respectively satisfy a relational expression (3) and a relational expression (4);
relation (3):
Figure BDA0001574866180000021
in relation (3):
Figure BDA0001574866180000022
to account for the concentration of convection-dispersion liquid phase lixiviant cations, D is the hydrodynamic dispersion coefficient, u is the average pore flow rate, k is the time node, k is 0,1,2, …, p-1, p is the maximum time node, Δ t is the time step, i is the coordinate node, i is 1,2, …, q-1, q is the maximum z coordinate node, Δ z is the z coordinate step;
relation (4):
Figure BDA0001574866180000023
in relation (4):
Figure BDA0001574866180000024
for taking convection-dispersion into accountThe concentration of liquid phase rare earth ions, D is a hydrodynamic dispersion coefficient, u is an average pore flow velocity, k is a time node, k is 0,1,2, …, p-1, p is a maximum time node, delta t is a time step, i is a z coordinate node, i is a maximum z coordinate node, i is …, q-1, q is a maximum z coordinate node, and delta z is a z coordinate step;
at the initial moment, the concentrations of the liquid-phase mineral leaching agent cations and the liquid-phase rare earth ions in the ore body are both 0, and the concentrations of the liquid-phase mineral leaching agent cations and the liquid-phase rare earth ions at different moments and different coordinates in the convection-dispersion process can be obtained according to the relation (3) and the relation (4) by combining the boundary condition of actual injection;
the fifth step: the concentrations of cations of the liquid-phase mineral leaching agent and the liquid-phase rare earth ions are calculated by considering the ion exchange process,
on the basis of the fourth step, considering the ion exchange process, the difference between the mole number of the cations of the solid-phase mineral leaching agent after the ion exchange and before the ion exchange and the mole number of the rare earth ions of the liquid phase after the ion exchange and before the ion exchange should satisfy the equivalent relation, and a relational expression (5) can be obtained;
relation (5):
Figure BDA0001574866180000025
in relation (5): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a z-coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure BDA0001574866180000026
and
Figure BDA0001574866180000027
respectively considering the concentrations of the solid-phase mineral leaching agent cation and the liquid-phase rare earth ion of the ion exchange,
Figure BDA0001574866180000031
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, each coordinate node is divided into one unit, and the unit at the coordinate node i is called as a single unitElement i, msiIs the mass of the ore body in the unit volume i, VLiIs the volume of the liquid phase in the unit volume i, VLi/msi＝n/ρbV (1-n), n is porosity, pbIs the density of the ore body soil particles, MNAnd MRRespectively the molar mass of the cation of the mineral leaching agent and the molar mass of the rare earth ion;
before and after ion exchange in the unit body i, a system formed by a liquid phase and a solid phase, the mass conservation of mineral leaching agent cations and rare earth ions is satisfied, and in the unit body i, the sum of the mass of the liquid phase mineral leaching agent cations and the mass of the solid phase mineral leaching agent cations before ion exchange reaction is equal to the sum of the mass of the liquid phase mineral leaching agent cations and the mass of the solid phase mineral leaching agent cations after reaction and can be expressed by a relational expression (6);
relation (6):
Figure BDA0001574866180000032
in relation (6): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure BDA0001574866180000033
and
Figure BDA0001574866180000034
respectively considering the concentrations of the cation of the liquid-phase mineral leaching agent and the rare earth ion of the liquid phase in ion exchange,
Figure BDA0001574866180000035
and
Figure BDA0001574866180000036
concentration of liquid phase mineral leaching agent cation and liquid phase rare earth ion, M, respectively, taking into account convection-dispersionNAnd MRRespectively the molar mass of the cation of the mineral leaching agent and the molar mass of the rare earth ion;
in the unit body i, the sum of the mass of the liquid-phase rare earth ions before the ion exchange reaction and the mass of the solid-phase rare earth ions is equal to the sum of the mass of the liquid-phase rare earth ions after the ion exchange reaction and the mass of the solid-phase rare earth ions, and can be represented by a relational expression (7);
relation (7):
Figure BDA0001574866180000037
in relation (7): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure BDA0001574866180000038
and
Figure BDA0001574866180000039
respectively considering the concentration of solid-phase rare earth ions and liquid-phase rare earth ions of ion exchange,
Figure BDA00015748661800000310
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, each coordinate node is divided into a unit, and the unit at the coordinate node i is called a unit body i, msiIs the mass of ore body in unit volume i, VLiIs the volume of the liquid phase in the unit volume i, VLi/msi＝n/ρbV (1-n), n is porosity, pbIs the density of ore body soil particles;
at the initial moment, the concentration of solid-phase rare earth ions of any coordinate in an ore body is the concentration of the solid-phase rare earth ions before ore leaching, the concentration of solid-phase ammonium ions of any coordinate in the ore body is 0, the concentration gradient of solid-phase mineral leaching agent cations and the solid-phase rare earth ions at the bottom end of the ore body is 0, and then the boundary conditions of the solid-phase mineral leaching agent cations and the solid-phase rare earth ions are expressed by a relational expression (8) and a relational expression (9);
relation (8):
Figure BDA00015748661800000311
relation formula(8) The method comprises the following steps:
Figure BDA00015748661800000312
in order to consider the concentration of cations of the solid-phase mineral leaching agent of ion exchange, L is the thickness of an ore body of an ore block, L is determined by mineral exploration data, t is time, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, and the vertical direction is positive;
relation (9):
Figure BDA0001574866180000041
in relation (9):
Figure BDA0001574866180000042
to take into account the concentration of the ion-exchanged solid phase rare earth ions,
Figure BDA0001574866180000043
is the concentration of solid-phase rare earth ions at the initial moment, L is the thickness of an ore body of an ore block,
Figure BDA0001574866180000044
and L is determined by the prospecting data, t is time, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, and the vertical direction is positive;
when k is 0 and i is 1, the boundary condition is obtained from the relationship (3) and the relationship (4)
Figure BDA0001574866180000045
And
Figure BDA0001574866180000046
as can be seen from the relational expression (8) and the relational expression (9),
Figure BDA0001574866180000047
is equal to 0 and is equal to 0,
Figure BDA0001574866180000048
is equal to
Figure BDA0001574866180000049
After the selection coefficient is known,
Figure BDA00015748661800000410
And
Figure BDA00015748661800000411
in the case of substituting the relational expressions (5), (6) and (7) into the ion exchange model, the ion exchange model can be obtained
Figure BDA00015748661800000412
Solving the system of nonlinear equations to calculate
Figure BDA00015748661800000413
Obtained by
Figure BDA00015748661800000414
The corrected values can be calculated by substituting the values into relational expressions (5), (6) and (7)
Figure BDA00015748661800000415
And
Figure BDA00015748661800000416
when k is 0 and i is 2, the boundary conditions are combined with the first two steps, and similarly, the calculation may be performed
Figure BDA00015748661800000417
And
Figure BDA00015748661800000418
by analogy, any time and any position can be calculated
Figure BDA00015748661800000419
And
Figure BDA00015748661800000420
and a sixth step: the concentration of the mineral leaching agent is calculated,
on the basis of determining basic parameters in the first step, the second step and the third step, according to the methods in the fourth step and the fifth step, an initial value of the concentration of the leaching agent is given, a penetration curve of rare earth ions can be calculated, the rare earth leaching rate corresponding to the concentration of the leaching agent is calculated according to the penetration curve of the rare earth ions, the concentration of the leaching agent is changed, a relation graph of different concentrations of the leaching agent and the rare earth leaching rate can be obtained, a target leaching rate is set, and when the calculated leaching rate is larger than the target leaching rate, the concentration of the leaching agent is determined.
The method fully considers the field condition, uses the convection-dispersion model to describe the migration process of the cations and the rare earth ions of the mineral leaching agent in the ore body on the basis of determining the ion exchange model and the selection coefficient through the cup leaching test, and considers the hydrodynamic parameters, the ore body thickness and the grade of the actual mine. The invention reduces the dosage of the mineral leaching agent on the premise of ensuring the rare earth leaching rate, reduces the mining cost, avoids the pollution of the excessive mineral leaching agent to the environment and is beneficial to the protection of water resources.
Drawings
FIG. 1 is a graph of concentration versus leaching rate for different ammonium sulfate solutions;
c in FIG. 1NSThe concentration of the ammonium sulfate solution is shown, and xi is the leaching rate of the rare earth.
Detailed Description
The method is applied to carry out an undisclosed test on certain ion type rare earth ore in Xinfeng, samples are taken in a test mine, ammonium sulfate solution is used as an ore leaching agent, an ion exchange model and a selection coefficient of the ore sample are determined by adopting a cup leaching test, a single-hole liquid injection test is carried out on an ore body, a saturated permeability coefficient of the ore body is tested by adopting an in-situ soil-water characteristic parameter testing method, the in-situ ore body is sampled, the porosity of the ore body is tested, the average pore flow rate and the hydrodynamic dispersion coefficient of the ore body are further determined, the thickness and the rare earth grade of the ore body of the mine are determined by utilizing ore exploration data, and the concentration of the ammonium sulfate solution of the ion type rare earth in-situ ore leaching is calculated by combining the ion exchange model and a convection-dispersion.
The first step is as follows: an ion exchange model of the ore body is determined,
sampling a certain ion type rare earth ore in Xinfeng, adopting a GZS-1 type high-frequency vibrating screen machine and a sieve with the aperture of 2mm to screen the ore sample, drying the screened ore sample in a drying oven at 110 ℃ for 10h, taking 20g of the ore sample, putting the ore sample into a 300mL volumetric flask, adding 100mL of ammonium sulfate solution with the concentration of 20g/L, shaking uniformly, putting the ore sample into an oscillating box, oscillating for 2h, taking the volumetric flask down, standing for 0.5h, separating the leachate and the ore sample by using medium-speed quantitative filter paper, taking 20mL of the leachate, testing the rare earth ion concentration of the leachate by adopting an EDTA titration method, determining the grade of the ore sample to be 0.56 thousandth, leaching the ore sample by adopting ammonium sulfate solutions with the mass concentrations of 2 g/L-20 g/L respectively, testing the rare earth ion concentrations leached by the ammonium sulfate solutions with different concentrations, obtaining a relation curve of the concentration of the ammonium sulfate solution and the rare earth ion concentration, and adopting a Kerr model, a Vanselow model, the results show that the average relative errors of the Kerr model are minimum and are respectively 3.91 percent, and the Kerr model is used as an ion exchange model for exchanging solid-phase rare earth ions by liquid-phase ammonium radical ions;
the second step is that: the selection coefficient of the ion exchange model is calculated,
determining an ion exchange model of the ore sample as a Kerr model in the first step, fitting a relation curve of the concentration of the ammonium sulfate solution and the concentration of the rare earth ions by using the Kerr model, and obtaining a selection coefficient of 12.59 multiplied by 10-10L2/g2。
The third step: the ore body is tested for average pore flow rate,
testing the saturated permeability coefficient of the ore body to be 0.51m/d by adopting an in-situ soil-water characteristic parameter testing method, obtaining the Darcy flow rate of the ore body to be 0.51m/d by the fact that the Darcy flow rate of the ore body is equal to the saturated permeability coefficient in value, sampling the ore body on site, testing the porosity of the ore body to be 0.46 by adopting a drying method, and determining the average pore flow rate of the ore body to be 1.11m/d according to the relation formula (1);
relation (1):
u＝v/n (1)，
in relation (1): u is the average pore flow rate, v is the darcy flow rate, and n is the porosity;
determining the hydrodynamic dispersion coefficient of the ore body at different coordinates as D ═ 0.111z by using the relation (2):
the relationship of the formula (2),
D＝0.1z·|u| (2)，
in relation (2): d is a hydrodynamic dispersion coefficient, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, the vertical direction is positive, u is the average pore flow velocity, and | u | is an absolute value operation on u;
the fourth step: the concentration of the liquid-phase mineral leaching agent cation and the concentration of the liquid-phase rare earth ion are calculated by considering the convection-dispersion process,
according to the prospecting data, the thickness L of an ore body is 8m, the average rare earth grade of a test ore block is 0.70 per thousand, the convection-dispersion process is considered, and the convection-dispersion equations of ammonium ions and rare earth ions are respectively a relational expression (3) and a relational expression (4);
relation (3):
Figure BDA0001574866180000051
in relation (3):
Figure BDA0001574866180000052
in order to consider the concentration of convective-diffusive liquid-phase ammonium ions, D is a hydrodynamic diffusion coefficient, u is an average pore flow rate, k is a time node, k is 0,1,2, …, p-1, p is a maximum time node, Δ t is a time step, i is a z-coordinate node, i is 1,2, …, q-1, q is a maximum z-coordinate node, and Δ z is a z-coordinate step;
relation (4):
Figure BDA0001574866180000053
in relation (4):
Figure BDA0001574866180000061
to consider the concentration of convective-diffusive liquid-phase rare earth ions, D is the hydrodynamic diffusion coefficient, u is the average pore flow rate, k is the time node, k is 0,1,2, …, p-1, p is the maximum time node, and Δ t is the timeStep length, i is a z coordinate node, i is 1,2, …, q-1, q is a maximum z coordinate node, and Δ z is a z coordinate step length;
at the initial moment, the concentrations of liquid-phase ammonium ions and liquid-phase rare earth ions in the ore body are both 0, the first-class boundary is adopted as a calculation boundary condition, and the concentrations of the liquid-phase ammonium ions and the liquid-phase rare earth ions at different moments and different coordinates can be obtained without considering the ion exchange process according to the relational expression (3) and the relational expression (4);
the fifth step: the concentrations of cations of the liquid-phase mineral leaching agent and the liquid-phase rare earth ions are calculated by considering the ion exchange process,
on the basis of the fourth step, considering the ion exchange process, the difference between the mole number of solid-phase ammonium ions after ion exchange and before ion exchange and the difference between the mole number of liquid-phase rare earth ions after ion exchange and before ion exchange should satisfy the equivalent relationship, and a relational expression (5) can be obtained;
relation (5):
Figure BDA0001574866180000062
in relation (5): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a z-coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure BDA0001574866180000063
and
Figure BDA0001574866180000064
respectively considering the concentration of solid-phase ammonium ions and liquid-phase rare earth ions of ion exchange,
Figure BDA0001574866180000065
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, each coordinate node is divided into a unit, and the unit at the coordinate node i is called a unit body i, msiIs the mass of the ore body in the unit volume i, VLiIs the volume of the liquid phase in the unit volume i, VLi/msi＝n/ρbV (1-n), n is porosity, pbTaking rho as the density of ore body soil particlesb＝2.71×103g/L，MNAnd MRRespectively the molar mass of ammonium ions and rare earth ions;
before and after ion exchange in the unit body i, a system formed by a liquid phase and a solid phase, ammonium ions and rare earth ions should meet mass conservation, and in the unit body i, the sum of the mass of the liquid phase ammonium ions and the mass of the solid phase ammonium ions before ion exchange reaction is equal to the sum of the mass of the liquid phase ammonium ions and the mass of the solid phase ammonium ions after reaction, and can be represented by a relational expression (6);
relation (6):
Figure BDA0001574866180000066
in relation (6): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a z-coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure BDA0001574866180000067
and
Figure BDA0001574866180000068
respectively considering the concentration of liquid-phase ammonium radical ions and liquid-phase rare earth ions of ion exchange,
Figure BDA0001574866180000069
and
Figure BDA00015748661800000610
concentration of liquid-phase ammonium ions and liquid-phase rare earth ions, M, respectively, taking into account convection-diffusionNAnd MRRespectively the molar mass of ammonium ions and rare earth ions;
in the unit body i, the sum of the mass of the liquid-phase rare earth ions before the ion exchange reaction and the mass of the solid-phase rare earth ions is equal to the sum of the mass of the liquid-phase rare earth ions after the ion exchange reaction and the mass of the solid-phase rare earth ions, and can be represented by a relational expression (7);
relation (7):
Figure BDA00015748661800000611
in relation (7): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure BDA0001574866180000071
and
Figure BDA0001574866180000072
respectively considering the concentration of solid-phase rare earth ions and liquid-phase rare earth ions of ion exchange,
Figure BDA0001574866180000073
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, each coordinate node is divided into a unit, and the unit at the coordinate node i is called a unit body i, msiIs the mass of the ore body in the unit volume i, VLiIs the volume of the liquid phase in the unit volume i, VLi/msi＝n/ρbV (1-n), n is porosity, pbIs the density of ore body soil particles;
at the initial moment, the concentration of solid-phase rare earth ions at any coordinate in an ore body is the concentration of the solid-phase rare earth ions before ore leaching, the concentration of solid-phase ammonium ions at any coordinate in the ore body is zero, the concentration gradient of the solid-phase ammonium ions and the solid-phase rare earth ions is zero at the bottom end of the ore body, and then the boundary conditions of the solid-phase ammonium ions and the solid-phase rare earth ions are expressed by a relational expression (8) and a relational expression (9);
relation (8):
Figure BDA0001574866180000074
in relation (8):
Figure BDA0001574866180000075
to consider ionsThe concentration of the exchanged solid-phase ammonium ions, L, the ore body thickness of the ore block, L, determined by the prospecting data, t, time, z, a vertical coordinate, the vertical coordinate taking the earth surface as an origin, and the vertical downward direction as the positive;
relation (9):
Figure BDA0001574866180000076
in relation (9):
Figure BDA0001574866180000077
to take into account the concentration of the ion-exchanged solid phase rare earth ions,
Figure BDA0001574866180000078
is the concentration of solid-phase rare earth ions at the initial moment, L is the thickness of an ore body of an ore block,
Figure BDA0001574866180000079
and L is determined by the prospecting data and is 0.6X 10 respectively-3g/g and 8m, t is time, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, and the vertical direction is positive;
when k is 0 and i is 1, the boundary condition is obtained from the relationship (3) and the relationship (4)
Figure BDA00015748661800000710
And
Figure BDA00015748661800000711
as can be seen from the relational expression (8) and the relational expression (9),
Figure BDA00015748661800000712
is equal to 0 and is equal to 0,
Figure BDA00015748661800000713
is equal to
Figure BDA00015748661800000714
After the selection coefficient is known,
Figure BDA00015748661800000715
And
Figure BDA00015748661800000716
in the case of substituting the relational expressions (5), (6) and (7) into the ion exchange model, the ion exchange model can be obtained
Figure BDA00015748661800000717
Solving the system of nonlinear equations to calculate
Figure BDA00015748661800000718
Obtained by
Figure BDA00015748661800000719
The corrected values can be calculated by substituting the values into relational expressions (5), (6) and (7)
Figure BDA00015748661800000720
And
Figure BDA00015748661800000721
when k is 0 and i is 2, the boundary conditions are combined with the first two steps, and similarly, the calculation may be performed
Figure BDA00015748661800000722
And
Figure BDA00015748661800000723
by analogy, any time and any position can be calculated
Figure BDA00015748661800000724
And
Figure BDA00015748661800000725
and a sixth step: the concentration of the mineral leaching agent is calculated,
on the basis of determining basic parameters in the first step, the second step and the third step, according to the method in the fourth step and the fifth step, the initial value of the concentration of the ammonium sulfate solution is given, the penetration curve of the rare earth ions can be calculated, the rare earth leaching rate corresponding to the concentration of the ammonium sulfate solution is calculated according to the penetration curve of the rare earth ions and the rare earth grade, the concentration of the ammonium sulfate solution is changed, a relation graph of the concentrations of different ammonium sulfate solutions and the rare earth leaching rate can be obtained, as shown in figure 1, the target leaching rate is set to be 90.00%, and when the calculated leaching rate is larger than the target leaching rate, the concentration of the mineral leaching agent is determined to be 8.0 g/L.
Effects of the implementation
Sampling rare earth ore of certain ion type in Xinfeng, taking ammonium sulfate solution as an ore leaching agent, testing the concentration of the rare earth ions under different ammonium sulfate concentrations through a cup leaching test, determining an ion exchange model as a Kerr model by adopting the method of the first step of the invention, and calculating the selection coefficient of the Kerr model of an ore body as 12.59 multiplied by 10 through the second step-10L2/g2The average pore flow rate of an ore body is tested to be 1.11m/d by using the method in the third step, on the basis of determining basic parameters in the first step, the second step and the third step, leaching rates corresponding to different ammonium sulfate solubilities are calculated by using the methods in the fourth step, the fifth step and the sixth step, a target leaching rate is set to be 90.00%, when the calculated leaching rate is larger than the target leaching rate, the concentration of a leaching agent is determined to be 8.0g/L, the average rare earth grade of an actual ore block is 0.70 per thousand, leaching is carried out by using the concentration of an ammonium sulfate solution of 8.0g/L, and after leaching is finished, the tailings are taken and tested, the average grade of the tailings is 0.06 per thousand, and the leaching rate is 91.42%.

Claims (1)

1. The method for calculating the concentration of the mineral leaching agent for in-situ ionic rare earth leaching is characterized by comprising the following steps of:
the first step is as follows: an ion exchange model of the ore body is determined,
(1) performing a cup leaching test on the ionic rare earth ore sample, performing a cup leaching test on the rare earth ore sample with the concentration of the leaching agent of 1.0-20.0 g/L, and testing the concentration of rare earth ions in the corresponding leachate to obtain a relation curve between the concentration of the leaching agent and the concentration of the rare earth ions in the leachate;
(2) fitting a relation curve of the concentration of the mineral leaching agent and the concentration of rare earth ions in the leaching solution by adopting an ion exchange model, and selecting the ion exchange model with the minimum average relative error as an ion exchange model for describing the rare earth sample leached by the mineral leaching agent;
the second step is that: the selection coefficient of the ion exchange model is calculated,
fitting a relation curve of the concentration of the mineral leaching agent and the concentration of rare earth ions in the leaching solution by using the ion exchange model determined in the first step by taking the selection coefficient as an unknown number to obtain the selection coefficient of the ion exchange model of the mineral sample;
the third step: the ore body is tested for average pore flow rate,
testing the saturated permeability coefficient of the ore body by adopting an in-situ soil-water characteristic parameter testing method, wherein the Darcy flow rate of the ore body is numerically equal to the saturated permeability coefficient, sampling the on-site ore body, testing the porosity of the ore body by adopting a drying method, and determining the average pore flow rate of the on-site ore body according to the relation (1);
relation (1):
u＝v/n (1)，
in relation (1): u is the average pore flow rate, v is the darcy flow rate, and n is the porosity;
determining the hydrodynamic dispersion coefficients of ore bodies at different coordinates by using a relation (2):
the relationship of the formula (2),
D ＝ 0.1z · |u| (2)
in relation (2): d is a hydrodynamic dispersion coefficient, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, the vertical direction is positive, u is the average pore flow velocity, and | u | is an absolute value operation on u;
the fourth step: the concentration of the liquid-phase mineral leaching agent cation and the concentration of the liquid-phase rare earth ion are calculated by considering the convection-dispersion process,
when the mineral leaching agent is transported in an ore body, the cations of the liquid-phase mineral leaching agent and the rare earth ions adsorbed on the surface of the soil particles are subjected to ion exchange reaction in the transporting process to replace the rare earth ions adsorbed on the surface of the soil particles of the ore body, and the whole process has not only a convection-dispersion process of the cations of the mineral leaching agent and the rare earth ions, but also an ion exchange process of the cations of the mineral leaching agent and the rare earth ions; firstly, calculating the distribution of cations and rare earth ions of the mineral leaching agent in a convection-dispersion process, and then calculating the exchange capacity of the cations and the rare earth ions of the mineral leaching agent, wherein the cations and the rare earth ions of the mineral leaching agent in the convection-dispersion process respectively satisfy a relational expression (3) and a relational expression (4);
relation (3):
Figure FDA0002943081770000012
in relation (3):
Figure FDA0002943081770000013
to account for the concentration of convection-dispersion liquid phase lixiviant cations, D is the hydrodynamic dispersion coefficient, u is the average pore flow rate, k is the time node, k is 0,1,2, …, p-1, p is the maximum time node, Δ t is the time step, i is the coordinate node, i is 1,2, …, q-1, q is the maximum z coordinate node, Δ z is the z coordinate step;
relation (4):
Figure FDA0002943081770000014
in relation (4):
Figure FDA0002943081770000021
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, D is a hydrodynamic diffusion coefficient, u is an average pore flow rate, k is a time node, k is 0,1,2, …, p-1, p is a maximum time node, Δ t is a time step, i is a z-coordinate node, i is 1,2, …, q-1, q is a maximum z-coordinate node, and Δ z is a z-coordinate step;
at the initial moment, the concentrations of the liquid-phase mineral leaching agent cations and the liquid-phase rare earth ions in the ore body are both 0, and the concentrations of the liquid-phase mineral leaching agent cations and the liquid-phase rare earth ions at different moments and different coordinates in the convection-dispersion process can be obtained according to the relation (3) and the relation (4) by combining the boundary condition of actual injection;
the fifth step: the concentrations of cations of the liquid-phase mineral leaching agent and the liquid-phase rare earth ions are calculated by considering the ion exchange process,
on the basis of the fourth step, considering the ion exchange process, the difference between the mole number of the cations of the solid-phase mineral leaching agent after the ion exchange and before the ion exchange and the mole number of the rare earth ions of the liquid phase after the ion exchange and before the ion exchange should satisfy the equivalent relation, and a relational expression (5) can be obtained;
relation (5):
Figure FDA0002943081770000022
in relation (5): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a z-coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure FDA0002943081770000023
and
Figure FDA0002943081770000024
respectively considering the concentrations of the solid-phase mineral leaching agent cation and the liquid-phase rare earth ion of the ion exchange,
Figure FDA0002943081770000025
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, each coordinate node is divided into a unit, and the unit at the coordinate node i is called a unit body i, msiIs the mass of the ore body in the unit volume i, VLiIs the volume of the liquid phase in the unit volume i, VLi/msi＝n/ρbV (1-n), n is porosity, pbIs the density of the ore body soil particles, MNAnd MRRespectively the molar mass of the cation of the mineral leaching agent and the molar mass of the rare earth ion;
before and after ion exchange in the unit body i, a system formed by a liquid phase and a solid phase, the mass conservation of mineral leaching agent cations and rare earth ions is satisfied, and in the unit body i, the sum of the mass of the liquid phase mineral leaching agent cations and the mass of the solid phase mineral leaching agent cations before ion exchange reaction is equal to the sum of the mass of the liquid phase mineral leaching agent cations and the mass of the solid phase mineral leaching agent cations after reaction and can be expressed by a relational expression (6);
relation (6):
Figure FDA0002943081770000026
in relation (6): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure FDA0002943081770000027
and
Figure FDA0002943081770000028
respectively considering the concentrations of the cation of the liquid-phase mineral leaching agent and the rare earth ion of the liquid phase in ion exchange,
Figure FDA0002943081770000029
and
Figure FDA00029430817700000210
concentration of liquid phase mineral leaching agent cation and liquid phase rare earth ion, M, respectively, taking into account convection-dispersionNAnd MRRespectively the molar mass of the cation of the mineral leaching agent and the molar mass of the rare earth ion;
in the unit body i, the sum of the mass of the liquid-phase rare earth ions before the ion exchange reaction and the mass of the solid-phase rare earth ions is equal to the sum of the mass of the liquid-phase rare earth ions after the ion exchange reaction and the mass of the solid-phase rare earth ions, and can be represented by a relational expression (7);
relation (7):
Figure FDA00029430817700000211
in relation (7): k is a time node, k is 0,1,2, …, p-1, p is the largest time node, i is a coordinate node, i is 1,2, …, q-1, q is the largest z-coordinate node,
Figure FDA0002943081770000031
and
Figure FDA0002943081770000032
respectively considering the concentration of solid-phase rare earth ions and liquid-phase rare earth ions of ion exchange,
Figure FDA0002943081770000033
in order to consider the concentration of convection-diffusion liquid-phase rare earth ions, each coordinate node is divided into a unit, and the unit at the coordinate node i is called a unit body i, msiIs the mass of ore body in unit volume i, VLiIs the volume of the liquid phase in the unit volume i, VLi/msi＝n/ρbV (1-n), n is porosity, pbIs the density of ore body soil particles;
at the initial moment, the concentration of solid-phase rare earth ions of any coordinate in an ore body is the concentration of the solid-phase rare earth ions before ore leaching, the concentration of solid-phase ammonium ions of any coordinate in the ore body is 0, the concentration gradient of solid-phase mineral leaching agent cations and the solid-phase rare earth ions at the bottom end of the ore body is 0, and then the boundary conditions of the solid-phase mineral leaching agent cations and the solid-phase rare earth ions are expressed by a relational expression (8) and a relational expression (9);
relation (8):
Figure FDA0002943081770000034
in relation (8):
Figure FDA0002943081770000035
in order to consider the concentration of the cation of the solid-phase mineral leaching agent of ion exchange, L is the thickness of an ore body of an ore block, L is determined by mineral exploration data, t is time, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin,the vertical direction is positive;
relation (9):
Figure FDA0002943081770000036
in relation (9):
Figure FDA0002943081770000037
to take into account the concentration of the ion-exchanged solid phase rare earth ions,
Figure FDA0002943081770000038
is the concentration of solid-phase rare earth ions at the initial moment, L is the thickness of an ore body of an ore block,
Figure FDA0002943081770000039
and L is determined by the prospecting data, t is time, z is a vertical coordinate, the vertical coordinate takes the earth surface as an origin, and the vertical direction is positive;
when k is 0 and i is 1, the boundary condition is obtained from the relationship (3) and the relationship (4)
Figure FDA00029430817700000310
And
Figure FDA00029430817700000311
as can be seen from the relational expression (8) and the relational expression (9),
Figure FDA00029430817700000312
is equal to 0 and is equal to 0,
Figure FDA00029430817700000313
is equal to
Figure FDA00029430817700000314
After the selection coefficient is known,
Figure FDA00029430817700000315
And
Figure FDA00029430817700000316
in the case of substituting the relational expressions (5), (6) and (7) into the ion exchange model, the ion exchange model can be obtained
Figure FDA00029430817700000317
Solving the system of nonlinear equations to calculate
Figure FDA00029430817700000318
Obtained by
Figure FDA00029430817700000319
The corrected values can be calculated by substituting the values into relational expressions (5), (6) and (7)
Figure FDA00029430817700000320
And
Figure FDA00029430817700000321
when k is 0 and i is 2, the boundary conditions are combined, and similarly, the calculation may be performed
Figure FDA00029430817700000322
And
Figure FDA00029430817700000323
by analogy, any time and any position can be calculated
Figure FDA00029430817700000324
And
Figure FDA00029430817700000325
and a sixth step: the concentration of the mineral leaching agent is calculated,
on the basis of determining basic parameters in the first step, the second step and the third step, according to the methods in the fourth step and the fifth step, an initial value of the concentration of the leaching agent is given, a penetration curve of rare earth ions can be calculated, the rare earth leaching rate corresponding to the concentration of the leaching agent is calculated according to the penetration curve of the rare earth ions, the concentration of the leaching agent is changed, a relation graph of different concentrations of the leaching agent and the rare earth leaching rate can be obtained, a target leaching rate is set, and when the calculated leaching rate is larger than the target leaching rate, the concentration of the leaching agent is determined.
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