Method of mining an element of interest by in-situ recovery

Abstract

Method of mining an element of interest by in situ recovery The mining method comprises: - a first mining phase during which current values ​​of state variables characterizing the loaded liquid collected in the collecting wells (12) are acquired periodically at determined times spaced between an initial time (T0) and a final time (Tf), the state variables including at least the concentration of said element of interest in the loaded liquid; - a phase of estimating control variables characterizing a geology of the mine, using the current values ​​of the state variables collected during the first mining phase, the control variables including at least an initial content of said element of interest in solid phase at the initial time (T0) at at least one point in the mine;The estimation phase comprises the following steps, repeated iteratively: - determination of estimated values ​​of the state variables at the specified times of the first exploitation phase, using a numerical model of reagent transport in the mine, with at least one set of control variables; - calculation of the difference between the estimated and actual values ​​of the state variables at the specified times of the first exploitation phase; - determination of at least one new set of control variables using the specified difference, by an optimization method, with at least one new set of control variables being used in the step of determining estimated values ​​of the state variables in the following iteration. Figure for the abstract: 1;

Description

Title of the invention: Method for exploiting a mine of an element of interest by in situ recovery

[0001] The invention relates to mining by in situ recovery (ISR).

[0002] In-situ recovery of metal is a mining technique that consists of recovering metal by direct leaching of the ore in place. The absence of mechanical extraction gives this approach the advantage of being quick to deploy, less expensive, and having a lower surface environmental impact than traditional mining techniques used in open-pit or underground mines.

[0003] Mines exploited by in situ recovery now supply 60% of the world's uranium production.

[0004] In situ recovery mining is particularly competitive for low-grade and medium-depth deposits, for example for roll-front uranium deposits in Kazakhstan or Uzbekistan.

[0005] This mining method is being used more and more frequently for other metals. It is widely used in China for rare earth deposits in the near subsoil, also called ion adsorption deposits.

[0006] The overall decrease in grades in exploited deposits makes it increasingly attractive for other metals such as copper or gold.

[0007] SRI could therefore become a major mining technique in the coming decades.

[0008] However, 1TSR has the drawback of providing an indirect view of the deposit. Operators have little information on the condition of the deposit. This information is limited to parameters measurable in the liquid extracted from the collector wells, in particular the metal concentration.

[0009] To allow for a better understanding of the state of the deposit, methods for simulating the operation by modeling reactive transport have been developed. In particular, Orano Mining has been developing an approach based on the HYTEC reactive transport code for nearly twenty years, developed with the geoscience center of the École des Mines de Paris. This model is based on solving the hydrodynamic equations and thermodynamic equilibria of water-rock systems, and on 3D geostatic models describing hydrogeochemical variabilities (permeability, facies, mineral content).

[0010] The demonstration of the feasibility and robustness of these simulations for 1TSR was carried out, in particular at Muyunkum and Tortkuduk, uranium mining sites in Kazakhstan operated by Orano Mining and Kazatomprom via their subsidiary KATCO. This modeling enabled the optimization of the well field (well field design, drilling of additional wells). It also improved mine planning and post-mining remediation.

[0011] It has been demonstrated that the simulations made it possible to reproduce uranium production satisfactorily on the scale of a technology block (about fifteen collector wells, about sixty injection wells), by manual calibration of the global geochemical parameters of the model (for example mineral content).

[0012] On the other hand, however, significant discrepancies may still exist between the model predictions at the scale of a collector well and reality.

[0013] Furthermore, a particular constraint for simulations used to estimate the variables characterizing the mine's geology is the computational and memory cost. Due to the complexity of geochemical speciation and the size of the models (up to several million cells), the calculations required are extremely resource-intensive. The number of calculations to be performed must therefore be kept as low as possible.

[0014] Another constraint arises from the fact that only a small amount of data is accessible, mainly from the analysis of the liquid extracted from the collector wells.

[0015] In this context, the invention aims to propose a method for exploiting a mine of an element of interest by in situ recovery, with implementation of an estimation of variables characterizing the geology of the mine which gives more precise results without requiring overly heavy calculations.

[0016] To this end, the invention relates to a method for exploiting a mine of an element of interest by in-situ recovery, the method comprising:

[0017] - a first phase of mine exploitation by injecting through injection wells in geological layers containing the element of interest an attack solution containing a reagent capable of extracting the element of interest and collecting a liquid charged with said element of interest in collecting wells, current values ​​of state variables characterizing the charged liquid collected in the collecting wells being acquired periodically at determined times of the first phase of operation staggered between an initial time and a final time, the state variables including at least the concentration of said element of interest in the charged liquid collected in the collecting wells;

[0018] - a phase of estimating control variables characterizing a geology of the mine, using the current values ​​of the state variables collected during the first phase of operation, the control variables having at least an initial content of said element of interest in solid phase at the initial time in at least a point in the mine, and preferably also comprising an initial concentration of said element of interest in liquid phase at the initial time in said at least one point in the mine;

[0019] - a second phase of mine exploitation, taking into account the variables of estimated controls at the estimation phase;

[0020] the estimation phase comprising the following steps, repeated iteratively:

[0021] - determination of estimated values ​​of the state variables at said determined times of the first phase of exploitation, by a numerical model of reagent transport in the mine, using at least one set of control variables;

[0022] - calculation of a difference between the estimated values ​​and the actual values ​​of the variables state at the said determined moments of the first phase of operation;

[0023] - determination of at least one new set of control variables using said deviation, by an optimization method, for example the adjoint state method or a gradient-free method, at least one new set of control variables being used in the step of determining estimated values ​​of the state variables of the next iteration.

[0024] The mining method thus makes it possible to estimate the variables characterizing the mine's geology, based on state variables, that is, quantities that can be measured. State variables are those accessible to the mine operator.

[0025] Several sets of control variables are successively estimated until a convergence criterion is satisfied or a stopping criterion is reached. Convergence is achieved after a moderate number of iterations, due to the use of an optimization method.

[0026] The operating method may further have one or more of the following characteristics, considered individually or in all possible combinations:

[0027] - the step of determining at least one new set of control variables includes the following sub-steps:..

[0028] * determination of adjoint variables, by an adjoint numerical transport model reactive in the mine, using the deviation calculated in the deviation calculation step, the adjoint variables comprising at least one error on the initial content of said element of interest in solid phase at the initial time at said at least one point in the mine, and preferably also comprising an error on the initial concentration of said element of interest in liquid phase at the initial time at said at least one point in the mine;

[0029] * determination of the new set of control variables using an approach optimization using a gradient calculated explicitly from adjoint variables and estimated values ​​of state variables;

[0030] - the adjunctive numerical model of reactive transport in the mine describes the backpropagation of the difference between the estimated values ​​and the current values ​​of the state variables, from the final time to the initial time;

[0031] - the numerical model of reagent transport includes at least one equation describing the hydraulic flow of the liquid in the geological layers, an equation describing the transport of the element of interest in the liquid phase in the geological layers, and an equation describing the dissolution and / or precipitation of the element of interest in the liquid phase from the geological layers, the adjunct numerical model comprising a backpropagation equation of the error corresponding to each of the equations of the numerical reagent transport model;

[0032] - the substep of determining the new set of control variables includes:

[0033] * an operation of calculating the gradient of an objective function with respect to the minus one of the control variables, using the estimated values ​​of the state variables, the current values ​​of the state variables and the determined adjoint variables;

[0034] * an operation to determine the new set of control variables using the calculated gradient(s);

[0035] - the operation of determining the new set of control variables is performed using a gradient descent algorithm, for example a conjugate gradient algorithm or a quasi-Newton algorithm;

[0036] - the step of determining estimated values ​​of the state variables, the calculation step of a difference between the estimated values ​​and the current values ​​of the state variables, and the step of determining at least one new set of control variables are repeated iteratively until the objective function satisfies a convergence criterion;

[0037] - at the stage of determining at least one new set of control variables, the determination of at least one new set of control variables is carried out using only said deviations, by a gradient-free method, for example an algorithm derived from the Gauss-Newton approach such as PCGA and ESMDA;

[0038] - the state variables include, in addition to the concentration of said element of interest in the loaded liquid collected in the collection wells, one or more of the following variables: the pH of the loaded liquid collected in the collection wells, a hydraulic head or pressure in the collection wells, the concentrations of species, ionic or colloidal, measurable in aqueous phase in the loaded liquid collected in the collection wells;

[0039] - the control variables include, for the point or each of said points of the mine, in addition to the initial content of said element of interest in solid phase at the initial time, one or more of the following variables: an initial concentration of said element of interest in liquid phase at the initial time, the effective porosity of the porous medium containing said element of interest; a hydraulic conductivity of the porous medium containing said element of interest; diffusion coefficients of the porous medium containing said element of interest; contents of the minerals composing the rock of the porous medium containing said element of interest; a spatial distribution of the rocks of the porous medium containing said element of interest;

[0040] - the element of interest is uranium or a rare earth element, a precious metal such as the copper or gold, or any other metal that can be recovered in situ;

[0041] - the second phase of exploitation includes one or more of the operations following:

[0042] * addition of additional injection wells at predetermined positions using the control variables estimated in the estimation phase;

[0043] * addition of additional collector wells at determined positions using the control variables estimated in the estimation phase;

[0044] * remediation of the mine using the control variables estimated at the phase estimation;

[0045] * closure of collector wells and injection wells at positions determined in using the control variables estimated in the estimation phase;

[0046] * adjustment of a reagent concentration in the attack solution injected by the injection wells at positions determined using the control variables estimated in the estimation phase;

[0047] * adjustment of the flow rate of the attack solution injected through injection wells and / or a flow rate of loaded liquid collected in collector wells, at positions determined using control variables estimated in the estimation phase.

[0048] Other features and advantages of the method of operating the invention will become apparent from the detailed description given below, by way of example and not limitation, with reference to the accompanying figures, among which: - [Fig-1] The [Fig. 1] is a step diagram illustrating the method of operating the invention; - [Fig.2] Fig.2 is a schematic perspective and cross-sectional view of the geological layers of a uranium mine and the mining facility for that mine; - [Fig. 3] Fig. 3 schematically illustrates some steps in the calculation of the method of exploitation of the [Fig.l]; - [Fig. 4] Fig. 4 illustrates the basic data used to construct a synthetic case on which the method of exploiting the invention was tested; - [Fig.5] The [Fig.5] illustrates the results obtained using the method of exploitation of the invention, for the synthetic case, employing the ASM and PCGA approaches; - [Fig.6] The [Fig.6] illustrates the results obtained using the method of exploitation of the invention, for the synthetic case, employing the ESMDA approach; - [Fig. 7] Figure 7 details the results obtained using the method of the invention (ASM approach); - [Fig. 8] Figure 8 illustrates the results obtained for the method of the invention using the ASM, PCGA, and ESMDA optimization approaches; and - [Fig.9] Fig.9 illustrates the computational cost of the results obtained for the method of the invention using the ASM, PCGA and ESMDA optimization approaches.

[0049] The method illustrated in [Fig.1] aims to exploit a mine of an element of interest by in situ recovery.

[0050] The element of interest is a metal, typically uranium.

[0051] Alternatively, the element of interest is a rare earth, or a precious metal such as copper or gold.

[0052] The method comprises a first exploitation phase S10, carried out by injecting into geological layers 8 containing the element of interest an attack solution containing a reagent capable of extracting the element of interest. The attack solution is injected through injection wells 10. A liquid laden with said element of interest is collected in collector wells 12 ([Fig.2]).

[0053] As illustrated in [Fig.2], the attack solution flows from the injection wells 10 to the collector wells 12 through geological layers 8 containing the element of interest.

[0054] In the example shown in [Fig. 2], the mine is a uranium mine. It is organized into several production cells, which are hexagonal in shape. The injection wells 10 are located at the six vertices of each hexagon. A collector well 12 is located at the center of each hexagon.

[0055] In the example of [Fig.2], the attack solution is sulfuric acid H2SO4, in solution in water.

[0056] The uranium-laden liquid extracted from the collection wells 12 is transferred to a separation plant 16, allowing the separation of a concentrated uranium solution from the aqueous sulfuric acid solution. This solution is then recycled to injection wells 10.

[0057] During the first exploitation phase S10, current values ​​of state variables characterizing the loaded liquid collected in the collector wells 12 are acquired periodically, at determined times spaced between an initial time T0 and a final time Tf.

[0058] The duration separating the initial moment from the final moment is typically between ten days and two hundred days, preferably between fifteen and one hundred days, and even more preferably between twenty and forty days.

[0059] The current values ​​of the state variables are acquired for example between once every four days and four times a day, preferably between once every three days and three times a day, even more preferably between once every two days and twice a day.

[0060] Typically, the current values ​​of the state variables are acquired for the loaded liquid collected in each collecting well. Alternatively, only the loaded liquid collected in certain collecting wells is analyzed.

[0061] The state variables include at least the concentration of said element of interest in the loaded liquid collected in the collecting wells.

[0062] Preferably, the state variables also include one or more of the following variables:

[0063] - the concentrations of the species, colloidal or ionic, measurable in phase aqueous in the loaded liquid collected in the collecting wells;

[0064] - the pH of the charged liquid collected in the collecting wells;

[0065] - the redox potential of the charged liquid collected in the collecting wells;

[0066] - a hydraulic charge or pressure in the collector wells.

[0067] Advantageously, the state variables include all the variables listed above.

[0068] The mining method further includes a phase S20 of estimating control variables characterizing the geology of the mine, using the current values ​​of the state variables collected during the first mining phase S10.

[0069] These control variables include at least an initial content of said element of interest in solid phase at the initial time T0 at at least one point in the mine.

[0070] Preferably, the control variables also include, for said at least one point of the mine, one or more of the variables below:

[0071] - an initial concentration of said element of interest in the liquid phase at time initial T0;

[0072] - the effective porosity of the porous medium containing said element of interest;

[0073] - the hydraulic conductivity of the porous medium containing said element of interest;

[0074] - the diffusion coefficients of the porous medium containing said element of interest;

[0075] - the mineral content composing the rock of the porous medium containing said element of interest;

[0076] - a spatial distribution of the rocks of the porous medium containing said element of interest.

[0077] The above control variables are typically estimated for a large number of points in the mine.

[0078] For example, all the control variables listed above are estimated for at least one point of the mine.

[0079] These points of the mine will be referred to as "calculation points" in the description below.

[0080] These points are typically regularly distributed throughout the area of ​​the mine that the mining method aims to simulate.

[0081] They therefore define a mesh of this area. This mesh is typically three-dimensional. In other words, the calculation points are distributed at different depths below the ground surface.

[0082] Alternatively, the mesh is two-dimensional, with all calculation points at the same depth below the ground surface or at the same ordinate.

[0083] According to another variant, the mesh is one-dimensional, with all calculation points being, for example, located on the same vertical line.

[0084] The calculation points typically define a parallelepiped mesh. The calculation points constitute the barycenters of these parallelepiped cells.

[0085] The dimensions of each mesh are a few meters in length, a few meters in width and a few meters in height. For example, each mesh has a length of 5 meters, a width of 5 meters and a height of 1 meter.

[0086] The geological layers 8 in which the element of interest is located are typically porous media. In other words, these layers are made of a solid material comprising a network of pores.

[0087] A liquid flow circulates within the pores. This liquid flow is supplied by the water table and by the attack solution injected into the injection wells. This flow is generally water, containing various dissolved chemical elements. These dissolved chemical elements include the element of interest, the reagent injected through the injection wells, and other chemical species.

[0088] In the case where the element of interest is uranium, these other chemical species are mainly composed of SO42, Ca2+, Fe2+, Fe3+, Mg2+, Al3+ ions or colloids.

[0089] The liquid stream can also be loaded with solid particles, typically particles torn from the solid material constituting the geological layer or precipitates.

[0090] The content of said element of interest in solid phase corresponds to the concentration of the element of interest in the solid matter, expressed in moles per litre.

[0091] The concentration of said element of interest in the liquid phase corresponds to the concentration of said element of interest in the liquid flow filling the pores, this concentration taking into account both dissolved elements and elements in the form of particles carried along with the liquid flow. It is expressed in moles per liter of solution in the porous medium according to the usual convention in geochemistry.

[0092] Porosity corresponds to the porosity of the material constituting the geological layer at the point considered, expressed as a fraction. Permeability corresponds to hydraulic conductivity, that is to say, the soil's capacity to allow a fluid to pass through, expressed in m / s.

[0093] As illustrated in [Fig.1], the mining method includes a second mining phase S30, carried out taking into account the control variables estimated in the estimation phase S20.

[0094] The S20 estimation phase will now be detailed.

[0095] The estimation phase S20 comprises the following steps, repeated iteratively:

[0096] - S21: determination of estimated values ​​of the state variables at said times determined from the first phase of exploitation S10, by a numerical model of reagent transport in the mine, using at least one set of control variables;

[0097] - S22: calculation of a difference between the estimated values ​​and the current values ​​of state variables audits instant determined from the first phase of operation S10;

[0098] - S23: determination of at least one new set of control variables using said gap, by an optimization method, for example the adjoint state method or a gradient-free method, at least one new set of control variables being used in step S21 of determining the estimated values ​​of the state variables of the next iteration.

[0099] The estimation phase S20 is performed after the first exploitation phase. More precisely, it is performed once the collection of current values ​​of the state variables between the initial time and the final time is complete. It is therefore performed after the final time.

[0100] The numerical transport model of the reactant used in step S21 takes into account various phenomena (see [Fig.3], left part of the step diagram):

[0101] - the flow of the liquid in the geological layers 8;

[0102] - the displacement of the chemical elements contained in the liquid, that is to say the transport of these chemical elements;

[0103] - the interaction between these chemical elements and solid matter, and the interactions of these chemical elements interacting with each other, that is to say, geochemistry.

[0104] The numerical reagent transport model thus comprises at least:

[0105] - equations describing the hydraulic flow of the liquid in the layers geological 8,

[0106] - an equation describing the transport of the element of interest in the liquid phase in the geological layers 8, and

[0107] - an equation describing the dissolution and / or precipitation of the element of interest in the liquid phase from the geological layers.

[0108] Typically, the numerical model of reagent transport also includes equations describing the transport, dissolution and / or precipitation of other chemical elements contained in the liquid stream flowing through the geological layers.

[0109] At step S21, as illustrated on the left side of [Fig. 3], the numerical model of reactant transport considers the state at T0 as the initial state. The equations are solved iteratively for all successively determined times, with a determined time step, from T0 to Tf. At each iteration, the equations describing the hydraulic flow are solved first, then the equation(s) describing the transport, and then the equation(s) describing the geochemistry.

[0110] Typically, the numerical transport model of the reagent used is the HYTEC code. This calculation code is well-known and will not be described in detail here. It is described in particular in the following references:

[0111] J. Nos, “Conceptual model of uranium mining by in situ recovery#; interpretation of production data and contribution of reactive transport modeling in heterogeneous media”, 2011. Available at: https: / / hal-mines-paristech.archives-ouvertes.fr / hal-00700218;

[0112] J. van der Lee, L. De Windt, V. Lagneau, and P. Goblet, “Module-oriented modeling of reactive transport with HYTEC”, Comput. Geosci., vol. 29, no. 3, p. 265-275, Apr. 2003, doi: 10.1016 / 80098-3004(03)00004-9.

[0113] The HYTEC code models the transport of the reagent in the mine using a large number of equations, as well as initial conditions.

[0114] The equations describing the hydraulic flow of the liquid are as follows: [0H5] Ssÿ =yK(Vh)+q

[0116] U=-KVh

[0117] The equation describing the transport of the element of interest in the liquid phase is as follows: [°118] = V • (wDVc-Ue) +s-

[0119] The equation describing the dissolution and / or precipitation of the element of interest in the liquid phase is as follows: C0120]

[0121] The initial conditions are as follows:

[0122] h{x, / = 0) = hMt{x)

[0123] c(x, / = 0) =cMt(x')

[0124] c(x,t = 0) = cMt(x)

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] The HYTEC model includes further equations describing the transport, dissolution and / or precipitation of other chemical elements, which are not reproduced here. These equations must be verified at each calculation point x of the simulated area. The first equation describes a transient saturated flow and allows us to determine the hydraulic head h (expressed in meters). Ss is the storage coefficient, expressed in m1, K is the hydraulic conductivity expressed in ms1, and q represents the sink / source term expressed in s'. The term well / source corresponds to the flow rate of liquid injected or extracted from each of the wells 10, 12. The second equation gives the Darcy velocities u, expressed in ms', calculated from the hydraulic heads h. The third equation describes the transport of the element of interest and incorporates various mechanisms: convection, diffusion, dispersion, source / sink terms, and chemical source terms. Convection corresponds to the transport of chemical elements in solution by the flow of the liquid containing them. Diffusion corresponds to the Fickian movement of chemical elements in solution from areas of high concentration to areas of low concentration. Dispersion corresponds to local fluctuations in flow velocity and numerical error. The chemical source term corresponds to the addition or removal of elements in solution due to precipitation or mineral dissolution, co is the dynamic porosity expressed as a percentage, D is the diffusion coefficient expressed in m² s⁻¹, c is the concentration of the element of interest in the liquid phase, and C is the content of the element of interest in the solid phase.s represents the source terms per well due to the injection of the attack solution and the pumping of the loaded liquid, and corresponds to the chemical source terms, i.e. t. d. the addition or disappearance of the element of interest in solution due to precipitation / dissolution of minerals.

[0131] The fourth equation describes the dissolution / precipitation of the element of interest. kv is the reaction rate of the element of interest expressed in mol.m 2.sl, As corresponds to the specific surface area of ​​the solid matter in m2.g ', and Ks is the solubility constant of the element of interest, expressed in mol.L *.

[0132] After step S21, and before step S22, a step S24 is provided for calculating an objective function J, using the estimated values ​​of the state variables and the current values ​​of the state variables. For example, the objective function is as follows:

[0133] 1 y |[2 1 / JA \Tni / j A \ — 2^11 %« It — 2 ( ^obs ” ^calc )^-( ^obs " “cale )

[0134] The number of current values ​​of the state variables considered for calculating the objective function J can be low or very high: it corresponds to the number of state variables considered (concentration of the element of interest in the collected slurry, pH in the collected slurry, hydraulic head, etc.), multiplied by the number of collecting wells, multiplied by the number of specific times at which the current values ​​are acquired. This number of points may vary depending on the time and / or the collecting well considered.

[0135] dobs is the vector of current values ​​of the state variables. Alternatively, when it is possible to directly measure certain control variables, the dobs vector also contains the measured values ​​of these control variables. This dobs vector has a dimension corresponding to the number of current values ​​of the state variables and measured values ​​of the control variables.

[0136] dcaic is the vector of estimated values ​​of the state variables. It typically has the same dimension as dobs.

[0137] R is the covariance matrix of the measurement noise.

[0138] This covariance matrix is ​​generally diagonal and has as its value the terms, on its diagonal, the square of the standard deviation of the noise of the measurements.

[0139] Steps S21, S22 and S23 are iterated until the objective function satisfies a convergence criterion or a stopping criterion.

[0140] For example, the convergence criterion is that the objective function J has been divided by 100 compared to the first iteration.

[0141] Other criteria may be used: division by a factor other than 100, reduction of less than 1% of the objective function between two successive iterations, etc.

[0142] For example, the stopping criterion is that the maximum number of iterations is reached. Other stopping criteria can be used: maximum number of reactive transport simulations, etc.

[0143] Following step S24, a step S25 is thus planned during which it is determined whether the objective function satisfies the convergence criterion. If so, step S20 is considered complete and the process proceeds directly to step S30. The set of control variables processed in the last iteration is considered the result of the control variable estimation phase.

[0144] On the contrary, if the convergence criterion is not satisfied, the S22 gap calculation step is executed.

[0145] The deviation calculated in step S22 is, for example, the simple difference between the estimated values ​​and the actual values ​​of the state variables at determined times in the first phase of operation. Alternatively, it is a percentage variance, or a variance calculated in any other way.

[0146] According to a first embodiment, the S23 step of determining the new set of control variables uses the adjoint state method (ASM method).

[0147] A single set of estimated values ​​for the state variables is determined in step S21.

[0148] A single new set of control variables is determined in step S23.

[0149] Step S23 of determining the new set of control variables includes In this case, the following sub-steps:

[0150] - S26: determination of adjoint variables, by an adjoint numerical model of transport of reagent in the mine, using the deviation calculated in calculation step S22, the adjoint variables including at least one error on the initial content of said element of interest in solid phase at the initial time at said at least one point in the mine, and preferably including an error on the initial concentration of said element of interest in liquid phase at the initial time at said at least one point in the mine;

[0151] - S27: determination of the new set of control variables using an approach optimization using a gradient calculated explicitly from adjoint variables and estimated values ​​of state variables.

[0152] The estimation phase of the control variables aims to bring the estimated values ​​as close as possible to the production history, that is, as close as possible to the current values ​​of the state variables. The estimation phase is approached as a constrained optimization problem. Its aim is to bring the objective function to convergence as quickly as possible.

[0153] The approach here consists of minimizing the objective function using an optimization algorithm.

[0154] This algorithm can, for example, be a descent direction algorithm. It is then necessary to determine the gradient of the objective function with respect to at least some control variables, in order to determine the new set of control variables.

[0155] The adjoint state method allows for the efficient calculation of the gradient of the objective function. The adjoint numerical model of reactant transport describes the backpropagation of the difference between the estimated and actual values ​​of the state variables, from the final time to the initial time.

[0156] The adjoint numerical model includes a backpropagation equation for the gap corresponding to each of the equations of the numerical reagent transport model.

[0157] The adjunctive numerical model used in step S26 takes into account various phenomena (see [Fig.3], right-hand part of the step diagram):

[0158] - the backpropagation of the gap for the interaction between chemical elements contained in the liquid and solid matter, and for the interactions of these chemical elements with each other (adjoining geochemistry stage);

[0159] - the backpropagation of the gap for the displacement of the contained chemical elements in the liquid, that is to say for the transport of these chemical elements (assisted transport stage);

[0160] - the backpropagation of the gap for the flow of the liquid in the layers geological 8 (adjunct flow stage).

[0161] The adjunctive digital model thus comprises at least:

[0162] - an equation describing the backpropagation of the gap for dissolution and / or the precipitation of the element of interest in the liquid phase from the geological layers

[0163] - an equation describing the backpropagation of the gap for the transport of the element of interest in the liquid phase in geological layers 8, and

[0164] - equations describing the backpropagation of the gap for the flow hydraulics of the liquid in geological layers 8.

[0165] Typically, the adjunct numerical model also includes equations describing the backpropagation of the gap for the transport, dissolution and / or precipitation of other chemical elements contained in the liquid stream flowing through the geological layers.

[0166] At step S26, as illustrated on the right-hand side of [Fig. 3], the adjoint numerical model of reagent transport considers the state at Tf as the initial state. The equations are solved iteratively for all successively determined times, with a determined time step, from Tf to T0. At each iteration, the equations describing the adjoint geochemistry are solved first, then the equation(s) describing the adjoint transport, and then the equation(s) describing the adjoint flow.

[0167] Typically, the adjoint variables include, in addition to the error in the initial content of said element of interest in the solid phase at the initial state at said at least one point in the mine and in addition to the error in the initial concentration of said element of interest in the liquid phase at the initial time at said at least one point in the mine, all or part of the following variables:

[0168] - error in the initial content of said element of interest in solid phase at said at minus one point of the mine at other determined times;

[0169] - error in the initial content of the other minerals composing the rock of the medium porous at said at least one point of the mine at the determined times;

[0170] - error in the initial concentration of said element of interest in liquid phase at said at least one point of the mine at the other determined times;

[0171] - error in the initial concentration of other chemical species in the liquid phase at said at least one point of the mine at the determined times;

[0172] - error in the hydraulic charge or pressure at said at least one point of the mine at each determined moment;

[0173] - error on the dynamic porosity at said at least one point of the mine;

[0174] - error on permeability at said at least one point of the mine;

[0175] The equation describing the backpropagation of the gap for the dissolution and / or precipitation of the element of interest in the liquid phase is as follows: 101761

[0177] The equation describing the backpropagation of the gap for the transport of the element of interest in the liquid phase is as follows:

[0178] ^4v; / \ nn ) 5 ( ç-çobs \

[0179] The equations describing the backpropagation of the gap for the hydraulic flow of the liquid are as follows:

[0180]

[0181] v ! h^\ vy

[0182] The initial conditions are as follows:

[0183] (X, tmax) = (4 tmax) ~ (^max) = 0 [° 184 ] ^(x,t mix ) =0

[0185] The adjoint model preferably includes yet other equations describing the backpropagation of the gap for the transport, dissolution and / or precipitation of other chemical elements, which are not reproduced here.

[0186] These equations must be verified at each calculation point x of the simulated area.

[0187] In the equations above:

[0188] - At is the error in the concentration of said element of interest in the liquid phase, the error in the content of said element of interest in solid phase;

[0189] - ^is the current value of the concentration of said element of interest in phase liquid ;

[0190] - is the current value of the hydraulic height;

[0191] - is the estimated acquisition error on the current value c°hs;

[0192] - is the estimated acquisition error on the current value;

[0193] _ is the error on the speeds of darcy.

[0194] Thus, in the adjoint numerical model, the system and the equations are solved in reverse order, contrary to the physical order ([Fig.3] on the right). The initial time has become the maximum time, and the sequential solution of the adjoint equations is performed from the

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203]

[0204] Adjoint chemistry extends to the adjoint flow. Furthermore, the terms "source" and "sink" have been replaced by terms called "adjoint sources," which represent deviations from production data. The adjoint problem can be viewed as a case where error is injected at observation points (the producing wells), propagating backward along streamlines to the injecting wells. These error terms are therefore negative at computational points where the liquid flow is zero. The gradient dependent on these error variables, its values, and the resulting fit will also be very small in areas where the liquid flow is zero. It is worth noting that the adjoint numerical model is discretized and solved in a very similar way to the reagent transport numerical model. Its solution will therefore have a computational cost equal to, or even lower than, that of the reagent transport numerical model. Substep S27 for determining the new set of control variables includes the following operations: - S28: an operation to calculate a gradient of the objective function with respect to at least one of the control variables, using the estimated values ​​of the state variables calculated in step S21, the current values ​​of the state variables, and the adjoint variables calculated in step S26; - S29: an operation to determine the new set of control variables using the calculated gradient(s). The gradient of the objective function is determined at least with respect to the initial content of the element of interest in the solid phase at the initial time, at each calculation point. For example, the gradient of the objective function is determined for each of the control variables. These gradients are obtained using equations that can be derived from the formula for calculating the objective function J, and the system of equations of the adjoint numerical model. These formulas can be established by a person skilled in the art who is familiar with numerical models of reagent transport in mines, without any particular difficulty. Therefore, they will not be detailed here. The equation for the gradient of the objective function with respect to the initial content of the element of interest in the solid phase at the initial time is as follows, at each calculation point: due _ ; 4 » / , C0 \ dc0 - dt + 1 - Ks / Once the gradients are known, the operation of determining the new set of control variables S29 is carried out, as described above, using a gradient descent algorithm, for example a conjugate gradient algorithm or a quasi-Newton algorithm.

[0205] The solver used for step S23 is, for example, the quasi-newton L-BFGS-B because of its good performance.

[0206] The solver is known and will not be described in detail here.

[0207] According to a second embodiment, in step S23 of determining at least one new set of control variables, the determination of at least one new set of control variables is carried out using only the deviations calculated in step S22, by a gradient-free method.

[0208] Several sets of estimated values ​​of the state variables are determined in step S21.

[0209] Several new sets of control variables are determined in step S23.

[0210] Step S23 thus comprises a single substep, during which several sets of control variables are determined without gradient, using for example the sets of control variables determined in step S23 in the previous iteration and the sets of estimated values ​​of the state variables determined in step S21.

[0211] Typically, step S23 is performed by an optimization algorithm that treats the reactive transport problem as a black box and does not require a gradient. For example, step S23 is performed using the principal component geostatistical approach (PCGA) or the ensemble smoother with multiple data assimilation (ESMDA). These optimization algorithms are known and will not be described in detail here.

[0212] PCGA is described in particular in the following references:

[0213] Kitanidis, P. K. and J. Lee (2014). “Principal Component Geostatistical Approach for Large-Dimensional Inverse Problems”. Water Resources Research 50:7, pp. 5428-5443. ISSN: 1944-7973. DOI: 10.1002 / 2013WR014630.

[0214] Lee, J. and P. K. Kitanidis (2014). “Large-Scale Hydraulic Tomography and Joint Inversion of Head and Tracer Data Using the Principal Component Geostatistical Approach (PCGA)”.

[0215] Water Resources Research 50:7, pp. 5410-5427. ISSN: 1944-7973. DOI: 10.1002 / 2014WR015483.

[0216] Et l’approche ESMDA est décrite notamment dans les références suivantes :

[0217] Emerick, A. A. and A. C. Reynolds (2012). “History Matching Time-Lapse Seismic Data Using the Ensemble Kalman Filter with Multiple Data Assimilations”. Computational Geosciences 16:3, pp. 639-659. ISSN: 1573-1499. DOI: 10.1007 / s 10596-012-9275-5.

[0218] - (2013a). “Ensemble Smoother with Multiple Data Assimilation”. Computers & Geosciences. Ensemble Kalman Filter for Data Assimilation 55, pp. 3-15. ISSN: 0098-3004. DOI: 10.1016 / j.cageo.2012.03.011.

[0219] The second S30 exploitation phase includes one or more of the following operations:

[0220] - addition of 10 additional injection wells at positions determined in using the control variables estimated in the estimation phase S20;

[0221] - addition of 12 additional collector wells at positions determined in using the control variables estimated in the estimation phase S20;

[0222] - closure of collector wells 12 and injection wells 10 at positions determined using the control variables estimated in the estimation phase S20;

[0223] - adjusting the concentration of a reagent in the attack solution injected by the injection wells 10 at positions determined using the control variables estimated in the estimation phase S20;

[0224] - adjustment of the flow rate of attack solution injected through injection wells 10 and / or a flow rate of loaded liquid collected in collector wells 12 at positions determined using the control variables estimated in the estimation phase S20;

[0225] - mine remediation using control variables estimated at phase S20 estimation;

[0226] In other words, the operation of the mine during the second phase of operation is optimized by taking into account the estimation of the control variables carried out during phase S20. This phase S20 makes it possible to better characterize the geology of the mine, in particular the grades and concentrations of the element of interest, in solid phase and in liquid phase, at the different calculation points of the mine.

[0227] An example of the application of the method of exploitation of the invention will now be detailed, with reference to figures 4 to 9.

[0228] The method of exploiting the invention is applied to a synthetic case, that is to say by using a set of current values ​​of the state variables obtained by calculation, and reflecting the real structure of a uranium mine.

[0229] This synthetic case is defined by a production block composed of seven hexagonal operating cells with a radius of 42 m, the radius being the distance separating the center of the hexagon from its vertices. An injection well is positioned at each vertex of the hexagons (black dots), and a collector well is positioned at the center of each hexagon (triangles), as illustrated in Figures 4d, 4e, and 4f. There are thus a total of seven collector wells and twenty-four injection wells.

[0230] The synthetic case is based on a regular grid of dimension (67 x 67 x 1) i.e. 4225 meshes having a size of (5 m x 5 m x 5 m).

[0231] The field of initial uranium contents in the solid phase is illustrated in Figure 4a (Reference).

[0232] Figure 4b (initial) illustrates the spatial distribution of the uranium considered initially for the estimation phase, i.e. considered at the initial time T0. This distribution differs significantly from that of Figure 4a.

[0233] This is generally the case during mining operations, since the operator has only partial knowledge of the actual uranium grades at different points in the mine. In an actual mine, initial grades are estimated by drilling, for example, using a grid with a side length of between 50 and 100 m. The uranium grade is generally calculated from a gamma logging signal. Two chemical elements contribute to this gamma signal: uranium (U) and radium (Ra). The ratio between uranium and radium can vary by an order of magnitude between different points in the mine. In practice, a single ratio is applied to all boreholes, which leads to significant errors in the estimated initial grades.

[0234] Figure 4c illustrates the U / Ra ratio for the synthetic case. The reconstructed initial concentrations shown in Figure 4b are determined assuming that a core sample is taken from the twelve core wells 18 shown in Figures 4a, 4b, and 4c. A U / Ra ratio of 0.65 is applied to the twelve samples corresponding to the twelve core samples. This ratio leads to a significant underestimation of the initial uranium concentrations. At the other points in the field covered by Figure 4b, the initial uranium concentrations are inferred from the values ​​determined for the twelve core wells 18.

[0235] Furthermore, a measurement error of 10% is assumed for the twelve available measurements. This leads to a significant underestimation of the quantity of uranium present in the production unit, as illustrated in comparative figures 4d and 4e. In the synthetic example, the production unit contains approximately 46.52 tonnes of uranium. With the initial concentrations considered in Figure 4b, the production unit contains only 38.82 tonnes of uranium, representing an error of -16.56%. This error averages ±3.66t in the production cells, or ±84.22% compared to the reference, as illustrated in Figure 4f.

[0236] The numerical model of reagent transport used in this example is defined by the system of four equations and by the three initial conditions defined above.

[0237] The main parameters for the numerical reagent transport model are shown in the following table. Parameter Value Unit Simulation duration (t) 300 days Time step (dt) 6 h Diffusion coefficient (D) 10 10 m2s 1 Hydraulic conductivity (Φ) 10⁴ ms Storage (Sy) 10³ m¹ Porosity (ε) 23% Density (P) 1.630 kg.r¹ Reaction rate (g) -6.9 x 10⁹ mol.m².s¹ Mineral molar mass (Ms) 270.0 g.mol¹ Specific surface area (As) 13.5 m².g¹ logK 3.2 - Solubility constant (Ks) 6.31 x 10⁴ mol

[0238] The adjoint numerical model used in this example is defined by the system of four equations and by the four initial conditions defined above.

[0239] The objective function is the function J whose equation is given above.

[0240] The new set of control variables is determined using only the gradient of the objective function with respect to the initial content of the element of interest in the solid phase at the initial time at each calculation point, according to the equation given above.

[0241] From the initial uranium concentration field in the solid phase, illustrated in Figure 4a, and using the numerical reagent transport model described above, it is possible to predict the characteristics of the loaded liquid collected in the different producing wells. In other words, it is possible to determine values ​​corresponding to the current values ​​of the state variables.

[0242] The simulation is carried out over three hundred days, and one thousand two hundred six-hour time steps. The initial flow rate imposed on the extraction wells is 12 m3 per hour, subsequently decreasing exponentially with a decay coefficient of -0.0015.

[0243] flow rate - flow rate x exp(coef xnt>idt}

[0244] The flow rates injected into the injection wells are calculated so as to obtain a perfect water balance.

[0245] The reference curves R on [Fig.5] represent the uranium concentrations thus calculated, in milligrams per litre, in the loaded liquid collected in the seven collecting wells.

[0246] The estimation phase S20 of the method for operating the invention is then implemented, using these data as current values ​​of the state variables. The time interval considered for the simulation, between the initial time T0 and the final time Tf, is shown in gray on the different curves in [Fig. 5]. Only the The values ​​obtained for the first thirty days of production are considered for the application of the S20 estimation phase. The following one hundred and seventy days are used only to validate the predictions.

[0247] For the application of the estimation phase, the current values ​​considered are either the R reference curves or the noisy reference curves. In the latter case, Gaussian white noise with a standard deviation of 2.7 mg / l is applied to the R reference curves.

[0248] The current values ​​are considered to be the noise-free (R curves) or noisy (circles in [Fig. 5]) uranium concentrations, calculated every six days for the period of one hundred and fifty days. There are therefore twenty-five measurements for each of the seven extraction wells, i.e., one hundred and seventy-five measurements in total, with or without noise.

[0249] The R' curves on [Fig. 5] correspond to the concentrations calculated using only the numerical reagent transport model and starting from the initial concentrations in Figure 4b. It can be seen that the uranium concentration in the loaded liquid collected in the extraction wells is either underestimated, overestimated, or correct.

[0250] The I and P curves in [Fig. 5] correspond to the values ​​predicted using the ASM and PCGA approaches respectively. They are extremely close to the reference curves R, and this is true for virtually all collector wells.

[0251] Figure 6 is similar to Figure 5. The gray curves I correspond to the predicted values ​​for different embodiments using the ESMDA approach, and curve P to the average of the predicted values ​​for these embodiments. The different embodiments correspond to different sets of control parameters, selected by random sampling. These multiple predictions characterize the uncertainty of the inverse content field on the predictions.

[0252] Figure 7 illustrates some results obtained by applying the method of exploitation of the invention with the ASM approach, in particular the estimation phase of the control variables S20, to the synthetic case defined above.

[0253] Figure 7a shows the initial gradient of the objective function at each calculation point considered. The initial gradient is the gradient determined at the end of the first iteration of the estimation phase. It appears that, for each calculation point considered, this gradient is zero, negative, or positive.

[0254] Negative values ​​indicate the need to increase the values ​​of the control variables while positive values ​​indicate the need to decrease the values ​​of the control variables.

[0255] The gradient value for the other iterations is not shown.

[0256] Figure 7b shows the initial solid-phase uranium contents determined at the outcome of the estimation phase.

[0257] Figure 7c shows the evolution of the objective function for each iteration of the estimation phase for the ASM approach (as a fraction of the value of the objective function after the first iteration).

[0258] The decay of the objective function is very rapid, reaching a factor of 100 after only twelve iterations (twelve calculations using the numerical model of reagent transport, alternating with twelve calculations using the adjoint numerical model). For iterations 1 to 14, the current values ​​from the reference curves R were taken into account in the calculations.

[0259] Figure 7d shows the uranium concentration simulated by the method of the invention (ordinate axis) using the ASM approach as a function of the reference concentrations (abscissa axis, observation, in milligrams per liter). The gray dots correspond to the values ​​after the first iteration. The black dots correspond to the final values ​​determined by simulation. Figure 7d shows that the prediction for each well has improved considerably.

[0260] Figure 8 compares the results obtained by the method of the invention, using the Adjoint State Approach (ASM), the PCGA approach and the ESMDA approach.

[0261] Figures 8a, 8b, 8c, and 8d show the initial solid-phase uranium contents for the reference, as estimated by the three approaches. Figures 8e, 8f, 8g, and 8h show the total amount of uranium in each production cell for the reference, as estimated by the three approaches. Figures 8j, 8k, and 81 show the error in the total amount of uranium in each production cell estimated by the three approaches.

[0262] The total estimated quantities of uranium in the production block for the three approaches are 46.60, 45.56 and 45.75 tonnes respectively, for a theoretical (reference) value of 46.52 tonnes. This is over or underestimated by less than 3% compared to -16.5% initially (Figure 4e), representing a significant improvement.

[0263] The quantity of uranium in the seven production cells is also correctly re-evaluated by the method of operation of the invention for the three approaches illustrated. The average deviation per production cell is respectively 1.14, 0.59 and 1.04 tonnes for the ASM, PCGA and ESMDA approaches, i.e. less than 20% error compared to 85% initially (Figure 4f).

[0264] According to another important aspect illustrated in [Fig. 9], the number of calculations required to achieve these results is only fourteen iterations with the ASM approach, representing twenty-eight simulations: fourteen using the numerical model of reagent transport, and fourteen using the adjoint numerical model. For the PCGA method, three hundred and twenty-five simulations are required. For the ESMDA method, one thousand one hundred simulations are required. The computation time and memory space required in the invention with the ASM approach are considerably reduced compared to the PCGA and ESMDA methods for similar inversion results.

Claims

1. Demands Method for exploiting a mine of an element of interest by in-situ recovery, the method comprising: - a first phase of mining by injecting through injection wells (10) into geological layers (8) containing the element of interest an attack solution containing a reagent capable of extracting the element of interest and by collecting a liquid loaded with said element of interest in collecting wells (12), current values ​​of state variables characterizing the loaded liquid collected in the collecting wells (12) being acquired periodically at determined times of the first phase of mining staggered between an initial time (T0) and a final time (Tf), the state variables including at least the concentration of said element of interest in the loaded liquid collected in the collecting wells (12); - an estimation phase of control variables characterizing a mine geology, using the current values ​​of the state variables collected during the first phase of exploitation, the control variables including at least an initial content of said element of interest in solid phase at the initial time (T0) at at least one point of the mine, and preferably also including an initial concentration of said element of interest in liquid phase at the initial time (T0) at said at least one point of the mine; - a second phase of mine operation, taking into account the control variables estimated in the estimation phase; the estimation phase comprising the following steps, repeated iteratively: - determination of estimated values ​​of state variables at said determined times of the first phase of exploitation, by a numerical model of reagent transport in the mine, using at least one set of control variables; - calculation of a difference between the estimated values ​​and the current values ​​of the state variables at the said determined times of the first phase of operation; - determination of at least one new set of control variables using said gap, by an optimization method, for example the adjoint state method or a gradient-free method, at least a new set of control variables being used in the step of determining estimated values ​​of the state variables of the next iteration.

2. A method of operation according to claim 1, wherein the step of determining at least one new set of control variables comprises the following substeps: - determination of adjoint variables, by an adjoint numerical model of reactive transport in the mine, using the error calculated in the step of calculating an error, the adjoint variables comprising at least one error on the initial content of said element of interest in solid phase at the initial time at said at least one point of the mine, and preferably also comprising an error on the initial concentration of said element of interest in liquid phase at the initial time at said at least one point of the mine; - determination of the new set of control variables using an optimization approach using a gradient calculated explicitly from the adjoint variables and the estimated values ​​of the state variables.

3. Method of operation according to claim 2, wherein the adjunctive numerical model of reactive transport in the mine describes the backpropagation of the difference between the estimated values ​​and the current values ​​of the state variables, from the final time to the initial time.

4. Method of operation according to claim 3, wherein the numerical reagent transport model comprises at least one equation describing the hydraulic flow of the liquid in the geological layers (8), one equation describing the transport of the element of interest in the liquid phase in the geological layers (8), and one equation describing the dissolution and / or precipitation of the element of interest in the liquid phase from the geological layers (8), the adjunct numerical model comprising a backpropagation equation of the gap corresponding to each of the equations of the numerical reagent transport model.

5. A method of operation according to any one of claims 2 to 4, wherein the substep of determining the new set of control variables comprises: - an operation of calculating the gradient of an objective function with respect to at least one of the control variables, using the estimated values ​​of state variables, current values ​​of state variables and determined adjoint variables; - an operation to determine the new set of control variables using the calculated gradient(s).

6. Method of operation according to claim 5, wherein the operation of determining the new set of control variables is carried out using a gradient descent algorithm, for example a conjugate gradient algorithm or a quasi-Newton algorithm.

7. A method of operation according to claim 5 or 6, wherein the step of determining estimated values ​​of the state variables, the step of calculating a difference between the estimated values ​​and the actual values ​​of the state variables, and the step of determining at least one new set of control variables are repeated iteratively until the objective function satisfies a convergence criterion.

8. Method of operation according to claim 1, wherein, in the step of determining at least one new set of control variables, the determination of at least one new set of control variables is carried out using only said deviations, by a gradient-free method, for example an algorithm derived from the Gauss-Newton approach such as PCGA and ESMDA.

9. A method of operation according to any one of the preceding claims, wherein the state variables include, in addition to the concentration of said element of interest in the loaded liquid collected in the collecting wells, one or more of the following variables: the pH of the loaded liquid collected in the collecting wells, a hydraulic head or pressure in the collecting wells, the concentrations of the species, ionic or colloidal, measurable in aqueous phase in the loaded liquid collected in the collecting wells.

10. A mining method according to any one of the preceding claims, wherein the control variables comprise, for the point or each of said points in the mine, in addition to the initial content of said element of interest in solid phase at the initial time, one or more of the following variables: an initial concentration of said element of interest in liquid phase at the initial time (T0), the effective porosity of the porous medium containing said element of interest; a hydraulic conductivity of the porous medium containing said element of interest; diffusion coefficients of the porous medium containing said element of interest; mineral contents composing the rock of the porous medium containing said element of interest; a spatial distribution of the rocks of the porous medium containing said element of interest.

11. A method of exploitation according to any one of the preceding claims, wherein the element of interest is uranium or a rare earth, a precious metal such as copper or gold, or any metal exploitable by in situ recovery.

12. A mining method according to any one of the preceding claims, wherein the second mining phase comprises one or more of the following operations: - adding additional injection wells (10) at predetermined positions using the control variables estimated in the estimation phase; - adding additional collector wells (12) at predetermined positions using the control variables estimated in the estimation phase; - remediation of the mine using the control variables estimated in the estimation phase; - closing collector wells (12) and injection wells (10) at predetermined positions using the control variables estimated in the estimation phase (S20); - adjusting a reagent concentration in the attack solution injected through the injection wells (10) at predetermined positions using the control variables estimated in the estimation phase (S20);- adjustment of a flow rate of attack solution injected through injection wells (10) and / or of a flow rate of loaded liquid collected in collector wells (12), at positions determined using the control variables estimated in the estimation phase (S20).;

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