DETERMINATION OF CONCENTRATIONS OF CHEMICAL COMPONENTS IN A DISTILLATION COLUMN

Abstract

The invention relates to a method for determining the concentrations of chemical components, in particular air, in a packed distillation column (14, 26). According to said method, a model is used to estimate the concentration of the components as a function of time and position along the longitudinal axis of the column (14, 26), said model exploiting a propagation term in relation to a convection of said components along the column (14, 26) and an axial diffusion term in relation to a diffusion of said components in the column (14, 26).

Description

The present invention relates to a method for determining the concentrations of chemical components, in particular air, in a packed distillation column, as well as a corresponding concentration determination device and air separation unit. By "concentrations" we mean more precisely here and in the rest of the text, "molar fractions". The term "concentrations" is retained for the purpose of simplification. The operation of air separation units, known by the English acronym ASU (Air Separation Units), requires knowledge of the concentrations and / or temperatures inside the packed distillation columns forming these units. There are sensors on the market, called concentration analyzers, which can measure the concentrations of chemical components at a specific location in a distillation column. However, in addition to their prohibitive cost, the use of these analyzers requires additional piping to take samples from the columns. For temperature measurements, the use of existing temperature probes is difficult at the cryogenic temperatures at which distillation is carried out. In addition, their installation requires drilling the columns. Adding pipes and drilling are undesirable because they deteriorate the column insulation. Therefore, the number of concentration analyzers and temperature probes that can be used in a column is limited, making it impossible to measure temperatures and concentrations everywhere along the column. The present application is thus concerned with the determination of concentrations. There is indeed a need to estimate in real time the concentrations at any location in a distillation column based on a limited number of sensors installed, taking into account, in particular, variations in the quantity of product treated by the distillation column. In the state of the art, three main families of solutions have been proposed to estimate concentrations of chemical components in a distillation column based on existing sensors. The first family of solutions consists of establishing a model, called a black box, in which the concentration to be estimated is considered as a function of the measurements made by the sensors. This function can be linear, polynomial, structured by a neural network, etc. The parameterization of this model consists of adjusting all its coefficients on the basis of experimental data. The time taken to establish the model is very long, and can take several weeks for an air separation unit. Furthermore, the black box model does not reflect the physical phenomena occurring in the column and generally does not account for nonlinearities in the column. However, distillation columns exhibit very strongly nonlinear behavior, especially when operating at high purity, for example to obtain very high purity oxygen from air separation. This makes the black box model relevant only for column operating conditions close to those used for its parameterization. Approaches have therefore been proposed to develop non-linear models. Thus, the second family of solutions consists of establishing a so-called tray model, in which a packed column is modeled as a tray column consisting of several theoretical stages. This model is quite satisfactory for a classical intensive simulation of the column, for example during its design, but it is insufficient for a real-time dynamic simulation. In addition, this model is complex in terms of calculation because it requires several sets of equations, each set corresponding to a theoretical stage of the column. In addition, this model requires the parameterization of a large number of parameters and its stability is not always guaranteed. The third family of solutions consists of establishing a model, called a wave model, expressing the distribution of concentrations along the column. According to In this model, distillation columns are considered as continuous beds along which concentration profiles move like waves propagating according to the gas and liquid flows. This results in concentration profiles with a general S-shaped shape along the column. This model has the advantage of being concise, with two equations being sufficient to describe the entire column. The wave model is parameterized with a parameter, called the shape factor, which adjusts the shape of the wave, in particular the flattening of its shape. Generally, the shape factor is considered constant in existing wave models. Thus, with this model, the wave slides in the column while its shape remains constant. However, this assumption is false when operating conditions change, particularly at high purity. To overcome this defect, there are corrective approaches linking the shape factor to the operating conditions using inferential models or online estimation that will allow adapting the shape of the curve. The article by S. Bian et al., “Nonlinear State Estimation and Model Predictive Control of Nitrogen Purification Columns,” Ind. Eng. Chem. Res. 2005, 44, 1 SOIS? describes a method for adjusting the waveform factor using a Kalman filter. However, this adjustment is applied uniformly over the entire column height. Thus, the wave model, even implementing a form factor adaptation strategy, remains insufficient to describe the physical phenomena occurring along a distillation column. The present invention aims to improve the situation. To this end, the subject of the present invention is a method for determining the concentrations of chemical components of a product, in particular air, in a packed distillation column, a method in which a model is implemented making it possible to estimate the concentration of the components as a function of time and position along the longitudinal axis of the column, said model exploiting a propagation term in relation to a convection of said components along the column and an axial diffusion term in relation to a diffusion of said components in the column. The diffusion term of the model of the invention results from the exchanges between the liquid and gaseous phases. Indeed, in a distillation column at packings, the rising gas or vapor flows are in contact with the descending liquid flows. This is simply modeled by a single vapor flow in contact with a single liquid flow, across a single contact interface. At the interface, the liquid and gas are concomitant and satisfy thermodynamic equilibrium at all times, which imposes the concentrations of the components in the liquid and gas phases. The further one is from the interface, the less thermodynamically coupled the fluids are. Therefore, far from the interface, the concentrations are different from the concentrations at the interface. In each phase, diffusion flows towards the interface tend to rehomogenize the concentrations.By taking into account not only the phenomenon of convection of the components along the column, but also their diffusion, the method of the invention provides more precise estimates of concentrations than those obtained with the methods of the state of the art. Furthermore, by bringing the expression of the diffusion phenomenon along the same axis as that along which the concentrations vary due to the propagation term, namely the longitudinal axis of the column, the weight of the calculations to be carried out is reduced and the simulation can more easily be implemented in real time. It can be noted that such a model comes from a microscopic analysis, in particular from an equation of some of the phenomena involving the concentration of components in an infinitesimal section of the column. The diffusion term of the model thus results, in particular, from microscopic exchanges between the liquid and gas phases. Most commonly, since the columns are oriented vertically, the position along the longitudinal axis of the column will represent the vertical position along the column. However, the invention will also find applications in columns with another orientation, particularly horizontal. For example, the model according to the invention delivers the value of the concentrations along an axis whose origin is placed at the end of the column at which the concentration of the least volatile compound is minimal and oriented in the increasing direction of the concentration of said least volatile compound. In other words, for air distillation columns with a vertical orientation, the least volatile compound is oxygen and the origin is the top of the column, the axis being oriented following the increasing oxygen concentration, that is, from top to bottom. It should be noted that, by packed distillation column, we understand distillation columns comprising elements in the form of metal sheets defining a network of channels for circulation of the liquid and gas flowing through the column, said sheets being configured so that said channels are strongly intertwined so as to promote contact between the liquid phases and the gaseous phases circulating in said channels. That being said, the invention applies more broadly to any distillation column technology comprising elements defining such a network of fluid circulation channels. Such a model exploits, for example, a partial differential equation which generally looks like this: = JL [_LX + Vk{Xl + \ôL v(X) ut uz oz^ L • Where t represents time; • z represents the position along the column axis; • L and V represent the respective flow rates of liquid and gas in the column ; • X is a vector representing an image of the concentration at time t, at position z; • k is a matrix of functions of X expressing the thermodynamic equilibrium between the liquid and gaseous phases of the components; • / and G are matrices of functions of X. By function matrices we mean applications of the set [0;1]A of real-valued vectors, in the interval [0;1], of dimension A, where A is the size of the vector X, into the set M(R)Axn of matrices with a value in the set of real numbers R, with A rows and N columns, N being 1 or A. Furthermore, G is parametrized by L and V. According to a preferred embodiment, when the mixture contains M components, the size of the vector X is equal to M-1, given that the sum of the concentrations of the components is equal to 1. For example, in an air separation unit, if the components of interest are oxygen, nitrogen and argon, the size of the vector X is equal to 2. In the case of a simplified binary mixture, for example a mixture of oxygen and nitrogen, the vector X is of size 1 and the partial differential equation is then purely scalar. According to a first aspect of the invention, the diffusion term is a function of the flow rate of liquid and gas in the column. According to a second aspect of the invention, the model uses an adjustment parameter making it possible to weight the effects of diffusion relative to the effects of propagation, so that said model allows consideration, at the macroscopic level, of the diffusion term along the longitudinal axis of the column. More precisely, the adjustment parameter, of very low value, in particular much lower than 1, makes it possible to weight the diffusion term. Advantageously, the model uses two different time scales to take into account both longitudinal circulation and circulation in a direction normal to the interface of the components in the infinitesimal section considered, that is to say, in a direction transverse to the longitudinal axis of the column, said circulation in a direction normal to the interface being faster than the longitudinal circulation. By using these two scales, all the physical phenomena occurring in the column are taken into account in the model while allowing simplifications reducing the weight of the calculations to be carried out. According to different modes of implementation of this aspect of the invention: - the model uses a partial differential equation of convection-diffusion linking a first derivative according to time, a first derivative and a second derivative according to the longitudinal position in the column of a value in relation to the concentration of said components in the column, said adjustment parameter being associated with said second derivative; - said model further uses an approximate expression of the concentration of said components as a function of an intermediate value resulting from the resolution of said equation; - said approximate expression is a limited development with respect to the adjustment parameter, said limited development comprising a term of order 0, expressing slow phenomena, and a term of order 1, perturbative; - from said equation a profile is derived, according to time and longitudinal position in said column, of said intermediate value and a profile is determined, according to time and longitudinal position in said column, of the concentration of the components in the column, by reporting said intermediate value in said approximate expression. For example, the partial differential equation has the following form: in which: • t represents time; • z represents the position along the column axis oriented from top to bottom; • L and V represent the respective flow rates of liquid and gas in the column; • X is a vector representing said intermediate value at time t, at position z; • k is a matrix of functions of X expressing the thermodynamic equilibrium between the liquid and gaseous phases of the components; • f and G are matrices of functions of X; and • s is the adjustment parameter. The functions f and G may depend on a vector of parameters o representing the liquid and gas retentions. According to one embodiment, o and / or L and / or V depend on the time t and / or the position z. Advantageously, k is a non-linear function. Preferably, the method comprises a step of numerically solving the partial differential equation. As an example, this numerical resolution uses a finite difference technique in time and space to ensure fast computation and low computational complexity. According to one embodiment, the time step used for the numerical resolution is between a value of the order of a second and a value of the order of a minute, approximately, and the spatial step is set at approximately 10 centimeters. The numerical scheme used to process the equation can be written in implicit or explicit form. To obtain calculated concentrations that are neither negative nor greater than 1, it may be preferable to use an implicit form method, even if it requires more calculations. According to one aspect of the invention, the column comprises feed and / or draw points for the product and / or all or part of the components of the product. Said model divides said column into several sections, called homogeneous sections, each provided between two neighboring feed and / or draw points according to the height of the column. Said convection term and / or said diffusion term are adapted to each homogeneous section. In particular, the parameter vector o may be adapted. Adapting the sets of parameters used to each homogeneous section makes it possible to improve the accuracy of the model. According to another aspect of the invention, the model exploits boundary conditions describing the principle of conservation of mass between two sections of the column, in particular between two homogeneous sections, and at the ends of said column. The boundary conditions thus complete the model at the ends of a homogeneous section of the packed column. Two cases arise. The first case is that in which the section is located at one end of the column. In this case, the boundary condition reflects a partial or total recycling of the flow leaving the column to obtain vapor at the upper end of the column and liquid at the lower end of the column. The second case is that in which the section is connected to another section. In this case, the boundary condition reflects a withdrawal or injection of liquid and / or gas between the two adjacent sections. According to another aspect of the invention, the method further comprises the steps of: measuring the concentration of at least one of said components at at least one location in the column; and model adjustment using a tuning parameter determined from the measured concentration. More specifically, the following steps can be carried out, particularly iteratively: the concentration of said component is estimated at said location of the column where the measurement takes place using said model with a first value of said adjustment parameter, an error is established between the estimated value and the measured value of the concentration, a second value of the adjustment parameter is established based on said error, the first value of the adjustment parameter is replaced by the second value in said model. Thus, the comparison of the concentrations measured at specific locations in the column, for example with a concentration analyzer, and concentrations determined at the same locations using the model of the invention provides estimation errors which are then used to adjust the model. The measured concentration may in particular be a concentration at the top and / or bottom of the column, a place of high purity of one of the components of the mixture. The invention also relates to a device for determining the concentrations of chemical components of a product, in particular air, in a packed distillation column, comprising means for implementing a model making it possible to estimate the concentration of the components as a function of time and position along the longitudinal axis of the column, said model exploiting a propagation term in relation to a convection of said components along the column and an axial diffusion term in relation to a diffusion of said components in the column. The invention also relates to an air separation unit comprising at least one air distillation column and a device for determining the concentrations of air components in the column according to the invention. The invention also relates to a computer program comprising instructions for implementing the method according to the invention, when the program is executed by a processor. The invention also relates to a recording medium in which the computer program according to the invention is stored. We will now describe examples of embodiments of the invention in a more precise, but non-limiting manner, with reference to the appended drawings in which: Figure 1 is a block diagram illustrating the structure and operation of an air separation unit according to one embodiment of the invention; Figure 2 is a graph illustrating the occurrence of a shock phenomenon; Figure 3 is a diagram illustrating an infinitesimal section of a column of the separation unit of Figure 1; Figure 4 is a diagram illustrating the phenomena at play in the infinitesimal section of Figure 3; Figure 5 is a diagram illustrating the operation of the method for determining concentrations according to one embodiment of the invention; Figure 6 is a graph illustrating examples of concentration profiles estimated by the method of the invention; and Figure 7 is a graph illustrating the dynamic adjustment of the model established according to the method of the invention. Figure 1 illustrates a cryogenic air separation unit according to one embodiment of the invention. This unit makes it possible to obtain practically pure oxygen, nitrogen and argon from air, whether in liquid or gaseous form. In a known manner, this separation unit 2 comprises a first distillation column 14 with packings, called the high pressure column, and a second distillation column 26 with packings, located here in the vertical continuity of the high pressure column 14. It also comprises a third distillation column 34 with packings, called the crude argon column, and a fourth distillation column 36 with packings, called the pure argon column. The high-pressure column 14 comprises several homogeneous sections 16, 18, 20, here three. The low-pressure column 26 also comprises several homogeneous sections, here five. The crude argon column here comprises a single homogeneous section. The pure argon column comprises several homogeneous sections, here two. At each end of a homogeneous section of one of the columns, there is either an introduction of air or an introduction of one or more components, resulting from the distillation in one of the other columns, or a draw of one or more components resulting from the distillation in the column in question, this in liquid phase and / or in gaseous phase. This ensures a distillation of the type known as reflux distillation. Without going into further detail, the high-pressure column 14 is supplied with air in the liquid phase, as illustrated by the arrow associated with the word AIR 1, and in the gas phase, as illustrated by the arrow associated with the word AIR 2. The supply of air in the gas phase is carried out at the bottom of the column and the supply of air in liquid form is carried out above the homogeneous section 16 located just above the bottom 24 of the high-pressure column 14. Liquid nitrogen, almost pure, denoted LIN in FIG. 1, is recovered at the top of the high-pressure column 14. Liquid oxygen, almost pure, denoted LOX, is recovered at the bottom 28 of the low-pressure column 26. Liquid rich in argon, denoted LAR, is recovered at the bottom of the pure argon column 36. The separation unit 2 may further comprise a heat exchanger 30 at which some of the flows introduced and / or drawn from the high and / or low pressure columns 14, 26 exchange heat. Said high and low pressure columns may furthermore be configured to allow heat exchange between the top of said high pressure column 14 and the bottom of said low pressure column 26 in order to respectively allow liquefaction and vaporization of the components located at this level. Advantageously, three oxygen concentration analyzers 41, 42, 43 are placed at determined locations in the low pressure column 26 and two analyzers 44, 45 are placed at determined locations in the high pressure column 14. Furthermore, the separation unit 2 comprises a device 50 for determining the concentrations of the chemical components of the air at any location in the high pressure 14 and low pressure 26 columns. This device 50 notably comprises a processor enabling the establishment of a model describing the variation in the concentrations of the components as a function of time and position along each of these columns 14, 26. The operation of this device 50 according to the invention is detailed in the remainder of the description. In this description, the term column without further specification will designate one of the columns 14, 26 of figure 1. The model established by device 50 includes the following partial differential equation (1): in which: • t represents time; • z represents the position along the column axis oriented from top to bottom; • L and V represent the respective flow rates of liquid and gas in the column; • X is a vector representing an intermediate value linked to the concentration of the components at time t, at position z; • k is a matrix of functions expressing the thermodynamic equilibrium between the liquid and gaseous phases of the components; • f and G are matrices of functions of X; and • s is a tuning parameter. The function k can be non-linear. For example, it is expressed as follows: ax l+(al)x in which a is the relative volatility of the component in question compared to the compound of rank M whose concentration is not calculated but deduced from the calculated concentration of the other compounds, as explained above. The first term of equation (1) is a propagation term. Indeed, by setting s = 0, equation (1) becomes a pure convection equation. In this case, the liquid L and gas V flow rates impose the propagation speed of the concentration along the column, as in the state-of-the-art wave model. In the wave model, the shape of the concentration profile is imposed instead of obtaining this profile by solving a partial differential equation. This avoids the occurrence of a shock phenomenon. According to the invention, since the function k is not linear, the propagation speed depends on the local concentration in the column. As a result, the propagation direction can change inside the column, thus creating a shock wave. This phenomenon of creating a shock wave is shown in Figure 2. In this figure, the abscissa axis represents z, that is, the position along the axis of the column oriented from top to bottom, and the ordinate axis represents the oxygen concentration. Curve 60 represents the initial concentration profile, arrows 62, 64, 66, 68, 70, 72, 74 represent the local propagation speed of the oxygen concentration profile. Arrow 68 is here a point, indicating that the speed is zero at the corresponding location z of the column. It thus appears clearly that the direction of propagation changes at this location of the column. The resulting concentration profile 76 presents a discontinuity that does not correspond to physical reality. The second term in equation (1) is an axial diffusion term. Taking this diffusion into account prevents the appearance of the shock wave. It comes from taking into account a rapid microscopic phenomenon, namely transverse microscopic diffusion, after simplification. In equation (1), it is the adjustment parameter s which allows the effects of diffusion to be modulated in relation to the effects of convection. The microscopic origins of equation 1 will now be detailed with reference to figures 3 and 4. For clarity of description, the mixture is considered to be binary oxygen / nitrogen, so that equation 1 is scalar, x and y corresponding to the concentration of oxygen, respectively in the liquid phase and in the gas phase. Figure 3 represents an infinitesimal section S of height dz of column 14, 26 in which the phenomena of convection and diffusion are studied. In the packed distillation column 14, 26, the rising gas flows are in contact with the descending liquid flows. With reference to Figure 4, this physical phenomenon can be modeled simply as a single gas stream 80 in contact with a single liquid stream 82 through a single contact interface 84. Arrows 86, 88 show the vertical displacement from bottom to top of the gas flow 80 and arrows 90, 92 show the vertical displacement from top to bottom of the liquid flow 82, the abscissa axis representing the distance to the liquid / gas interface and the ordinate axes X and Y representing the liquid and gas concentrations respectively. At the interface 84, the liquid and the gas are concomitant and in thermodynamic equilibrium at all times, which imposes the concentrations at the interface according to the relation (2): (2) in which the asterisk indicates that it is a variable evaluated at interface 84. Far from the interface, the fluids are no longer thermodynamically coupled so that the concentrations are different from the concentrations at the interface. The downward movement of liquid represented by arrows 90, 92 is described by relation (3): dx d( Lx] Xt dt dz e (3) in which oL represents the liquid phase retention of the component in question and XL represents a liquid phase diffusion coefficient. Similarly, the upward displacement of gas represented by arrows 86, 88 is described by relation (4): It — — - |-- Ut UZ 6 (4). in which ov represents the vapor phase retention of the component in question and Xv represents a vapor phase diffusion coefficient. If we only consider this vertical displacement, neglecting the rapid dynamics, we would find the speed of the state-of-the-art wave model leading to the appearance of a shock wave, as described previously. Remarkably, the model of the invention does not simply place itself in a slow time scale, in which the phenomenon of radial diffusion allowing an exchange of mass between the liquid and gaseous phases is neglected because it is too rapid. On the contrary, the model of the invention also uses a rapid scale to describe this circulation phenomenon represented by the arrows 94, 96, 98. In each phase, diffusion flows 94, 98 tend to rehomogenize the concentrations. The diffusion then ends up affecting the interface 84 which cannot accumulate or create matter. Thus, a mass exchange flow 96 must cross the interface 84 and thus allows the diffusion flows of each phase to be coupled. This mass exchange between the 2 phases is expressed by the relation (5): (5). The adjustment parameter s is very small, notably much lower than 1. The term Xv / £ is comparable to the diffusion coefficient associated with diffusion flows in the gas phase, and the term KJs is comparable to the diffusion coefficient associated with diffusion flows in the liquid phase. The assumption that the diffusion coefficients are very large is reasonable when the column packing is efficient. With this assumption, the system of equations (2) to (5) can be simplified. To achieve this simplification, a technique called invariant manifold is used here, in particular a technique called center manifold. This technique makes it possible to preserve an overall mass balance. It also makes it possible not to make one phase preponderant over the other in the structure of the model, in particular from the point of view of liquid / vapor retentions and from the point of view of thermodynamic equilibrium. The reduction then leads to equation (1), in which the function G makes it possible to link the operating conditions of the column to the effects of diffusion. The function G can be expressed as follows: k'm 2 + kVQ G(X) =------^XavL + aL V)2 (6) in which k' is the function derived from the function k. It allows us to highlight the local effects of L and V on diffusion. The function f can be expressed as follows: (?) It should be noted that the parameters o, L and V may depend on the time t and the position z. The model also allows to describe the concentrations in each phase. More precisely, for this purpose, an approximate expression of the concentration of said components is used as a function of the intermediate value resulting from the resolution of equation (1). Said approximate expression is, for example, a limited development with respect to the adjustment parameter, said limited development comprising a term of order 0, expressing the slow phenomena, and a term of order 1, perturbative. This means that the term of order 0 expresses an operation of the system in which the fast phenomena are considered as instantaneous and the term of order 1, perturbative, takes into account at least partially the non-instantaneity of said fast phenomena. The concentration x in the liquid phase can be expressed, for example, as follows: , , w G(X} ÛX x(z, t)=X — eay------- Cy L + CT£ v OZ (g) The concentration y in the gas phase can be expressed, for example, as follows: (9) Thus, to estimate the concentrations in the liquid phase and in the gas phase of a component, it will be possible to derive from equation (1) a profile, according to time and vertical position in the column, of said intermediate value X and then determine a profile, according to time and vertical position in said column, of the concentration x in the liquid phase and y in the gas phase of the components in the column, by reporting said intermediate value X in said approximate expression (8) and / or (9). This is the approach implemented in Device 50. In addition to equation (1), the model includes boundary conditions describing here the principle of conservation of mass between two sections, in particular between two homogeneous sections, of the column and at the ends of said column. More particularly, the effects of diffusion in equation (1) must be preserved at these boundary locations. Figure 5 illustrates the operation of the device 50 for determining the oxygen concentration profile in the air separation unit 2. Known data 100 are provided to the determination device 50. These include temperatures and / or pressures and / or flow rates of liquid and / or gas at specific locations in the separation unit 2. In addition, the concentration analyzers 41, 42, 43, 44, 45 provide the determination device 50 with discrete concentration measurements 102 of oxygen in determined locations of the columns 14, 26. An initial version of the model is thus established. Alternatively, arbitrary starting values ​​can also be chosen. From these data, the determination device 50 equipped with the model represented by equation (1) iteratively estimates the oxygen concentration profile in the columns 14, 26. In the first iteration, the adjustment parameter s is set to a certain value. The determination device 50 estimates an oxygen concentration profile 104 using the model incorporated therein with this value of the adjustment parameter. Then, the determination device 50 compares the estimated concentrations at the determined locations with the discrete measurements and deduces estimation errors (block 106 in FIG. 5) which it uses to adapt the adjustment parameter s (block 108 in FIG. 5). Thus, initially, during the very first iterations, the concentration profile may be very imprecise. After a certain time, the parameter s is correctly adjusted. The determination device 50 then provides an accurate concentration profile. Preferably, each column 14, 26 has its own adjustment parameter s. When estimating the concentration profile, the determination device 50 numerically solves the partial differential equation (1). To do this, it uses a finite difference technique in time and space to ensure a fast, low-complexity calculation. The time step chosen for the numerical resolution is set here at about one second and the spatial step is set at about 10 centimeters. The numerical scheme used to process the equation is written so that the calculated concentrations are neither negative nor greater than 1, for example using an implicit scheme. According to a preferred embodiment, the principle of adaptation 108 of the adjustment parameter is as follows: if the tuning parameter has a correct value, then the mathematical model of equation (1) is realistic. In this case, the estimation errors are zero; If the estimation errors are not zero, then the mathematical model is not correct. Therefore, it is necessary to change the value of the tuning parameter s. Here, the determination device 50 uses an additional equation (10): — = M (10) dt in which M is a function of estimation errors and possibly other parameters. Equation (10) allows the tuning parameter s to be changed continuously in order to keep the estimation errors as small as possible. The M function can, for example, directly use one or more estimation errors and can take into account other parameters such as liquid and / or gas flow rates, pressures, etc. A simple linear function M depending only on a single estimation error can be used. It is also possible to use a more complex structure for the function M to accelerate the reduction of estimation errors. Figure 6 shows the concentration profiles in the low pressure column 26 estimated by the determination device 50. In this figure, the abscissa axis represents the height in the low pressure column 26 oriented from top to bottom and the ordinate axis represents the concentration. Curves 110, 112 represent the oxygen concentrations in the liquid phase and in the gas phase respectively. As expected and as it appears on these curves 110, 112, at the top of the low pressure column 26, there is almost no oxygen. The concentration of oxygen in the liquid phase and in the gas phase increases towards the bottom of the column to be maximum, that is to say tending towards 1, at the very bottom of the low pressure column 26 where the liquid oxygen is recovered. Curves 114, 116 represent the nitrogen concentrations in the liquid phase and in the gas phase respectively. It appears from these curves 114, 116 that the nitrogen concentration is maximum, that is to say tending towards 1, at the very top of the low pressure column 26. The nitrogen concentration decreases towards the bottom of the column until it becomes zero at the very bottom of the low pressure column 26. Curves 118, 120 represent the argon concentrations in the liquid phase and in the gas phase respectively. It appears from these curves 118, 120 that the argon concentrations are very low, notably less than 2%, at the ends of the low pressure column 26 and are at their maximum, notably around 14%, in the middle of the low pressure column 26. The graphs in Figure 7 relate to the estimation of the oxygen concentration profile in the high pressure column 14. This estimation is carried out by the determination device 50 using the discrete measurements provided by the concentration analyzers 44 and 45. Figure 7 focuses more particularly on the dynamic operation of the determination device 50 through the adaptation of the adjustment parameter s. Figure 7 comprises three parts. The upper part comprises two curves 130, 132. The middle part comprises two curves 134, 136 and the lower part comprises a curve 138. Curve 130 represents the oxygen concentration, estimated by the device 50 at the position of the analyzer 44, i.e. at the top of the high pressure column 14, as a function of time expressed in hours. Curve 132 represents the oxygen concentration measured by analyzer 44 as a function of time expressed in hours. Curve 134 represents the oxygen concentration, estimated by the device 50 at the position of the analyzer 45 as a function of time expressed in hours. Curve 136 represents the oxygen concentration measured by analyzer 45 as a function of time expressed in hours. Curve 138 represents the evolution of the adjustment parameter s as a function of time expressed in hours. The determination device 50 here uses only the measurement from the analyzer 44 to obtain an estimation error and adapt the adjustment parameter s as a function of this error. As can be seen by looking at curves 130, 132 and 138, the adjustment parameter s varies continuously so that the estimated concentration (curve 130) is kept close to the measured concentration (curve 132). The consequence of this adaptation using only the measurement from the analyzer 44 at the top of the high pressure column 14 is that the estimate made by the determination device 50 remains very precise everywhere else in the column 14. This is visible by looking at curves 134, 136 showing that the concentration estimated by the determination device 50 is close to the concentration measured by the analyzer 45 although the estimation error at this point is not used for the adjustment of the device 50.

Claims

Claims 1. Method for determining the concentrations of chemical components of a product, in particular air, in a packed distillation column (14, 26), in which method the concentration of the components is estimated as a function of time and position along the longitudinal axis of the column (14, 26) by means of a model exploiting a propagation term in relation to a convection of said components along the column (14, 26) and an axial diffusion term in relation to a diffusion of said components in the column (14, 26), the model exploits an adjustment parameter making it possible to weight the effects of diffusion in relation to the effects of propagation and further comprising the steps of: - measuring the concentration of at least one of said components in at least one location of the column (14, 26); and - adjustment of the model using the adjustment parameter determined from the measured concentration.

2. Method according to claim 1, in which the model uses a partial differential equation of convection-diffusion linking a first derivative according to time, a first derivative and a second derivative according to the longitudinal position in the column (14, 26) of a value in relation to the concentration of said components in the column (14, 26), said adjustment parameter being associated with said second derivative.

3. Method according to claim 2, comprising a step of numerically solving the partial differential equation.

4. Method according to any one of claims 2 or 3, in which the model further uses an approximate expression of the concentration of said components as a function of an intermediate value resulting from the resolution of said equation.

5. Method according to claim 4, in which said approximate expression is a limited development with respect to the adjustment parameter, said limited development comprising a term of order 0, expressing slow phenomena, and a term of order 1, perturbative.

6. Method according to claim 4 or 5, in which a profile is obtained from said equation, according to time and longitudinal position in said column (14, 26), of said intermediate value and a profile is determined, according to time and longitudinal position in said column (14, 26), of the concentration of the components in the column (14, 26), by reporting said intermediate value in said approximate expression.

7. Method according to any one of the preceding claims, in which the column (14, 26) comprises feed and / or drawing of the product and / or of all or part of the components of the product, said model dividing said column into several sections (16, 18, 20), called homogeneous sections, each provided between two neighboring feed and / or drawing points according to the height of the column, said convection term and / or said diffusion term being adapted to each homogeneous section.

8. Method according to claim 2 or 3, in which the model exploits boundary conditions describing the principle of conservation of mass between two sections of the column (14, 26) and at the ends of said column (14, 26).

9. Method according to claim 1 in which: - the concentration of said component is estimated at said location of the column (14, 26) where the measurement takes place using said model with a first value of said adjustment parameter, an error is established between the estimated value and the measured value of the concentration, - a second value of the adjustment parameter is established based on said error, - the first value of the adjustment parameter is replaced by the second value in said model.

10. Device (50) for determining the concentrations of chemical components of a product, in particular air, in a packed distillation column (14, 26) which is an air distillation column, said device comprising means for estimating the concentration of the components as a function of time and position along of the longitudinal axis of the column (14, 26) by means of a model exploiting a propagation term in relation to a convection of said components along the column (14, 26) and an axial diffusion term in relation to a diffusion of said components in the column (14, 26) and a device (50) for determining the concentrations of air components in the column (14, 26).

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