FR2991054A1 - Method for determining concentrations of e.g. oxygen, of air in distillation column of cryogenic air separation unit, involves estimating concentration of components according to time and position along longitudinal axis of column - Google Patents

Abstract

The method involves estimating concentration of components according to time and a position along a longitudinal axis of packing distillation column e.g. high pressure column (14), and low pressure column (26) by a model operating a propagation term in relation to a convection of the components along the column and an axial diffusion term in relation to diffusion of the components in the column. An adjustment parameter is operated by a model to balance effects of diffusion with respect to propagation effects. Independent claims are also included for the following: (1) a device for determining concentrations of chemical components of a product in a packing fractionating column (2) a computer program comprising a set of instructions for implementing a method for determining concentrations of chemical components of a product (3) a recording medium for storing a program comprising a set of instructions for implementing a method for determining concentrations of chemical components of a product.

Description

The present invention relates to a method for determining the concentrations of chemical components, especially air in a packed distillation column, as well as a device for determining concentrations and a separating unit. corresponding air.

By "concentrations" is meant more precisely here and in the rest of the text, "molar fractions". The term "concentrations" is kept for the purpose of simplification. The operation of air separation units, known by the 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, known as concentration analyzers, which measure the concentrations of chemical components at a specific point in a distillation column. However, in addition to their prohibitive cost, the use of these analyzers requires the provision of additional pipes to take samples in 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 implementation requires drilling the 25 columns. The addition of pipes and drilling are not desirable because they deteriorate the insulation of the columns. As a result, the number of concentration analyzers and temperature probes that can be used in a column is limited, thus making it impossible to measure temperatures and concentrations anywhere along the column. The present application is thus concerned with the determination of the concentrations. There is indeed a need to estimate in real time the concentrations at any point of a distillation column based on a limited number of sensors installed, this taking into account, in particular, variations in the amount of product. treated by the distillation column. In the state of the art, three main families of solutions have been proposed for estimating concentrations of chemical components in a distillation column on the basis of existing sensors. The first family of solutions is to establish 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 network of neurons, etc. The parameterization of this model consists in adjusting all its coefficients on the basis of experimental data. The setup time of the model is very long, which can take several weeks for an air separation unit. In addition, the black box model does not reflect the physical phenomena occurring in the column and it does not generally account for nonlinearities in the column. However, the distillation columns exhibit a very strongly non-linear behavior all the more when they operate at high purity, for example to obtain oxygen of very high purity from a separation of air. This makes the black box model relevant only for the operating conditions of the column close to those used for its parameterization. Approaches have therefore been proposed to develop nonlinear models. Thus, the second family of solutions consists in establishing a so-called plate model in which a packed column is modeled as a plate 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 dynamic simulation in real time. 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 in establishing a model, called wave model, expressing the distribution of concentrations along the column. According to this model, the distillation columns are considered as continuous beds along which the concentration profiles move as waves propagating according to the flow of gas and liquid. This results in concentration profiles with a general S-shape along the column. This model has the advantage of being concise, two equations being sufficient to describe the entire column. The wave model is parameterized with a parameter, called form factor, which adjusts the shape of the wave, including the smoothing of its pace. Generally, the form 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 remedy this defect, there are corrective approaches linking the form factor to the operating conditions by using inferential models or online estimation that will allow to adapt the shape of the curve. The article by S. Bian & Al., "Nonlinear State Estimation and Predictive Control Model of Nitrogen Purification Columns", Ind. Eng. Chem. Res. 2005, 44, 153167 discloses a method of adjusting the shape factor of the wave pattern using a Kalman filter. This adjustment is however reflected uniformly over the entire height of the column. Thus, the wave model, even implementing a strategy for adapting the form factor, remains insufficient to describe the physical phenomena taking place all along a distillation column. The present invention aims to improve the situation.

For this purpose, the subject of the present invention is a process for determining the concentrations of chemical components of a product, in particular air, in a packed distillation column, in which process a model is used which makes it possible to estimating 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 exchanges between the liquid and gaseous phases. In fact, in a packed distillation column, the rising gas or vapor flows are in contact with the descending liquid flows. This is modeled simply by a single stream of vapor in contact with a single stream of liquid, through a single contact interface. At the interface, the liquid and the gas are concomitant and satisfy at each instant the thermodynamic equilibrium, which imposes the concentrations of the components in the liquid phase and in the gas phase. The further one is from the interface, the less the fluids are coupled thermodynamically. 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 the concentrations than those obtained with the methods of the state. of the technique.

In addition, by reducing the expression of the diffusion phenomenon along the same axis along which the concentrations vary due to the propagation term, namely the longitudinal axis of the column, the weight of the calculations to be performed is reduced. and the simulation can more easily be implemented in real time.

It may 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 the components in an infinitesimal section of the column. The diffusion term of the model results in this way, in particular, microscopic exchanges between the liquid and gaseous phases.

Most commonly, the columns being oriented vertically, the position along the longitudinal axis of the column will represent the vertical position along the column. The invention will however also find its applications in columns having a different orientation, including horizontal. By way of 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 having a vertical orientation, the least volatile compound is oxygen and the origin is the top of the column, the axis being oriented according to the increasing concentration of oxygen, c that is, from top to bottom. It should be noted that, by packed distillation column, distilling columns comprising elements in the form of metal sheets defining a network of liquid circulation channels and gas flowing through the column, said sheets being configured to said channels are strongly interlocked so as to promote contacting of the liquid phases and the gaseous phases circulating in said channels. However, 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 in the following general way: 0 / (x) 0 2 = [-LX + Vk (X)] + at az a2 - Where t represents time; z represents the position along the axis of the column; - 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; f and C are function matrices of X. Function matrices are applications of the set [0; 1] A to real-valued vectors, in the interval [0; 1], of dimension A, where A is the size of the vector X, in the set M (R) AXN of the matrices with value in the set of reals R, at A rows and N columns, N being 1 or A. Moreover, 30 is parameterized 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, since the sum of the concentrations of the components is equal to 1. For example, in a separation unit of air, 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 oxygen, 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 of liquid and gas in the column. According to a second aspect of the invention, the model uses a setting parameter that makes it possible to weight the effects of the diffusion with respect to the effects of the propagation, so that the model makes it possible to take account, at the macroscopic level, of the diffusion term along the longitudinal axis of the column. More precisely, the setting parameter, of very low value, in particular much less than 1, makes it possible to weight the diffusion term. Advantageously, the model uses two different time scales to take account of both the longitudinal circulation and the circulation in a direction normal to the interface of the components in the infinitesimal section considered, that is to say, according to a direction transverse to the longitudinal axis of the column, said circulation in a direction normal to the interface being faster than the longitudinal flow. Thanks to the use of these two scales, all the physical phenomena occurring in the column are taken into account in the model while allowing simplifications decreasing the weight of the calculations to be performed. According to various embodiments of this aspect of the invention: the model exploits a partial differential convection-diffusion equation linking a first derivative according to time, a first derivative and a second derivative according to the longitudinal position in the column a value in relation to the concentration of said components in the column, said setting parameter being associated with said second derivative; said model also exploits an approximate expression of the concentration of said components as a function of an intermediate value resulting from the resolution of said equation; said approximated expression is a development limited with respect to the adjustment parameter, said limited development comprising a term of order 0, expressing slow phenomena, and a term of order 1, which is perturbative; from said equation, a profile is obtained, according to the time and the longitudinal position in said column, of said intermediate value and a profile is determined, according to the time and the longitudinal position in said column, of the concentration of the components in the column; by plotting said intermediate value in said approximate expression. By way of example, the partial differential equation has the following form: X + Vk (X) 1 Ot z in which: t represents the time; z represents the position along the axis of the column 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 function matrices of X; and - this is the setting parameter. The functions f and G may depend on a vector of parameters a representing the reservoirs of liquid and gas. According to one embodiment, a and / or L and / or V depend on the time t and / or on the position z.

Advantageously, k is a non-linear function. Preferably, the method comprises a step of numerical resolution of the partial differential equation.

For example, this digital resolution uses a technique of finite differences in time and space to ensure a fast calculation and low computational complexity. In one embodiment, the time step used for the digital resolution is between a value of the order of one second to a value of about one minute, and the spatial pitch is fixed at about 10 centimeters. The numerical scheme used to process the equation can be written implicitly or explicitly. To have calculated concentrations that are neither negative nor superior to 1, we may prefer the use of an implicit form method, even if it requires more calculations. According to one aspect of the invention, the column comprises feed points and / or pulling the product and / or all or part of the product components. Said model divides said column into several sections, called homogeneous sections, each provided between two feeding points and / or neighboring prints depending on the height of the column. Said convection term and / or said diffusion term are adapted to each homogeneous section. In particular, the vector of parameters a may be adapted. Adapting the sets of parameters used to each homogeneous section improves the accuracy of the model. According to another aspect of the invention, the model exploits boundary conditions describing the principle of conservation of the 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 where the section is at one end of the column. In this case, the limiting condition translates a partial or total recycling of the flow leaving the column to obtain steam at the high end of the column and the liquid at the lower end of the column. The second case is where the section is connected to another section. In this case, the limit condition reflects a sampling 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 in at least one location of the column; and - setting the model using a setting parameter determined from the measured concentration.

More precisely, the following steps can be carried out, in particular 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, establishes an error between the estimated value and the measured value of the concentration, - a second value of the adjustment parameter is established as a function of the said error, the first value of the adjustment parameter is replaced by the second value in the said model. Thus, comparison of the concentrations measured at particular 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 subject of the invention is also 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 with 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. Exemplary embodiments of the invention will now be described more specifically, but not limitatively, with reference to the accompanying drawings, in which: FIG. 1 is a block diagram illustrating the structure and operation of a separation unit; of air according to one embodiment of the invention; FIG. 2 is a graph illustrating the appearance of a shock phenomenon; Figure 3 is a diagram illustrating an infinitesimal section of a column of the separation unit of Figure 1; FIG. 4 is a diagram illustrating the phenomena involved in the infinitesimal section of FIG. 3; FIG. 5 is a diagram illustrating the operation of the concentration determination method according to one embodiment of the invention; FIG. 6 is a graph illustrating examples of concentration profiles estimated by the method of the invention; and FIG. 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 an embodiment of the invention. This unit makes it possible to obtain oxygen, nitrogen and argon, practically pure, from the air, whether in liquid or gaseous form. In a known manner, this separation unit 2 comprises a first packed distillation column 14, called a high pressure column, and a second packed distillation column 26, located here in the vertical continuity of the high pressure column 14. It comprises still a third packed distillation column 34, said crude argon column, and a fourth packed distillation column 36, said 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 takes place either an introduction of air or an introduction of one or components, resulting from the distillation in one of the other columns, or a draw of one or components derived from distillation in the column in question, this in the liquid phase and / or in the gas phase. In this way, distillation of the type known as reflux distillation is provided. Without going into more detail, the high pressure column 14 is supplied with air in the liquid phase, as illustrated by the arrow associated with the mention AIR 1, and in the gas phase, as illustrated by the arrow associated with the mention AIR 2. L The air supply in the gas phase is carried out at the bottom of the column and the air supply in liquid form is carried out above the homogeneous section 16 located just above the bottom 24 of the high pressure column 14. Nitrogen LIQUID, almost pure, noted LIN in Figure 1, is recovered at the top of the high pressure column 14. Liquid oxygen, almost pure, noted LOX, is recovered at the bottom 28 of the low pressure column 26. Rich liquid argon, noted 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 pulled from the columns high and / or or low pressure 14, 26 ech heat. Said high and low pressure columns may also be configured to allow a heat exchange between the top of said high pressure column 14 and the bottom of said low pressure column 26 to respectively allow liquefaction and vaporization of the components at this point. level.

Advantageously, three oxygen concentration analyzers 41, 42, 43 are placed at specific locations in the low pressure column 26 and two analyzers 44, 45 are placed at specific 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 point of the high pressure and low pressure columns 14. This device 50 comprises in particular a processor enabling the establishment of a model describing the variation of 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 following description. In this description, the term column without further precision will designate one of the columns 14, 26 of FIG. 1. The model established by the device 50 comprises the following partial differential equation (1): f (X) Ot I- LX + Vk (X)] + G in which: - t represents time; z represents the position along the axis of the column 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 related to the concentration of the components at time t, at the z position; k is a matrix of functions expressing the thermodynamic equilibrium between the liquid and gaseous phases of the components; f and G are function matrices of X; and - it is a setting parameter. The function k can be non-linear. By way of example, it is expressed as follows: k 1+ (-1) x where a is the relative volatility of the component in question relative to the compound of rank M whose concentration is not calculated but deduced from the calculated concentration of the other compounds, as explained above. (1) The first term of equation (1) is a propagation term. Indeed, by setting c = 0, equation (1) becomes a pure convection equation. In this case, the flow rates of liquid L and of gas V impose the rate of propagation of the concentration along the column, as in the wave model of the state of the art. In the wave model, we impose the shape of the concentration profile instead of obtaining this profile by solving a partial differential equation. This avoids the appearance 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 direction of propagation can change inside the column, creating a shock wave. This phenomenon of creation of a shock wave is represented in FIG. 2. In this figure, the abscissa axis represents z, that is to say the position along the axis of the column oriented from above. down and the y-axis represents the oxygen concentration. Curve 60 represents the initial concentration profile, arrows 62, 64, 66, 68, 70, 72, 74 represent the local propagation velocity of the oxygen concentration profile. The arrow 68 is here a point, indicating that the speed is zero at the z location of the corresponding column. It is clear that the direction of propagation changes at this point in the column. The resulting concentration profile 76 has a discontinuity that does not correspond to physical reality. The second term of equation (1) is an axial diffusion term. Taking into account this diffusion prevents an appearance of the shock wave. It comes from the taking into account of a fast microscopic phenomenon, namely the transverse microscopic diffusion, this after simplification. In equation (1), it is the setting parameter c that modulates the effects of diffusion with respect to the effects of convection.

The microscopic origins of equation 1 will now be detailed with reference to FIGS. 3 and 4. For the sake of clarity, the mixture is considered as binary oxygen / nitrogen, so that equation 1 is scalar, x and y corresponding to the oxygen concentration, respectively in the liquid phase and in the gas phase.

FIG. 3 represents an infinitesimal section S of height dz of the column 14, 26 in which the phenomena of convection and diffusion are studied. In the packed distillation column 14, 26, the rising gas streams are in contact with the downward liquid streams. With reference to FIG. 4, this physical phenomenon can be modeled simply as a single gas flow 80 in contact with a single flow of liquid 82 through a single contact interface 84. The arrows 86, 88 show the vertical displacement of low at the top of the gas flow 80 and the arrows 90, 92 show the vertical displacement from top to bottom of the flow of liquid 82, the abscissa axis representing the distance at the liquid / gas interface and the X and Y ordinate axes representing the concentrations of liquid and gas respectively. At the interface 84, the liquid and the gas are concomitant and at thermodynamic equilibrium at all times, which imposes the concentrations at the interface according to the relation (2): k ((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 the arrows 90, 92 is described by the relation (3): t OZ + E- x) a (Lx) AL (3) where a represents the liquid phase hold of the component in question and AL represents a diffusion coefficient in the liquid phase. In the same way, the upward movement of gas represented by the arrows 86, 88 is described by the relation (4): cr ay VY) v Ot OZ (4). where o-v represents the vapor phase retention of the component in question and Av represents a vapor diffusion coefficient.

If we only considered this vertical displacement by neglecting the fast dynamics, we would find the speed of the wave model of the state of the art resulting in the appearance of a shock wave, as described above.

Remarkably, the model of the invention is not content to be placed in a slow time scale, in which the radial diffusion phenomenon allowing a mass exchange between the liquid and gaseous phases is neglected because it is too fast. On the contrary, the model of the invention also uses a fast scale to describe this circulation phenomenon represented by the arrows 94, 96, 98. In each phase, diffusion streams 94, 98 tend to rehomogenize the concentrations. The diffusion then ends up affecting the interface 84 which can not accumulate or create matter. Thus, a mass exchange flux 96 must pass through the interface 84 and thus makes it possible to couple the diffusion fluxes of each phase. This mass exchange between the two phases is expressed by the relation (5): 4, e (17 * -17) -F -1 -X) = 0 (5). The setting parameter c is very small, in particular much smaller than 1. The term Δv / c is comparable to the diffusion coefficient associated with the diffusion fluxes in the gaseous phase, and the term Mc is comparable to the diffusion coefficient associated with the flows. of diffusion in the liquid phase. The assumption that diffusion coefficients are very large is reasonable when column packing is effective. With this assumption, the system of equations (2) to (5) can be simplified. To achieve this simplification, a so-called invariant manifold technique is used here, including a so-called center manifold technique. This technique makes it possible to preserve an overall mass balance. It also makes it possible not to make one phase predominant with respect to 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 function G makes it possible to relate the operating conditions of the column to the effects of diffusion. The function G can be expressed in the following way: k, (x) 2 k '(X) G (X) = m Av +)) 2 L + V 2 AL n-life (X (6) in which k is the function derived from the function K. It makes it possible to highlight the local effects of L and V on the diffusion The function f can be expressed in the following way: f (X) = aL + avk '(X (7) It should be noted that the parameters a, L and V may depend on the time t and on the position z. The model also makes it possible to describe the concentrations in each phase, more precisely using an approximate expression of the concentration of said components as a function of the intermediate value resulting from the resolution of equation (1). Said approximate expression is, for example, a development limited with respect to the adjustment parameter, said limited development comprising a 0-term term , expressing the slow phenomena, and a term of order 1, which is perturbative, by which we mean that the term of order 0 expresses a function of the system in which the fast phenomena are considered instantaneous and the term of order 1, perturbative, takes into account at least partially the non instantaneousness of said fast phenomena. The concentration x in liquid phase can be expressed, for example, in the following way: o-vL LV (8) The concentration y in the gas phase can be expressed, for example, as follows: Y k (X) Therefore, to estimate the liquid phase and gas phase concentrations of a component, it will be possible to derive the equation (1) a profile, according to the time and the vertical position in the column, of said intermediate value X and then determining a profile, according to the time and the vertical position in said column, of the concentration x in the liquid phase and y in the gaseous phase of the components in the column, by transferring said intermediate value X into said approximate expression (8) and / or (9), this approach being implemented in the device 50. In addition to the equation (1 ), the model includes boundary conditions describing here the principle of conservation of the mass between two sections, in particular between two sections homogeneous, of the column and at the ends of said column. In particular, the effects of diffusion in equation (1) must be preserved at these boundary locations. FIG. 5 illustrates the operation of the device 50 for determining the oxygen concentration profile in the air separation unit 2. Known data 100 are supplied 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 concentration measurements. Discrete 102 oxygen in specific locations of columns 14, 26. This establishes an initial version of the model. Alternatively, one can also choose arbitrary starting values. From these data, the determination device 50 provided with the model 25 represented by the equation (1) iteratively estimates the oxygen concentration profile in the columns 14, 26. During the first iteration, the setting parameter it is set to a certain value. The determining device 50 estimates an oxygen concentration profile 104 using the model incorporated therewith with this setting parameter value. Then, the determination device 50 compares the estimated concentrations at the determined locations with the discrete measurements and deduces from them estimation errors (block 106 in FIG. 5) that it uses to adapt the adjustment parameter c (block 108 on the Figure 5).

Thus, initially, during the first few iterations, the concentration profile can be very imprecise. After a while, the E parameter is set correctly. The determination device 50 then provides a precise concentration profile.

Preferably, each column 14, 26 has its own setting parameter E. When estimating the concentration profile, the determining device 50 digitally resolves the partial derivative equation (1).

It uses a technique of finite differences in time and space to ensure a fast calculation of low complexity. The time step chosen for the digital resolution is set here to about one second and the spatial pitch is fixed 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 adaptation principle 108 of the adjustment parameter is as follows: if the adjustment parameter c has a correct value, then the mathematical model of the 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 setting parameter E. Here, the determining device 50 uses an additional equation (10): dt M (10) in which M is a function of the estimation errors and possibly of other parameters. Equation (10) allows the setting parameter c to be changed continuously so as to keep the estimation errors as low as possible.

The function M 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 solely dependent on a single estimation error can be used. It is also possible to use a more complex structure for the M function in order to accelerate the decline in estimation errors. FIG. 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 Y axis represents the concentration. The 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 15 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, while at the bottom of the low pressure column 26 where the liquid oxygen is recovered. Curves 114, 116 represent the liquid phase and gas phase nitrogen concentrations, respectively. It appears on these curves 114, 116 that the concentration of nitrogen is maximum, that is to say, tending to 1, at the very top of the low pressure column 26. The nitrogen concentration decreases going down from the column to become zero at the bottom of the low pressure column 26. The curves 118, 120 represent the argon concentrations in the liquid phase and in the gas phase, respectively. It appears on these curves 118, 120 that the concentrations of argon are very low, especially less than 2%, at the ends of the low pressure column 26 and are at their maximum, especially around 14%, in the middle of the lower column. pressure 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 by using the discrete measurements provided by the concentration analyzers 44 and 45. FIG. 7 is more particularly concerned with the dynamic operation of the determination device 50 through the adaptation of the adjustment parameter. E. Figure 7 comprises three parts. The upper part comprises two curves 130, 132. The middle part comprises two curves 134, 136 and the bottom part comprises a curve 138.

The curve 130 represents the oxygen concentration, estimated by the device 50 at the position of the analyzer 44, that is to say at the top of the high pressure column 14, as a function of the time expressed in hours. Curve 132 represents the oxygen concentration measured by analyzer 44 as a function of time expressed in hours.

The curve 134 represents the oxygen concentration, estimated by the device 50 at the position of the analyzer 45 as a function of the 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 setting parameter c as a function of the time expressed in hours. The determination device 50 here only uses the measurement of the analyzer 44 to obtain an estimation error and to adapt the adjustment parameter c as a function of this error. As can be seen by looking at the curves 130, 132 and 138, the setting parameter c 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 of 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 the 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 (15)

REVENDICATIONS1. A process for determining the concentrations of chemical components of a product, especially air, in a packed column (14, 26), wherein the component concentration 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 with a diffusion of said components in the column (14, 26). 2. The method of claim 1, wherein the model uses a setting parameter to weight the effects of diffusion against the effects of propagation. A method according to claim 2, wherein the model uses a partial derivative time-derivative derivative convection-diffusion equation, a first derivative and a second derivative according to the longitudinal position in the column (14, 26) of the invention. a value in relation to the concentration of said components in the column (14, 26), said setting parameter being associated with said second derivative. 4. Method according to claim 3, comprising a step of numerical resolution of the partial differential equation. 5. Method according to any one of claims 3 or 4, wherein the model further exploits an approximate expression of the concentration of said components as a function of an intermediate value resulting from the resolution of said equation. 6. The method of claim 5, wherein said approximated expression is a development limited with respect to the setting parameter, said limited development comprising a term of order 0, expressing slow phenomena, and a term of order 1, perturbative. The method according to claim 5 or 6, wherein from said equation is derived a profile, according to the time and the longitudinal position in said column (14, 26), of said intermediate value and a profile is determined according to the time and the longitudinal position in said column (14, 26) of the concentration of the components in the column (14, 26), plotting said intermediate value in said approximate expression. A method according to any one of the preceding claims, wherein the column (14, 26) comprises feed points and / or draw points of the product and / or all or part of the product components, said model dividing said column in several sections (16, 18, 20), said homogeneous sections, each provided between two feed points and / or neighboring draws depending on the height of the column, said convection term and / or said diffusion term being adapted to each homogeneous section. The method of claim 3 or 4, wherein the model operates boundary conditions describing the principle of conservation of the mass between two sections of the column (14, 26) and at the ends of said column (14, 26). The method of any one of claims 2 to 9, 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 - setting the model using the setting parameter determined from the measured concentration. 30 11. The method of claim 10 wherein: - 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, establishes an error between the estimated value and the measured value of the concentration, - a second value of the adjustment parameter is established as a function of the said error, the first value of the adjustment parameter is replaced by the second value in the said model. 12. Device for determining (50) the concentrations of chemical components of a product, in particular air, in a packed distillation column (14, 26), said device comprising means for estimating the concentration of the components 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). 13. Air separation unit (2) comprising at least one air distillation column (14, 26) and a device (50) for determining concentrations of air components in the column (14, 26) according to claim 12. 14. Computer program comprising instructions for carrying out the method according to any one of claims 1 to 11, when the program is executed by a processor. Recording medium in which the program according to claim 14 is stored.