CN115280094A

CN115280094A - Method and device for determining fouling of a heat exchanger

Info

Publication number: CN115280094A
Application number: CN202180020015.2A
Authority: CN
Inventors: 乔纳斯·考布; 丹尼尔·拉比施
Original assignee: Siemens AG
Current assignee: Siemens AG
Priority date: 2020-03-09
Filing date: 2021-03-05
Publication date: 2022-11-01
Also published as: US20230122608A1; EP4088077C0; EP4088077B1; EP4088077A1; WO2021180581A1

Abstract

In order to increase the accuracy of determining fouling in a heat exchanger (1) in which heat is transferred from a first medium (S) to a second medium (P), a variable (R) characterizing fouling is determined from the value of a first variable (k) and the value of a second variable (X) influenced by fouling_f) The value of (c). The flow rate (F) of the first medium (S) and/or the second medium (P) through the heat exchanger (1) is set in this case_S，F_P) Is at least partially compensated by the second variable (X). The first variable can be a heat transfer resistance or a heat transfer capacity (or a heat transfer coefficient (k value)) in this case, wherein the first variable and the second variable are derived from measured values of the temperature and the flow rate of the first medium, andthe first and second variables are derived without using the material properties of the first and second media and the structural properties of the heat exchanger.

Description

Method and device for determining fouling of a heat exchanger

Technical Field

The present invention relates to a method and an apparatus for deriving fouling of a heat exchanger according to

claims

1 and 2 and claims 14 and 15.

Background

Heat exchangers, also commonly referred to as heat transporters, are technical devices for heating or cooling a medium. For this purpose, heat is transferred from the hotter first medium to the cooler second medium. Depending on the way of construction, the functional principle of the heat exchanger is different. The most common configuration is classified as one of three functional groups, a straight flow, a counter flow or a cross flow heat exchanger.

The medium to be heated or cooled is often also referred to as "product medium", and the heating or cooling medium is often also referred to as "service medium". For example, the service medium can be heated steam or cooled water. The service medium generally flows through a line arrangement arranged in the product medium or around a line arrangement through which the product medium flows.

The first and second media are guided through the heat exchanger, wherein the two media flow through, usually separated from each other by a wall, and wherein the heat of the warmer medium is transferred to the cooler medium through the wall.

One core problem of heat exchangers is the so-called "fouling", i.e. the formation of deposits or coatings on the inner walls of the heat exchanger. The cause of such deposits can be physical, chemical or biological. In many cases they are unavoidable, for example due to given frame conditions on the product side. The deposits inhibit heat transfer between the media, thereby reducing the efficiency of the heat exchanger. If a certain degree of contamination is reached, chemical or mechanical cleaning or even replacement of the heat exchanger is necessary. This problem is particularly evident in process-technical process installations (for example, installations in the chemical, petrochemical, glass, paper, metal production or cement industries) or in large industrial heat exchangers used in power plants, whose heat transfer power is usually designed to exceed 100kW.

It is difficult to determine the degree of contamination inside the heat exchanger from the outside, and therefore the heat exchanger cannot be cleaned or replaced as desired. The temperature control circuit is able to compensate to some extent for the effect of fouling so that fouling does not show up immediately from the outlet temperature of the product medium. Due to this imperceptibility, it is often not possible to clean or replace the heat exchanger as required.

Up to now, the heat exchanger affected by the contamination has therefore to be cleaned or replaced regularly, i.e. without knowing the actual state of contamination. In this process, the maintenance intervals cannot be adjusted according to different contamination levels. Thus, for example, cleaning or replacement of the heat exchanger may be performed prematurely, even if only a small amount of deposits are present. While this will ensure efficient operation of the heat exchanger, it will be uneconomical due to the direct cost of maintenance work and the indirect cost due to the additional damage of the continuous operation of the plant in which the heat exchanger is used. If appropriate measures are performed too late, excessive deposits in the heat exchanger will result in a significant reduction in heat transfer. The result is that for the same heat flow to be transferred, a much larger flow of the service medium is required than in the case when the heat exchanger is clean. This results in an increased energy consumption for providing the service medium, i.e. the heating and pumping power, which is also a cost factor. Furthermore, in the case of the formation of large amounts of deposits, there is also a risk of deterioration of the quality of the product medium, since, for example, the temperature specifications are not fully complied with.

EP2128551A1 discloses a method for monitoring the effectiveness of a heat exchanger with respect to fouling, in which the current heat flow of the product medium is recorded

Or current heat flow of the service medium

And compared with at least one reference heat flow

The reference heat flow corresponds to a predetermined degree of contamination of the heat exchanger, for example a zero degree of contamination and a maximum allowable degree of contamination. Corresponding reference heatFlow of

Is derived from a characteristic map previously set up and stored for different operating points by means of a simulation program, depending on the current operating point of the heat exchanger, the flow rate F of the two media passing through the operating point of the heat exchanger_S，F_PAnd their temperature T at the inlet of the heat exchanger_p,Ein，T_s,EinAnd (6) obtaining the result. By using a simulation program, for example, the operating point dependency of the heat that can be transferred can be pre-calculated at several hundred interpolation points, without having to carry out corresponding time-consuming measurements in the actual plant.

From WO2019/001683A1 a method for monitoring a heat exchanger is known, in which the flow rates, the inlet temperatures and the outlet temperatures of the service and product media represent process variables, wherein at least one process variable is variable on the product side and the inlet temperature is determined on the service side and the other process variables are variable. In order to monitor the heat exchanger without temperature measurement on the service side, it is proposed that the variable process variable(s) of the product medium and the flow rate of the service medium are measured and a characteristic map for the interdependence of the variable process variable(s) of the product medium and the flow rate of the service medium is derived and stored from the measured values obtained in the reference state of the heat exchanger. In this case, the distance of the measured value tuple formed from the measured values obtained in the currently unknown state of the heat exchanger from the characteristic map is determined as a measure of the deviation of the current state of the heat exchanger from a reference state.

"Einstatz des Kessel-Diagnose-Systems KEDI im Kraft Staudinger 5", VGB Power plant technology, essen, germany, vol.75, no. 9, 9/1 in 1995, p.755-762, ISSN:0372-5715, DE19502096A1, U.S. Pat. No. 4,390,058A or EP0470676A2, it is known to monitor heat exchangers taking into account the heat transfer coefficient or k value. Heat flow transferred in heat exchanger

Is dependent onk value, exchange area A and so-called logarithmic temperature difference Δ T for driving heat transfer_M. The k-value and the logarithmic temperature difference depend on the operating point of the heat exchanger and therefore on the flow rate F of the product and service medium_P，F_PAnd its temperature T at the time of entry into the heat exchanger_p,Ein，T_s,Ein。

In the case of DE19502096A1, the current K value for each heating surface is derived from the calculated thermal power, logarithmic temperature difference and heating surface size. The cleaning state CF is calculated from the relation CF = K/Kref by comparing the current K value with the stored reference K value Kref of "cleanest possible state". The reference value Kref is stored in the memory depending on the load and alternatively depending on the fuel. The reference value Kref can be corrected with a correction factor depending on some current state variable. Thus, for example, a correction is made in accordance with the steam speed. However, it is not clear at present how the reference values are obtained.

In that

In this case, the so-called "heating surface value FV" is defined as a measure of the contamination of the heating surface. This is defined as the ratio of the actual evaluation factor fist to the base evaluation factor fbais. The actual evaluation factor fist is the ratio of the "measured" heat transfer coefficient Kist to the theoretical heat transfer coefficient ktheirie. The "measured" heat transfer coefficient Kist is determined from the medium temperature and the dimensions of the heated surface. The theoretical heat transfer coefficient, ktheirie, is derived from geometric data such as the size, width and length divisions of the tube. The basic assessment factor fbais is derived and stored from the optimum operating conditions for which it is believed that there is substantial contamination, for example, acceptance testing of the steam generator. The calculation of the reference state involves the use of basic data stored in the system and some current process data (such as feedwater, live steam and

-parameters) recalculation of the steam generator. However, the precise details of the process data used are not disclosed.

DE102016225528A1 discloses a method for monitoring the state of contamination in a heat exchanger, which uses an additional temperature sensor arranged in or on the wall of the heat exchanger. The temperature sensor detects a working wall temperature of the heat exchanger. The working wall temperature is corrected and a deviation between the corrected working wall temperature and a reference wall temperature is derived. The correction of the working wall temperature takes into account variations in the measured values, for example deviations in the fluid temperature or in the volume flow of the fluid, which occur as a result of working conditions deviating from the reference conditions. The working wall temperature and the reference wall temperature are values measured at and/or preset for the same point of the heat exchanger.

Current fouling resistance R_fCan be measured from the current heat transfer resistance l/k_istAnd heat transfer resistance l/k_sollThe difference between the two is calculated, and the difference is obtained in the cleaning state of the heat exchanger:

however, it has been shown that the evaluation of the fouling resistance on this basis is inaccurate. For example, without obvious causes, the level of heat transfer resistance jumps, such as occurs when cleaning or replacing heat exchangers.

Disclosure of Invention

The object of the invention is therefore to provide a method and a device with which the fouling in a heat exchanger can be determined more precisely.

This object is achieved by a method according to claim 1 and according to claim 2 and by an apparatus according to claim 14 and according to claim 15. A computer program is the subject of claim 16. Advantageous embodiments are specified in the dependent claims.

In the method according to the invention, for ascertaining fouling, a value of a variable characterizing fouling is ascertained from a value of a first variable affected by fouling and a value of a second variable, wherein a change in the first variable caused by a change in a property of the first and/or second medium, in particular by a change in the flow rate of the first and/or second medium through the heat exchanger, is at least partially compensated by the second variable.

The variable indicative of fouling is preferably heat transfer resistance or heat transfer capacity. However, it can also be a flow resistance, for example.

The invention is based on the finding that a horizontal jump in the variable characterizing fouling can generally be explained by a change in the flow rate of the first and/or second medium. The reason is that when the flow rate is changed, the flow velocity and the flow type at the point of heat transfer from the first medium to the second medium also change. Then, depending on the type of flow occurring (e.g. laminar flow, weak turbulence, strong turbulence) and the flow velocity, the value of the first variable affected by fouling may also vary. Even in one flow type, mixing and heat transfer will vary depending on flow rate. For example, the turbulence also forms a laminar boundary layer at the edge region, the size of which and the effects resulting therefrom depend, for example, on the flow rate or flow velocity. In order to derive more precisely the values of the variables characterizing the fouling, these variations are therefore taken into account according to the invention. For this purpose, a change in the first variable caused by a change in the flow of the first and/or second medium through the heat exchanger is at least partially compensated by the second variable. In other words, a change in the flow rate of the first and/or second medium causes a corresponding change in the second variable, which is then used to compensate for the effect of the change in flow rate on the first variable. Here, the (previously unexplained) horizontal jumps of the first variable calculated from the measurement data can be well explained and compensated for.

The present invention is able to reliably quantify fouling resistance even for different heat exchanger flow variations. Here, no knowledge of the material or structural properties of the heat exchanger is required. The invention works entirely on the basis of measurement data. Instead of using only the heat transfer resistance or heat transfer capacity (or heat transfer coefficient (k value)) or flow resistance as an indicator of fouling, the present invention uses this variable while combining the influence of the flow dynamics of the two media on the end result.

Since according to the invention not the heat flow but the heat transfer resistance or heat transfer capacity (or heat transfer coefficient (k value)) or flow resistance is taken into account, the fouling resistance contained therein is advantageously independent of the operating point.

Furthermore, no heat exchanger models are required which are laborious to make by experts. All results and intermediate steps can also be displayed in a family of 2D or 3D characteristics. For the calculation, a non-intuitive family of multidimensional characteristic curves is not required.

The invention does not require any special additional measuring instruments (for example temperature sensors on the heat exchanger wall) but rather the use of instruments which are usually present in heat exchangers is sufficient.

Furthermore, one of the measurements of the flow rate and the inlet/outlet temperature of the medium can be dispensed with, so that even a complete meter is not required.

Individual process variables (e.g., inlet temperature) of the product medium or the service medium also need not be measured if they are determined according to a given framework condition and therefore can be assumed to be unchanged.

It is not necessary and therefore not ready to record other variables, such as the material properties of the two media or the structural properties of the heat exchanger. Instead, the present invention assumes that these are unknown. Any constant can be assumed for this purpose, which, when expressed in absolute values, results in incorrect values for the first variable, the second variable and the variable characterizing fouling, but finally the relative changes of these variables are decisive for the operation and success of the process. In most cases this will also be sufficient in practice.

With the present invention, in the example of an industrial heat exchanger, significantly better results can be obtained when deriving fouling than using conventional calculations. Thus, the results can help plant operators make better estimates of fouling resistance. Advantageously, the invention can be applied not only to thermal balancing, but also to the consideration of pressure differences and therefore flow resistance.

A particularly good compensation for changes in the flow rate can be achieved if the second variable is a variable which is not affected by dirt.

According to a first alternative of the invention, the first variable affected by the fouling is the heat transfer resistance or the heat transfer capacity (or the heat transfer coefficient, also commonly referred to as "k-value"). The heat transfer resistance or heat transfer capacity (or k-value) can be derived particularly easily from the temperature measurements of the first medium and the second medium at the inlet and outlet of the heat exchanger.

For example, when heat is transferred from a first medium to a second medium through a wall, the k value theoretically consists of:

or

Wherein, the first and the second end of the pipe are connected with each other,

R_f: fouling resistance (m)²K/W)

S: wall thickness (m)

λ_W: thermal conductivity of wall (W/mK)

α 1: first medium to wall heat transfer coefficient (W/m)²K)

α 2: second medium to wall coefficient of thermal conductivity (W/m)²K)

A change in the flow of the first and/or second medium through the heat exchanger causes a change in the flow velocity and flow type, resulting in a heat transfer coefficient alpha₁，₂A change in (c).

By using

To obtain

1/k＝X+R_f

Here, the fouling resistance R_fCan be calculated by the following formula

R_f＝1/k-X

In this case, the amount of the solvent to be used,

R_f: a parameter that is characteristic of the fouling,

1/k: is a first variable

X: a second parameter unaffected by fouling.

The second variable is therefore preferably a measure of the heat transfer coefficient between the first medium and the wall, the heat transfer coefficient of the wall and the heat transfer coefficient between the second medium and the wall.

According to a second alternative of the invention, the variable affected by fouling is the flow resistance of the first or second medium through the heat exchanger. The flow resistance can be derived particularly easily from the pressure measurements of the first medium and the second medium at the inlet and at the outlet of the heat exchanger.

According to a particularly advantageous first embodiment of the method (hereinafter referred to as "method 1"), the value of the second variable is changed at the point in time of the change in flow rate, in particular at the point in time of the sudden change, such that the value of the variable characterizing the fouling remains unchanged.

Each time the heat exchanger is initially commissioned or cleaned, i.e. when there is no fouling, an initial value for the first variable can be derived (or "learned") and the second variable can be set to correspond to the initial value for the first variable. The two variables then fully compensate each other. Then, when the value of the first variable increases in further operation of the heat exchanger due to fouling and flow changes, the flow changes cause corresponding changes in the second variable, which results in a corresponding compensation of the first variable.

The method is particularly suitable for operating heat exchangers having a plurality of operating phases, in which the flow rates are each constant in segments and then change abruptly. This corresponds, for example, to the relatively common case of regulating the product medium flow, wherein the setpoint value is permanently preset for this purpose. Constant flow variations can only be handled in segments. However, continuous adjustment can then be made by interpolation between changes in the segments. The advantage is that the change of the medium after cleaning does not affect the result and does not require any learning data.

According to a particularly advantageous second embodiment of the method (hereinafter referred to as "method 2"), a function can be defined which assigns the value of the flow through the heat exchanger of the first and/or second medium to the value of the second variable, respectively.

This function can be derived or "learned" during a time interval after initial commissioning of the heat exchanger or after cleaning of the heat exchanger of fouling. The function is preferably formed by a regression of the flow rate measurements and the associated values of the second variable over the time interval. The regression can be, for example, a linear regression (when the flow rate of only one of the two media changes) or a 3D regression (when the flow rates of the two media change). This approach can also take into account constant variations, be relatively insensitive to deviations in normal operation, and also require multiple cleanings (and subsequently multiple different flow rate variations) to "learn" the function. He can also achieve a comparison between the quality of multiple cleanings.

According to a particularly advantageous third embodiment of the method (hereinafter referred to as "method 3"), value ranges are defined for the flow rate, which value ranges are respectively assigned to the values of the second variable. In this case, the assignment between the value of the second variable and the flow rate is advantageously derived or "learned" within a time interval after the initial commissioning of the heat exchanger or after the cleaning of the heat exchanger. Alternatively, the transitions between the values of the second variable can be filtered at the range boundaries so they do not change strongly. It is also possible to interpolate between different learning points instead of quantising in order to create a "smoother" transition.

The time interval for defining the function or zone specific value assignment depends on the speed of the fouling process and can be, for example, between a few hours (in the case of a fast fouling process, this would result, for example, in cleaning the heat exchanger weekly) and between a few days (in the case of a slow fouling process, this would result, for example, in cleaning the heat exchanger monthly).

Combinations and extensions of the three approaches described above are also possible. For example, method 1 can be used whenever a flow change occurs, and the degree of mutation and the degree of compensation can be considered as new learning points in

methods

2 and 3. Therefore, the learning point can be in a dirty state.

According to a further advantageous embodiment of the method, a characteristic curve of the relationship between the second variable and the flow rate of one of the two media is determined, wherein, in order to determine the characteristic curve, in a first step a characteristic curve of the mathematical derivative of the first variable is determined from the flow rate of the media, and in a second step the characteristic curve obtained in the first step is integrated again with respect to the flow rate of the media.

This method takes advantage of the fact that the variables that characterize fouling follow a slow and reasonably stable trend. The relationship between the first variable and the flow is therefore constantly changing, so that it is not possible to directly estimate this relationship. There is therefore a problem of estimating the characteristic curve (static relationship) between two variables. In addition to static relationships, additive trends also affect dependent variables.

The basic idea to solve this problem is to estimate the derivative of the first variable from the flow (e.g. (d l/k)/dF)) and thereby be able to calculate the fouling. The integration of the derivative then provides the actual relationship again, wherein the absolute value is obviously lost. However, this is also not necessary in applications, as only the relative change in flow needs to be compensated for.

In a further advantageous embodiment of the method, a first characteristic curve of the relationship between the second variable and the flow rate of the first medium and a second characteristic curve of the relationship between the second variable and the flow rate of the second medium are simultaneously determined, wherein, in order to determine the characteristic curves for both media in the first step, a characteristic curve of the mathematical derivative of the first variable is determined in each case as a function of the flow rate of the respective medium, and in the second step the characteristic curve determined in the first step is integrated again with respect to the flow rate of the respective medium.

This method is particularly advantageous when the flow rates of both media are changed simultaneously. Here, two characteristic curves (static relationships) between the two variables are therefore each estimated. In addition to static relationships, additive trends also affect dependent variables. Applied to the heat exchanger, the effects of the two characteristic curves of the second variable are superimposed according to the flow rate of the respective media.

The latter two embodiments of the method have the advantage that they do not depend on the characteristic curve after the cleaning, since the fouling effect is compensated for to a large extent by the formation of derivatives.

The apparatus according to the invention for carrying out the above-described method according to the invention comprises

-means for receiving measured values of the heat exchanger or variables derived therefrom and

an evaluation device, which is provided to derive from the measured values or the derived variables the values of the variables characterizing the fouling from the values of the first variables and the values of the second variables influenced by the fouling, wherein a change in the flow of the first medium and/or the second medium through the heat exchanger causes a change in the first variables to be at least partially compensated by the second variables.

The first variable can be the resistance to heat transfer or the capacity to heat transfer (or the heat transfer coefficient (k value)), the first variable and the second variable being composed of several measured variables:

temperatures of the first medium and the second medium at the inlet and outlet of the heat exchanger, and

-the flow of the first medium and the second medium through the heat exchanger, and the material properties of the first medium and the second medium and the structural properties of the heat exchanger are not used in deriving the first and second variables.

However, the first variable can also be the flow resistance, the first variable and the second variable being composed of the following measured variables:

-the pressure of the first medium and the second medium at the inlet and outlet of the heat exchanger, and

-the flow rates of the first and second media through the heat exchanger, and the material properties of the first and second media and the structural properties of the heat exchanger are not used in deriving the first and second variables.

The "derived variable" can be, for example, a statistical variable, such as an average, minimum, maximum, etc., of the measured values.

The computer program according to the invention comprises instructions which, when the program is run on a computer, cause the computer to carry out the method according to the invention as described above.

A corresponding computer program product comprises a storage medium having stored thereon instructions which, when the program is executed on a computer, cause the computer to carry out the method according to the invention described above.

Drawings

The invention and further advantageous embodiments of the invention according to the features of the dependent claims are explained in more detail below with reference to the embodiments in the drawings; in which is shown:

figure 1 shows a block diagram of a heat exchanger and an apparatus for deriving fouling in a heat exchanger,

figure 2 shows a time curve of normalized k-values for an industrial heat exchanger according to the prior art,

figure 3 shows a time curve of the fouling resistance in principle without flow changes in the calculation of the method 1 according to the invention,

figure 4 shows a principal time curve of the fouling resistance in the case of a flow change in the calculation of the method 1 according to the invention,

figure 5 shows a time curve of the 1/k value of the industrial heat exchanger according to figure 1 in the calculation of the method 1 according to the invention,

figure 6 shows an application of an exemplary linear regression using the industrial heat exchanger of figure 2,

FIG. 7 shows the fouling resistance R of the industrial heat exchanger of FIG. 2 in the calculation of the method 2 according to the invention_fIs measured in the time curve of (a),

FIG. 8 shows the fouling resistance R of the industrial heat exchanger of FIG. 2 in a calculation according to method 3 of the present invention_fIs measured in the time curve of (a),

figure 9 shows the time curve of the correcting variable X of the industrial heat exchanger of figure 2 in the calculation of the method 4 according to the invention,

figure 10 shows a time curve of the flow rates of a service medium and a product medium of an industrial heat exchanger for deriving fouling according to another embodiment of the invention,

figure 11 shows a time curve of the temperatures of the service medium and the product medium in relation to the flow according to figure 10,

figure 12 shows a time curve of the variables characterizing the fouling according to the method 5 of the invention according to the flow and the temperature of figures 10 and 11,

figure 13 shows a time curve of the flow rates of the service medium and of the product medium of an industrial heat exchanger for deriving fouling according to a further embodiment of the invention,

figure 14 shows a time curve of the temperatures of the service medium and the product medium in relation to the flow according to figure 13,

figure 15 shows a time curve of the variables characterizing the fouling according to the method 6 of the invention according to the flow and the temperature of figures 13 and 14,

FIG. 16 shows a block diagram of a heat exchanger and a cloud-based apparatus for deriving fouling in the heat exchanger.

Detailed Description

Fig. 1 shows, by way of example and in a simplified representation, a heat exchanger 1 for transferring heat or cold from a service medium S to a product medium P. The heat exchanger 1 is shown as a counter-flow heat exchanger, but other designs of heat exchanger are possible. Product medium P flows through line 2. In the flow direction before the heat exchanger 1, the flow rate F of the product medium_P(or flow rate or volume flow) and its temperature T_P,EinMeasured by means of a flow sensor 4 and a temperature sensor 5. A further temperature sensor 6 arranged downstream of the heat exchanger 1 in the flow direction measures the temperature T of the product medium P leaving the heat exchanger 1_P,Aus。

The product medium P is heated or cooled by the service medium S, which is supplied from the heating or coolant supply to the heat exchanger 1. Flow rate F of working medium in the flow direction upstream of the heat exchanger 1_S(or flow rate or volume flow) and its temperature T_S,EinBefore entering the heat exchanger is measured by means of a flow sensor 7 and a temperature sensor 8. A further temperature sensor 9 arranged downstream of the heat exchanger 1 in the flow direction measures the temperature T of the service medium S leaving the heat exchanger 1_S,Aus。

For monitoring fouling of the heat exchanger 1, a flow measurement F of the product medium P_PAnd a temperature measurement value T_P,Ein，T_P,AusAnd a measured flow rate value Fs and a measured temperature value T of the service medium S_S,Ein，T_S,AusIs transmitted to the device 10. When a single process variable of the product medium P or the service medium S,e.g. its inlet temperature T_P,EinOr T_S,EinAre determined on the basis of given framework conditions, so they can be assumed to be invariant and do not need to be measured.

For heat flow on the product and service side

And

and

C_P,Pis the heat capacity of the medium of the product,

C_P,Sis the thermal capacity of the service medium,

ρ_Pis the density of the medium of the product,

ρ_Sis the density of the service medium.

Neglecting losses, all the heat given off by the service medium S is transferred to the product medium P, so that the two heat flows are equal

Alternatively, the heat flow can also be calculated using the following formula, which is derived from the mechanical structure of the heat exchanger:

this applies here to:

k: coefficient of heat transfer (W/m)²K)

A: heat generationArea available for exchange (m)²)

ΔT_m: mean logarithmic temperature difference

Heat flow.

Mean logarithmic temperature difference Δ T_mIs defined as

Wherein, delta T_ARepresenting the temperature difference on the inlet side (from the product medium point of view), Δ T_BRepresenting the temperature difference at the outlet side.

The heat flow transferred can thus be calculated in three ways, such as:

a) Heat flow from the medium 1

b) Heat flow through heat exchanger 1

c) Heat flow from the medium 2

Thereby following:

c_P，Pρ_PF_P(T_P，Aus-T_P，Ein)＝k·A·ΔTm＝-c_P，Sρ_SF_S(T_S，Aus-T_S，Ein)

in general, it is now assumed that the fouling resistance is independent of the operating point. Can be based on the current heat transfer resistance 1/k_istWith heat transfer resistance 1/k derived in the clean state_sollThe difference between the two values is used for obtaining and calculating the current dirt resistance.

Therefore, the k value can be calculated by the following formula

Wherein for the case of a convective heat exchanger, Δ T is utilized_A＝T_P，Ein-T_S，AusAnd Δ T_B＝T_P，Aus-T_s，Ein。

If A, C_P，P，C_P，S，ρ_PAnd ρ_SIs regarded as a constant, the relative value of k can therefore only be calculated by means of the inlet-side and outlet-side temperature measurements and the flow rates of the two media.

Fig. 2 shows an exemplary plot of the 1/k value of an industrial heat exchanger over time t. For simplicity, it is found that at time t₀K value k present when =0₀And FIG. 2 shows the sum of the initial value k₀The associated value 1/k'. Here, the vertical line shows the cleaning time. Here, a 1/k' drop due to fouling can be seen in certain areas. However, there is a horizontal jump at the point marked with an arrow, which makes it difficult to accurately estimate the dirt resistance.

As has already been proven, the fouling resistance can be derived more precisely by also taking into account flow variations in the product and/or the service medium in the evaluation.

When heat is transferred from the first medium to the second medium through the wall, the k value theoretically consists of:

or

Wherein the content of the first and second substances,

R_f: fouling resistance (m)²K/W)

S_W: wall thickness (m)

λ_W: thermal conductivity of the wall (W/mK)

α 1: coefficient of heat transfer from the first medium to the wall (W/m)²K)

α 2: coefficient of heat transfer from the second medium to the wall (W/m)²K)

The flow rate variation and thus the flow type or variations in the flow type result in a heat transfer coefficient alpha_1，2A change in (c).

By using

Obtaining

1/k＝X+R_f。

In this case, the amount of the solvent to be used,

R_f: a parameter that is characteristic of the fouling,

1/k: first parameter

X: a second parameter unaffected by fouling.

The second variable is thus preferably a measure of the heat transfer coefficient between the first medium and the wall, the thermal conductivity of the wall and the heat transfer coefficient between the second medium and the wall.

According to the invention, the change in the first variable (here the calculated k value) caused by the change in the flow rate is at least partially compensated by means of the second variable (here the value of the variable X).

According to fig. 3 to 10, three methods or ways of how to consider the flow are now shown:

method 1

In method 1, the value of X is adjusted for each sudden flow change. Here, the following assumptions are made:

wall thickness and its thermal conductivity (S)_W/λ_W= constant) does not change during operation,

the properties of the medium do not change or do not change significantly,

in normal operation, the dirt resistance does not decrease or increase significantly if there is no particular reason (e.g. cleaning).

In the learning phase after cleaning, the initial value of X is learned:

at certain time intervals after cleaning, the dirt resistance R can be assumed_f＝0。

In this range, l/α 1, l/α 2 and S are learned_W/λ_WIs (summarized in value X). By means of R_f=0 and X = l/α 1/α 2+ S_W/λ_WNow, it is possible to utilize the previously calculated k value k₀Determining X of an initial interval (or after a cleaning interval)₀。X₀＝1/k₀This applies here.

Case 1: the flow is not changed

In this case, the value of α does not change either, i.e. X remains constant. Thus, any change in the 1/k value can be attributed to fouling. Thus, the formula R can be used_fFouling resistance was calculated as 1/k-X. FIG. 3 shows exemplary 1/k, X and R_fVarying over time t. The value of X is constant and results in 1/k and R_fA constant difference between them.

Case 2: flow at time t₀Variations in

At a point in time t₀Fouling resistance R_f(t₀) Kept constant for a short time, e.g. by X_neu＝1/k-R_f(t₀) Calculating X_neu。

For 1/k, the slave t can now be used₀To t₀Average value of the interval of + x. Or, X_neuIt can also be calculated as follows: x_neu＝X_alt-(1/k_alt-1/k_neu)。

1/_kaltAnd 1/k_neuRepresenting the average 1/k value in the interval before or after the flow change. Both methods showed almost the same results.

In a further process, R is then reused_f＝1/k_neu-X_neuAnd calculating dirt resistance.

FIG. 4 exemplarily shows 1/k, X and R_fA change over time t. As shown, this approach provides a fouling resistance R_fAt a point in time t₀Rather than causing a horizontal jump, the jump in traffic of (1) continues steadily.

If the method is now used to calculate the 1/k value, X and R of the industrial heat exchanger of FIG. 2_fAnd plotted over time t, results in the curve shown in fig. 5. Only relative values are shown here. Here again, the vertical line shows the cleaning time point. For the sake of simplicity, it is found that at time t₀ Initial value 1/k present when =0₀And X₀Fig. 5 shows the values 1/k 'and X' associated with these initial values.

When calculating the 1/k' value, a horizontal jump again occurs at the position marked by the arrow, but the relative dirt resistance R is calculated_fThe change in the value of X' largely compensates for this horizontal jump.

The method is particularly suitable for heat exchanger operation with operating phases in which the flow rate is constant in sections and then changes abruptly. Constant flow variations can only be handled in segments. However, continuous adjustment can then be made by interpolation between piecewise changes. Advantageously, changes in the media after cleaning have no effect on the results and do not require learning data.

Method 2

As previously mentioned, the dirt resistance after cleaning can be roughly assumed to be ≈ 0. Here, X (F) =1/k is applied. This initial interval is now used to find the relationship between X and F (flow) for different flows in the form of a function F. Even if the flow rate changes during this interval. For this purpose, regression, in particular linear regression, and even better nonlinear regression, can be used. Using the result of this interpolation, a corresponding X value can be calculated for an arbitrary flow rate.

FIG. 6 schematically illustrates a linear regression application using the industrial heat exchanger of FIG. 2. In order to create a linear regression and thus define the function F, a plurality of average flow values F for the product side after cleaning the heat exchanger_PThe relevant X values (marked with an "-" in fig. 6) were obtained. Here, the flow rate change in the interval is considered. Therefore, the following applies: x = F (F)_p) Wherein the function F is from F_pAnd linear regression of X.

If the method is now used to calculate the relative fouling resistance R of the industrial heat exchanger of FIG. 2_fAnd plotted together with the value X, obtained by means of linear regression over time t, a curve is obtained as shown in figure 7. For the sake of simplicity, it is also assumed here that the time t is₀Initial value X where =0 exists₀Fig. 7 shows a value X' associated with the initial value.

As shown, this approach has shown satisfactory results over a wide range.

Here again, the vertical lines show the cleaning points in time.

For example, the function f can be formed by a linear regression (when only one of the two media changes, see fig. 6) or by a 3D regression of the measured values of the flow rate and the associated values of the second measurement in the time interval after the initial commissioning or cleaning. This approach can also account for constant variations, which are relatively insensitive to deviations in normal operation, but also requires multiple purges (and then multiple different flow rates) to "learn" the function f. He can also compare the quality of multiple cleanings.

Method 3

The value of X learned after initial commissioning or cleaning can be used to form a range of values for flow. Within such a range, each flow value is assigned a learned X value. Thus, the transition between the two X values does not become too abrupt, and this X value can be filtered slightly over time.

If the method is now used to calculate the relative fouling resistance R of the industrial heat exchanger from FIG. 2_fAnd X and plotted over time t, the result is the curve shown in figure 8.For the sake of simplicity, it is found that at the point in time t₀ Initial value 1/k where =0 exists₀And X₀And figure 5 shows the values 1/k 'and X' associated with these initial values. The calculation is based on the heat on the product side. Here again, the vertical lines show the cleaning points in time. As shown, this approach also has shown satisfactory results in many respects.

The value of the second variable and the distribution of the flow are advantageously derived in a time interval after the initial commissioning of the heat exchanger or after the heat exchanger has been cleaned of fouling. Optionally, the transitions between the values of the second variable can be filtered at the range boundaries so that they do not change drastically. Interpolation between different learning points can also be performed instead of quantization to produce a "smoother" transition.

One optimization possibility is the so-called "interpolation point method". This method also represents a possibility of how the relation between the flow rate and the reference value can be analyzed. For this reason, a rough introduction is required, how the characteristic curve of the α value can be regarded as depending on the flow rate. In this case, it is already possible to find the boundary conditions of the subsequent characteristic curves or functions, for example the monotonicity of the curves. The first value for the analysis is obtained or derived in the state of cleaning after cleaning.

The new value is added at run-time. These are weighted with previous values in a certain area and the feature is updated. The weighting factor can be the number of points of a region so far or the current dirt resistance.

In addition to these three methods, combining and expanding can also be used.

Combination of

methods

1 and 2

This combination can first derive the fouling resistance or X value of the heat exchanger using method 1, and then can calculate the X value in the middle phase by the ratio of the two methods (e.g., depending on the deviation between

methods

1 and 2, the variance of method 2, or the number of data points in method 2). In the long term, method 2 alone is sufficient.

Method 4

With the aid of method 1, in the case of a breakthrough in the flow, the change in the X-value and the flow before and after the change are known. On the one hand, it is now possible to calculate the sudden flow change (Δ F)₁) And the value of X (Δ X)₁) The level of (c). Thus, the effect relative to the previous X value can be calculated for each future (also constant) flow change. If there are multiple mutations available,. DELTA.F is used₁And Δ X₁Linear regression between. To this end, fig. 9 shows the assignment of the value of X to the flow F over time t.

To calculate the final X value, interpolation can be performed between different sampling points to avoid abrupt curves (see dashed lines in fig. 9). Thus, the combination of method 1 and method 4 provides particular advantages.

Method 5

According to one embodiment of the method, referred to as method 5, a characteristic curve of the relationship between the second variable and the flow rate of one of the two media is determined, wherein, in order to determine the characteristic curve, in a first step a characteristic curve of the mathematical derivative of the first variable is determined from the flow rate of the media, and in a second step the characteristic curve obtained in the first step is integrated again with respect to the flow rate of the media.

This method takes advantage of the fact that the variables that characterize fouling follow a slow and reasonably steady trend. The relationship between the first variable and the flow is therefore constantly changing and therefore cannot be directly estimated. There is therefore a problem of estimating the characteristic curve (static relationship) between the two variables. In addition to static relationships, additive trends also affect dependent variables.

The basic idea to solve this problem is to estimate the derivative of the first variable from the flow (e.g., (dl/k)/dF)) and thereby be able to calculate the fouling. The integral of the derivative then provides the actual relationship again, and the absolute value is obviously lost. However, this is also not necessary in applications, as only the relative change in flow needs to be compensated for.

The inverse of the k value is assumed to consist of the sum of the fouling resistance and X

Where X combines all other thermal resistances. The derivative over time gives

thus is suitable for

For phi₁(t)≠Φ₂(t) application

At X₀，F₀Location, adapted to unique but unknown relationships

Independent of Φ (t) and κ (t).

Therefore, the temperature of the molten metal is controlled,

adapted for all phi₁(t)≠Φ₂(t)。

Therefore, it is necessary to vary Φ for two different flows₁(t)≠Φ₂(t) calculation of

The difference of the varying weights.

To determine the characteristic curve, it is proposed to do so at F₀All F radicals nearbyAll of the secondary collection have

And is a pair of phi₁(t)≠Φ₂(t) respectively give

The sought characteristic is then generated by integration of the derivative characteristic integrals.

Advantageously, the absolute value is irrelevant here, so that the initial value does not have to be taken into account in the integration.

Due to the simpler parameterization, the modeling is only carried out qualitatively, i.e. 1/k is determined without exact material data or heat exchanger properties. Therefore, only the relative change in the k value can be calculated. However, the determined characteristic curve can be used precisely for the relative change in the flow rate.

One feature of this method is that the actual task of determining fouling is initially unobtrusive and to estimate the X-F characteristics, the effect of fouling can be compensated for. Only then can the 1/k characteristic be used to derive fouling. Advantageously, the characteristic curve can be easily implemented so that nothing prevents online evaluation.

Fig. 10 to 12 show simulations of an industrial heat exchanger in the case of a flow variation.

In this case, fig. 10 shows the flow rate F of the product medium through the heat exchanger_PAnd flow of service medium F_STime profile of the (simulated) measured values of (c).

FIG. 11 shows the temperature T of the product medium at the inlet of the heat exchanger_P,EinAnd the temperature T of the product medium at the outlet of the heat exchanger_P,AusIs measured by the (analogue) measurement. Furthermore, the temperature T of the service medium at the inlet of the heat exchanger is shown_S,EinAnd the temperature T of the service medium at the outlet of the heat exchanger_S,AusIs measured (simulated).

FIG. 12 shows 1/k and fouling resistance R_fRelative value of the correlation calculation.

The 1/k value shows a significant dependence on the flow change, regardless of which side of the heat exchanger. The trend of the overlay can still be seen in the idealized data. However, depending on the severity of the fouling, a reliable conclusion cannot be drawn from the 1/k value alone.

By using the characteristic curve and compensating for the associated flow dependence, an estimated dirt profile is obtained (shown as shifted up for better visibility). In addition to measuring noise, a linear trend can be seen. Fouling can therefore be derived very reliably. It is to be noted here that at the beginning the changes of the two flow rates are mutually independent, so that the two flow rate characteristics can also be well estimated in sequence and independently of each other.

Method 6

According to a design of the method, which is referred to as method 6, a first characteristic curve of the relationship between the second variable and the flow rate of the first medium and a second characteristic curve of the relationship between the second variable and the flow rate of the first medium are simultaneously obtained. In order to obtain the characteristic curves for the two media in the first step, a characteristic curve of the mathematical derivative of the first variable is obtained in each case as a function of the flow rate of the respective medium, and in the second step the characteristic curve obtained in the first step is integrated again with respect to the flow rate of the respective medium.

This method is particularly advantageous when the flow rates of both media are changed simultaneously. Thus, two characteristic curves (static relationships) between the respective two variables are estimated here. In addition to static relationships, additive trends also affect dependent variables. Applied to the heat exchanger, the effects of the two characteristic curves of the second variable are superimposed according to the flow rates of the respective media.

In the case of a heat exchanger, two characteristic curves X_P＝f_P(F_P) And X_S＝f_S(F_S) The influence on the 1/k value is additive, wherein

The derivative of 1/k with respect to time gives

Wherein, X = X_P+X_S。

Now look for the derivative characteristic

N of (A) to (B)_pInterpolation point (dx)_Pi，F_Pi) And derivative characteristic curve

N of (a)_SInterpolation point (dx)_Si，F_Si)。

For this purpose, for each point in time t, it applies

Or

With three unknowns (dx)_Pi，dx_SiM) yields the equation:

n_Dthe equations can then be summarized in a matrix expression where the corresponding flow must be noted at the interpolation point. Therefore, it is applicable to

c＝[κ(t₁)...κ(t_m)]

For a better understanding, one row of a is given. In thatAt a suitable point in time, should_FP≈F_P5And F_S≈F_S7Wherein n is_P=10 and n_S=20. Then the rows of A correspond to

Where columns 5 and 17 (= 10+ 7) and there are non-zero entries in the last column.

If the existing measurements now cover all the traffic ranges on both the service side and the product side, then there is at least one data point in each column of A. Assuming a has the maximum level, the system of equations can be solved from the unknowns in the vector b, for example by means of a pseudo-inverse.

Then, two derivative characteristic curves can be regenerated from the vector b and the characteristic curve X is obtained by integrating them_P＝f_P(F_P) And X_S＝f_S(F_S)。

If there are two characteristic curves, it is possible to determine the characteristic curve by first determining

And by using characteristic curves

A method of calculating fouling to estimate fouling.

As already briefly outlined, the absolute value of the characteristic curve is unknown due to integration. Due to the simpler parameterization, the modeling can only be carried out qualitatively anyway, i.e. 1/k is determined without exact material data or heat exchanger properties. Therefore, only the relative change in the value of k can be calculated. However, the determined characteristic curve can be used accurately for the relative change in flow.

Here, the actual task of deriving the fouling is initially unnoticeable, in particular the influence of the fouling is compensated for in order to estimate the two X-F characteristic curves. Only then is fouling determined by means of the 1/k characteristic curve. Advantageously, the characteristic curve can be implemented very simply, so that nothing prevents an online evaluation.

Fig. 13-15 show simulations of an industrial heat exchanger with varying flow rates.

FIG. 13 shows the flow F of the product medium through the heat exchanger_PAnd flow F of the service medium_STime profile of the (simulated) measured values of (d).

FIG. 14 shows the temperature T of the product medium at the inlet of the heat exchanger_P,EinAnd the temperature T of the product medium at the outlet of the heat exchanger_P,AusThe relevant (analog) measurement of (c). In addition, the temperature T of the service medium at the inlet of the heat exchanger is shown_S,EinAnd the temperature T of the service medium at the outlet of the heat exchanger_S,AusIs measured (simulated).

FIG. 15 shows the relative values of 1/k and fouling resistance Rf thus calculated.

The 1/k value shows a significant dependence on the flow change, no matter which side of the heat exchanger. The superimposed trend can still be seen in the idealized data. However, depending on the severity of the fouling, a reliable conclusion cannot be drawn from the 1/k value alone. Obtaining an estimated fouling curve R by using the characteristic curve and compensating for the associated flow dependence_f. In addition to the measurement noise, a linear trend can be seen. Thus, fouling can be derived very reliably even if both flows are changed simultaneously.

In principle, the same method can also be applied to take account of pressure differences. Flow resistance also increases with fouling, but also depends on flow rate.

These methods can reliably quantify fouling resistance even if the flow rates of different heat exchangers vary. Here, no knowledge of the material or structural properties of the heat exchanger is required. These methods are purely data-based. So far, only pure k values have been used as indicators of fouling. These methods use this variable, including the effect of the flow dynamics of both media on the final result.

Furthermore, no laborious preparation by experts is requiredThe heat exchanger model of (1). All results and intermediate steps can also be displayed in a family of 2D or 3D characteristics. A non-intuitive family of multidimensional characteristic curves is not required for the calculation. In addition, measurement F can also be omitted_P、F_S、T_P,Ein、T_P,Aus、T_S,Ein、T_S,AusOne, and therefore does not require a complete instrument. If the flow rate changes of the two media are compensated, the temperature measurement can of course be dispensed with here only.

Using these methods, in the case of industrial heat exchangers, the results obtained when fouling were obtained were clearly superior to conventional calculations. Thus, this result can help plant operators to better assess fouling resistance. Advantageously, these methods cannot be applied to thermal equilibrium, nor to taking into account pressure differences and therefore flow resistance.

The method according to the invention can be provided as a stand-alone application in a process plant or can be integrated into a process control system of a process plant. The method can also be provided in a local or remote computer system ("cloud"), for example as a "software as a service" by a service provider.

In fig. 1, a device 10 according to the invention for detecting fouling is schematically shown, comprising:

for receiving a measured value T of the heat exchanger 1_P,Ein、T_P,Aus、T_S,Ein、T_S,AusApparatus 20, and

an evaluation device 30, which is provided to derive and output a resistance to fouling R from these measured values by means of the method described above_fThe value of (c). Additionally or alternatively, the evaluation device can also serve as a monitoring device: he can monitor whether the derived dirt resistance exceeds a threshold value and if so, output a signal indicating, for example, that cleaning is required.

To this end, the evaluation device 30 comprises a processor unit 31, a memory 32 for storing the received measurement data and a memory 33 in which a program 34 with instructions is stored, which when executing one of the above-described methods, is executed by the processor unit 31. The processor unit stores the measured values M received from the device 20 in the memory 32.

Without detecting other variables, e.g. A, C_P,P，C_P,S，ρ_PAnd ρ_S. Instead, the method according to the invention assumes that these are unknown. Any constant can be assumed which will result in an incorrect value of k as seen from the absolute value, but eventually the relative change in this value of k is decisive for the operation and success of the method.

The apparatus 10 shown in FIG. 1 can be provided, for example, as a stand-alone application in a process plant or can be integrated into a process control system of a process plant.

Conversely, the apparatus for deriving fouling 100 shown in fig. 16 can be provided by a local or remote computer system ("cloud"), for example, to provide a service provider's derivation of fouling as "software as a service". Here, the receiving device 20 is located on site in the process installation of the heat exchanger 1, while the evaluation device 30 is located on a local or remote computer system ("cloud"). For this purpose, the receiving device 20 stores the received measured values in a memory 21 and transmits them to the evaluation device 30 via a transmission device 22, for example via the internet or an intranet.

The evaluation device 30 comprises a processor unit 31, a memory 32 for storing the received measurement data and a memory 33, in which a program 34 with instructions is stored, which, when executed, performs one of the above-described methods by means of the processor unit 31.

The processor unit 31 stores the measured values M received from the device 20 via the interface 36 in the memory 32 and, if necessary, other input variables received via a separate interface 37. The dirt resistance R derived by the program 34 is output via the interface 38_fA value and/or a signal indicating that cleaning is required.

Interfaces

36, 37 and 38 can also be provided by a single common interface, for example to an intranet or intranet.

By detecting the measurements and calculating fouling resistance in near real time, continuous data-based fouling analysis and fouling monitoring can be performed as the system or heat exchanger is operated. However, offline fouling analysis, which is time-shifted with respect to the actual operation of the facility, is also feasible.

Claims

1. A method for deriving fouling in a heat exchanger (1) in which heat is transferred from a first medium (S) to a second medium (P),

characterized in that a variable (R) characterizing the fouling is derived from the value of a first variable (k) and the value of a second variable (X) influenced by the fouling_f) Wherein the flow rate (F) due to the first medium (S) and/or the second medium (P) through the heat exchanger (1)_S，F_P) Is at least partially compensated by the second variable (X), wherein the first variable (k) is a heat transfer resistance or a heat transfer capacity (or a heat transfer coefficient, k-value), and wherein the first variable (k) and the second variable (X) are derived from measured values of a plurality of measured variables,

-the temperature (T) of the first medium (S) and of the second medium (P) at the inlet and at the outlet of the heat exchanger (1)_p,Ein，T_p,Aus，T_s,Ein，T_s,Aus) And an

-a flow rate (F) of the first medium (S) and the second medium (P) through the heat exchanger (1)_S，F_P)，

And, in deriving the first and second variables, the material properties of the first and second media (S, P) and the structural properties of the heat exchanger (1) are not used.

2. Method for deriving fouling in a heat exchanger (1) according to claim 1, in which heat is transferred from a first medium (S) to a second medium (P),

characterized in that a variable (R) characterizing said fouling is derived from the value of a first variable (k) and the value of a second variable (X) influenced by said fouling_f) Wherein the flow rate (F) due to the first medium (S) and/or the second medium (P) through the heat exchanger (1)_S，F_P) Is at least partially compensated by the second variable (X), wherein the first variable is the flow resistance, and wherein the first variable (k) and the second variable (X) are derived from measured values of a plurality of measured variables,

-the pressure of the first medium (S) and the second medium (P) at the inlet and outlet of the heat exchanger (1), and

-the flow rate (F) of the first medium (S) and the second medium (P) through the heat exchanger (1)_S，F_P)，

And not using the material properties of the first medium (S) and the second medium (P) and the structural properties of the heat exchanger (1) when deriving the first variable and the second variable.

3. Method according to claim 1 or 2, wherein the point in time (t) of flow variation₀) The value of the second variable (X) is changed, thereby characterizing the fouling variable (R)_f) The value of (c) is kept constant.

4. Method according to claim 3, wherein the initial value (k) of the first variable (k) is derived after an initial commissioning and respectively after cleaning of the heat exchanger (1)₀) And setting the value of the second variable (X) to an initial value (X)₀) The initial value corresponding to the initial value (k) of the first variable (k)₀)。

5. Method according to any one of the preceding claims, wherein a function (f) is defined which assigns a value of the second variable (X) to the value of the flow of the first medium (S) and/or the second medium (P), respectively.

6. Method according to claim 5, wherein the function (f) is derived at time intervals (T) after initial commissioning or after cleaning of the heat exchanger (1) of fouling.

7. Method according to claim 5 or 6, wherein the function (F) is formed by regression, in particular linear regression or 3D regression, of the measured values of the flow rate (F) and the associated values of the second variable (X) in a time interval (T).

8. Method according to any one of the preceding claims, wherein a range of values is defined for the flow rate (F), each associated with a value of a second variable (X).

9. Method according to claim 8, wherein an assignment of the value of the second variable (X) to the flow rate (F) within a time interval (T) after an initial commissioning or after cleaning of the heat exchanger (1) of fouling is derived.

10. Method according to any of the preceding claims, wherein a characteristic curve of the relation between the second variable (X) and the flow rate (F) of one of the two media (S, P) is derived, wherein, in order to derive the characteristic curve, in a first step a characteristic curve of the mathematical derivative of the first variable (K) is derived from the flow rate (F) of the medium (S or P), and in a second step the characteristic curve obtained in the first step is integrated again with respect to the flow rate (F) of the medium (S or P).

11. Method according to any one of the preceding claims, wherein a first characteristic curve for the relationship between the second variable (X) and the flow rate (F) of the first medium (S or P) and a second characteristic curve for the relationship between the second variable (X) and the flow rate (F) of the second medium (P or S) are simultaneously derived, wherein, for deriving a characteristic curve for each of the two media (S, P) in a first step, a characteristic curve for the mathematical derivative of the first variable (k) is derived from the flow rate (F) of the respective medium (S or P), respectively, and the characteristic curves obtained in the first step are integrated in a second step again with respect to the flow rate (F) of the respective medium (S or P).

12. Method according to any one of the preceding claims, wherein a variable (R) characteristic of the fouling_f) Is the heat transfer resistance.

13. Method according to any one of the preceding claims, wherein only the variable (R) characterizing the fouling is derived_f) A relative change of the first variable (k) and the second variable (X).

14. An apparatus (10, 100) for performing the method according to any one of claims 1 and 3 to 13, the apparatus comprising

-means (20) for receiving a measured value (M) of the heat exchanger (1) or a variable derived from said measured value, and

-an evaluation device (30) provided for deriving from the measured value (M) or the derived variable a variable (R) characterizing the fouling from the values of a first variable (k) and a second variable (X) influenced by the fouling_f) Wherein the flow rate (F) of the first medium (S) and/or the second medium (P) through the heat exchanger (1)_S，F_P) Is at least partially compensated by the second variable (X), and wherein the first variable (k) and the second variable (X) are derived from measured values of a plurality of measured variables,

-the temperature (T) of the first medium (S) and the second medium (P) at the inlet and outlet of the heat exchanger (1)_p,Ein，T_p,Aus，T_s,Ein，T_s,Aus) And an

-a flow (F) of the first medium (S) and the second medium (P) through the heat exchanger (1)_S，F_P)，

And the material properties of the first medium (S) and the second medium (P) and the structural properties of the heat exchanger (1) are not used in deriving the first variable and the second variable.

15. An apparatus (10, 100) for performing the method according to any one of claims 2 to 13, the apparatus comprising:

-an evaluation device (30) provided for deriving from the measured value (M) or the derived variable a variable (R) characterizing the fouling from a value of a first variable (k) and a value of a second variable (X) influenced by the fouling_f) Wherein the flow rate (F) of the first medium (S) and/or the second medium (P) through the heat exchanger (1)_S，F_P) Is at least partially compensated by the second variable (X), wherein the first variable is the flow resistance, and wherein the first variable (k) and the second variable (X) are derived from measured values of a plurality of measured variables,

16. A computer program comprising instructions which, when executed on a computer, cause the computer to carry out the method according to any one of claims 1 to 13.