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

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 deriving fouling of a heat exchanger

technical field

The invention relates to a method and a device for decontamination of heat exchangers according to claims 1 and 2 and claims 14 and 15 .

Background technique

A heat exchanger, often also called a heat transmitter, is a technical device for heating or cooling a medium. For this, heat is transferred from a first, warmer medium to a second, cooler medium. Depending on how they are constructed, the functional principle of the heat exchanger differs. The most common configurations fall into one of the three functional groups of once-through, counter-flow or cross-flow heat exchangers.

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 heating steam or cooling water. The service medium usually flows through a line arrangement arranged in the product medium or around a line arrangement through which the product medium flows.

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

A central problem with heat exchangers is so-called "fouling", 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 cannot be avoided, eg due to given framework conditions on the product side. Deposits inhibit heat transfer between media, thereby reducing the efficiency of the heat exchanger. If a certain level of contamination is reached, chemical or mechanical cleaning or even replacement of the heat exchanger is necessary. This problem is especially noticeable in process facilities in process technology (for example, those 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, so it is not possible to clean or replace the heat exchanger as needed. The temperature control circuit is able to compensate the effect of fouling to a certain extent, so the fouling is not immediately apparent from the outlet temperature of the product medium. Because of this unknowability, it is often not possible to clean or replace heat exchangers as required.

So far, heat exchangers affected by contamination have therefore been regularly cleaned or replaced, ie the actual state of contamination has not been known. In this process, it is not possible to adjust maintenance intervals to different degrees of contamination. Thus, cleaning or replacement of, for example, heat exchangers may be carried out prematurely, even if only a small amount of deposits are present at this time. While this would ensure efficient operation of the heat exchanger, it would be uneconomical due to the direct costs of maintenance work and the indirect costs due to additional damage from ongoing operation of the plant using the heat exchanger. Excessive deposits in the heat exchanger will lead to a significant reduction in heat transfer if appropriate measures are carried out too late. The consequence is that, for the same heat flow to be transferred, a much greater flow of service medium is required than would be the case if the heat exchanger were clean. This leads to increased energy consumption for providing the service medium, ie heating and pumping power, which is also a cost factor. Furthermore, in the event of formation of large deposits, there is also a risk of deterioration of the quality of the product medium, since eg temperature specifications are not sufficiently observed.

或服务介质的当前热流

并与至少一个参考热流进行比较

参考热流对应于热交换器的预定污染程度，例如零污染程度和最大允许污染程度。相应的参考热流

是根据热交换器的当前工作点由之前利用模拟程序为不同的工作点设立和存储的特征曲线族得出的，其中，热交换器的工作点通过两个介质的流量F_S，F_P和他们在热交换器的入口的温度T_p,Ein，T_s,Ein得出的。通过使用模拟程序，例如能够在几百个插值点处预先计算能够传递的热量的工作点相关性，而不必在实际工厂中执行相应的耗费时间的测量。From EP2128551A1 a method is known for monitoring the effectiveness of a heat exchanger with respect to fouling, wherein the current heat flow of the product medium is recorded

or the current heat flow of the service medium

and compared to at least one reference heat flow

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

According to the current working point of the heat exchanger, it is obtained from the characteristic curve family set up and stored for different working points by using the simulation program before, where the working point of the heat exchanger passes through the flow rates of the two media F _S , F _P and They are derived from the temperatures T _p,Ein and T _s,Ein at the inlet of the heat exchanger. By using a simulation program, it is possible, for example, to precalculate the operating point dependence of the heat transferable at several hundred interpolation points without having to carry out corresponding time-consuming measurements in the actual plant.

A method for monitoring a heat exchanger is known from WO 2019/001683 A1, wherein the flow rates of the service and product medium, the inlet temperature and the outlet temperature represent process variables, wherein at least one process variable is variable on the product side and on the The service side inlet temperature is determined and other process variables are variable. Proposed for monitoring the heat exchanger without temperature measurement on the service side, the variable process variable(s) of the product medium and the flow of the service medium are measured and obtained from the reference state of the heat exchanger The measured values determine and store characteristic curves for the interdependence of the variable process variable(s) of the product medium and the flow of the service medium. In this case, for the measured values obtained in the currently unknown state of the heat exchanger, the distance of the resulting measured value tuple from the characteristic curve is obtained as a measure of the deviation of the current state of the heat exchanger from the reference state.

取决于该k值、交换面积A以及驱动热传递的所谓对数温差ΔT_M。k值和对数温差都取决于热交换器的工作点，因此取决于产品和服务介质的流量F_P，F_P及其进入热交换器时的温度T_p,Ein，T_s,Ein。"Einsatz des Kessel-Diagnose-Systems KEDI im Kraftwerk Staudinger 5" by Zolzer K et al., VGB Power Plant Technology, Essen, Germany, Vol. 75, No. 9, September 1, 1995, pp. 755-762 Page, ISSN: 0372-5715, DE19502096A1, US4,390,058A or EP0470676A2, are known to take into account the heat transfer coefficient or k-value to monitor heat exchangers. Heat flow transferred in the heat exchanger

Dependent on this k value, the exchange area A and the so-called logarithmic temperature difference ΔT _M driving the heat transfer. Both the k-value and the logarithmic temperature difference depend on the operating point of the heat exchanger and therefore on the product and service medium flow rates F _P , F _P and their temperatures T _p,Ein , T _s,Ein as they enter the heat exchanger.

In the case of DE19502096A1, the current K value for each heating surface is derived from the calculated heating power, the logarithmic temperature difference and the heating surface dimensions. By comparing the current K value with the stored "cleanest possible" reference K value Kref, the cleanliness state CF is calculated according to the relationship CF=K/Kref. The reference value Kref is stored in a memory depending on the load and or depending on the fuel. The reference value Kref can be corrected with correction factors according to some current state variables. Thus, for example, a correction is made according to the steam velocity. However, it is unclear how the reference value was obtained.

的情况中，所谓的“受热面值FV”被限定为受热面污染的量度。这被限定为实际评估因子fist与基础评估因子fBasis的比。实际评估因子fist是“测量的”传热系数Kist与理论的传热系数KTheorie的比。“测出的”传热系数Kist根据介质温度和受热面尺寸来得出。理论的传热系数KTheorie根据管道尺寸、宽度和长度划分等几何数据来得出。基础评估因子fBasis是根据被认为存在基本污染的最佳的运行状态得出并保存的，例如蒸汽发生器的验收测试。参考状态的计算包括利用存储在系统中的基本数据和一些当前的过程数据(如给水、新鲜蒸汽和

-参数)对蒸汽发生器的重新计算。然而，没有披露所使用的过程数据的精确细节。exist

In the case of , the so-called "heated surface value FV" is defined as a measure of the contamination of the heated surface. This is defined as the ratio of the actual evaluation factor fist to the base evaluation factor fBasis. The actual evaluation factor fist is the ratio of the "measured" heat transfer coefficient Kist to the theoretical heat transfer coefficient KTheorie. The "measured" heat transfer coefficient Kist is derived from the temperature of the medium and the dimensions of the heating surface. The theoretical heat transfer coefficient KTheorie is derived from geometric data such as pipe size, width and length division. The basic evaluation factor fBasis is derived and stored based on the best operating conditions where basic contamination is considered to be present, eg acceptance tests of steam generators. The calculation of the reference state involves using the basic data stored in the system and some current process data (such as feed water, live steam and

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

DE 10 2016 225 528 A1 discloses a method for monitoring the state of contamination in a heat exchanger using an additional temperature sensor arranged in or on the heat exchanger wall. The temperature sensor detects the working wall temperature of the heat exchanger. The working wall temperature is corrected and the deviation between the corrected working wall temperature and the reference wall temperature is derived. The correction of the working wall temperature takes into account measured value changes that occur due to working conditions deviating from reference conditions, for example deviations in the fluid temperature or in the volume flow of the fluid. The working wall temperature and the reference wall temperature are values measured at and/or preset for the same point of the heat exchanger.

The current fouling resistance R _f can be calculated from the difference between the current heat transfer resistance l/k _ist and the heat transfer resistance l/k _soll obtained in the heat exchanger clean state:

However, the assessment of dirt resistance on this basis has proven to be inaccurate. For example, the level of resistance to heat transfer jumps for no apparent reason, such as when cleaning or replacing a heat exchanger.

Contents of the invention

It is therefore the object of the present invention to propose a method and a device with which fouling in heat exchangers can be determined more precisely.

This object is achieved by a method according to claim 1 and according to claim 2 and by a device according to claim 14 and according to claim 15 . A computer program is the subject matter of claim 16 . Advantageous refinements are given in the dependent claims.

In the method according to the invention, in order to obtain the fouling, the value of the variable characterizing the fouling is derived from the value of the first variable affected by the fouling and the value of the second variable, wherein, from the first and/or the second medium Changes in properties, in particular changes in the first variable caused by changes in the flow of the first and/or second medium through the heat exchanger, are at least partially compensated by the second variable.

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

The invention is based on the discovery that jumps in the level of a fouling-characterizing variable can often be explained by changes in the flow of the first and/or second medium. The reason is that when the flow rate changes, the flow velocity and flow type at the point of transfer from the first medium to the second medium also changes. Then, depending on the type of flow occurring (e.g. laminar, weakly turbulent, highly turbulent) and the velocity of the flow, the value of the first variable affected by fouling may also change. Even within one flow type, mixing and heat transfer will vary depending on the flow rate. For example, turbulence also forms a laminar boundary layer at the edge region, the size and thus the influence of which depends, for example, on the flow or flow velocity. These variations are therefore taken into account according to the invention in order to more precisely determine the value of the variable characterizing the fouling. For this purpose, changes in the first variable caused by changes in the flow of the first and/or second medium through the heat exchanger are at least partially compensated by the second variable. In other words, a change in the flow of the first and/or second medium causes a corresponding change in the second variable, which is then used to compensate the effect of the flow change on the first variable. Here, the (previously unexplained) level jump of the first variable calculated from the measured data is well explained and compensated.

The invention enables reliable quantification of fouling resistance even for flow variations of different heat exchangers. 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 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 final result .

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

Furthermore, there is no need for heat exchanger models laboriously produced by experts. All results and intermediate steps can also be displayed in 2D or 3D characteristic curves. For calculations, non-intuitive multidimensional characteristic curve families are not required.

Here, the invention does not require any special additional measuring devices (eg temperature sensors on the heat exchanger wall), but it is sufficient to use the devices normally present in the heat exchanger.

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

Individual process variables of the product medium or service medium (eg inlet temperature) also do not need to be measured if they are determined according to given frame conditions and can therefore be assumed to be constant.

It is not necessary and therefore not intended to record further variables, such as the material properties of the two media or the structural properties of the heat exchanger. Instead, the present invention assumes these are unknown. Arbitrary constants can be assumed for this, which, when expressed in absolute values, lead to incorrect values of the primary, secondary and fouling-characterizing variables, but ultimately the relative changes of these variables are decisive for the operation and success of the process. In most cases, this is also sufficient in practice.

With the 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 assessments of fouling resistance. Advantageously, the invention can be applied not only to heat balances, but also to the consideration of pressure differences and thus of flow resistance.

A particularly good compensation for flow changes can be achieved when the second variable is a variable that is not influenced by fouling.

According to a first alternative of the invention, the first variable affected by fouling is the heat transfer resistance or heat transfer capacity (or heat transfer coefficient, often also called "k-value"). The heat transfer resistance or heat transfer capacity (or k-value) can be deduced particularly easily from 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 through a wall from a first medium to a second medium, then the value of k theoretically consists of:

or

in,

R _f : Fouling resistance (m ² K/W)

S: wall thickness (m)

λ _W : thermal conductivity of the wall (W/mK)

α1: thermal conductivity from the first medium to the wall (W/m ² K)

α2: Thermal conductivity from the second medium to the wall (W/m ² K)

A change in the flow rate of the first and/or second medium through the heat exchanger causes a change in flow velocity and flow type, resulting in a change in the heat transfer coefficient α ₁ , ₂ .

use

get

1/k=X+R _f

Here, the fouling resistance R _f can be calculated by the following formula

R _f =1/kX

here,

R _f : parameter characterizing the fouling,

1/k: is the first variable

X: Second parameter not affected by dirt.

Thus, the second variable is 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 determined particularly easily from the pressure measurements of the first medium and the second medium at the inlet and 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 a point in time of a flow change, in particular at a point in time of a sudden change, such that the value of the variable characterizing the fouling constant.

After each initial commissioning or cleaning of the heat exchanger, i.e. when there is no fouling, here an initial value of the first variable can be derived (or "learned") and the second variable can be set to correspond to the first variable the initial value of . The two variables then fully compensate each other. Then, when the value of the first variable increases during further operation of the heat exchanger due to fouling and flow changes, the flow change causes a corresponding change of the second variable, which leads to a corresponding compensation of the first variable.

The method is particularly suitable for the operation of heat exchangers with several operating phases, in which the flow is respectively sectionally constant and then changes abruptly. This corresponds, for example, to the relatively common case of regulating the product medium flow, wherein a setpoint value is constantly preset for this. Constant flow changes can only be handled in sections. However, continuous adjustments can then be made by interpolation between changes in segments. The advantage is that changes in the medium after washing do not affect the results and do not require any learning data.

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

This function can be derived or "learned" at a time interval after the initial commissioning of the heat exchanger or after the heat exchanger has been descaled. The function is preferably formed from a regression of the flow measurement values in the time interval and the associated value of the second variable. The regression can eg be a linear regression (when the flow of only one of the two media changes) or a 3D regression (when the flow of both media changes). This approach can also account for constant variation, is relatively less prone to drift in normal operation, and also requires multiple cleanings (and subsequent multiple different flow changes) to "learn" the function. He also enables comparisons between the quality of multiple cleanings.

According to a particularly advantageous third embodiment of the method (referred to below as "method 3"), a value range is defined for the flow rate, which is respectively assigned to the value of the second variable. In this case, the assignment between the value of the second variable and the flow is advantageously ascertained or “learned” within a time interval after initial commissioning of the heat exchanger or after cleaning of the heat exchanger. Optionally, transitions between values of the second variable can be filtered at range boundaries, so they do not vary strongly. It is also possible to interpolate rather than quantize between different learning points in order to create "smoother" transitions.

The time interval for defining a function- or area-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 a weekly cleaning heat exchange heat exchanger) and between a few days (in the case of a slow fouling process, this leads, for example, to cleaning the heat exchanger every month).

Combinations and extensions of the above three methods are also feasible. For example, method 1 can be used whenever a flow change occurs, and the degree of abrupt change and compensation can be considered as new learning points in methods 2 and 3. Therefore, a learning point can also be in a dirty state.

According to a further advantageous refinement of the method, a characteristic curve of the relationship between the second variable and the flow rate of one of the two media is obtained, wherein, in order to obtain the characteristic curve, the flow rate of the medium is derived in a first step A characteristic curve of the mathematical derivative of the first variable, and in a second step the characteristic curve obtained in the first step is again integrated with respect to the flow rate of the medium.

The method exploits the fact that variables characterizing fouling follow slow and reasonably stable trends. The relationship between the first variable and the flow is thus constantly changing, making it impossible to estimate the relationship directly. There is thus the problem of estimating a characteristic curve (static relationship) between two variables. In addition to static relationships, additive trends also affect the dependent variable.

The basic idea to solve this problem is to estimate the derivative of the first variable from the flow rate (eg (d l/k)/dF)), from which fouling can be calculated. The integral of the derivative then provides the actual relationship again, where the absolute value is obviously lost. However, this is also not necessary in the application, since only relative changes in flow need be compensated.

In a further advantageous refinement of the method, a first characteristic curve for the relationship between the second variable and the flow of the first medium and a second characteristic curve for the relationship between the second variable and the flow of the second medium are simultaneously obtained. Characteristic curves, wherein, in order to obtain the characteristic curves for the two media in the first step, the characteristic curves of the mathematical derivatives of the first variable are respectively obtained as a function of the flow rate of the corresponding medium and in the second step again with respect to the corresponding The flow rate of the medium is integrated over the characteristic curve obtained in the first step.

This method is particularly advantageous when the flow rates of both media are changed simultaneously. Here, therefore, two characteristic curves (static relations) between the two variables are respectively estimated. Here, in addition to the static relationship, an additive trend also affects the dependent variable. Applied to heat exchangers, the influence of the two characteristic curves of the second variable is superimposed depending on the flow of the respective medium.

The latter two configurations of the method have the advantage of not relying on the characteristic curve after learning cleaning, since fouling effects are largely compensated by the formation of derivatives.

According to the device of the present invention, for implementing the above-mentioned method according to the present invention, the device comprises

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

- An evaluation device, which is configured to derive a value for a variable characterizing the fouling from the measured value or the derived variable from the value of the first variable influenced by the fouling and the value of the second variable, wherein the first medium and/or A change in the flow of the second medium through the heat exchanger causes a change in the first variable to be at least partially compensated by the second variable.

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

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

The flow rates of the first medium and the second medium through the heat exchanger, without using the material properties of the first medium and the second medium and the structural properties of the heat exchanger for deriving the first and second variables.

However, the first variable can also be flow resistance, the first variable and the second variable consisting 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 medium and the second medium through the heat exchanger, without using the material properties of the first medium and the second medium and the structural properties of the heat exchanger for deriving the first and second variables.

“Derived variables” can be, for example, statistical variables such as mean values, minimum values, maximum values, etc. of measured values.

A 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 on which are stored instructions which, when the program is executed on a computer, cause the computer to carry out the method according to the invention as described above.

Description of drawings

Further advantageous embodiments of the invention and the invention according to the features of the dependent claims are explained in more detail below on the basis of the embodiments in the drawings; where it is shown:

Figure 1 shows a block diagram of a heat exchanger and a device for deriving fouling in the heat exchanger,

Figure 2 shows the time curve of the normalized k-value of an industrial heat exchanger according to the prior art,

Figure 3 shows the principle time curve of the fouling resistance without flow change in the calculation according to method 1 of the invention,

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

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

Figure 6 shows the application of linear regression using the example of the industrial heat exchanger of Figure 2,

Fig. 7 shows the time curve of the fouling resistance R _f of the industrial heat exchanger of Fig. 2 in the calculation according to method 2 of the present invention,

Fig. 8 shows the time curve of the fouling resistance R _f of the industrial heat exchanger of Fig. 2 in the calculation according to method 3 of the present invention,

Fig. 9 shows the time curve of the correction variable X of the industrial heat exchanger of Fig. 2 in the calculation according to the method 4 of the present invention,

FIG. 10 shows time curves of the flow rates of service medium and product medium of an industrial heat exchanger for fouling according to another embodiment of the invention,

Figure 11 shows the time profile of the temperature of the service medium and the product medium in relation to the flow rate according to Figure 10,

Figure 12 shows the time curves of the variables characterizing the fouling obtained according to the method 5 of the invention according to the flow and temperature of Figures 10 and 11,

FIG. 13 shows a time profile of the flow of the service medium and the product medium of an industrial heat exchanger for fouling according to another embodiment of the invention,

Figure 14 shows the time profile of the temperature of the service medium and the product medium in relation to the flow rate according to Figure 13,

Figure 15 shows the time curves of the variables characterizing the fouling obtained according to the method 6 of the invention according to the flow and temperature of Figures 13 and 14,

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

Detailed ways

Figure 1 shows exemplarily and in a simplified diagram 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 exchangers are also possible. Product medium P flows through line 2 . In the direction of flow upstream of the heat exchanger 1 , the flow FP (or flow rate or volume flow) of the product medium and its temperature T _{P ,Ein} are measured 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 _P,Aus of the product medium P leaving the heat exchanger 1 .

The product medium P is heated or cooled by a service medium S which is supplied to the heat exchanger 1 from a heating or coolant supply. In the flow direction upstream of the heat exchanger 1 , the flow F _S (or flow rate or volume flow) of the working medium and its temperature T _S,Ein are measured before entering the heat exchanger 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 _S,Aus of the service medium S leaving the heat exchanger 1 .

To monitor the fouling of the heat exchanger 1, flow measurements F _P and temperature measurements T _P,Ein ,T _P,Aus of the product medium P and flow measurements Fs and temperature measurements T _S,Ein ,T of the service medium S _S,Aus is transmitted to the device 10 . When individual process variables of the product medium P or service medium S, such as its inlet temperature T _P,Ein or T _S,Ein , are determined on the basis of given framework conditions, so that they can be assumed to be constant, then no They need to be measured.

和

For the heat flow on the product and service side

and

and

in,

C _P,P is the heat capacity of the product medium,

C _P,S is the heat capacity of the service medium,

_ρP is the density of the product medium,

_ρS is the density of the serving medium.

Neglecting the loss, all the heat released by the service medium S is transferred to the product medium P, so the two heat flows are equal

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

This applies to:

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

A: Available heat exchange area (m ² )

ΔT _m : mean logarithmic temperature difference

热流。

heat flow.

The mean logarithmic temperature difference ΔT _m is defined as

Among them, ΔT _A represents the temperature difference on the inlet side (from the point of view of the product medium), and ΔT _B represents the temperature difference on the outlet side.

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

a) Heat flow output by medium 1

b) Heat flow through heat exchanger 1

c) Heat flow output by medium 2

Follow from this:

c _{P, P} ρ _P F _P (T _{P, Aus} -T _{P, Ein} ) = k·A·ΔTm=-c _{P, S} ρ _S F _S (T _{S, Aus} -T _{S, Ein} )

In general, it is now assumed that dirt resistance is independent of the operating point. The current fouling resistance can be derived and calculated from the difference between the current heat transfer resistance 1/k _ist and the heat transfer resistance 1/k _soll obtained in the clean state.

Therefore, the value of k can be calculated using the following formula

Wherein, for the case of a convective heat exchanger, ΔT _A =T _{P, Ein} −T _{s, Aus} and ΔT _B =T _{P, Aus} −T _{s, Ein} are used.

If the values of A, C _{P, P} , C _{P, S} , ρ _P and ρ _S are considered constant, the relative value of k can therefore only be made with the help of temperature measurements on the inlet and outlet sides and the flow rates of the two media to calculate.

FIG. 2 exemplarily shows a typical curve of the 1/k value over time t for an industrial heat exchanger. For the sake of simplicity, the k value k ₀ present at time t ₀ =0 is derived, and FIG. 2 shows the value 1/k′ in relation to the initial value k ₀ . Here, the vertical line shows the cleaning time. Here, a 1/k' drop due to fouling can be seen in certain regions. However, there is a horizontal jump at the point marked with an arrow, which makes it difficult to accurately assess dirt resistance.

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

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

or

in,

R _f : Fouling resistance (m ² K/W)

S _W : Wall thickness (m)

λ _W : thermal conductivity of the wall (W/mK)

α1: Thermal conductivity from the first medium to the wall (W/m ² K)

α2: Thermal conductivity from the second medium to the wall (W/m ² K)

A change in flow rate and thus a change in or within a flow type results in a change in the heat transfer coefficient α _1,2 .

use

get

1/k=X+R _f .

here,

R _f : parameter characterizing the fouling,

1/k: first parameter

X: Second parameter not affected by dirt.

Thus, the second variable is 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, changes in the first variable (here the calculated value of k) caused by flow changes are at least partially compensated by means of the second variable (here the value of the variable X).

According to Figures 3 to 10, three methods or ways of how traffic is considered 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:

- the wall thickness and its thermal conductivity (S _W /λ _W = constant) do not change during operation,

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

- In normal operation, if there is no special reason (such as cleaning), the dirt resistance will not decrease or increase significantly.

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

During a certain time interval after washing, the resistance to fouling R _f =0 can be assumed.

In this range, the values of l/α1, l/α2 and _Sw / _λw (summarized in value X) are learned. With _Rf = 0 and X = 1/α1+1/α2+S _W /λ _W , X _{0 for the initial interval (or after cleaning interval) can now be determined using the previously calculated k-value k 0 .} X ₀ =1/k ₀ applies here.

Case 1: No change in traffic

In this case, the value of α also does not change, i.e. X remains constant. Therefore, any variation in the 1/k value can be attributed to fouling. Therefore, the fouling resistance can be calculated using the formula R _f =1/kX. FIG. 3 exemplarily shows the variation of 1/k, X and R _f over time t. The value of X is constant and results in a constant difference between 1/k and _Rf .

Case 2: The flow rate changes at time point t ₀

At time t ₀ , the fouling resistance R _f (t ₀ ) is briefly held constant, and X _neu is calculated, for example, using X _neu =1/kR _f (t ₀ ).

For 1/k, it is now possible to use the mean of the interval from t ₀ to t ₀ +x. Alternatively, X _neu can also be calculated as follows: X _neu =X _alt -(1/k _alt -1/k _neu ).

1/ _kalt and 1/k _neu represent the average 1/k value in the interval before or after the flow change. Both methods show almost identical results.

In a further procedure, the fouling resistance is then calculated again using R _f =1/k _neu -X _neu .

FIG. 4 exemplarily shows the variation of 1/k, X and R _f over time t. As shown, this approach enables the fouling resistance R _f to continue steadily at the jump in flow at time point t ₀ , rather than causing a horizontal jump.

If this method is now used to calculate the 1/k value, X and R _f for the industrial heat exchanger of FIG. 2 and plotted over time t, the curve shown in FIG. 5 results. Only relative values are shown here. Here again, the vertical line shows the cleaning time. For the sake of simplicity, the initial values 1/k ₀ and X ₀ which exist at time t ₀ =0 are derived, and FIG. 5 shows the values 1/k' and X' associated with these initial values.

When calculating the 1/k' value, a horizontal jump occurs again at the position marked by the arrow, but this horizontal jump is largely compensated by the change in the X' value when calculating the relative dirt resistance _Rf .

The method is particularly suitable for the operation of heat exchangers with operating phases in which the flow rate is constant in sections and then changes abruptly. Constant flow changes can only be handled in sections. However, continuous adjustments can then be made by interpolation between segmental changes. Advantageously, changes in the medium after cleaning have no effect on the results, and no learning data is required.

Method 2

As mentioned earlier, it can be roughly assumed that the dirt resistance after cleaning is ≈0. Here, X(F)=1/k holds true. 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 traffic changes during this interval. For this purpose regression can be used, in particular linear regression, and even better non-linear regression. Using the result of this interpolation, the corresponding X value can be calculated for any flow.

FIG. 6 exemplarily shows the application of linear regression using the industrial heat exchanger in FIG. 2 . In order to create the linear regression and thus define the function _f , the relevant X values (marked with "*" in FIG. 6 ) are derived for a plurality of averaged flow values FP on the product side after cleaning the heat exchanger. Here, the flow change within this interval is considered. Therefore, the following applies: X=f(F _p ), where the function f comes from the linear regression of F _p and X.

If the relative fouling resistance R _f of the industrial heat exchanger of FIG. 2 is now calculated using this method and plotted together with the value X obtained by means of linear regression over time t, the curve shown in FIG. 7 is obtained. For the sake of simplicity, an initial value X ₀ which exists at time t ₀ =0 also results here, and FIG. 7 shows the value X′ associated with this initial value.

As shown, this method also shows satisfactory results in many ranges.

Here again, the vertical line shows the cleaning time.

For example, the function f can be obtained by a linear regression of the measured values of the flow in the time interval after the initial commissioning or cleaning and the assigned value of the second measurement (when only one of the two media changes, see Figure 6) or by a 3D come back to form. This approach is also able to account for constant variation and is relatively less prone to bias in normal operation, but also requires multiple washes (and then multiple different flows) to "learn" the function f. He was also able to 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. So that the transition between the two X values doesn't become too abrupt, being able to filter the X value a bit over time.

If this method is now used to calculate the relative fouling resistance _Rf and X of the industrial heat exchanger from Figure 2 and plotted over time t, the result is the curve shown in Figure 8. For the sake of simplicity, the initial values 1/k ₀ and X ₀ that exist at the time t ₀ =0 are derived, and FIG. 5 shows the values 1/k' and X' associated with these initial values. Calculations are based on heat on the product side. Here again, the vertical line shows the cleaning time. As shown in the figure, this method also shows satisfactory results in many aspects.

The assignment of the value of the second variable to the flow is advantageously made within a time interval after initial commissioning of the heat exchanger or after the heat exchanger has been descaled. Optionally, transitions between values of the second variable can be filtered at range boundaries so that they do not change drastically. It is also possible to interpolate, rather than quantize, between different learning points to produce "smoother" transitions.

One optimization possibility is the so-called "interpolation point method". This approach also represents a possibility of how the relationship between the flow rate and the reference value can be analyzed. For this purpose, it is briefly necessary to describe how the characteristic curve for the α value can be considered as a function of the flow rate. Here, it is already possible to find boundary conditions of the subsequent characteristic curve or function, for example the monotonicity of the curve. The first value for analysis is obtained or derived in the cleaned state after cleaning.

Add new values at runtime. These are weighted with previous values in a certain area and update the feature. The weighting factor can be the number of points so far in an area or the current dirt resistance.

In addition to these three methods, composition and extension can also be used.

Combination of methods 1 and 2

This combination enables the fouling resistance or X value of the heat exchanger to be derived first using method 1, and then the X value can be calculated in the interim 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 run, method 2 alone will suffice.

Method 4

With the help of method 1, in case of a flow breakthrough, the change in X value and before and after the flow change are known. On the one hand, it is now possible to calculate the levels of flow breaks (ΔF ₁ ) and X-values (ΔX ₁ ). Thus, the impact relative to previous X values can be calculated for each future (also constant) flow change. If multiple mutations were available, a linear regression between ΔF ₁ and ΔX ₁ was used. To this end, FIG. 9 shows the assignment of the value of X to the flow F at time t.

To calculate the final X value, an interpolation can be performed between different sampling points to avoid abrupt curves (see dashed line in Fig. 9). Therefore, the combination of method 1 and method 4 offers particular advantages.

Method 5

According to the design of the method called method 5, a characteristic curve of the relationship between the second variable and the flow rate of one of the two media is obtained, wherein, in order to obtain this characteristic curve, in a first step according to the flow rate of the medium A characteristic curve of the mathematical derivative of the first variable is obtained, and in a second step the characteristic curve obtained in the first step is integrated again with respect to the flow rate of the medium.

The method exploits the fact that variables characterizing fouling follow slow and reasonably stable trends. The relationship between the first variable and flow is thus constantly changing, so this relationship cannot be estimated directly. There is thus the problem of estimating a characteristic curve (static relationship) between two variables. Here, in addition to the static relationship, an additive trend also affects the dependent variable.

The basic idea to solve this problem is to estimate the derivative of the first variable from the flow rate (eg (dl/k)/dF)), from which the fouling can be calculated. The integral of the derivative then provides the actual relationship again, the absolute value is obviously lost. However, this is also not necessary in the application, since only relative changes in flow need be compensated.

Assume the reciprocal of the value of k consists of the sum of dirt resistance and X

where X combines all other thermal resistances. The derivative in time gives

in,

therefore applies to

For Φ ₁ (t)≠Φ ₂ (t) apply

不取决于Φ(t)和κ(t)。At X ₀ , F ₀ position, applies unique but unknown relation

Does not depend on Φ(t) and κ(t).

therefore,

This applies to all Φ ₁ (t)≠Φ ₂ (t).

变化的加权的差。Therefore, it is necessary to calculate for two different flow changes Φ ₁ (t)≠Φ ₂ (t)

Change the weighted difference.

的数据，并为成对的Φ₁(t)≠Φ₂(t)分别得出

然后通过对导数特征曲线积分的整合生成所求的特征曲线。In order to determine the characteristic curve, it is recommended to sequentially collect all _Fs with

, and for the pairs of Φ ₁ (t)≠Φ ₂ (t), we get

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

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

Due to the simpler parameterization, modeling is only done qualitatively, i.e. 1/k is determined without exact material data or heat exchanger properties. Therefore, only relative changes in k values can be calculated. However, the determined characteristic curve can be accurately used for relative changes in flow.

A feature of this approach is that the actual task of determining the fouling is initially unnoticed and the effect of fouling can be compensated for in order to estimate the X-F characteristics. Only then can the dirt be derived using the characteristic curve of 1/k. Advantageously, characteristic curves can be realized easily, so that nothing prevents the online evaluation.

Figures 10 to 12 show simulations of industrial heat exchangers with varying flow rates.

In this case, FIG. 10 shows the time profile of the (simulated) measured values of the flow _FP of product medium and the flow _FS of service medium through the heat exchanger.

FIG. 11 shows the associated (simulated) measured values for the temperature T _P,Ein of the product medium at the inlet of the heat exchanger and the temperature T _P,Aus of the product medium at the outlet of the heat exchanger. Furthermore, (simulated) measured values of the temperature T _S,Ein of the service medium at the inlet of the heat exchanger and of the temperature T _S,Aus of the service medium at the outlet of the heat exchanger are shown.

Figure 12 shows the relative values of 1/k and the correlation calculation of the fouling resistance _Rf .

The 1/k value shows a significant dependence on the change in flow regardless of which side of the heat exchanger. Overlapping trends can still be seen in idealized data. However, depending on the severity of fouling, no reliable conclusions can be drawn from the 1/k value alone.

By using the characteristic curve and compensating for the associated flow dependence, an estimated fouling curve (shown offset upwards for better visibility) is obtained. In addition to measuring noise, a linear trend can also be seen. Dirt can thus be drawn off very reliably. At this point, it should be noted that initially the changes of the two flows are independent of each other, so that the two flow characteristics can also be well estimated successively and independently of each other.

Method 6

According to the design scheme of the method called method 6, the first characteristic curve of the relationship between the second variable and the flow rate of the first medium and the second characteristic curve of the relationship between the second variable and the flow rate of the first medium are simultaneously obtained. characteristic curve. Wherein, in order to obtain the characteristic curves for two media in the first step, the characteristic curves of the mathematical derivatives of the first variable are obtained respectively according to the flow rate of the corresponding medium, and in the second step again with respect to the corresponding medium The flow rate is integrated over the characteristic curve obtained in the first step.

This method is particularly advantageous when the flow rates of both media are changed simultaneously. Thus, two characteristic curves (static relations) between the corresponding two variables are estimated here. Here, in addition to the static relationship, an additive trend also affects the dependent variable. Applied to heat exchangers, the influence of the two characteristic curves of the second variable is superimposed depending on the flow rate of the respective medium.

In the case of heat exchangers, the influence of the two characteristic curves X _P =f _P (F _P ) and X _S =f _S (F _S ) on the value of 1/k is superimposed, where

The derivative of 1/k with respect to time gives

Wherein, X=X _P +X _S .

的n_p插值点(dx_Pi，F_Pi)和导数特征曲线

的n_S插值点(dx_Si，F_Si)。Now find the derivative characteristic curve

The n _p interpolation points (dx _Pi , F _Pi ) and the derivative characteristic curve

n _S interpolation points of (dx _Si , F _Si ).

或

具有三个未知量(dx_Pi，dx_Si，m)的方程产生：To do this, for each time point t, apply

or

An equation with three unknowns (dx _Pi , dx _Si , m) yields:

The _nD equation is then summarized in a matrix-able expression, where the corresponding flows have to be noted at the interpolation points. Therefore, apply

c=[κ(t ₁ )...κ(t _m )]

For better understanding, a row of A is given. At an appropriate point in time, it should be _F P ≈ F _P5 and F _S ≈ F _S7 , where n _P =10 and n _S =20. Then the rows of A correspond to

Among them, there are non-zero entries in the 5th column, the 17th column (=10+7) and the last column.

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

Two derivative characteristic curves can then be regenerated from the vector b and by integrating them the characteristic curves X _P =f _P (F _P ) and X _S =f _S (F _S ) are obtained.

并且通过使用特征曲线If there are two characteristic curves, then it can be determined by first determining

and by using the characteristic curve

来计算污垢的方法来估计污垢。

To calculate the dirt method to estimate the dirt.

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

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

Figures 13-15 show simulations of industrial heat exchangers with varying flow rates.

FIG. 13 shows the time curve of the (simulated) measured values of the flow _FP of the product medium and the flow _FS of the service medium through the heat exchanger.

FIG. 14 shows the associated (simulated) measured values for the temperature T _P,Ein of the product medium at the inlet of the heat exchanger and T _P,Aus of the product medium at the outlet of the heat exchanger. In addition, the (simulated) measured values of the temperature T _S,Ein of the service medium at the inlet of the heat exchanger and the temperature T _S,Aus of the service medium at the outlet of the heat exchanger are shown.

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

The 1/k value shows a significant dependence on the change in flow, no matter on which side of the heat exchanger. Overlapping trends can still be seen in idealized data. However, depending on the severity of fouling, no reliable conclusions can be drawn from the 1/k value alone. An estimated fouling curve R _f is obtained by using the characteristic curve and compensating for the associated flow dependencies. Aside from the measurement noise, a linear trend can be seen. Therefore, fouling can be drawn very reliably even if both flow rates change at the same time.

In principle, the same approach can also be applied to take pressure differences into account. Flow resistance also increases with dirt, but also depends on flow.

These methods are able to reliably quantify fouling resistance even with varying flow rates across different heat exchangers. 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 while including the influence of the flow dynamics of the two media on the final result.

Furthermore, there is no need for heat exchanger models laboriously produced by experts. All results and intermediate steps can also be displayed in 2D or 3D characteristic curves. Unintuitive multidimensional characteristic curve families are not required for calculation. Furthermore, it is also possible to omit measuring one of F _P , F _S , T _P,Ein , T _P,Aus , T _S,Ein , T _S,Aus , so that a complete instrument is not required. Of course the only thing that can be dispensed with here is the temperature measurement if the flow changes of the two media are to be compensated.

Using these methods, using the example of an industrial heat exchanger, significantly better results were obtained when deriving fouling than conventional calculations. Therefore, the results can help plant operators better assess fouling resistance. Advantageously, these methods cannot be applied to heat balance, nor can they be applied to take into account pressure differences and thus flow resistance.

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

In Fig. 1 schematically shows a device 10 according to the invention for deriving dirt, the device comprising:

- means 20 for receiving measured values T _P,Ein , T _P,Aus , T _S,Ein , T _S,Aus of the heat exchanger 1 , and

An evaluation device 30 , which is designed to derive and output a value for the dirt resistance R _f from these measured values by means of the method described above. Additionally or alternatively, the evaluation device can also be used as a monitoring device: it can monitor whether the resulting dirt resistance exceeds a threshold value and, if it does, output a signal which, for example, indicates 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, when one of the methods described above is executed, by the processor unit 31 Carry out the method described previously. The processor unit stores the measured values M received from the device 20 in a memory 32 .

There is no need to detect other variables such as A, C _P,P , C _P,S , ρ _P and ρ _S . Instead, the method according to the invention assumes that these are unknown. Arbitrary constants can be assumed, which will lead to k values that are incorrect in absolute terms, but ultimately the relative change in this k value is decisive for the operation and success of the method.

The device 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 device 100 for deriving dirt shown in FIG. 16 can be provided by a local or remote computer system ("the cloud"), for example in order to offer derivation of dirt as "software as a service" by a service provider. 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”). To this end, 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 received measurement data and a memory 33 in which is stored a program 34 with instructions which, when executed, carry out one of the methods described above by the processor unit 31 .

The processor unit 31 stores the measured values M received via the interface 36 from the device 20 in the memory 32 and, if necessary, other input variables received via a separate interface 37 . The value of the resistance to fouling _Rf determined by the program 34 and/or a signal indicating the need for cleaning is output via the interface 38 . The interfaces 36, 37 and 38 can also be provided by a single common interface, for example to an intranet or intranet.

By detecting measurements and calculating fouling resistance in near real time, continuous data-based fouling analysis and fouling monitoring is enabled as the system or heat exchanger operates. However, offline fouling analysis with a time offset relative to the actual operation of the facility is also feasible.

Claims (16)

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 the value of the variable (R _f ) characterizing the fouling is derived from the value of the first variable (k) influenced by the fouling and the value of the second variable (X), wherein, due to the second A change in said first variable (k) caused by a change in flow (FS, F _P ) of a medium ( _S ) and/or said second medium (P) through said heat exchanger (1) is at least Partly compensated by said second variable (X), wherein said first variable (k) is heat transfer resistance or heat transfer capacity (or heat transfer coefficient, k value), and wherein said first variable (k) and said second variable (X) are derived from the measured values of the following measured variables, - the temperatures of said first medium (S) and said second medium (P) at the inlet and outlet of said heat exchanger (1) (T _p,Ein , T _p,Aus , T _s,Ein , T _{s, Aus} ), and - the flows (FS, F _P ) of said first medium ( _S ) and said second medium (P) through said heat exchanger (1), Also, the material properties of the first medium (S) and the second medium (P) and the heat exchanger (1) are not used in deriving the first and second variables. Structural properties. 2. Method according to claim 1 for deriving fouling in the heat exchanger (1) in which heat is transferred from a first medium (S) to a second medium (P ), characterized in that the value of the variable (R _f ) characterizing the fouling is derived from the value of the first variable (k) influenced by the fouling and the value of the second variable (X), wherein, due to the second A change in said first variable (k) caused by a change in flow (FS, F _P ) of a medium ( _S ) and/or said second medium (P) through said heat exchanger (1) is at least Partially compensated by said second variable (X), wherein said first variable is flow resistance, and wherein said first variable (k) and said second variable (X) are measured by The measured value of the variable yields, - the pressure of said first medium (S) and said second medium (P) at the inlet and outlet of said heat exchanger (1), and - the flows (FS, F _P ) of said first medium ( _S ) and said second medium (P) through said heat exchanger (1), And in deriving said first variable and said second variable, the material properties of said first medium (S) and said second medium (P) and the structure of said heat exchanger (1) are not used characteristic. 3. A method according to claim 1 or 2, wherein at the point in time (t ₀ ) of the change in flow, the value of the second variable (X) changes, thereby characterizing the variable (R _f ) of the fouling value remains constant. 4. The method according to claim 3, wherein the initial value (k ₀ ) of the first variable (k) is obtained after initial commissioning and after cleaning the heat exchanger (1), respectively, and the The value of said second variable (X) is set to an initial value (X ₀ ) corresponding to the initial value (k ₀ ) of said first variable (k). 5. The method according to any one of the preceding claims, wherein a function (f) is defined as a function of the flow of the first medium (S) and/or the second medium (P) Values are each assigned a value of said second variable (X). 6. Method according to claim 5, wherein the function (f) is derived at time intervals (T) after initial commissioning or after descaling of the heat exchanger (1). 7. The method according to claim 5 or 6, wherein the function (f) is regressed by the measured value of the flow (F) in the time interval (T) and the associated value of the second variable (X) , especially linear regression or 3D regression forms. 8. The method according to any one of the preceding claims, wherein a value range is defined for the flow rate (F) which is respectively associated with a value of the second variable (X). 9. Method according to claim 8, wherein the value of the second variable (X) is derived for a time interval (T) after initial commissioning or after cleaning the heat exchanger (1) of dirt with the distribution of the flow (F). 10. The method according to any one of the preceding claims, wherein a characteristic curve of the relationship between the second variable (X) and the flow (F) of one of the two media (S, P) is derived , wherein, in order to obtain the characteristic curve, in the first step, the characteristic curve of the mathematical derivative of the first variable (K) is obtained according to the flow rate (F) of the medium (S or P), and in the second step In a step, the characteristic curve obtained in the first step is then integrated with respect to the flow (F) of the medium (S or P). 11. The method according to any one of the preceding claims, wherein the relationship between the second variable (X) and the flow (F) of the first medium (S or P) is derived simultaneously 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), wherein, in order to Deriving a characteristic curve for each of the two media (S, P), deriving the mathematical derivative of said first variable (k) from the flow (F) of the corresponding medium (S or P), respectively The characteristic curve obtained in the first step is then integrated in a second step with respect to the flow rate (F) of the respective medium (S or P). 12. The method according to any one of the preceding claims, wherein the variable ( _Rf ) characterizing the fouling is heat transfer resistance. 13. The method according to any one of the preceding claims, wherein only the relative values of the variable (R _f ), the first variable (k) and the second variable (X) characterizing the fouling are derived Variety. 14. An apparatus (10, 100) for performing the method according to any one of claims 1 and 3 to 13, said apparatus comprising - means (20) for receiving measured values (M) of said heat exchanger (1) or variables derived from said measured values, and - evaluation means (30), said evaluation means being arranged for, from the value of the first variable (k) influenced by dirt and the value of the second variable (X) from said measured value (M) or said derived variable value to obtain the value of the variable (R _f ) characterizing the fouling, wherein the flow rate of the first medium (S) and/or the second medium (P) through the heat exchanger (1) (F Changes in said first variable (k) caused by changes in _S , F _P ) are at least partially compensated by said second variable (X), and wherein said first variable (k) and said second variable (X) is derived from the measured values of the following multiple measured variables, - the temperatures of said first medium (S) and said second medium (P) at the inlet and outlet of said heat exchanger (1) (T _p,Ein , T _p,Aus , T _s,Ein , T _{s, Aus} ), and - the flows (FS, F _P ) of said first medium ( _S ) and said second medium (P) through said heat exchanger (1 ), 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, said apparatus comprising: - means (20) for receiving a measured value (M) of said heat exchanger (1) or a variable derived from said measured value, and - evaluation means (30), said evaluation means being arranged for, from the value of the first variable (k) influenced by dirt and the value of the second variable (X) from said measured value (M) or said derived variable Values yield the value of the variable (R _f ) characterizing the fouling, where the flow of the first medium (S) and/or the second medium (P) through the heat exchanger (1) ( Changes in said first variable (k) caused by changes in F _S , F _P ) are at least partially compensated by said second variable (X), wherein said first variable is flow resistance, and wherein said The first variable (k) and said second variable (X) are derived from measured values of the following measured variables, - the pressure of said first medium (S) and said second medium (P) at the inlet and outlet of said heat exchanger (1), and - the flows (FS, F _P ) of said first medium ( _S ) and said second medium (P) through said heat exchanger (1 ), 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 . 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.

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