Method and device for detecting fouling of a heat exchanger

Abstract

In order to improve the accuracy of the determination of fouling in a heat exchanger (1), in which heat is transferred from a first medium (S) to a second medium (P), a variable (R) for characterizing fouling is derived from the value of a first variable (k) affected by fouling and the value of a second variable (X). f ) value. Here, 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). The first variable can be a heat transfer resistance or a heat transfer capacity (or a heat transfer coefficient (k value)), wherein the first variable and the second variable are derived from measured values ​​of the temperature and the flow rate of the first medium, and the material properties of the first medium and the second medium and the structural properties of the heat exchanger are not used when deriving the first variable and the second variable.

Description

Technical Field

[0001] The invention relates to a method and a device for detecting fouling of a heat exchanger. Background Art

[0002] Heat exchangers, also often called heat transfer devices, are technical devices used to heat or cool a medium. To this end, heat is transferred from a first, hotter medium to a second, colder medium. Depending on the type of construction, the heat exchanger functions in different ways. The most common types of construction fall into one of three functional groups: direct-flow, counter-flow or cross-flow heat exchangers.

[0003] 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 pipe arrangement arranged in the product medium or flows around a pipe arrangement through which the product medium flows.

[0004] The first and second media are conducted through the heat exchanger, wherein the two media usually flow past each other separated by a wall and heat from the warmer medium is transferred via the wall to the cooler medium.

[0005] A central problem of heat exchangers is so-called "fouling", i.e. the formation of deposits or coatings on the inner walls of the heat exchanger. The causes of the formation of such deposits can be physical, chemical or biological. In many cases, they cannot be avoided, for example due to given framework conditions on the product side. The deposits inhibit the heat transfer between the media and thus reduce 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 facilities in process technology (e.g. facilities in the chemical, petrochemical, glass, paper, metal production or cement industries) or in large industrial heat exchangers used in power plants, which are usually designed for a heat transfer capacity of more than 100 kW.

[0006] 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 required. The temperature control circuit is able to compensate for the effects of fouling to a certain extent, so fouling is not immediately apparent from the outlet temperature of the product medium. Due to this unknowability, it is usually not possible to clean or replace the heat exchanger as required.

[0007] Until now, heat exchangers affected by contamination were therefore cleaned or replaced at regular intervals, i.e. without knowing the actual state of contamination. In this process, it was not possible to adjust the maintenance intervals to the different degrees of contamination. Therefore, for example, the cleaning or replacement of the heat exchanger could be carried out too early, even if only small deposits were present at this time. Although this would ensure the efficient operation of the heat exchanger, it would be uneconomical due to the direct costs of the maintenance work and the indirect costs due to additional damage to the continued operation of the plant using the heat exchanger. If appropriate measures are carried out too late, excessive deposits within the heat exchanger will lead to a significant reduction in heat transfer. As a result, for the same heat flow to be transferred, a much larger flow of service medium is required than would be the case when the heat exchanger was clean. This leads to an increased energy consumption for providing the service medium, i.e. the heating and pumping power, which is also a cost factor. In addition, in the case of the formation of large amounts of deposits, there is also the risk of a deterioration in the quality of the product medium, because, for example, temperature specifications are not fully complied with.

[0008] EP 2 128 551 A1 discloses a method 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 with 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 permissible degree of contamination. It is derived from the characteristic curve family previously established and stored for different operating points using the simulation program according to the current operating point of the heat exchanger, where the flow rate F of the two media through the operating point of the heat exchanger is S , F P and their temperature at the inlet of the heat exchanger T p,Ein , T s,Ein By using a simulation program, the operating point dependency of the transferable heat can be calculated in advance, for example, at several hundred interpolation points, without having to carry out corresponding time-consuming measurements in the actual plant.

[0009] A method for monitoring a heat exchanger is known from WO2019 / 001683A1, in which the flow rate, inlet temperature and outlet temperature 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 to measure the (multiple) variable process variables of the product medium and the flow rate of the service medium, and to derive and store a family of characteristic curves for the mutual dependence of the variable (multiple) process variables of the product medium and the flow rate of the service medium from the measured values ​​obtained in the reference state of the heat exchanger. Here, for the measured values ​​obtained in the current unknown state of the heat exchanger, the distance between the measured value tuple formed thereby and the family of characteristic curves is derived as a measure of the deviation of the current state of the heat exchanger from the reference state.

[0010] It is known to monitor heat exchangers by taking into account the heat transfer coefficient or k-value, from "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, 1 September 1995, pp. 755-762, ISSN: 0372-5715, DE 19502096 A1, US 4,390,058 A or EP 0 470 676 A2. The heat transfer coefficient or k-value is the heat flow transferred in the heat exchanger. The k value depends on the exchange area A and the so-called logarithmic temperature difference ΔT that drives the heat transfer. M Both the k value and the logarithmic temperature difference depend on the operating point of the heat exchanger and therefore on the flow rates F of the product and service media. P , F P and its temperature T when it enters the heat exchanger p,Ein , T s,Ein .

[0011] In the case of DE 195 02 096 A1, the current K value for each heating surface is derived from the calculated thermal power, the logarithmic temperature difference and the size of the heating surface. The cleanliness state CF is calculated according to the relationship CF=K / Kref by comparing the current K value with a stored reference K value Kref of the "cleanest possible state". 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 a correction factor depending on some current state variables. Thus, for example, a correction is made depending on the steam velocity. However, it is not clear how the reference value is obtained.

[0012] exist In the case of a 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 basic 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 medium temperature and the dimensions of the heating surface. The theoretical heat transfer coefficient KTheorie is derived from geometric data such as pipe dimensions, width and length divisions. The basic evaluation factor fBasis is derived and saved based on the best operating conditions in which basic contamination is assumed to exist, such as the acceptance test of a steam generator. The calculation of the reference state involves the use of the basic data stored in the system and some current process data (such as feed water, live steam and However, the precise details of the process data used are not disclosed.

[0013] DE102016225528A1 discloses a method for monitoring the contamination state in a heat exchanger, which method uses an additional temperature sensor arranged in or on the wall of the heat exchanger. 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 the measured value changes that occur due to working conditions that deviate from the reference conditions, such as deviations in the fluid temperature or the volume flow of the fluid. The working wall temperature and the reference wall temperature are values ​​measured at the same point of the heat exchanger and / or preset for the same point.

[0014] Current dirt resistance R f The current heat transfer resistance l / k ist and heat transfer resistance l / k soll The difference between is calculated, which is obtained in the clean state of the heat exchanger:

[0015]

[0016] However, it turns out that the assessment of fouling resistance on this basis is inaccurate. For example, the level of heat transfer resistance can jump for no apparent reason, such as when cleaning or replacing a heat exchanger. Summary of the invention

[0017] It is therefore an object of the present invention to provide a method and a device with which fouling in heat exchangers can be determined more accurately.

[0018] In the method according to the invention, in order to derive the fouling, the value of a variable characterizing the fouling is derived from the value of a first variable affected by the fouling and the value of a second variable, wherein a change in the first variable caused by a change in the properties 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.

[0019] The variable characterizing fouling is preferably the heat transfer resistance or heat transfer capacity. However, it can also be, for example, the flow resistance.

[0020] The invention is based on the discovery that the level jump of the variable characterizing fouling can usually be explained by the flow change of the first and / or second medium. The reason is that when the flow changes, the flow velocity and the flow type at the hot transfer point 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 change. Even in one flow type, mixing and heat transfer will change depending on the flow velocity. For example, turbulence also forms a laminar boundary layer at the edge area, the size of which and the resulting influence depend on, for example, the flow rate or the flow velocity. In order to more accurately derive the value of the variable characterizing fouling, these changes are therefore taken into account according to the invention. For this purpose, the change of the first variable caused by the change of 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, the change of the flow of the first and / or second medium causes a corresponding change of the second variable, which is then used to compensate for the influence of the flow change on the first variable. Here, the (previously unexplained) level jump of the first variable calculated from the measurement data can be well explained and compensated.

[0021] The invention enables reliable quantification of the fouling resistance even for different heat exchanger flow variations. Knowledge of the material properties or structural characteristics of the heat exchanger is not required. The invention works entirely on the basis of measured 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 invention uses this variable while combining the influence of the flow dynamics of the two media on the final result.

[0022] Since according to the invention it is not the heat flow that is taken into account but the heat transfer resistance or heat transfer capacity (or heat transfer coefficient (k value)) or flow resistance, the fouling resistance contained therein is advantageously independent of the operating point.

[0023] Furthermore, laborious heat exchanger models produced by experts are not necessary. All results and intermediate steps can also be displayed in 2D or 3D characteristic curve families. For the calculation, unintuitive multidimensional characteristic curve families are not required.

[0024] The invention does not require any special additional measuring instruments (eg temperature sensors on the heat exchanger wall) here, but it is sufficient to use the instruments which are usually present in the heat exchanger.

[0025] Furthermore, one of the measurements of the flow rate and the inlet / outlet temperature of the medium can be omitted, so that even a complete instrument is not required.

[0026] If individual process variables of the product medium or service medium (eg inlet temperature) are determined according to given framework conditions and can therefore be assumed to be constant, they also do not need to be measured.

[0027] It is not necessary and therefore not intended to record other variables, such as the material properties of the two media or the structural properties of the heat exchanger. On the contrary, the invention assumes that these are unknown. It is possible to assume arbitrary constants for this, which, when expressed in absolute values, would lead to incorrect values ​​for the first variable, the second variable and the variable characterizing fouling, but ultimately the relative changes in these variables are decisive for the operation and success of the process. In most cases, this is also sufficient in practice.

[0028] With the invention, in the example of an industrial heat exchanger, significantly better results can be obtained when deriving fouling than with conventional calculations. The results can thus help the plant operator to make a better assessment of the fouling resistance. Advantageously, the invention can be applied not only to the heat balance, but also to the consideration of the pressure difference and thus to the consideration of the flow resistance.

[0029] A particularly good compensation of flow rate changes can be achieved if the second variable is a variable which is not affected by fouling.

[0030] 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 derived particularly easily from the temperature measurements of the first medium and the second medium at the inlet and outlet of the heat exchanger.

[0031] For example, when heat is transferred from a first medium to a second medium through a wall, the k value is theoretically composed as follows:

[0032]

[0033] or

[0034]

[0035] in,

[0036] R f :Dirt resistance(m 2 K / W)

[0037] S: wall thickness (m)

[0038] λ W : Thermal conductivity of the wall (W / mK)

[0039] α1: Thermal conductivity from the first medium to the wall (W / m 2 K)

[0040] α2: Thermal conductivity from the second medium to the wall (W / m 2 K)

[0041] A change in the flow rate of the first and / or second medium through the heat exchanger will cause a change in the flow rate and flow type, resulting in a change in the heat transfer coefficient α 1，2 changes.

[0042] use

[0043]

[0044] get

[0045] 1 / k=X+R f

[0046] Here, the dirt resistance R f It can be calculated by the following formula

[0047] R f =1 / kX

[0048] Here,

[0049] R f : Parameters that characterize fouling,

[0050] 1 / k: is the first variable

[0051] X: The second parameter that is not affected by dirt.

[0052] 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.

[0053] 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 pressure measurements of the first and second medium at the inlet and outlet of the heat exchanger.

[0054] 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 time of a flow change, in particular a sudden change, such that the value of the variable characterizing fouling remains unchanged.

[0055] After each initial commissioning or cleaning of the heat exchanger, i.e. when there is no fouling, an initial value of the first variable can be determined (or "learned") and the second variable can be set to the initial value corresponding to the first variable. The two variables then completely compensate for each other. If, in the further operation of the heat exchanger, the value of the first variable then increases due to fouling and flow changes, the flow changes cause a corresponding change in the second variable, which results in a corresponding compensation of the first variable.

[0056] The method is particularly suitable for the operation of heat exchangers with multiple operating phases, in which the flow is respectively constant in sections and then changes suddenly. This corresponds, for example, to the relatively common case of regulating the flow of a product medium, for which a setpoint value is constantly preset. Constant flow changes can only be handled in sections. However, continuous adjustment can then be made by interpolation between the sectioned changes. The advantage is that changes in the medium after cleaning do not affect the result and no learning data are required.

[0057] 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.

[0058] The function can be derived or "learned" in a time interval after the initial commissioning of the heat exchanger or after the heat exchanger has been defouled. The function is preferably formed by a regression of the flow measurement values ​​and the associated values ​​of the second variable in this time interval. The regression can be, for example, 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 method can also take into account constant changes, which are relatively prone to deviations in normal operation and also require multiple cleanings (and subsequently multiple different flow changes) to "learn" the function. It also enables a comparison between the qualities of multiple cleanings.

[0059] According to a particularly advantageous third embodiment of the method (hereinafter referred to as "method 3"), value ranges are defined for the flow, which are respectively assigned to the values ​​of the second variable. Advantageously, the assignment between the values ​​of the second variable and the flow is determined or "learned" in a time interval after the initial commissioning of the heat exchanger or after cleaning of the heat exchanger. Optionally, the transitions between the values ​​of the second variable can be filtered at the range boundaries, so that they do not change strongly. It is also possible to interpolate between different learning points instead of quantizing in order to create a "smoother" transition.

[0060] The time intervals for defining function- or area-specific value assignments depend on the speed of the fouling process and can, for example, be between a few hours (in the case of a rapid fouling process, which would, for example, result in weekly cleaning of the heat exchanger) and between a few days (in the case of a slow fouling process, which would, for example, result in monthly cleaning of the heat exchanger).

[0061] Combinations and extensions of the above three methods are also possible. For example, as long as a flow change occurs, method 1 can be used, and the degree of mutation and compensation can be considered as new learning points in methods 2 and 3. Therefore, the learning point can also be in a dirty state.

[0062] According to another advantageous design 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, in a first step, a characteristic curve of the mathematical derivative of the first variable is obtained according to the flow rate of the medium, and in a second step, the characteristic curve obtained in the first step is integrated with respect to the flow rate of the medium.

[0063] This method exploits the fact that the variables characterizing 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 estimate this relationship directly. There is therefore the problem of estimating the characteristic curve (static relationship) between the two variables. In addition to the static relationship, additive trends can also affect the dependent variable.

[0064] The basic idea to solve this problem is to estimate the derivative of the first variable according to the flow rate (e.g. (dl / k) / dF)), from which the fouling can be calculated. The integration 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 rate need to be compensated.

[0065] In another 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 derived, wherein, in order to derive the characteristic curves for the two media in a first step, characteristic curves of the mathematical derivatives of the first variable are derived respectively according to the flow rates of the corresponding media and in a second step the characteristic curves obtained in the first step are integrated again with respect to the flow rates of the corresponding media.

[0066] This method is particularly advantageous when the flow rates of both media change simultaneously. In this case, two characteristic curves (static relationships) are therefore estimated respectively between the two variables. In this case, in addition to the static relationship, additive trends also influence the dependent variable. Applied to heat exchangers, the influence of the two characteristic curves of the second variable is superimposed depending on the flow rates of the respective media.

[0067] The last two embodiments of the method have the advantage that they are independent of the characteristic curve after learning the cleaning, since the effects of dirt are largely compensated by the formation of the derivative.

[0068] The device according to the present invention is used to implement the method according to the present invention, and the device comprises

[0069] - means for receiving measured values ​​of the heat exchanger or variables derived therefrom and

[0070] - an evaluation device, which is designed to derive a value for a variable characterizing fouling from measured values ​​or derived variables from values ​​of a first variable influenced by fouling and values ​​of a second variable, wherein a change in the flow rate of the first medium and / or the second medium through the heat exchanger causes a change in the first variable which is at least partially compensated by the second variable.

[0071] The first variable can be the 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:

[0072] - the temperature of the first medium and the second medium at the inlet and outlet of the heat exchanger, and

[0073] - the flow rates of the first medium and the second medium through the heat exchanger, and material properties of the first medium and the second medium and structural properties of the heat exchanger are not used in deriving the first and second variables.

[0074] However, the first variable can also be the flow resistance, and the first variable and the second variable are composed of the following measured variables:

[0075] - the pressures of the first medium and the second medium at the inlet and outlet of the heat exchanger, and

[0076] - the flow rates of the first medium and the second medium through the heat exchanger, and material properties of the first medium and the second medium and structural properties of the heat exchanger are not used in deriving the first and second variables.

[0077] A “derived variable” can be, for example, a statistical variable such as a mean value, a minimum value, a maximum value, etc. of measured values.

[0078] The computer program according to the invention comprises instructions which, when the program is run on a computer, cause the computer to execute the method according to the invention as described above.

[0079] The corresponding computer program product comprises a storage medium on which instructions are stored. When the program is executed on a computer, the instructions cause the computer to execute the method according to the present invention described above. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] The present invention and other advantageous embodiments of the present invention are explained in more detail below based on the embodiments in the accompanying drawings; wherein:

[0081] Figure 1 A block diagram showing a heat exchanger and an apparatus for detecting fouling in the heat exchanger,

[0082] Figure 2 shows the time curve of the normalized k value for an industrial heat exchanger according to the prior art,

[0083] Figure 3 shows the principle time curve of the fouling resistance without flow change in the calculation according to method 1 of the invention,

[0084] Figure 4 shows the principle time curve of the fouling resistance with a flow rate change in the calculation according to method 1 of the invention,

[0085] Figure 5 It is shown that in the calculation according to the method 1 of the present invention, Figure 1 Time curve of the 1 / k value of an industrial heat exchanger,

[0086] Figure 6 Shows the use of Figure 2 Application of linear regression to an example of an industrial heat exchanger,

[0087] Figure 7 It is shown that in the calculation according to the method 2 of the present invention Figure 2 The fouling resistance R of industrial heat exchangers f The time curve of

[0088] Figure 8 The calculation method 3 according to the present invention is shown in FIG. Figure 2 The fouling resistance R of industrial heat exchangers f The time curve of

[0089] Fig. 9 The calculation method 4 according to the present invention is shown in FIG. Figure 2 Time curve of the correction variable X of an industrial heat exchanger,

[0090] Fig.10 shows a time curve of the flow rate of the service medium and the product medium of a fouled industrial heat exchanger for determining the flow rate according to another embodiment of the present invention,

[0091] Fig.11 Shown according to Fig.10 Time curves of the flow-dependent temperatures of the service and product media,

[0092] Fig.12 Shows the characterization according to Fig.10 and Fig.11 The time curve of the fouling variable of flow rate and temperature obtained according to method 5 of the present invention,

[0093] Fig.13 shows a time curve of the flow rate of the service medium and the product medium of an industrial heat exchanger for detecting fouling according to another embodiment of the present invention,

[0094] Fig.14 Shown according to Fig.13 Time curves of the flow-dependent temperatures of the service and product media,

[0095] Fig.15 Shows the characterization according to Fig.13 and Fig.14 The time curve of the fouling variable of flow rate and temperature obtained according to method 6 of the present invention,

[0096] Fig.16 A block diagram of a heat exchanger and a cloud-based device for deriving fouling in the heat exchanger is shown. DETAILED DESCRIPTION

[0097] Figure 1 By way of example and in a simplified diagram, a heat exchanger 1 for transferring heat or cold from a service medium S to a product medium P is shown. The heat exchanger 1 is shown as a countercurrent heat exchanger, but other designs of heat exchangers are also possible. The product medium P flows through the 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,Ein The flow rate is 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 of the product medium P leaving the heat exchanger 1. P,Aus .

[0098] The product medium P is heated or cooled by means of a service medium S which is supplied to the heat exchanger 1 from a heating or cooling agent supply. In the flow direction upstream of the heat exchanger 1, the flow rate F of the working medium S (or flow rate or volume flow) and its temperature T S,Ein Before entering the heat exchanger, it 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 .

[0099] In order to monitor the fouling of the heat exchanger 1, the flow rate F of the product medium P is measured. P and the temperature measurement value T P,Ein , TP,Aus and the flow measurement value Fs and temperature measurement value T of the service medium S S,Ein , T S,Aus is transmitted to the device 10. When a single process variable of the product medium P or the 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 they can be assumed to be constant and there is no need to measure them.

[0100] Heat flow for product and service sides and

[0101]

[0102] and

[0103]

[0104] in,

[0105] C P,P is the heat capacity of the product medium,

[0106] C P,S is the heat capacity of the serving medium,

[0107] ρ P is the density of the product medium,

[0108] ρ S is the density of the serving medium.

[0109] Ignoring losses, all the heat released by the service medium S is transferred to the product medium P, so the two heat flows are equal

[0110] Alternatively, the heat flow can also be calculated using the following formula, which results from the mechanical design of the heat exchanger:

[0111]

[0112] This applies to:

[0113] k: heat transfer coefficient (W / m 2 K)

[0114] A: Available area for heat exchange (m 2 )

[0115] ΔT m : Mean logarithmic temperature difference

[0116] Heat flow.

[0117] Average logarithmic temperature difference ΔT mLimited to

[0118]

[0119] Where, ΔT A Represents the temperature difference on the inlet side (from the perspective of the product medium), ΔT B Represents the temperature difference on the outlet side.

[0120] The transferred heat flow can therefore be calculated in three ways, such as:

[0121] a) Heat flow from medium 1

[0122]

[0123] b) Heat flow through heat exchanger 1

[0124]

[0125] c) Heat flow from medium 2

[0126]

[0127] Follow from this:

[0128]

[0129] In general, it is now assumed that the fouling resistance is independent of the operating point. It can be calculated based on the current heat transfer resistance 1 / k ist The heat transfer resistance 1 / k obtained in the clean state soll The difference between them is obtained and the current dirt resistance is calculated.

[0130]

[0131]

[0132] Therefore, the k value can be calculated using the following formula

[0133]

[0134] In the case of a countercurrent heat exchanger, ΔT A =T P,Ein -T S，Aus and ΔT B =T P，Aus -T S,Ein .

[0135] If A, C P,P , C P,S , ρ P and ρ SIf the value of is considered as a constant, the relative value of k can therefore only be calculated with the aid of the temperature measurements on the inlet and outlet sides and the flow rates of the two media.

[0136] Figure 2 A typical curve of the 1 / k value over time t for an industrial heat exchanger is shown by way of example. For simplicity, the k value k0 present at time t0=0 is assumed, and Figure 2 The value 1 / k' is shown in relation to the initial value k0. Here, the vertical line shows the cleaning time. Here, a drop in 1 / k' caused by 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 assess the fouling resistance.

[0137] As has been demonstrated, the fouling resistance can be determined more precisely by also taking into account flow changes in the product and / or service medium in the evaluation.

[0138] When heat is transferred from the first medium to the second medium through the wall, the k value is theoretically composed of:

[0139]

[0140] or

[0141]

[0142] in,

[0143] R f :Dirt resistance(m 2 K / W)

[0144] S W :Wall thickness(m)

[0145] λ W : Thermal conductivity of the wall (W / mK)

[0146] α1: Thermal conductivity from the first medium to the wall (W / m 2 K)

[0147] α2: Thermal conductivity from the second medium to the wall (W / m 2 K)

[0148] Changes in flow rate and therefore changes in flow type or within flow type result in a heat transfer coefficient α 1，2 changes.

[0149] use

[0150]

[0151] get

[0152] 1 / k=X+Rf ..

[0153] Here,

[0154] R f : Parameters that characterize fouling,

[0155] 1 / k: the first parameter

[0156] X: The second parameter that is not affected by dirt.

[0157] 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.

[0158] According to the invention, changes in the first variable (here the calculated k value) caused by changes in the flow rate are at least partially compensated by means of the second variable (here the value of the variable X).

[0159] according to Figures 3 to 10 , now show three methods or ways of how to consider traffic:

[0160] Method 1

[0161] In method 1, the value of X is adjusted for each sudden flow change. Here, the following assumptions are made:

[0162] - Wall thickness and its thermal conductivity (S W / λ W = constant) does not change during operation,

[0163] - the properties of the medium do not change or do not change significantly,

[0164] _In normal operation, the fouling resistance will not decrease or increase significantly without special reasons (such as cleaning).

[0165] In the learning phase after cleaning, the initial value of X is learned:

[0166] During a certain time interval after cleaning, it can be assumed that the fouling resistance R f =0.

[0167] In this range, 1 / α1, 1 / α2 and S are learned W / λ W The value of (summarized in value X). Using R f = 0 and X = 1 / α1 + 1 / α2 + S W / λ W , X0 can now be determined for the initial interval (or after a cleaning interval) using the previously calculated k value k0. X0=1 / k0 applies here.

[0168] Case 1: Traffic remains unchanged

[0169] In this case, the value of α does not change either, i.e. X remains constant. Therefore, any changes in the value of 1 / k can be attributed to fouling. Therefore, the formula R can be used f =1 / kX to calculate the dirt resistance. Figure 3 1 / k, X and R are shown as examples. f changes over time t. The value of X is constant and results in 1 / k being related to R f The constant difference between .

[0170] Case 2: Traffic changes at time t0

[0171] At time t0, the dirt resistance R f (t0) is briefly kept constant and, for example, is used to neu =1 / kR f (t0) Calculate X neu .

[0172] For 1 / k, we can now use the average value of the interval from t0 to t0+x. Or, X neu It can also be calculated as follows: X neu =X alt -(1 / k alt -1 / k neu ).

[0173] 1 / kalt and 1 / k neu represents the average 1 / k value in the interval before or after the flow change. The two methods show almost the same results.

[0174] In the further process, R f =1 / k neu -X neu Calculate the fouling resistance.

[0175] Figure 4 1 / k, X and R are shown as examples f As shown in the figure, this method makes the fouling resistance R f The jump in flow at time t0 continues steadily, rather than causing a level jump.

[0176] If we now use this method to calculate Figure 2 1 / k value, X and R of industrial heat exchangers f and plotted at time t, we get Figure 5 The curve shown in . Only relative values ​​are shown here. Here again, the vertical line shows the cleaning time. For simplification, the initial values ​​1 / k0 and X0 existing at time t0=0 are obtained, Figure 5The values ​​1 / k' and X' are shown in relation to these initial values.

[0177] When calculating the 1 / k′ value, a horizontal jump occurs again at the position marked by the arrow, but in the calculation of the relative fouling resistance R f The change in the value of X′ largely compensates for the horizontal jump.

[0178] The method is particularly suitable for heat exchanger operation with operating phases in which the flow is piecewise constant and then changes suddenly. Constant flow changes can only be processed piecewise. However, continuous adjustment can then be made by interpolation between the piecewise changes. Advantageously, changes in the medium after cleaning have no influence on the results and no learning data is required.

[0179] Method 2

[0180] As mentioned above, it can be roughly assumed that the dirt resistance after cleaning is ≈0. Here, X(F)=1 / k applies. This initial interval is now used to find the relationship between X and F(flow) in the form of a function f for different flow rates. Even if the flow rate changes within this interval. For this purpose, regression can be used, in particular linear regression, or even better nonlinear regression. Using the result of this interpolation, the corresponding X value can be calculated for any flow rate.

[0181] Figure 6 The example shows the use of Figure 2 In order to create a linear regression and thus define the function f, a number of average flow values ​​F on the product side after cleaning the heat exchanger are taken. P Get the relevant X value (in Figure 6 Here, the flow variation within this interval is taken into account. Therefore, the following applies: X = f (F p ), where function f comes from F p and linear regression of X.

[0182] If we now use this method to calculate Figure 2 Relative fouling resistance R of industrial heat exchangers f , and plotted together with the value X obtained by linear regression at time t, we obtain Figure 7 For simplicity, the initial value X0 at time t0=0 is also obtained here. Figure 7 The value X' is shown relative to this initial value.

[0183] As shown in the figure, this method also shows satisfactory results in many ranges.

[0184] Here again, the vertical lines show the cleaning times.

[0185] For example, the function f can be obtained by linear regression of the measured value of the flow rate in the time interval after initial commissioning or cleaning and the associated value of the second measurement (when only one of the two media changes, see Figure 6 ) or by 3D regression. This method can also take into account constant variations and is relatively resistant to deviations in normal operation, but it also requires multiple cleanings (and then multiple different flow rates) to "learn" the function f. It also makes it possible to compare the quality of multiple cleanings.

[0186] Method 3

[0187] The X-values ​​learned during initial commissioning or after cleaning can be used to form a value range for the flow rate. Within such a range, each flow rate value is assigned a learned X-value. This makes it possible to filter this X-value slightly over time so that the transition between two X-values ​​does not become too abrupt.

[0188] If we now use this method to calculate the Figure 2 Relative fouling resistance R of industrial heat exchangers f and X and plotted against time t, the result is Figure 8 For simplicity, the initial values ​​1 / k0 and X0 existing at time t0 = 0 are obtained, and Figure 5 The values ​​1 / k' and X' are shown in relation to these initial values. The calculation is based on the heat on the product side. Here again, the vertical lines show the cleaning times. As the figure shows, this method also shows satisfactory results in many respects.

[0189] The assignment of the value of the second variable to the flow rate is advantageously derived over a time interval after the heat exchanger has been initially commissioned 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. It is also possible to interpolate between different learning points, rather than quantizing, to produce a "smoother" transition.

[0190] One optimization possibility is the so-called "method of interpolation points". This method also represents a possibility, namely how the relationship between the flow rate and the reference value can be analyzed. For this purpose, it is necessary to briefly explain how the characteristic curve of the α value can be regarded as dependent on the flow rate. In this case, the boundary conditions of the subsequent characteristic curve or function can already be found, such as the monotonicity of the curve. The first value for the analysis is obtained or determined in the clean state after cleaning.

[0191] New values ​​are added at runtime. These are weighted with the previous values ​​in a certain area and the feature is updated. The weight factor can be the number of points in an area so far or the current dirt resistance.

[0192] In addition to these three methods, combinations and extensions can also be used.

[0193] Combination of Methods 1 and 2

[0194] This combination enables to first derive the fouling resistance or X-value of the heat exchanger using method 1, and then to calculate the X-value in the medium term 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, only method 2 may be sufficient.

[0195] Method 4

[0196] With the help of method 1, in case of a flow break, the X-value change and the flow before and after the change are known. On the one hand, it is now possible to calculate the level of the flow mutation (ΔF1) and the X-value (ΔX1). Thus, it is possible to calculate the impact relative to the previous X-value for each future (also constant) flow change. If there are multiple mutations available, a linear regression between ΔF1 and ΔX1 is used. For this purpose, Fig. 9 The assignment of the value of X to the flow F at time t is shown.

[0197] To calculate the final X value, it is possible to interpolate between different sampling points to avoid abrupt curves (see Fig. 9 Therefore, the combination of method 1 and method 4 provides particular advantages.

[0198] Method 5

[0199] According to a design 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 obtained, wherein, in order to obtain the characteristic curve, in a first step, a characteristic curve of the mathematical derivative of the first variable is obtained according to the flow rate of the medium, 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.

[0200] This method exploits the fact that the variable characterizing fouling follows a slow and reasonably stable trend. The relationship between the first variable and the flow is therefore constantly changing and cannot be estimated directly. There is therefore the problem of estimating the characteristic curve (static relationship) between the two variables. Here, in addition to the static relationship, an additive trend also affects the dependent variable.

[0201] The basic idea to solve this problem is to estimate the derivative of the first variable according to the flow rate (e.g. (dl / k) / dF)), from which the fouling can be calculated. The integration 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 rate need to be compensated.

[0202] Assume that the inverse of the k value is composed of the sum of the fouling resistance and X

[0203]

[0204] where X combines all other thermal resistances. The derivative with respect to time gives

[0205]

[0206] in,

[0207] Therefore, it is applicable to

[0208]

[0209] For Φ1(t)≠Φ2(t)

[0210] At X0, F0 position, for a unique but unknown relationship Does not depend on Φ(t) and κ(t).

[0211]

[0212] Therefore, it applies to all Φ1(t)≠Φ2(t).

[0213] Therefore, it is necessary to calculate for two different flow changes Φ1(t)≠Φ2(t) The weighted difference of the changes.

[0214] In order to determine the characteristic curve, it is recommended to collect all the Fs with data, and for pairs of Φ1(t)≠Φ2(t) Then the desired characteristic curve is generated by integrating the integral of the derivative characteristic curve.

[0215] Advantageously, the absolute value is irrelevant here, so that no initial value has to be taken into account in the integration.

[0216] Due to the simpler parameterization, the modeling is only performed qualitatively, i.e. 1 / k is determined without exact material data or heat exchanger characteristics. Therefore, only relative changes in the k value can be calculated. However, the determined characteristic curve can be used accurately for relative changes in the flow rate.

[0217] A feature of this method is that the actual task of determining fouling is initially unnoticed and, in order to estimate the XF characteristic, the influence of fouling can be compensated. Only then can the fouling be derived using the 1 / k characteristic curve. Advantageously, the characteristic curve can be easily implemented so that nothing hinders the online evaluation.

[0218] Figures 10 to 12 A simulation of an industrial heat exchanger with varying flow rates is shown.

[0219] Here, Fig.10 shows the flow rate F of the product medium through the heat exchanger P and the flow rate F of the service medium S Time curve of the (simulated) measured values.

[0220] Fig.11 shows the temperature T of the product medium at the heat exchanger inlet P,Ein and the temperature of the product medium at the heat exchanger outlet T P,Aus In addition, the temperature T of the service medium at the heat exchanger inlet is also shown. S,Ein and the temperature of the service medium at the heat exchanger outlet T S,Aus The (simulated) measured value of .

[0221] Fig.12 shows 1 / k and fouling resistance R f The relative value of the correlation calculation.

[0222] The 1 / k value shows a significant dependence on the flow rate change, regardless of 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, no reliable conclusions can be drawn from the 1 / k value alone.

[0223] By using the characteristic curve and compensating the associated flow dependency, an estimated fouling curve is obtained (shown offset upwards for better visibility). Apart from the measurement noise, a linear trend can be seen. The fouling can thus be derived very reliably. It should be noted here that at the beginning, the changes in the two flows are independent of each other, so that the two flow characteristics can also be well estimated sequentially and independently of each other.

[0224] Method 6

[0225] According to a refinement 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 derived. In this case, in order to derive the characteristic curves for the two media in a first step, characteristic curves of the mathematical derivative of the first variable are derived in each case as a function of the flow rate of the respective medium, and in a second step, the characteristic curves obtained in the first step are integrated again with respect to the flow rate of the respective medium.

[0226] This method is particularly advantageous when the flow rates of both media change simultaneously. Therefore, two characteristic curves (static relationships) are estimated between the two variables in question. In addition to the static relationship, additive trends also influence the dependent variable. Applied to heat exchangers, the influence of the two characteristic curves of the second variable is superimposed depending on the flow rates of the respective media.

[0227] In the case of a heat exchanger, the two characteristic curves X P =f P (F P ) and X S =f S (F S ) has an additive effect on the 1 / k value, where

[0228]

[0229] The time derivative of 1 / k gives

[0230]

[0231] Where X = X P +X S .

[0232] Now find the derivative characteristic curve n p Interpolation point (dx Pi , F Pi ) and derivative characteristic curve n S Interpolation point (dx Si , F Si ).

[0233] To do this, for each time point t, it is applicable to or

[0234] There are three unknown quantities (dx Pi , dx Si , m) produces:

[0235]

[0236] n D The equations can then be summarized in a matrix expression, where the corresponding flows must be noted at the interpolation points. Therefore, it applies

[0237] Ab=c

[0238]

[0239] c=[κ(t1)…κ(t m )]

[0240]

[0241] For better understanding, a row of A is given. At the appropriate point in time, F P ≈F P5 And F S ≈F S7, where n P =10 and n S = 20. Then the rows of A correspond to

[0242]

[0243] Among them, there are non-zero entries in the 5th and 17th columns (=10+7) and the last column.

[0244] If the existing measurements now cover the entire flow range on the service side and the product side, there is at least one data point in each column of A. Assuming A has maximum level, the system of equations can be solved for the unknowns in vector b, for example by means of a pseudo-inverse.

[0245] Then two derivative characteristic curves can be generated again from the vector b,

[0246] And by integrating it, we get the characteristic curve X P =f P (F P ) and X S =f S (F S ).

[0247] If there are two characteristic curves, then And by using the characteristic curve

[0248] To calculate the dirt method to estimate the dirt.

[0249] As has already been briefly outlined, due to the integration, the absolute value of the characteristic curve is unknown. Due to the simpler parameterization, modeling can only be performed qualitatively anyway, i.e. 1 / k is determined without exact material data or heat exchanger characteristics. Therefore, only relative changes in the k value can be calculated. However, the determined characteristic curve can be used accurately for relative changes in the flow rate.

[0250] Here, the actual task of determining the fouling is initially not taken into account, in particular the influence of the fouling is compensated in order to estimate the two XF characteristic curves. Only in this way can the fouling be determined with the aid of the 1 / k characteristic curve. Advantageously, the characteristic curve can be realized very simply so that nothing hinders the online evaluation.

[0251] Figure 13-15 A simulation of an industrial heat exchanger is shown with varying flow rates.

[0252] Fig.13 shows the flow rate F of the product medium through the heat exchanger P and the flow rate F of the service medium S Time curve of the (simulated) measured values.

[0253] Fig.14 shows the temperature T of the product medium at the heat exchanger inlet P,Ein and the temperature of the product medium at the heat exchanger outlet T P,Aus In addition, the temperature T of the service medium at the heat exchanger inlet is also shown. S,Ein and the temperature of the service medium at the heat exchanger outlet T S,Aus The (simulated) measured value of .

[0254] Fig.15 The relative values ​​of 1 / k and fouling resistance Rf calculated therefrom are shown.

[0255] The 1 / k value shows a significant dependence on the flow rate variation, regardless of which side of the heat exchanger. In the idealized data, the superimposed trend can still be seen. However, depending on the severity of the fouling, no reliable conclusions can be drawn from the 1 / k value alone. An estimated fouling curve R is obtained by using the characteristic curve and compensating for the relevant flow rate dependence f Apart from the measurement noise, a linear trend can be seen. Therefore, even if both flow rates change simultaneously, fouling can be determined very reliably.

[0256] In principle, the same approach can also be applied to take into account the pressure difference. The flow resistance also increases with fouling, but also depends on the flow rate.

[0257] These methods are able to reliably quantify the fouling resistance even if the flow rates vary from one heat exchanger to another. Knowledge of the material properties or the structural characteristics of the heat exchanger is not required here. These methods are purely data-based. So far, only the pure k value has been used as an indicator for fouling. These methods use this variable and simultaneously include the influence of the flow dynamics of the two media on the final result.

[0258] Furthermore, laborious heat exchanger models produced by experts are not necessary. All results and intermediate steps can also be displayed in 2D or 3D characteristic curves. Unintuitive multidimensional characteristic curves are not required for the calculation. Furthermore, the measurement of F P 、F S 、T P,Ein 、T P,Aus 、T S,Ein 、T S,Aus If the flow changes of the two media are to be compensated, the only thing that can be omitted here is of course the temperature measurement.

[0259] Using these methods, the results obtained when deriving fouling, for example for industrial heat exchangers, are significantly better than those obtained with conventional calculations. The results can therefore help plant operators to better assess the fouling resistance. Advantageously, these methods cannot be applied to heat balances or to take into account pressure differences and therefore flow resistance.

[0260] 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 by a service provider as "software as a service".

[0261] exist Figure 1 Schematically shown in FIG. 1 is a device 10 according to the present invention for extracting dirt, the device comprising:

[0262] - for receiving the measured value T of the heat exchanger 1 P,Ein 、T P,Aus 、T S,Ein 、T S,Aus The device 20, and

[0263] An evaluation device 30 is provided for determining and outputting a value for the fouling resistance R from these measured values ​​by means of the above-described method. f Additionally or alternatively, the evaluation device can also be used as a monitoring device: it can monitor whether the resulting fouling resistance exceeds a threshold value and, if so, output a signal which, for example, indicates that cleaning is required.

[0264] To this end, the evaluation device 30 comprises a processor unit 31, a memory 32 for storing received measurement data, and a memory 33 in which a program 34 with instructions is stored, which, when one of the above methods is executed, is executed by the processor unit 31. The processor unit stores the measurement values ​​M received from the device 20 in the memory 32.

[0265] No need to detect other variables, such as A, C P,P , C P,S , ρ P and ρ S In contrast, the method according to the invention assumes that these are unknown. Arbitrary constants can be assumed, which will lead to incorrect k values ​​from an absolute point of view, but ultimately the relative change of this k value is decisive for the operation and success of the method.

[0266] Figure 1 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 the process plant.

[0267] On the contrary, Fig.16The device 100 for determining fouling shown in FIG can be provided by a local or remote computer system (“cloud”), for example, in order to provide the determination of fouling by a service provider as “software as a service”. In this case, the receiving device 20 is located on-site in the process plant of the heat exchanger 1, and 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.

[0268] The evaluation device 30 comprises a processor unit 31 , a memory 32 for storing received measurement data and a memory 33 in which a program 34 with instructions is stored, which, when executed, causes one of the above-described methods to be performed by the processor unit 31 .

[0269] 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, stores further input variables received via a separate interface 37. The fouling resistance R determined by the program 34 is output via the interface 38. f Values ​​and / or signals 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.

[0270] By detecting the measured values ​​and calculating the fouling resistance in almost real time, continuous data-based fouling analysis and fouling monitoring can be performed as the system or heat exchanger is running. However, offline fouling analysis with a time offset relative to the actual operation of the facility is also feasible.

Claims

1. A method for detecting fouling in a heat exchanger (1) in which heat is transferred from a first medium to a second medium, It is characterized in that The value of a variable characterizing the fouling is derived from the value of a first variable and a value of a second variable affected by the fouling, wherein a change in the first variable due to a change in the flow rate of the first medium and / or the second medium through the heat exchanger (1) is at least partially compensated by the second variable, wherein the first variable is a heat transfer resistance or a heat transfer capacity or a heat transfer coefficient, and wherein the first variable and the second variable are derived from measured values ​​of a plurality of measured variables: - the temperature of the first medium and the second medium at the inlet and outlet of the heat exchanger (1), and - the flow rates of the first medium and the second medium through the heat exchanger (1), Furthermore, when deriving the first variable and the second variable, the material properties of the first medium and the second medium and the structural properties of the heat exchanger (1) are not used.

2. The method according to claim 1, wherein: At the time point when the flow rate changes, the value of the second variable changes, so that the value of the variable characterizing the fouling remains constant.

3. The method according to claim 2, wherein: After initial commissioning and respectively after cleaning of the heat exchanger (1), an initial value of the first variable is determined and the value of the second variable is set to an initial value corresponding to the initial value of the first variable.

4. The method according to claim 1, wherein: A function is defined which assigns a value of the second variable to each value of the flow rate of the first medium and / or the second medium.

5. The method according to claim 4, wherein: The function is determined at time intervals after initial commissioning or after defouling the heat exchanger (1).

6. The method according to claim 4, wherein: The function is formed by regression of the measured values ​​of the flow rate and the associated values ​​of the second variable in a time interval.

7. The method according to claim 6, wherein: The regression is either a linear regression or a 3D regression.

8. The method according to claim 1, wherein: Value ranges are defined for the flow rate, which are respectively associated with values ​​of the second variable.

9. The method according to claim 8, wherein: The distribution of the value of the second variable to the flow rate is determined within a time interval after initial commissioning or after cleaning the heat exchanger (1) from fouling.

10. The method according to claim 1, wherein: 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, a characteristic curve of a mathematical derivative of the first variable is obtained according to the flow rate of the medium in a first step, 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.

11. The method according to claim 1, wherein: At the same time, a first characteristic curve for the relationship between the second variable and the flow rate of the first medium and a second characteristic curve for the relationship between the second variable and the flow rate of the second medium are obtained, wherein, in order to obtain the characteristic curve for each of the two media in the first step, a characteristic curve of the mathematical derivative of the first variable is obtained according to the flow rate of the corresponding medium, and in the second step, the characteristic curve obtained in the first step is integrated with respect to the flow rate of the corresponding medium.

12. The method according to claim 1, wherein: The variable that characterizes the fouling is the resistance to heat transfer.

13. The method according to claim 1, wherein: Only the relative changes of the variable characterizing the fouling, the first variable and the second variable are derived.

14. A method for detecting fouling in a heat exchanger (1) in which heat is transferred from a first medium to a second medium, It is characterized in that The value of a variable characterizing the fouling is derived from the value of a first variable and a value of a second variable influenced by the fouling, wherein a change in the first variable due to a change in the flow rate of the first medium and / or the second medium through the heat exchanger (1) is at least partially compensated by the second variable, wherein the first variable is a flow resistance, and wherein the first variable and the second variable are derived from measured values ​​of a plurality of measured variables: - the pressures of the first medium and the second medium at the inlet and outlet of the heat exchanger (1), and - the flow rates of the first medium and the second medium through the heat exchanger (1), Furthermore, when deriving the first variable and the second variable, the material properties of the first medium and the second medium and the structural properties of the heat exchanger (1) are not used.

15. The method according to claim 14, wherein: At the time point when the flow rate changes, the value of the second variable changes, so that the value of the variable characterizing the fouling remains constant.

16. The method according to claim 15, wherein: After initial commissioning and respectively after cleaning of the heat exchanger (1), an initial value of the first variable is determined and the value of the second variable is set to an initial value corresponding to the initial value of the first variable.

17. The method according to claim 14, wherein: A function is defined which assigns a value of the second variable to each value of the flow rate of the first medium and / or the second medium.

18. The method according to claim 17, wherein: The function is determined at time intervals after initial commissioning or after defouling the heat exchanger (1).

19. The method according to claim 17, wherein: The function is formed by regression of the measured values ​​of the flow rate and the associated values ​​of the second variable in a time interval.

20. The method according to claim 19, wherein: The regression is either a linear regression or a 3D regression.

21. The method according to claim 14, wherein: Value ranges are defined for the flow rate, which are respectively associated with values ​​of the second variable.

22. The method according to claim 21, wherein: The distribution of the value of the second variable to the flow rate is determined within a time interval after initial commissioning or after cleaning the heat exchanger (1) from fouling.

23. The method according to claim 14, wherein: 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, a characteristic curve of a mathematical derivative of the first variable is obtained according to the flow rate of the medium in a first step, 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.

24. The method according to claim 14, wherein: At the same time, a first characteristic curve for the relationship between the second variable and the flow rate of the first medium and a second characteristic curve for the relationship between the second variable and the flow rate of the second medium are obtained, wherein, in order to obtain the characteristic curve for each of the two media in the first step, a characteristic curve of the mathematical derivative of the first variable is obtained according to the flow rate of the corresponding medium, and in the second step, the characteristic curve obtained in the first step is integrated with respect to the flow rate of the corresponding medium.

25. The method of claim 14, wherein: The variable that characterizes the fouling is the resistance to heat transfer.

26. The method of claim 14, wherein: Only the relative changes of the variable characterizing the fouling, the first variable and the second variable are derived.

27. A device for performing the method according to any one of claims 1 to 13, the device comprising - means for receiving measured values ​​of the heat exchanger (1) or variables derived from said measured values, and - an evaluation device (30) which is configured to derive, from the measured value or the derived variable, a value of a variable characterizing the fouling from the value of a first variable and a value of a second variable influenced by the fouling, wherein: The change of the first variable caused by the change of the flow rate of the first medium and / or the second medium through the heat exchanger (1) is at least partially compensated by the second variable, and wherein the first variable and the second variable are obtained from the measured values ​​of the following multiple measured variables: - the temperature of the first medium and the second medium at the inlet and outlet of the heat exchanger (1), and - the flow rates of the first medium and the second medium through the heat exchanger (1), Furthermore, the material properties of the first medium and the second medium and the structural properties of the heat exchanger (1) are not used when deriving the first variable and the second variable.

28. An apparatus for performing the method according to any one of claims 14 to 26, the apparatus comprising: - means for receiving measured values ​​of the heat exchanger (1) or variables derived from said measured values, and - an evaluation device (30) which is arranged to derive, from the measured values ​​or the derived variables, a value of a variable characterizing the fouling from the value of a first variable and a value of a second variable influenced by the fouling, wherein a change in the first variable caused by a change in the flow rate of the first medium and / or the second medium through the heat exchanger (1) is at least partially compensated by the second variable, wherein the first variable is a flow resistance, and wherein the first variable and the second variable are derived from measured values ​​of a plurality of measured variables: - the pressures of the first medium and the second medium at the inlet and outlet of the heat exchanger (1), and - the flow rates of the first medium and the second medium through the heat exchanger (1), Furthermore, the material properties of the first medium and the second medium and the structural properties of the heat exchanger (1) are not used when deriving the first variable and the second variable.

29. A computer program product having a computer program, the computer program comprising instructions which, when executed on a computer, cause the computer to perform the method according to any one of claims 1 to 26.

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