US20230122608A1 - Method and Device for Determining Fouling in a Heat Exchanger - Google Patents

Abstract

A device and method for increasing accuracy in the determination of fouling in a heat exchanger in which heat is transferred from a first medium to a second medium, wherein a value for a variable characterizing the fouling is determined from a value for a first variable influenced by the fouling and a value for a second variable, where the second variable compensates for a change in the first variable caused by a change in flow of the first and/or second mediums through the heat exchanger, where the first variable can be a thermal transmission resistance, a thermal transmittance or a thermal transmission coefficient, where the first and second variable are determined from values measured totemperaturesr and flows of the first and second mediums without using material properties of the first and second mediums and structural properties of the heat exchanger when determining the first and second variables.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS
• This is a U.S. national stage of application No. PCT/EP2021/055563 filed 5 Mar. 2021. Priority is claimed on European Application No. 20161837.8 filed 9 Mar. 2010, the content of which is incorporated herein by reference in its entirety.
BACKGROUND OF THE INVENTION 1. Field of the Invention
• The invention relates to a method and a device for determining fouling in a heat exchanger.
2. Description of the Related Art
• Heat exchangers are technical apparatuses used to heat or cool a medium. To this end, heat is transferred from a warmer first medium to a cooler second medium. Depending on their construction, heat exchangers differ in their functional principle. The most frequent constructions are classified into one of three function groups: direct current, reverse current or cross-flow heat exchangers.
• The medium to be heated or cooled is frequently also referred to as “product medium” and the heating or cooling medium is frequently also referred to as “service medium”. The service medium can be heating steam or cooling water, for example. The service medium normally flows either through an arrangement of lines that is arranged inside the product medium, or flows around an arrangement of lines through which the product medium flows.
• The first and the second medium are conducted through the heat exchanger, where both the media normally flow past one another, separated by a wall, and thereby the heat of the warmer medium is dissipated to the colder medium through the wall.
• A key problem with heat exchangers is represented by what is known as “fouling”, in which deposits or coatings form on the inner walls of the heat exchanger. The reasons why such deposits occur may be of a physical, chemical or biological nature. In many cases, it is not possible to prevent them, for example, because of the given basic product-related conditions. The coatings impede the thermal transmission between the media and thereby reduce the efficiency of the heat exchanger. Once a particular degree of contamination is reached, chemical or mechanical cleaning is necessary, or where appropriate the heat exchanger may even need to be replaced. This problem is particularly prevalent in the case of large industrial heat exchangers that are employed in process engineering plants (i.e., for example, plants in the chemical, petrochemical, glass, paper, metal production or cement industries) or in power plants, where they are normally designed for a thermal transmission capacity of more than 100 kW.
• From the outside, it is very difficult to determine the extent of the contamination in the interior of the heat exchanger, so that it is not possible to clean or replace the heat exchanger based on need. A temperature control circuit can to a certain extent compensate for the effects of the contamination, so that the contamination is not immediately apparent from the outlet temperature of the product medium. Because of this lack of knowledge, it is frequently not possible to clean or replace the heat exchanger based on need.
• Until now, heat exchangers affected by contamination have therefore been cleaned or replaced at regular intervals, i.e., without knowing the actual state of contamination. In this procedure, the maintenance intervals cannot be adjusted as a function of different degrees of contamination. Consequently, the heat exchanger may, for example, be cleaned or replaced too early, even though only minor deposits are present up to this point. Although this would ensure the efficient operation of the heat exchanger, it would however be uneconomical, because not only are direct costs for the maintenance work incurred, but also indirect costs because of the additional adverse effect on the ongoing operation of the plant in which the heat exchanger is employed. If corresponding measures are taken too late, excess deposits in the interior of the heat exchanger already result in a significantly reduced thermal transmission. The consequence is that for the same heat flow to be transmitted a much larger flow of the service medium is required than is the case when the heat exchanger is in a clean state. This results in an increased energy input that is expended for the provision of the service medium, i.e., heat output and pumping capacity, which likewise represents a cost factor. Furthermore, when there is a heavy formation of deposits there is also the risk that the quality of the product medium will be impaired, because specified temperatures cannot be appropriately adhered to, for example.
• EP 2 128 551 Al discloses a method for monitoring the effectiveness of a heat exchanger with respect to fouling, in which a current heat flow {dot over (Q)}_P of the product medium or {dot over (Q)}_s of the service medium is detected and compared with at least one reference heat flow {dot over (Q)}_Ref that corresponds to a predetermined degree of contamination, for example, the zero degree of contamination and a maximum permitted degree of contamination, of the heat exchanger. The respective reference heat flow {dot over (Q)}_Ref is determined as a function of the current operating point of the heat exchanger from a characteristic field previously created and stored with the help of a simulation program for different operating points, where the operating point of the heat exchanger is determined by the flows F_P, F_s of both media and their temperatures T_{P, In}, T_{S, In} on entry into the heat exchanger. By using the simulation program, the operating point dependency of the transferrable amount of heat can, for example, be precalculated at several hundred interpolation points, without having to perform correspondingly time-consuming measurements in the real plant.
• WO 2019/001683 A1 discloses a method for monitoring a heat exchanger, in which the flows, inlet temperatures and outlet temperatures of service and product medium represent process variables, at least one process variable of which is variable on the product side and the inlet temperature is fixed on the service side and the remaining process variables are variable. In order to monitor the heat exchanger without measuring the temperature on the service side, the variable process variable(s) of the product medium and the flow of the service medium are measured, and a characteristic field for the mutual dependence of the variable process variable(s) of the product medium and of the flow of the service medium is ascertained from the measured values obtained in this case in a reference state of the heat exchanger, and is stored. For the measured values obtained in a current unknown state of the heat exchanger, a distance of the measured value tuple formed from the measured values to the characteristic field is ascertained as a measurement of the deviation of the current state of the heat exchanger from the reference state.
• From Zölzer K et al. “Application of the boiler diagnosis system KEDI at Staudinger 5 power station”, VGB Kraftwerkstechnik, Essen, Germany, Vol. 75, No. 9, 1 September 1995, pages 755-762, ISSN: 0372-5715, and from DE 195 02 096 Al, US 4 390 058 A or EP 0 470 676 A2 it is known for the thermal transmission coefficient or k value to be taken into consideration when monitoring heat exchangers. The heat flow {dot over (Q)}=k·A·OT_M transferred within the heat exchanger depends on this k value, on the exchange surface A and on what is known as the logarithmic temperature difference ΔT_m driving the thermal transmission. Both the k value and the logarithmic temperature difference are each dependent on the operating point of the heat exchanger and thus on the flows F_P, F_s of the product and service medium and their temperatures T_{P, In}, T_{S, In} on entry into the heat exchanger.
• In the case of DE 195 02 096 A1, a current K value is determined for each heating surface from a calculated heat output, a logarithmic temperature difference and the size of the heating surface. By comparing the current K value with a stored reference K value Kref for the “cleanest possible state”, a cleaning state CF is calculated in accordance with the relationship CF=K/Kref. The reference values Kref are stored in a memory as a function of the load and possibly as a function of the fuel. The reference values Kref can be corrected using correction factors in accordance with certain current state variables. Thus, for example, a correction is performed in accordance with the steam velocity. However, how the reference values are obtained remains an open question.
• In the case of Zolzer, a “heating surface valency FV” is defined as a measurement for heating surface contamination. This is defined as the ratio of an actual evaluation factor factual to a base evaluation factor fbase. The actual evaluation factor factual is the ratio of a “measured” thermal transmission coefficient Kactual to a theoretical thermal transmission coefficient Ktheory. The “measured” thermal transmission coefficient Kactual is ascertained based on the media temperatures and the size of the heating surface. The theoretical thermal transmission coefficient Ktheory is determined, for instance, based on the geometry data, such as pipe dimension, width separation and/or longitudinal separation, of the heating surface. The base evaluation factor fbase is determined from an operating state deemed to be optimal with basic contamination present, for example, an acceptance test of the steam generator, and is stored. The calculation of the reference state includes a recalculation of the steam generator with the basic data stored in the system and certain current process data, such as feedwater parameters, fresh steam parameters and repeater parameters. Precise details of the process data used are not however disclosed.
• DE 10 2016 225 528 A1 discloses a method for monitoring a contamination state in a heat exchanger with the help of an additional temperature sensor, which is arranged in or on the heat exchanger wall. The temperature sensor detects an operating wall temperature of the heat exchanger. This operating wall temperature is correctively calculated and a deviation between the correctively calculated operating wall temperature and a reference wall temperature is determined. The correction of the operating wall temperature takes account of changes in measured values that occur as a result of operating conditions deviating from reference conditions, for example deviations in the fluid temperatures or in the volume flows of the fluids. Operating wall temperature and reference wall temperature are values that are measured at the same point and/or are predetermined for the same point on the heat exchanger.
• A current fouling resistance R_f can be calculated from the difference between a current thermal transmission resistance 1 / k_actual and a thermal transmission resistance 1/k_target, which was determined in the clean state of the heat exchanger:
• $R_f=\frac{1}{k_{\mathrm{actual}}}-\frac{1}{k_{\mathrm{target}}}$
• It has, however, been found that an evaluation of the fouling resistance on this basis is inaccurate. For example, changes in level of the thermal transmission resistance occur without any apparent particular reason, as would be present, for example, during cleaning or while the heat exchanger is being replaced.
SUMMARY OF THE INVENTION
• In view of the foregoing, it is therefore an object of the present invention to provide a method and device with which an even more accurate determination of fouling in a heat exchanger can occur.
• This and other objects and advantages are achieved in accordance with the invention by a , computer program, device and method in which, in order to determine fouling, a value for a variable characterizing the fouling is determined from a value for a first variable affected by the fouling and a value of a second variable, where a change in the first variable caused by a change in a property of the first and/or of the second medium, in particular of a flow of the first and/or of the second medium through the heat exchanger, is compensated for at least in part by the second variable.
• The variable characterizing the fouling is preferably a thermal transmission resistance or a thermal transmittance. However, it can also be a flow resistance, for example.
• The invention is based on the finding that changes in the level of the variable characterizing the fouling can frequently be explained by changes in the flow of the first and/or second medium. The reason for this is that, when there are changes in flow, the flow velocity and the flow type at the points in the thermal transmission can change from the first to the second medium. Depending on the flow type that then occurs (for example, laminar flow, weakly turbulent flow, or strongly turbulent flow) and flow velocity this can however also result in changes in the value of the first variable affected by the fouling. Even within one flow type, the mixing and thus the thermal transmission can change as a function of the flow velocity. For example, a turbulent flow at the edge regions also forms laminar border layers, the size and thus the effect of which thus, for example, depend on the flow or the flow velocity. For a more accurate determination of a value of the variable characterizing the fouling, these changes are therefore taken into account in accordance with the invention. To this end, a change in the first variable caused by a change in a flow of the first and/or second medium through the heat exchanger is compensated for at least in part 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 for the effect of the change in flow on the first variable. As a result, changes in level of the first variable that are calculated from measured data and that until now have been inexplicable can be very readily explained and compensated for.
• In the event of a change in flow, the invention also enables a reliable quantification of the fouling resistance for different heat exchangers. Here, no knowledge of material properties or structural properties of the heat exchanger is necessary. The invention operates purely on the basis of measured data. Instead of using only the thermal transmission resistance or the thermal transmittance (or the thermal transmission coefficient (k value)) or the flow resistance as an indicator of the fouling, the invention uses this variable and at the same time also integrates the effect of the flow dynamic of both the media on the final result.
• In accordance with the invention, it is not the heat flow but the thermal transmission resistance or the thermal transmittance (or a thermal transmission coefficient (k value)) or the flow resistance that is taken into account. As a result, the fouling resistance contained therein is of advantage regardless of the operating point.
• Furthermore, there is no requirement for a model of the heat exchanger, which would have to be laboriously prepared by an expert. All results and interim steps can furthermore be represented in 2D or 3D characteristic fields. No abstract multidimensional characteristic fields are required for the calculation.
• The invention does not require any special additional measuring instruments (for example, a temperature sensor on a heat exchanger wall), but gets by with the instrumentation normally present for heat exchangers.
• Furthermore, it is also possible to dispense with one of the measurements of flows and input/output temperatures of the media, so that not even full instrumentation is required.
• If individual process variables of the product medium or service medium, such as the inlet temperature, are determined based on given basic conditions and hence can be accepted as unchanging, they likewise do not need to be measured.
• It is not necessary to detect further variables such as material properties of both the media or structural properties of the heat exchanger and thus no provision is made for this either. On the contrary, the invention assumes that these are not known. Any constants can be assumed for this, which then when seen in absolute terms result in false values for the first variable, the second variable and the variable characterizing the fouling, but ultimately the relative changes in these variables are decisive for the functioning and the success of the method. This is also sufficient in practice in most cases.
• Using the example of an industrial heat exchanger, a significantly better result can be achieved with the invention in the determination of fouling than with a conventional calculation. The results can thus help a plant operator to obtain a significantly better evaluation of the fouling resistance. The invention can advantageously be applied not only to the heat balances but also to the consideration of the pressure differences and thus of the flow resistances.
• A particularly good or optimal compensation of the changes in flow can be achieved if the second variable is a variable unaffected by the fouling.
• The first variable affected by the fouling is, in accordance with a first alternative embodiment of the invention, a thermal transmission resistance or a thermal transmittance (or a thermal transmission coefficient, frequently also referred to as a “k value”). The thermal transmission resistance or the thermal transmittance (or the k value) can be determined particularly easily from measured values of temperatures of the first medium and second medium at an inlet and at an outlet of the heat exchanger, in each case.
• If the heat is transmitted from the first medium to the second medium through a wall, the k value is then, for example, theoretically composed as follows:
• $k=\frac{1}{\frac{1}{\alpha 1}+\frac{s_w}{{\lambda }_w}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2}+R_f}$ $\mathrm{or}$ $\frac{1}{{ }_{.}k}=\frac{1}{\alpha 1}+\frac{s_w}{{ }_{.}{\lambda }_w}+\frac{1}{\alpha 2}+R_f$
• where
• • R_f: fouling resistance (in m²K/W)
  • s_w: wall thickness (in m))
  • λ_w: thermal conductivity of the wall (in W/mK)
  • a₁: thermal transmission coefficient from the first medium to the wall (in W/m²K)
  • a₂: thermal transmission coefficient from the second medium to the wall (in W/m²K)
• Changes in the flow of the first and/or second medium through the heat exchanger may result in changes in the flow velocity and flow type and thus in changes in the thermal transmission coefficient a_1,2.
• Where
• $X=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00002.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_1}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2}+\frac{s_w}{{\lambda }_w}$
• this gives
• 
  1/k=X+R _f
• The fouling resistance R_f can then be calculated by
• 
  R _f=1/k−X.
• Here, the following apply:
• R_f: the variable characterizing the fouling,
• 1/k: the first variable,
• X: the second variable.
• The second variable X is here consequently a variable unaffected by the fouling.
• The second variable is preferably thus a measure of the thermal transmission coefficient between the first medium and the wall, the thermal conductivity of the wall and the thermal transmission coefficient between the second medium and the wall.
• In accordance with a second embodiment of the invention, the variable affected by the fouling is a flow resistance of the first or second medium through the heat exchanger. A flow resistance can be determined particularly easily from measured values of pressures of the first and second mediums at an input and at an output of the heat exchanger in each case.
• In accordance with a particularly advantageous first embodiment of the method (referred to as “Method 1” below) at the time of a change in flow, in particular of an abrupt change, the value of the second variable is to this end changed such that the value of the variable characterizing the fouling remains constant.
• In each case after an initial startup or cleaning of the heat exchanger, i.e., when no fouling is present, an initial value of the first variable can be determined (or “learned”) and the second variable can be set to an initial value that corresponds to the initial value of the first variable. Both the variables then fully compensate one another. If in the further operation of the heat exchanger the value of the first variable increases because of fouling and because of changes in flow, then the changes in flow bring about a corresponding change in the second variable, and result in a corresponding compensation of the first variable.
• This method is particularly suitable for operation of the heat exchanger with operating phases, in which the flow is in each case piecewise constant and then changes abruptly. For example, this corresponds to the relatively common case in which the flow of the product medium is regulated, where the target values for this are predetermined as constant. A constant change in flow can only be processed in a piecewise manner. However, a continuous adjustment could then occur via an interpolation between the piecewise changes. It is advantageous that changes in the medium after cleaning have no effect on the result and nor is any learning data required.
• In accordance with a particularly advantageous second embodiment of the method (referred to below as “Method 2”) a function can be defined that in each case assigns a value for the second variable to a value for a flow through the heat exchanger of the first and/or of the second medium.
• This function can be determined or “learned” in a time interval after an initial startup of the heat exchanger or after cleaning the heat exchanger of fouling. The function is preferably formed by a regression of measured values of the flow and associated values of the second variable in the time interval. The regression can, for example, be a linear regression (if only the flow of one of the two media changes) or a 3D regression (if the flows of both media change). This method can also take account of constant changes and is relatively resistant to deviations in normal operation, but for this also requires several cleaning operations (and thereafter several different changes in flow) to “train” the function. The method also enables comparisons between the quality of cleaning operations.
• In accordance with a particularly advantageous third embodiment of the method (referred to below as “Method 3”), value ranges are defined for the flow, to which in each case a value for the second variable is assigned. Here, the assignment of the values of the second variable to the flow is advantageously determined or “learned” here in a time interval after an initial startup of the heat exchanger or after cleaning the heat exchanger of fouling. The transitions between values of the second variable can optionally be somewhat filtered at the range boundaries, so that they do not change too sharply. It is also possible to interpolate between the various learned points, instead of quantizing, in order to create a “smoother” transition.
• The time interval for defining the function or the range by range value assignments depends on the speed of the fouling processes and may, for example, be between a few hours (in the case of rapid fouling processes, which result in weekly cleaning of the heat exchanger, for example) and a few days (in the case of slow fouling processes, which result in monthly cleaning of the heat exchanger, for example).
• Combinations and extensions of the three aforementioned methods are also possible. For example, Method 1 can always be used when a change in flow occurs and the step height and compensation height can be taken into account as a new learning point in Method 2 and 3. Thus learning points in a contaminated state are also possible.
• In accordance with a further advantageous embodiment of the method, a characteristic curve for a relationship between the second variable and the flow of one of the two media is determined, where for the determination of the characteristic curve in a first step a characteristic curve of a mathematical derivation of the first variable after the flow of the medium is determined and, in a second step, the characteristic curve contained in the first step is again integrated with respect to the flow of the medium.
• The presently contemplated embodiment of the method makes use of the fact that the variable characterizing the fouling follows a slow and reasonably steady trend. The relationship between the first variable and the flow thus shifts continually, so that it is not possible to estimate the relationship directly. The problem therefore exists of estimating a characteristic curve (static relationship) between two variables. Besides the static relationship, an additive trend also acts on the dependent variable in this case.
• The basic idea for solving this problem is to estimate the derivation of the first variable after the flow (for example, (d 1/k)/dF)), from which the fouling can be subtracted. The integration of the derivation then again supplies the actual relationship, the absolute value obviously being lost. This is, however, also not necessary in the application, because only relative changes in flow have to be compensated for.
• In a further advantageous embodiment of the method, a first characteristic curve for a relationship between the second variable and the flow of the first medium and a second characteristic curve for a relationship between the second variable and the flow of the second medium are determined at the same time, where for the determination of the characteristic curves, in a first step, a characteristic curve of a mathematical derivation of the first variable after the flow of the respective medium is determined for each of the two media and, in a second step, the characteristic curves contained in the first step are again integrated with respect to the flow of the respective medium.
• The presently contemplated embodiment of the method is particularly advantageous in the event of simultaneous changes in the flows of both media. Thus, two characteristic curves (static relationships) between two variables each have to be estimated here. Besides the static relationships, an additive trend additionally acts on the dependent variable in this case. Applied to the heat exchanger, the effects of both the characteristic curves for the second variable overlap as a function of the flow of the respective medium.
• The advantage of both the last-mentioned embodiments of the method is that there is no reliance on learning the characteristic curves after cleaning, because the fouling effect is largely compensated for by the formation of derivations.
• It is also an object of the invention to provide a device for the implementing the disclosed embodiments of the method, where the device comprises a further device for receiving measured values or variables of the heat exchanger derived therefrom. The device also includes an evaluation device that is configured to determine, from the measured values or the derived variables, a value for a variable characterizing the fouling from a value for a first variable affected by the fouling and a value of a second variable, where a change in the first variable caused by a change in a flow of the first medium and/or the second medium through the heat exchanger is compensated for at least in part by the second variable.
• The first variable can, in this case, be a thermal transmission resistance or a thermal transmittance (or a thermal transmission coefficient (k value)), where the first variable and the second variable are determined from a plurality of the following measured variables (i) temperatures of the first and second mediums at the inlet and at the outlet of the heat exchanger and (ii) flows of the first and second mediums through the heat exchanger, and without using material properties of the first medium and second mediums and structural properties of the heat exchanger in the determination of the first and the second variable.
• The first variable can, however, also be a flow resistance, wherein the first variable and the second variable are determined from a plurality of the following measured variables (i) pressures of the first and second mediums at the inlet and at the outlet of the heat exchanger and (ii) flows of the first and second mediums through the heat exchanger, where the determination of the first and the second variable occur without using material properties of the first medium second mediums and structural properties of the heat exchanger.
• The “derived variables” can, for example, be statistical variables such as mean values, minima, maxima of measured values.
• It is also an object of the invention to provide a computer program that comprises instructions which, when the program is executed on a computer including a processor and memory, cause the computer to execute an inventive method as described above.
• A corresponding computer program product comprises a storage medium, on which a program containing instructions is stored which, when the program is executed on a computer including a processor and memory, cause the computer to execute an inventive method as described above.
• Other objects and features of the present invention will become apparent from the following detailed description considered in conjunction with the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims. It should be further understood that the drawings are not necessarily drawn to scale and that, unless otherwise indicated, they are merely intended to conceptually illustrate the structures and procedures described herein.
BRIEF DESCRIPTION OF THE DRAWINGS
• The invention and further advantageous embodiments of the invention are explained in greater detail below in the figures using exemplary embodiments, in which:
• FIG. 1 shows a block diagram of a heat exchanger and of a device for determining fouling in the heat exchanger in accordance with the invention
• FIG. 2 shows a temporal progression of a standardized k value for an industrial heat exchanger in accordance with the prior art;
• FIG. 3 shows a schematic temporal progression of the fouling resistance without any change in flow in a calculation in accordance with Method 1 of the invention;
• FIG. 4 shows a schematic temporal progression of the fouling resistance with a change in flow in a calculation in accordance with Method 1 of the invention;
• FIG. 5 shows a temporal progression of the 1/k value for the industrial heat exchanger in accordance with FIG. 1 in a calculation in accordance with Method 1 of the invention;
• FIG. 6 shows an application of a linear regression using the example of the industrial heat exchanger in FIG. 2 ;
• FIG. 7 shows a temporal progression of the fouling resistance R_f for the industrial heat exchanger in FIG. 2 in a calculation in accordance with Method 2 of the invention;
• FIG. 8 shows a temporal progression of the fouling resistance R_f for the industrial heat exchanger in FIG. 2 in a calculation in accordance with Method 3 of the invention;
• FIG. 9 shows a temporal progression of the correction variable X for the industrial heat exchanger in FIG. 2 in a calculation in accordance with Method 4 of the invention;
• FIG. 10 shows a temporal progression of flows of a service medium and a product medium for an industrial heat exchanger for determination of fouling in accordance with a further embodiment of the invention;
• FIG. 11 shows a temporal progression of temperatures of the service medium and of the product medium in relation to the flows in accordance with FIG. 10 ,
• FIG. 12 shows a temporal progression of a variable characterizing the fouling determined in accordance with Method 5 of the invention from the flows and temperatures in accordance with FIG. 10 and FIG. 11 ;
• FIG. 13 shows a temporal progression of flows of a service medium and of a product medium for an industrial heat exchanger for a determination of fouling in accordance with a further embodiment of the invention;
• FIG. 14 shows a temporal progression of temperatures of the service medium and of the product medium in relation to the flows in accordance with FIG. 13 ′
• FIG. 15 shows a temporal progression of a variable characterizing the fouling determined in accordance with Method 6 of the invention from the flows and temperatures in accordance with FIG. 13 and FIG. 14 ;
• FIG. 16 shows a block diagram of a heat exchanger and a Cloud-based device for determining fouling in a heat exchanger in accordance with the invention; and
• FIG. 17 is a flowchart of the method in accordance with the invention.
DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS
• FIG. 1 shows by way of example and in a simplified representation a heat exchanger 1 for the transmission of heat or cold from a service medium S to a product medium P. The heat exchanger 1 is represented by way of example as a reverse current heat exchanger, but other constructions of heat exchangers are also possible. The product medium P flows through a line 2. In the direction of flow, upstream of the heat exchanger 1, the flow F_P (or the flowrate or the volume flow) of the product medium and its temperature T_{P, In} are measured upstream of the inlet into the heat exchanger 1 via a flow sensor 4 and a temperature sensor 5. A further temperature sensor 6 arranged in the direction of flow downstream of the heat exchanger 1 measures the temperature T_{P, Out} of the product medium P exiting from the heat exchanger 1.
• The product medium P is heated or cooled via a service medium S, which is supplied to the heat exchanger 1 from a supply of heating or coolant. In the direction of flow, upstream of the heat exchanger 1, the flow F_S (or the flowrate or the volume flow) of the service medium and its temperature T_{S, In} are measured upstream of the inlet into the heat exchanger 1 via a flow sensor 7 and a temperature sensor 8. A further temperature sensor 9 arranged in the direction of flow, downstream of the heat exchanger 1, measures the temperature T_{S, Out} of the service medium S exiting from the heat exchanger 1.
• To monitor the heat exchanger 1 for fouling, the flow measured value F_P and the temperature measured values T_{P, In}, T_{P, Out} of the product medium P and the flow measured value F_S, as well as the temperature measured values T_{S, In}, T_{S, Out} of the service medium S, are transferred to a device 10 for determining fouling. If individual process variables of the product medium P or of the service medium S, for example, its inlet temperature T_{P, In} or T_{S, In}, are established based on given basic conditions and hence can be assumed to be unchanging, they do not need to be measured.
• The following applies for the product-related and service-related heat flows {dot over (Q)}_P and {dot over (Q)}_S:
• 
  {dot over (Q)} _P =c _{P, P}·ρ_P ·F _P·(TP, _out −T _{P, In})
• and
• 
  {dot over (Q)} _S =−c _{P, S}·ρ_S ·F _S·(T _{S, Out} −T _{S, In}).
• Where
• c_{P, P} thermal capacity of the product medium,
• c_{P, S} thermal capacity of the service medium,
• ρ_P density of the product medium,
• ρ_S density of the service medium.
• Ignoring losses, the entire amount of heat dissipated from the service medium S is transferred to the product medium P, so that both heat flows are identical ({dot over (Q)}_P={dot over (Q)}_S={dot over (Q)}). Alternatively, the heat flow can also be calculated using the following relationship, which stems from the mechanical structure of the heat exchanger:
• 
  {dot over (Q)}=k·A·ΔT _m.
• The following applies here:
• k: thermal transmission coefficient (in W/m²K)
• A: available surface for heat exchange (in m²)
• ΔT_m: mean logarithmic temperature difference
• Q: heat flow.
• The mean logarithmic temperature difference ΔT_m is defined as:
• $\Delta T_m=\frac{\Delta T_A-\Delta T_B}{\ln \left(\frac{\Delta T_A}{\Delta T_B}\right)},$
• where ΔT_A stands for the temperature difference of the inlet side (from the perspective of the product medium) and ΔT_B for that of the outlet side.
• Thus, the transferred heat flow can be calculated in three variants, as:
• a) heat flow dissipated by Medium 1
• 
  {dot over (Q)} _P =−c _{P, P}ρ_P F _P (T _{P, Out} −T _{P, In})
• b) heat flow passing through the heat exchanger 1
• 
  {dot over (Q)}=k·A·ΔT _m
• c) heat flow dissipated by Medium 2
• 
  {dot over (Q)} _S =−c _{P, S}ρ_S F _S(T _{S, Out} −T _{S, In})
• It follows from this that:
• 
  c _{P, P}ρ_P F _P(T _{P, Out} −T _{P, In})=k·A·ΔT _m =−c _{P, S}ρ_S F _S(T _{S, Out} −T _{S, In}).
• In general, it is now assumed that the fouling resistance is independent of the operating point. The current fouling resistance can be calculated from the difference between the current thermal transmission resistance 1/k_actual and the thermal transmission resistance 1/k_target that was determined in the clean state.
• $R_f=\frac{1}{k_{\mathrm{actual}}}-\frac{1}{k_{\mathrm{target}}}$ $k=\frac{1}{\frac{1}{{\alpha }_i}+\frac{s_w}{{\lambda }_w}+\frac{1}{{\alpha }_a}+R_f}$
• Thus the k value can be calculated using the relationship:
• $k=\stackrel{.}{Q}\frac{1}{A}\frac{\ln \left(\frac{\Delta T_A}{\Delta T_B}\right)}{\Delta T_A-\Delta T_B}$
• where
• 
  ΔT _A =T _{P, In} −T _{S, Out} and ΔT _B =T _{P, Out} −T _{S, In}
• in the case of a reverse current heat exchanger.
• In the case of values for A, c_{P, P}, c_{P, S}, ρ_P and ρ_S regarded as constant, a relative value for k can thus be corrected merely with the help of the measured values of the input-side and output-side temperatures and of the flows of both the media.
• FIG. 2 shows by way of example a typical progression of the 1/k value over the time t for an industrial heat exchanger. For simplification, a k value k₀ present at the time t₀=0 has been determined, and in FIG. 2 a value 1/k′ related to the initial value k₀ is represented. Perpendicular lines in this case show the cleaning time points. In some ranges, a dissipation of 1/k′ caused by fouling can be identified here. Level changes are, however, apparent at the points marked with an arrow, which make an accurate evaluation of the fouling resistance more difficult.
• As has been found, the determination of the fouling resistance can occur more accurately by additionally taking changes in flow in the product medium and/or service medium into account during the evaluation.
• If the heat is transmitted from the first medium to the second medium through a wall, the k value is then in theory composed as follows:
• $k=\frac{1}{\frac{1}{\alpha 1}+\frac{s_w}{{\lambda }_w}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2}+R_f}$ $\mathrm{or}$ $\frac{1}{ k}=\frac{1}{\alpha 1}+\frac{s_w}{ {\lambda }_w}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2}+R_f$
• where
• • R_f: fouling resistance (in m²K/W)
  • s_w: wall thickness (in m))
  • λ_w: thermal conductivity of the wall (in W/mK)
  • a₁: thermal transmission coefficient from the first medium to the wall (in W/m²K)
  • a2: thermal transmission coefficient from the second medium to the wall (in W/m²K).
• Changes in flow and thus changes in the flow type or within a flow type can result in changes in the thermal transmission coefficient a_1,2.
• Where
• $X=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00002.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_1}+\frac{1}{{\mathrm{<figure-callout\; id="2"\; label="\alpha "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_2}+\frac{s_w}{{\lambda }_w}$
• the following is produced:
• 
  1/k=X+R _f.
• The fouling resistance R_f can then be calculated by:
• 
  R _f=1/k−X.
• In this case
• R_f: is a variable characterizing the fouling,
• 1/k: is a first variable which is affected by the flow,
• X: is a second variable which is not affected by the fouling.
• The second variable X is thus a measurement of the thermal transmission coefficient between the first medium and the wall, the thermal conductivity of the wall and the thermal transmission coefficient between the second medium and the wall.
• In accordance with the invention, changes in the first variable caused by changes in flow, here changes in the calculated k value, are compensated for at least in part with the help of a second variable, here a value of the variable X.
• Three methods for how the flow can be taken into account are now presented here based on FIGS. 3 to 10 :
• Method 1
• In Method 1 the value for X is adjusted at each abrupt change in flow. Here, the following assumptions are made:
• • the wall thickness and the thermal conductivity thereof (sw/λw=const.) do not change in operation,
  • the properties of the media do not change, or only insignificantly,
  • the fouling resistance does not significantly decrease or increase without a particular reason (for example cleaning) in normal operation.
• In a learning phase, immediately after cleaning, an initial value for X is learned.
• For a certain time interval after cleaning, it can be assumed that the fouling resistance is Rf=0.
• In this range, the values for ¹/a₁, 1/a₂ and s_w/λ_w are learned (aggregated in the value X). Where R_f=0 and X=1/a₁+1/a₂+s_w/λ_w, X₀ for the initial interval (or after a cleaning interval) can now be determined using the previously calculated k value k₀. X₀=1/k₀ applies here.
• Case 1: The flows do not change
• In this case, the values of a also do not change, i.e., X remains constant. Each change in the 1/k value can thus be attributed to fouling. The fouling resistance can thus be calculated using the relationship R_f=1/k−X. FIG. 3 to this end shows by way of example a progression of 1/k, X and R_f over the time t. The value X is constant and results in a constant difference between 1/k and R_f.
• Case 2: A flow changes at the time t₀
• At the time t₀, the fouling resistance R_f(t₀) is briefly kept constant and X_new is calculated, for example, with X_new=1/k−R_f(t₀).
• For 1/k a mean value for an interval from t₀ to t₀+x can now be used. Alternatively, X_new can also be calculated as follows:
• 
  X _new =X _old−(1/k _old−1/k _new).
• 1/kola and 1/knew here stand for an averaged 1/k value in an interval prior to or after a change in flow. Both approaches show almost identical results.
• In the subsequent progression, the fouling resistance is then calculated again using R_f=1/k_new−X_new.
• FIG. 4 to this end shows by way of example a progression of 1/k, X and R_f over the time t. As is apparent, with this method the fouling resistance R_f is continued steadily in the event of a change in the flow at the time t₀, instead of resulting in a change in level.
• If this method is now used to calculate the 1/k value, X and R_f for the industrial heat exchanger in FIG. 2 and this is plotted over the time t, the progressions shown in FIG. 5 are produced. Only relative values are shown here. Perpendicular lines in this case again show the cleaning times. For simplification, initial values 1/k₀ and X₀ present at the time t₀=0 have now been determined and values 1/k′ and X′ related to these initial values are represented in FIG. 5 .
• In the calculation of the 1/k′ value, level changes are again apparent at the points marked with an arrow, but in the calculation of the relative fouling resistance R_f are largely compensated for by changes in the X′ value.
• This method is particularly suitable for an operation of the heat exchanger with operating phases in which the flow is in each case piecewise constant and then changes abruptly. A constant change in flow can only be processed in a piecewise manner. A continuous adjustment could then, however, occur via an interpolation between the piecewise changes. Changes in the medium after cleaning advantageously have no effect on the result, and nor is any learning data required.
• Method 2
• As already described, as a rough approximation it can be assumed that the fouling resistance after cleaning is ≈0. X(F)=1/k here. This initial interval is now used for different flows to find a relationship between X and F (flow) in the form of a function f. Even if the flow changes within this interval. A regression, in particular a linear regression, or even better a nonlinear regression, can be used for this. A corresponding X value can be calculated for any flows with the result of this interpolation.
• FIG. 6 shows by way of example an application of the linear regression, using the example of the industrial heat exchanger in FIG. 2 . To create the linear regression and thus to define the function f, the associated X values have been determined (marked with “*” in FIG. 6 ) after cleaning of the heat exchanger for a number of averaged flow values F_P of the product side. Changes in flow within this interval are taken into account in this case. The following thus applies: X=f(F_p), where the function f is a product of the linear regression of F_p and X.
• If this method is now used to calculate the relative fouling resistance R_f for the industrial heat exchanger in FIG. 2 and is plotted over the time t together with the values X determined via the linear regression, the product is a progression shown in FIG. 7 . For simplification, the initial value X₀ present at the time t₀=0 has been determined here too and a value X′ related to this initial value is represented in FIG. 7 .
• As is apparent, this method also produces a satisfactory result in many ranges.
• Perpendicular lines in this case again show the cleaning times.
• The function f can, for example, be formed by a linear regression (if only the flow of one of the two media changes, see FIG. 6 ) or a 3D regression (if the flows of both media change) of measured values of flows and associated values of the second variable in the time interval after an initial startup or cleaning. This method can also take account of constant changes, and is relatively resistant to deviations in normal operation, but for this also requires a plurality of cleaning operations (and following this a plurality of different flows) to “train” the function f. It also enables comparisons between the quality of cleaning operations.
• Method 3
• The X values learned after an initial startup or cleaning can be used to form value ranges for the flow. Within such a range each flow value is assigned a learned X value. So that the transitions between two X values do not become too abrupt, this X value can be filtered somewhat over time.
• If this method is now used to calculate the relative fouling resistance R_f and X for the industrial heat exchanger in FIG. 2 and to plot this resistance over the time t, the product is a progression shown in FIG. 8 . For simplification, initial values 1/k₀ and X0 present at the time t₀=0 have been determined and values 1/k′ and X′ related to these initial values are shown in FIG. 5 . The calculation was performed using the heat quantity of the product side. Perpendicular lines in this case again show the cleaning times. As is apparent, this method again produces a satisfactory result in many ranges.
• The assignments of the values of the second variable to the flow are advantageously determined here in a time interval after an initial startup of the heat exchanger or after cleaning the heat exchanger of fouling. The transitions between values of the second variable can optionally be somewhat filtered at the range boundaries, so that they do not change too sharply. It is also possible to interpolate between the various learned points, instead of quantizing, in order to create a “smoother” transition.
• What is known as the “interpolation points method” represents an opportunity for optimization here. This method likewise represents an opportunity for how the analysis of a relationship between flow and reference value could be implemented. To this end, a rough presentation is required of how the characteristic curve of the a value could look as a function of the flow velocity. Basic conditions for the subsequent characteristic curve or function could already be found here, such as monotonicity of the curve. First values for the analysis are obtained and plotted in the clean state after cleaning operations.
• New values are added during the runtime. These are brought together in a particular range, weighted with the previous values, and the characteristic curve is updated. The weighting factor can be the number of previous points in a range or the current fouling resistance.
• In addition to the three methods, combinations and extensions can also be applied.
• Combination of Methods 1 and 2
• This combination could be used to determine the fouling resistance or the X value for the heat exchanger first with Method 1 and then in the medium term the X value thanks to a ratio between both methods (as a function, for example, of the deviation between Method 1 and 2, the variance of Method 2 or the number of data points in Method 2). In the long term Method 2 alone should then suffice.
• Method 4
• With the help of Method 1 the X value changes and the changes in flow before and after are known in the event of flow changes. The amount of the flow change (ΔF₁) and of the X value (ΔX₁) can now firstly be calculated. Thus, for each future (and constant) change in flow, the effects relative to the previous X value can be calculated. If there is a plurality of usable changes, a linear regression between ΔF₁ and ΔX₁ is used. FIG. 9 to this end shows an assignment of values for X to the flow F over the time t.
• To work out the final X value, it is possible to interpolate between the different sampling points, in order to avoid an abrupt progression (see dashed line in FIG. 9 ). A combination of Method 1 and Method 4 therefore offers particular advantages.
• Method 5
• In accordance with an embodiment of the method, referred to as Method 5, a characteristic curve for a relationship between the second variable and the flow of one of the two media is determined, where to determine the characteristic curve, in a first step, a characteristic curve of a mathematical derivation of the first variable after the flow of the medium is determined and, in a second step, the characteristic curve obtained in the first step is again integrated with respect to the flow of the medium.
• This method makes use of the fact that the variable characterizing the fouling follows a slow and reasonably steady trend. The relationship between the first variable and the flow thus shifts continually, so that it is not possible to estimate the relationship directly. The problem therefore exists of estimating a characteristic curve (static relationship) between two variables. Besides the static relationship, an additive trend also acts on the dependent variable in this case.
• The basic idea for solving this problem is to estimate the derivation of the first variable after the flow (for example, (d 1/k)/dF)), from which the fouling can be subtracted. The integration of the derivation then again supplies the actual relationship, the absolute value obviously being lost. This is, however, also not necessary in the application, because only relative changes in flow have to be compensated for.
• It is assumed that the reciprocal k value is composed of the sum of the fouling resistance and X:
• $\frac{1}{k}=X+R_f,$
• where X is composed of all further thermal resistances. The time derivation produces:
• $\frac{d\frac{1}{k}}{\mathrm{dt}}=\frac{\mathrm{dX}}{\mathrm{dF}}\frac{\mathrm{dF}}{\mathrm{dt}}+\frac{{\mathrm{dR}}_f}{\mathrm{dt}}$ $\kappa \left(t\right)=\frac{\mathrm{dX}}{\mathrm{dF}}\Phi \left(t\right)+m,$
• wherein
• $\kappa \left(t\right)=\frac{d\frac{1}{k}}{\mathrm{dt}},\Phi \left(t\right)=\frac{\mathrm{dF}}{\mathrm{dt}},m=\frac{{\mathrm{dR}}_f}{\mathrm{dt}}.$
• Thus, the following applies:
• $\frac{\mathrm{dX}}{\mathrm{dF}}=\frac{\kappa \left(t\right)-m}{\Phi \left(t\right)}$
• For Φ₁(t)≠Φ₂(t), the following applies:
• $\frac{1}{{\Phi }_1-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2}\left({\mathrm{<figure-callout\; id="1"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00002.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_1\frac{dX}{dF}-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2\frac{dX}{dF}\right)=\frac{dX}{dF}$
• At a point X₀, F₀ the unambiguous but unknown relationship
• ${\frac{\mathrm{dX}}{\mathrm{dF}}❘}_{{\mathrm{<figure-callout\; id="0"\; label="X"\; filenames="US20230122608A1-20230420-D00002.png,US20230122608A1-20230420-D00004.png"\; state="\{\{state\}\}">X</figure-callout>}}_0,{\mathrm{<figure-callout\; id="0"\; label="F"\; filenames="US20230122608A1-20230420-D00002.png,US20230122608A1-20230420-D00004.png"\; state="\{\{state\}\}">F</figure-callout>}}_0}$
• applies, regardless of Φ(t) and κ(t).
• Hence the following applies:
• $\frac{dX}{dF}=\frac{1}{{\Phi }_1-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2}\left({\mathrm{<figure-callout\; id="1"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00002.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_1\frac{dX}{dF}-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2\frac{dX}{dF}\right)=\frac{1}{{\Phi }_1-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2}\left({\mathrm{<figure-callout\; id="1"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00002.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_1\frac{{\kappa }_1\left(t\right)-m}{{\Phi }_1\left(t\right)}-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2\frac{{\kappa }_2\left(t\right)-m}{{\Phi }_2\left(t\right)}\right)=\frac{1}{{\Phi }_1-{\mathrm{<figure-callout\; id="2"\; label="\Phi "\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00001.png"\; state="\{\{state\}\}">\Phi </figure-callout>}}_2}\left({\kappa }_1\left(t\right)-{\kappa }_2\left(t\right)\right)$
• for all Φ₁(t)≠Φ₂(t).
• It is therefore necessary to calculate the thus weighted difference in the
• $\frac{1}{k}$
• changes, tor two aiiierent changes in flow Φ₁(t)≠Φ₂(t).
• To now therefore determine a characteristic curve, it is proposed successively to compile all data with
• $\frac{\mathrm{dF}}{\mathrm{dt}}>c_F,$
• for all F in the environment of an F₀, and in each case to determine
• $\frac{\mathrm{dX}}{\mathrm{dF}}$
• for paired Φ₁(t)≠Φ₂(t). By integrating the derivation characteristic curve, the characteristic curve that is desired is then created.
• In this case, the absolute value is advantageously irrelevant, so that an initial value need not be taken into account in the integration.
• Because of the simpler parameterization the modeling is undertaken only qualitatively, i.e., 1/k is determined without exact material data or properties of the heat exchanger. Thus only relative changes in the k value can be calculated. The determined characteristic curves are however exactly applicable for relative changes in the flows.
• A particular feature of this method is that the actual task of determining the fouling is initially pushed into the background and it is the effect of fouling that is compensated for, in order to estimate the X-F characteristic curve. Only then is the fouling determined with the help of the characteristic curve from 1/k. A characteristic curve can advantageously be easily implemented, so that nothing stands in the way of even an online evaluation.
• FIGS. 10 to 12 to this end show a simulation of an industrial heat exchanger with variation in a flow.
• FIG. 10 in this case shows a temporal progression of (simulated) measured values of the flow F_P of the product medium and of the flow F_S of the service medium through the heat exchanger.
• FIG. 11 shows the associated (simulated) measured values for the temperature T_{P, In} of the product medium at the inlet and the temperature T_{P, Out} of the product medium at the outlet of the heat exchanger. In addition, (simulated) measured values of the temperature T_{S, In} of the service medium at the inlet and of the temperature T_{S, Out} of the service medium at the outlet of the heat exchanger are shown.
• FIG. 12 shows the associated calculated relative values for 1/k and the fouling resistance R_f.
• In the event of changes in flow, the 1/k value shows a significant dependency, no matter which side of the heat exchanger the changes are on. It is true that an overlaid trend is still apparent in the idealized data. Depending on the extent of the fouling, it is not however possible to derive any reliable information from the 1/k value alone.
• By applying the characteristic curves and compensating for the associated flow dependencies, the estimated fouling progression is produced (shown offset upward for better visibility). Except for the measurement noise, a linear trend is apparent. The fouling can thus be ascertained very reliably. It should be noted here that at the start both flows have been changed independently of one another, so that it was also possible to successively estimate both flow characteristic curves independently of one another.
• Method 6
• In accordance with an embodiment of the method referred to as Method 6, a first characteristic curve for a relationship between the second variable and the flow of the first medium and a second characteristic curve for a relationship between the second variable and the flow of the second medium are determined, where to determine the characteristic curves, in a first step, in each case a characteristic curve of a mathematical derivation of the first variable after the flow of the respective medium is determined for each of the two media and, in a second step, the characteristic curves obtained in the first step are again integrated in respect of the flow of the respective medium.
• This method is particularly advantageous in the event of simultaneous changes in the flows of both media. Thus, two characteristic curves (static relationships) between two variables are each to be estimated here. Besides the static relationships, an additive trend additionally acts on the dependent variable in this case. When applied to the heat exchanger, the effects of both the characteristic curves for the second variable overlap one another as a function of the flow of the respective medium.
• In the case of a heat exchanger, the effects of both the characteristic curves X_P=f_P(F_P) and X_S=f_S(F_S) on the 1/k value overlap one another where
• $\frac{1}{k}=X_P+X_S+R_f.$
• The derivation of 1/k after the time produces
• $\frac{d\frac{1}{k}}{\mathrm{dt}}=\frac{\mathrm{dX}}{{\mathrm{dF}}_p}\frac{{\mathrm{dF}}_p}{\mathrm{dt}}+\frac{dX}{d{F}_S}\frac{d{F}_S}{dt}+\frac{d{R}_f}{dt}$
• where X=X_P+X_S.
• n_P interpolation points (dx_pi, F_pi) of the derivation characteristic curve
• $\frac{{\mathrm{dX}}_P}{{\mathrm{dF}}_P}=\stackrel{-}{f_P}\left(F_P\right)$
• and n_S interpolation points (dx_si, F_si) of the derivation characteristic curve
• $\frac{{\mathrm{dX}}_S}{{\mathrm{dF}}_S}=\overline{f_S}\left(F_S\right)$
• are now sought.
• To this end, for each time t for which
• $\frac{{\mathrm{dF}}_P}{\mathrm{dt}}>\mathrm{dFpLimit}\mathrm{or}\frac{{\mathrm{dF}}_S}{\mathrm{dt}}>\mathrm{dFsLimit}$
• applies, an equation with three unknowns (dx_pi,dx_si,m) is generated:
• $\frac{d\frac{1}{k}}{\mathrm{dt}}=d{x}_{Pi}\frac{d{F}_P}{dt}+d{x}_{\mathrm{Si}}\frac{d{F}_S}{dt}+m$
• n_D, equations can then be combined in matrix notation, where the respective flow has to be taken into account for the interpolation points. Thus the following applies:
• $Ab=c$ ${{{{{b=[\frac{d{X}_P}{d{F}_P}❘}_{{\mathrm{<figure-callout\; id="1"\; label="F\; P"\; filenames="US20230122608A1-20230420-D00000.png,US20230122608A1-20230420-D00002.png"\; state="\{\{state\}\}">F</figure-callout>}}_{P_{}}},\dots ,\frac{d{X}_P}{d{F}_P}❘}_{F_{P_{n_p}}},\frac{d{X}_S}{d{F}_S}❘}_{F_{s_1}},\dots ,\frac{d{X}_S}{d{F}_S}❘}_{F_{s_{n_s}}},m]}^T$ $c=\left[\kappa \left(t_1\right)\dots \kappa \left(t_m\right)\right]$ $A\in R^{n_D\times \left(n_p+n_s+1\right)}$
• For better understanding, a row of A is specified. At the corresponding time, it should be the case that F_P≈F_P5 and F_S≈F_S7, where n_P=10 and n_S=20. The row of A then corresponds to:
• ${{{[0,\dots ,0,\frac{d{X}_P}{d{F}_P}❘}_{F_{P5}},0,\dots 0,\frac{d{X}_S}{d{F}_S}❘}_{F_{S7}},0,\dots ,0,1]}^T$
• where there are entries different from zero only in the 5^th and 17^th (=10+7) and last column.
• If the measured values present now cover all flow ranges on the service and product side, then there is at least one data point in each column of A. Assuming that A has the maximum ranking, the equation system can be resolved in accordance with the unknown in the vector b, such as via a pseudoinverse.
• The two derivation characteristic curves can then again be generated from the vector and integrating these produces the characteristic curves X_P=f_P(F_P) and X_S=f_S(F_S).
• If both characteristic curves are present, then the fouling can be estimated, by first determining 1/k, and the fouling is calculated by applying the characteristic curves:
• $R_f=\frac{1}{k}-X_P-X_S$
• As already outlined in brief, the absolute values of the characteristic curves are unknown by the integration. Because of the simpler parameterization, the modeling is in any case implemented only qualitatively, i.e., 1/k is determined without precise material data or properties of the heat exchanger. Thus, only relative changes in the k value can be calculated. The determined characteristic curves can, however, be applied precisely for relative changes in the flows.
• Here, the actual task of determining the fouling is also initially pushed into the background and it is the effect of fouling that is compensated for, in order to estimate both the X-F characteristic curves. Only then is the fouling determined with the help of the characteristic curves from 1/k. Characteristic curves can advantageously be easily implemented, so that an evaluation can even be carried out online.
• FIGS. 13-15 to this end show a simulation of an industrial heat exchanger with variation in the flows.
• FIG. 13 in this case shows a temporal progression of (simulated) measured values of the flow F_P of the product medium and of the flow F_S of the service medium through the heat exchanger.
• FIG. 14 shows the associated (simulated) measured values for the temperature T_{P, In} of the product medium at the inlet and the temperature T_{P, Out} of the product medium at the outlet of the heat exchanger. In addition, (simulated) measured values of the temperature T_{S, In} of the service medium at the inlet and the temperature T_{S, Out} of the service medium at the outlet of the heat exchanger are shown.
• FIG. 15 shows the relative values calculated therefrom for 1/k and the fouling resistance R_f.
• The 1/k value shows a significant dependency in the case of changes in flow, no matter which side of the heat exchanger said changes are on. It is true that an overlaid trend is still apparent in the idealized data. Depending on the extent of the fouling, it is not however possible to derive any reliable information from the 1/k value alone. By applying the characteristic curves and compensating for the associated flow dependencies, the estimated fouling progression Rf is produced. Except for the measurement noise, a linear trend is apparent. The fouling can thus be determined very reliably, even if both flows change at the same time.
• The same methods can in principle also be transferred to the consideration of the pressure difference. The flow resistance also increases in the case of fouling, but also depends on the flow.
• The disclosed embodiments of the methods enable a reliable quantification of the fouling resistance for different heat exchangers even in the event of a change in flow. In this case, no knowledge of material properties or structural properties of the heat exchanger is necessary. The disclosed embodiments of the method all work purely on the basis of data. Hitherto, only the pure k value has been used as an indicator for fouling. The disclosed embodiments of the method use this variable and at the same time also incorporate the effect of the flow dynamic of both the media into the final result.
• Furthermore, there is no requirement for a model of the heat exchanger, which would have to be laboriously prepared by an expert. All results and interim steps can furthermore be represented in 2D or 3D characteristic fields. No abstract multidimensional characteristic fields are required for the calculation. Furthermore, it is also possible to dispense with one of the measurements F_P, F_S, T_{P, In}, T_{P, Out}, T_{S, In}, T_{S, Out}, so that full instrumentation is not required. If a compensation takes place with respect to changes in the flow of both media, then it should be understood only one temperature measurement can be dispensed with in this case.
• Using the example of an industrial heat exchanger, it was possible to achieve a significantly better result with these disclosed embodiments of the methods in the determination of fouling than with a conventional calculation. The results could thus help a plant operator to obtain a significantly better evaluation of the fouling resistance. The methods can advantageously be applied not only to the heat balances but also to the consideration of the pressure differences and thus of the flow resistances.
• The inventive embodiments of the method can be provided as a standalone application in a processing system or can be integrated into a process control system of a processing system. It can also be provided in a local or remote computer system (“Cloud”), for example by a service provider as “Software as a Service”.
• An inventive device 10 for determining fouling shown by way of example in FIG. 1 comprises a device 20 for receiving the measured values T_{P, In}, T_{P, Out}, T_{S, In}, T_{S, Out}, F_P, F_S of the heat exchanger 1 and an evaluation device 30 which is configured to determine and output a value for the fouling resistance R_f from these measured values via a method in accordance with the disclosed embodiments. Additionally or alternatively the evaluation device can also act as a monitoring device: it can monitor the determined fouling resistance to see whether a threshold value has been exceeded and if this threshold value is exceeded can thn emit a signal, which for example signals a need for cleaning.
• To this end, the evaluation device 30 comprises a processor unit 31, a memory 32 for storing the received measured data, and a memory 33 in which a program 34 containing instructions is stored, which when executed via the processor unit 31 executes the method in accordance with the disclosed embodiments. The processor unit 31 stores the measured values M received by the device 20 in the memory 32.
• It is not necessary to detect further variables, such as c_{P, P}, c_{P, S}, ρ_P, ρ_S. On the contrary, the disclosed embodiments of the method assumes that these are not known. Any constants can be assumed, which then when seen in absolute terms result in a false value, but ultimately the relative changes in this k-value are decisive for the functioning and the success of the method in accordance with disclosed embodiments.
• The device 10 shown in FIG. 1 can, for example, be provided as a standalone application in a processing system or can be integrated into a process control system of a processing system.
• A device 100 shown in FIG. 16 for determining fouling can in contrast be provided by a local or remote computer system (“Cloud”), for example, in order to offer the determination of fouling by a service provider as “Software as a Service”. The receiving device 20 is, in this case, located in situ in the processing system of the heat exchanger 1 and 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 sends the measured values M (or variables derived therefrom) to the evaluation device 30 (for example, at regular intervals in time, on an event-driven basis or on request by the evaluation device 30) via a transmission device 22, such as over the Internet or an intranet.
• The evaluation device 30 comprises a processor unit 31, a memory 32 for storing the received measured data, and a memory 33, in which a program 34 containing instructions is stored, which when executed via the processor unit 31 executes the method in accordance with disclosed embodiments of the invention.
• The processor unit 31 stores the measured values M received from the device 20 via an interface 36 in the memory 32, and where appropriate for further input variables that are received via a separate interface 37. The values for the fouling resistance R_f determined with the program 34 and/or a signal that signals a need for cleaning are output via an interface 38. The interfaces 36, 37 and 38 can in this case also be provided by a single shared interface, for example, to the Internet or an intranet.
• FIG. 17 is a flowchart of the method for determining fouling in a heat exchanger 1, in which heat from a first medium S is transferred to a second medium P.
• The method comprises determining a value for a variable characterizing the fouling Rf from a value for a first variable k affected by the fouling and from a value of a second variable X, as indicated in step 1710.
• Next, a change in the first variable k caused by a change in a flow FS, FP of either the first medium S and/or the second medium P through the heat exchanger 1 is compensated for at least in part by the second variable X, as indicated in step 1720.
• In accordance with the method of the invention, the first variable k is either a thermal transmission resistance, a thermal transmittance or a thermal transmission coefficient k value, where the first variable k and the second variable X are determined from measured values of a plurality of the measured variables comprising (i) temperatures TP, In, TP, Out, TS, In, TS, Out of the first medium S and the second medium P at an inlet and at an outlet of the heat exchanger 1 and (ii) flows FP, FS of the first medium S and the second medium P through the heat exchanger 1, and where the determination of the first and the second variable occurs without using material properties of the first medium S and the second medium P and structural properties of the heat exchanger 1.
• Thanks to virtually realtime detection of the measured values and calculation of the fouling resistance a continuous running data-based fouling analysis and monitoring of the fouling can take place, accompanying the operation of the plant or of the heat exchanger. However, an offline fouling analysis with a time offset to the real operation of the plant is also possible.
• Thus, while there have been shown, described and pointed out fundamental novel features of the invention as applied to a preferred embodiment thereof, it will be understood that various omissions and substitutions and changes in the form and details of the methods described and the devices illustrated, and in their operation, may be made by those skilled in the art without departing from the spirit of the invention. For example, it is expressly intended that all combinations of those elements and/or method steps which perform substantially the same function in substantially the same way to achieve the same results are within the scope of the invention. Moreover, it should be recognized that structures and/or elements and/or method steps shown and/or described in connection with any disclosed form or embodiment of the invention may be incorporated in any other disclosed or described or suggested form or embodiment as a general matter of design choice. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.

Claims (22)

1.-16.

17. A method for determining fouling in a heat exchanger, in which heat from a first medium is transferred to a second medium, the method comprising:

determining a value for a variable characterizing the fouling from a value for a first variable affected by the fouling and from a value of a second variable; and

compensating for a change in the first variable caused by a change in a flow of at least one of (i) the first medium and (ii) the second medium through the heat exchanger at least in part by the second variable, the first variable being one of a thermal transmission resistance, a thermal transmittance and a thermal transmission coefficient, the first variable and the second variable being determined from measured values of a plurality of the measured variables comprising (i) temperatures of the first medium and the second medium at an inlet and at an outlet of the heat exchanger and (ii) flows of the first medium and the second medium through the heat exchanger, and the determination of the first and the second variable occurring without using material properties of the first medium and the second medium and structural properties of the heat exchanger.

18. A method for determining fouling in a heat exchanger, in which heat is transferred from a first medium to a second medium, the method comprising:

determining a value for a variable characterizing the fouling from a value for a first variable affected by the fouling and from a value of a second variable; and

compensating for a change in the first variable caused by a change in a flow of at least one of (i) the first medium and (ii) the second medium through the heat exchanger at least in part by the second variable, the first variable being a flow resistance, and the first variable and the second variable being determined from measured values of a plurality of measured variables comprising (i) pressures of the first medium and the second medium at an inlet and at an outlet of the heat exchanger and (ii) flows of the first medium and the second medium through the heat exchanger, and the determination of the first and the second variable occurring without utilizing material properties of the first medium and the second medium and structural properties of the heat exchanger.

19. The method as claimed in claim 17, wherein at a time of a change in flow, the value of the second variable is changed such that the value of the variable characterizing the fouling remains constant.

20. The method as claimed in claim 18, wherein at a time of a change in flow, the value of the second variable is changed such that the value of the variable characterizing the fouling remains constant.

21. The method as claimed in claim 19, wherein after an initial startup and after a cleaning operation of the heat exchanger an initial value of the first variable is determined in each case and the value of the second variable is set to an initial value which corresponds to the initial value of the first variable.

22. The method as claimed in claim 17, wherein a function is defined which in each case assigns a value for the second variable to a value for a flow of at least one of the first medium and the second medium.

23. The method as claimed in claim 22, wherein the function is determined in a time interval after an initial startup or after cleaning the heat exchanger of fouling.

24. The method as claimed in claim 22, wherein the function is formed by a regression of measured values of the flow and associated values of the second variable in the time interval.

25. The method as claimed in claim 23, wherein the function is formed by a regression, in particular a linear or a 3D regression, of measured values of the flow and associated values of the second variable in the time interval.

26. The method as claimed in claim 24, wherein the regression comprises a linear or a 3D regression.

27. The method as claimed in claim 25, wherein the regression comprises a linear or a 3D regression.

28. The method as claimed in claim 17, wherein value ranges for the flow are defined, to each of which a value for the second variable is assigned.

29. The method as claimed in claim 28, wherein assignments of the values of the second variable to the flow are determined in a time interval after an initial startup or after cleaning the heat exchanger of fouling.

30. The method as claimed in claim 17, wherein a characteristic curve for a relationship between the second variable and the flow of one of the two media is determined; and

wherein, for the determination of the characteristic curve, a characteristic curve of a mathematical derivation of the first variable after the flow of the medium is initially determined and the characteristic curve initially obtained is subsequently again integrated with respect to the flow of the medium.

31. The method as claimed in claim 17, wherein a first characteristic curve for a relationship between the second variable and the flow of the first medium and a second characteristic curve for a relationship between the second variable and the flow of the second medium are simultaneously determined; and

wherein for the determination of the characteristic curves for each of the first and second media a characteristic curve of a mathematical derivation of the first variable after the flow of the respective first and second medium are each determined and the characteristic curves initially obtained are subsequently again integrated with respect to the flow of the respective medium.

32. The method as claimed in claim 17, wherein the variable characterizing the fouling is a thermal transmission resistance.

33. The method as claimed in one claim 17, wherein only relative changes in the variable characterizing the fouling, the first variable and the second variable are determined.

34. A device for determining fouling in a heat exchanger, in which heat from a first medium is transferred to a second medium, the device comprising:

a further device for receiving measured values or variables derived therefrom of the heat exchanger; and

an evaluation device which is configured to determine from the received measured values or the derived variables a value for a variable characterizing the fouling from a value for a first variable affected by the fouling and from a value of a second variable;

wherein a change in the first variable caused by a change in a flow of at least one of (i) the first medium and (ii) the second medium through the heat exchanger is compensated for at least in part by the second variable; and

wherein the first variable and the second variable are determined from measured values of a plurality of measured variables comprising (i) temperatures of the first medium and the second medium at an inlet and at an outlet of the heat exchanger and (ii) flows of the first medium and the second medium through the heat exchanger, and the determination of the first and the second variable occurring without utilizing material properties of the first medium and the second medium and structural properties of the heat exchanger being utilized.

35. The device for determining fouling in a heat exchanger, in which heat is transferred from a first medium to a second medium, the device comprising:

a further device for receiving measured values or variables derived therefrom of the heat exchanger; and

an evaluation device which is configured to determine from the measured values or the derived variables a value for a variable characterizing the fouling from a value for a first variable affected by the fouling and from a value of a second variable;

wherein a change in the first variable caused by a change in a flow of at least one of (i) the first medium and (ii) the second medium through the heat exchanger is compensated for at least in part by the second variable;

wherein the first variable is a flow resistance;

wherein the first variable and the second variable are determined from measured values of a plurality of measured variables comprising (i) pressures of the first medium and the second medium at an inlet and at an outlet of the heat exchanger and (ii) flows of the first medium and of the second medium through the heat exchanger, and the determination of the first and the second variables occurring without utilizing material properties of the first medium and the second medium and structural properties of the heat exchanger.

36. A computer program comprising instructions which, when executed by a processor of a computer, cause the computer to execute the method as claimed in claim 17.

37. A computer program comprising instructions which, when executed by a processor of a computer, cause the computer to execute the method as claimed in claim 18.

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