Method and Device for Ascertaining Fouling in a Heat Exchanger

Abstract

Device and method for ascertaining fouling in a heat exchanger in which heat is transferred from a first medium to a second medium through a wall, wherein a function is used with at least one parameter that describes the dependence of a first variable, which is influenced by the fouling, on the flow and/or temperature of the first medium and/or the second medium, in particular the simultaneous influence of changes in the flow and temperature on the first variable, wherein a value for the at least one parameter is ascertained using measurement values of the first and/or the second medium such that the precision when ascertaining fouling in a heat exchanger, in which heat is transferred from a first medium to a second medium, is increased.

Claims

1-17. (canceled)

18. A method for ascertaining fouling in a heat exchanger in which heat is transferred from a first medium to a second medium through a wall, the method comprising: utilizing a function with at least one parameter, said function describing a dependence of a first variable influenced by the fouling on at least one of a flow rate and a temperature of at least one of the first medium and the second medium comprising a simultaneous influence of changes in flow rate and temperature on the first variable; and ascertaining a value for the at least one parameter aided by measured values of at least one of the first mediums and the second medium.

19. The method as claimed in claim 18, wherein the first variable is ascertained from a heat balance of the heat exchanger.

20. The method as claimed in claim 18, wherein a value for a variable characterizing the fouling is ascertained from a value for the first variable influenced by the fouling and a value of a second variable which compensates an influence of a dependence of the first variable on at least one of a flow rate and a temperature of at least one of the first medium and the second medium comprising a simultaneous influence of changes in flow rate and temperature on the first variable and wherein the value of the second variable is ascertained aided by the function with the at least one parameter.

21. The method as claimed in claim 18, wherein said ascertaining the at least one parameter is based on measured values of temperatures of (i) at least one of the first medium and the second medium and (ii) at least one of flow rates of the at last one of the first medium and the second medium.

22. The method as claimed in claim 18, wherein the function with the at least one parameter for at least one side of a wall, preferably for both sides of the wall, takes into account dependence of a heat transfer coefficient of a respective side on at least one of the flow rate and the temperature of the first or second medium which are each conducted past the side of the wall.

23. The method as claimed in claim 22, wherein the dependence of the heat transfer coefficient on the flow rate of the medium which is conducted past the respective wall is in accordance with the relationship:
?(F)=a.Math.F(t).sup.b; wherein F is the flow rate of the medium at the respective side of the wall, t is time and a, b are parameters.

24. The method as claimed in claim 22, wherein the dependence of the heat transfer coefficient on the temperature of the medium conducted past the respective wall in accordance with the relationship:
?(T)=a.Math.(T(t)+b).sup.c; wherein T is a mean temperature of the medium at the respective side of the wall, t is time and a, b, c are parameters.

25. The method as claimed in claim 22, wherein the dependence of the heat transfer coefficient on at least one of the flow rate and the temperature of the medium conducted past the respective wall is in accordance with the relationship:
?(F, T)=a.Math.F.sup.b.Math.(T+c).sup.d; wherein F is a time-dependent flow rate and T is a time-dependent mean temperature of the medium at the respective side of the wall and a, b, c, d are parameters.

26. The method as claimed in claim 18, wherein said ascertaining the at least one parameter comprises: providing a target function based on the function with the at least one parameter, ascertaining the value of the at least one parameter by optimizing the target function based on measured values of at least one of flow rates and temperatures of at least one of the first and seconds medium aided by a parameter optimization algorithm.

27. The method as claimed in claim 26, wherein the target function is based on an at least first-order time derivative of the function with the at least one parameter.

28. The method as claimed in claim 26, wherein particle swarm optimization or an evolution strategy algorithm is utilized the parameter optimization algorithm.

29. The method as claimed in claim 27, wherein particle swarm optimization or an evolution strategy algorithm is utilized the parameter optimization algorithm.

30. The method as claimed in claim 18, wherein a value of a variable characterizing the fouling is ascertained without using material data for the first and second medium or without using geometry data for the heat exchanger.

31. The method as claimed in claim 18, wherein a value of a variable characterizing the fouling is ascertained without using the material data or the geometry data.

32. The method as claimed in claim 18, wherein a value of a variable characterizing the fouling is ascertained, preferably exclusively, from measured values of several of the following measured variables: (i) temperatures of the first medium and the second medium at an inlet and outlet of the heat exchanger, and (ii) flow rates of the first medium and the second medium through the heat exchanger.

33. The method as claimed in claim 18, wherein only relative values for a variable characterizing the fouling are ascertained.

34. The method as claimed in claim 18, wherein heat transfer resistance or heat-transfer conductivity is utilized as a variable characterizing the fouling.

35. A device for ascertaining fouling in a heat exchanger in which heat is transferred from a first medium to a second medium through a wall, said device comprising: a facility for receiving measured values or variables of the heat exchanger derived therefrom; and an evaluating facility in which a function with at least one parameter describing a dependence of a first variable influenced by the fouling on at least one of a flow rate and a temperature of at least one of the first medium and the second medium comprising a simultaneous influence of changes in the flow rate and temperature on the first variable, is stored; wherein the evaluating facility is configured to ascertain a value for the at least one parameter aided by the measured values or the variables derived therefrom of at least one of the first medium and the second medium.

36. A computer program comprising instructions which, when executed on a computer, cause the computer to execute the method as claimed in claim 18.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The invention and further advantageous embodiments of the invention according to features of the subclaims are explained below with reference to exemplary embodiments in the figures, in which:

[0065] FIG. 1 is a block diagram of a heat exchanger and a device for ascertaining fouling in the heat exchanger in accordance with the invention,

[0066] FIG. 2 is a graphical plot of a time profile of flow rates and temperatures of a service medium and a product medium for an industrial heat exchanger in accordance with the invention;

[0067] FIG. 3 is a graphical plot of a time profile of a normalized k-value for the flow rates and temperatures of FIG. 2;

[0068] FIG. 4 is graphical plot of a time profile of normalized fouling resistance ascertained with the method in accordance with the invention compared to the graphical plot of the normalized k-value of FIG. 3;

[0069] FIG. 5 is a graphical plot of a time profile of the normalized fouling resistance of FIG. 4 ascertained with the method in accordance with the invention compared to normalized fouling resistance ascertained by rigorous modeling;

[0070] FIG. 6 is a block diagram of a heat exchanger and a cloud-based device for ascertaining fouling in a heat exchanger in accordance with the invention; and

[0071] FIG. 7 is a flowchart of the method in accordance with the invention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

[0072] FIG. 1 shows by way of example and in a simplified representation a heat exchanger 1 for transferring heat or cold from a service medium S to a product medium P. The heat exchanger 1 is represented by way of example as a counterflow heat exchanger, but other heat exchanger configurations 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 rate F.sub.P (or the volume flow) of the product medium and its temperature T.sub.P,in are measured before entry into the heat exchanger 1 via a flow rate 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.sub.P,out of the product medium P leaving the heat exchanger 1.

[0073] The product medium P is heated or cooled via a service medium S, which is supplied to the heat exchanger 1 from a heating or cooling medium supply. In the direction of flow upstream of the heat exchanger 1, the flow rate Fs (or the volume flow) of the service medium and its temperature T.sub.S,in are measured before entry into the heat exchanger 1 by means of a flow rate 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.sub.S,out of the service medium S leaving the heat exchanger 1.

[0074] To monitor the heat exchanger 1 with regard to fouling, the flow rate measured value F.sub.P and the temperature measured values T.sub.P,in, T.sub.P,out of the product medium P and the flow rate measured value F.sub.S and the temperature measured values T.sub.S,in, T.sub.S,out of the service medium S are transferred to a device 10 for ascertaining fouling. If individual process variables of the product medium P or the service medium S, such as its inlet temperature T.sub.P,in or T.sub.S,in, are fixed due to given framework conditions and therefore can be assumed to be invariable, they do not need to be measured.

[0075] The following applies to the product-related and service-related heat flows {dot over (Q)}.sub.P and {dot over (Q)}.sub.S:

{dot over (Q)}.sub.P=c.sub.P,P.Math.?.sub.P.Math.F.sub.P.Math.(T.sub.P,out?T.sub.P,in)

and

{dot over (Q)}.sub.S=?c.sub.P,S.Math.?.sub.S.Math.F.sub.S.Math.(T.sub.S,out?T.sub.S,in).

where [0076] c.sub.P,P is the thermal capacity of the product medium, [0077] c.sub.P,S is the thermal capacity of the service medium, [0078] ?.sub.P is the density of the product medium, and [0079] ?.sub.S is the density of the service medium.

[0080] Disregarding losses, the total amount of heat dissipated by the service medium S is transferred to the product medium P so that both heat flows are identical ({dot over (Q)}.sub.P={dot over (Q)}.sub.S={dot over (Q)}).

[0081] Alternatively, the heat flow can also be calculated with the following relationship resulting from the mechanical design of the heat exchanger:

{dot over (Q)}=k.Math.A.Math.?T.sub.m.

[0082] Herein: [0083] k: is the heat transfer coefficient (in W/m.sup.2K), [0084] A: is the available surface for heat exchange (in m.sup.2), [0085] ?T.sub.m: is the mean logarithmic temperature difference, and [0086] {dot over (Q)}: is the heat flow.

[0087] The mean logarithmic temperature difference ?T.sub.m is defined as

[00004]$?T_m=\frac{?T_A-?T_B}{\ln \left(\frac{?T_A}{?T_B}\right)},$

where ?T.sub.A is the temperature difference of the inlet side (from the perspective of the product medium) and ?T.sub.B is that of the outlet side.

[0088] Thus, the transferred heat flow can be calculated in three variants as: [0089] c) heat flow dissipated by medium 1

{dot over (Q)}.sub.P=c.sub.P,P?.sub.PF.sub.P(T.sub.P,Aus?T.sub.P,Ein) [0090] b) heat flow passing through the heat exchanger 1

{dot over (Q)}=k.Math.A.Math.?Tm [0091] c) heat flow dissipated by medium 2

{dot over (Q)}.sub.S=?c.sub.P,S?.sub.SF.sub.S(T.sub.S,Aus?T.sub.S,Ein)

[0092] As a result:

c.sub.P,P?.sub.PF.sub.P(T.sub.P,Aus?T.sub.P,Ein)=k.Math.A.Math.?Tm=?c.sub.P,S?.sub.SF.sub.S(T.sub.S,Aus?T.sub.S,Ein).

[0093] 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 heat transfer resistance 1/k.sub.ist and the heat transfer resistance 1/k.sub.soll, that was ascertained in clean state.

[00005]$R_f=\frac{1}{k_{\mathrm{ist}}}-\frac{1}{k_{\mathrm{soll}}}k=\frac{1}{\frac{1}{?s}+\frac{s_w}{{?}_w}+\frac{1}{{?}_P}+R_f}$

where [0094] s.sub.w: is the wall thickness (in m), [0095] ?.sub.w: is the thermal conductivity of the wall (in W/mK), [0096] ?.sub.S: is the heat-transfer coefficient from the service medium to the wall (in W/m.sup.2K), and [0097] ?.sub.P: is the heat transfer coefficient from the product medium to the wall (in W/m.sup.2K).

[0098] Hence, the k-value can be calculated with the relationship

[00006]$\begin{array}{cc}K=\stackrel{.}{Q}\frac{1}{A}\frac{\ln \left(\frac{?T_A}{?T_B}\right)}{?T_A-?T_B}& \left(1\right)\end{array}$

where

?T.sub.A=T.sub.P,A?T.sub.S,out and ?T.sub.B=T.sub.P,Aus?T.sub.S,Ein

for the case of a counterflow heat exchanger.

[0099] Hence, with values for A, c.sub.P,P, c.sub.P,S, ?.sub.P and ?.sub.S considered to be constant, a relative value for k can be calculated with the aid of only the measured values of the inlet and outlet temperatures and the flow rates of the two media.

[0100] To this end, FIG. 2 shows by way of example temporal profiles of measured values of flow rates and temperatures in an industrial shell-and-tube heat exchanger and FIG. 3 shows a profile of the 1/k-value calculated therefrom with a heat balance according to (1), where this has been normalized to a maximum value.

[0101] Although, the profile shows an in principle increasing trend, short-term fluctuations are significantly stronger than the trend. Thus, no statement regarding fouling can be made according to the data and operating point.

[0102] As has been found, this enables the fouling resistance to be ascertained more exactly because changes in the flow rate and/or temperature product and/or service medium are also taken into account in the evaluation.

[0103] If the heat is transferred from the service medium S to the product medium P through a wall, the the k-value is theoretically composed as follows:

[00007]$\begin{array}{cc}\frac{1}{k}=\frac{1}{{?}_P}+\frac{1}{{?}_S}+\frac{s_w}{{?}_w}+R_f,& \left(2\right)\end{array}$

[0104] Changes in the flow rate and or temperature and thus changes in the type of flow or within one type of flow can lead to changes in the heat transfer coefficient ?.sub.S,P.

[0105] Based on thermodynamic models and with the aid of simulation studies, if the design parameters a, b?R are chosen appropriately, then a dependence of the heat transfer coefficient ? on the flow rate can be described for both sides of the wall by the structure function

?(F)=a.Math.F(t).sup.b, (3)

where F is the flow rate of the respective medium and t is the time.

[0106] Furthermore, as has been found by thermodynamic models and with the aid of simulation studies, if the design parameters a, b?R are chosen appropriately, then it is moreover possible to describe a dependence of the heat transfer coefficient ? on the temperature by the structure function

?(T)=a.Math.(T(t)+b).sup.c, (4)

where T is the mean temperature of the respective medium and t is the time.

[0107] In the case of a simultaneous change in flow rate and temperature, the two above structures can be combined to form the overall structure function

?(F, T)=a.Math.F.sup.b.Math.(T+c).sup.d (5)

with the design parameters a, b, c, d?R and where F is the (time-dependent) flow rate and T is the (time-dependent) mean temperature of the respective medium. Hence, this function describes a dependence of the heat transfer coefficient ? on both the flow rate and temperature.

[0108] Validation with the aid of simulation data has shown that this overall structure function enables both flow rate dependencies and temperature dependencies to be depicted very accurately.

[0109] Since the fouling process has very slow dynamics, the fouling resistance can be disregarded in a first-order derivative of (2) with respect to time and the following is obtained

[00008]$\begin{array}{cc}\frac{d\frac{1}{k}}{\mathrm{dt}}=\frac{d\frac{1}{{?}_P}}{\mathrm{dt}}+\frac{d\frac{1}{{?}_S}}{\mathrm{dt}},& \left(6\right)\end{array}$

where, when the structure functions (3), (4) or (5) are inserted into (6), only the respective design parameters remain as unknown variables. Equation (6) produces the target function

[00009]$\begin{array}{cc}J=.Math.\frac{d\frac{1}{k}}{\mathrm{dt}}-\left(\frac{d\frac{1}{{?}_P}}{\mathrm{dt}}+\frac{d\frac{1}{{?}_S}}{\mathrm{dt}}\right).Math.& \left(7\right)\end{array}$

which is optimized (here minimized) with respect to design parameters with the aid of a parameter optimization algorithm for available operating data (measured values) of the heat exchanger. Here, optimization can occur exclusively with measured values of the temperatures T.sub.P,Ein, T.sub.P,Aus, T.sub.S,Ein, T.sub.S,Aus of the service medium S and the product medium P at the inlet and outlet of the heat exchanger 1 and the flow rates F.sub.P, F.sub.S of the service medium S and the product medium P through the heat exchanger 1.

[0110] Preferably, particle swarm optimization (PSO) or an evolution strategy algorithm is used as the parameter optimization algorithm.

[0111] The optimization (here minimization) results in the desired design parameters. These can then be used in the respective structure function (3), (4) or (5).

[0112] The respective structure function (3), (4) or (5) with the ascertained design parameters can then be used in (2).

[0113] Preferably, only relative values or relative changes in the fouling resistance are taken into account. Therefore, in (2), the constant thermal resistance Rw=s.sub.w/?.sub.w of the wall can be disregarded and the fouling resistance can then be calculated by

[00010]$\begin{array}{cc}{R}_f=\frac{1}{k}-\left(\frac{1}{{?}_P}+\frac{1}{{?}_S}\right).& \left(8\right)\end{array}$

[0114] The 1/k-value in (8) can be calculated with the aid of the heat balance according to (1). Only relative values or changes in the fouling resistance are considered. Consequently, all material parameters of the media S, P and all geometry parameters of the heat exchanger 1 can be set to 1 in (1). The k-value in (8) can be calculated or estimated with the aid of (1) exclusively from measured values of the temperatures T.sub.P,Ein, T.sub.P,Aus, T.sub.S,Ein, T.sub.S,Aus of the service medium S and the product medium P at the inlet and outlet of the heat exchanger 1 and the flow rates F.sub.P, F.sub.S of the service medium S and the product medium P through the heat exchanger 1.

[0115] To this end, FIG. 4 shows by way of example relative time profiles of 1/k-values ascertained with (1) and values for the fouling resistance R.sub.f calculated or estimated with (8) for the measured values of FIG. 2. Here, the values were normalized to the maximum of the 1/k-value. Compared to the 1/k-value, the increase in fouling resistance R.sub.f is very clearly apparent.

[0116] FIG. 5 shows a time profile of the normalized fouling resistance R.sub.f in FIG. 4 ascertained with the method in accordance with the invention compared to normalized fouling resistance R.sub.f,rig, calculated by rigorous white-box modeling taking into account all material properties and geometric variables for the measured values of FIG. 2. The comparison shows the high quality of the method in accordance with the invention.

[0117] Hence, the actual task of determining fouling is initially relegated to the background and it is precisely the effect of fouling that is compensated by derivation to ascertain the design parameters in the above. Only then, is the fouling determined with the aid of the structure.

[0118] It should be understood, it is always possible to add further data in order to better ascertain (or estimate) the design parameters.

[0119] The great advantage of the disclosed inventive method is that only very little information about the heat exchanger is required or very few assumptions need to be made. No material data or geometry data are required.

[0120] In principle,

[00011]$X=\frac{1}{{?}_S}+\frac{1}{{?}_P}+\frac{s_w}{{?}_w}\mathrm{and}1/k=X+R_f.$

enables the fouling resistance R.sub.f to be calculated by

R.sub.f=1/k?X.

[0121] Herein [0122] R.sub.f: is a variable characterizing the fouling, [0123] 1/k: is a first variable that is influenced by the flow rate, and [0124] X: is a second variable that is not influenced by the fouling.

[0125] The second variable X is hence a measure for 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.

[0126] Hence, the method in accordance with the invention enables values for the second variable X to be ascertained with which the influence of changes in the flow rate and/or temperature on the values of the first variable, here the 1/k-value calculated from measured values, can then be compensated. This can increase accuracy when ascertaining the fouling resistance, i.e., the variable characterizing the fouling.

[0127] The same methods can in principle also be transferred to the consideration of the pressure difference. The flow resistance also increases with fouling, but also depends on the flow rate.

[0128] With the example of an industrial heat exchanger, these methods were able to achieve a significantly better result when ascertaining fouling than that achieved with the conventional calculation. Thus, the results could help a plant operator to achieve a significantly better evaluation of the fouling resistance. Advantageously the methods can be applied not only to the heat balances, but also to the consideration of the pressure differences and thus the flow resistances.

[0129] The method in accordance with the invention can be provided as a stand-alone application in a process plant or integrated into a process control system of a process plant. It can also be provided in a local or remote computer system (cloud), for example, by a service provider as Software as a Service.

[0130] A device 10 in accordance with the invention shown in FIG. 1 by way of example for ascertaining fouling comprises a facility 20 for receiving the measured values T.sub.P,in, T.sub.P,out, T.sub.S,in, T.sub.S,out, F.sub.P, F.sub.S of the heat exchanger 1 and and evaluating facility 30 which is configured to ascertain and output a value for the fouling resistance R.sub.f from these measured values by means of an above-described method. Additionally or alternatively, the evaluating facility can also function as a monitoring device: it can monitor the ascertained fouling resistance to determine whether a threshold value has been exceeded and, if this is the case, output a signal that, for example, indicates the need for cleaning.

[0131] To this end, the evaluating facility 30 comprises a processor 31, a memory 32 for storing the received measured data, and a memory 33 in which a program 34 with instructions is stored that, when executed via the processor 31, cause the above-described method to be executed. The processor unit 31 stores the measured values M received from the facility 20 in the memory 32.

[0132] Although it is possible to detect further variables, such as A, c.sub.P,P, c.sub.P,S, ?.sub.P, ?.sub.S, this is not necessary. On the contrary, the method in accordance with the invention assumes that these are not known. Any constants can be assumed which, when seen in absolute terms, then result in an incorrect k-value, but ultimately the relative changes in this k-value are decisive for the mode of operation and success of the method.

[0133] The device 10 shown in FIG. 1 can, for example, be provided as a stand-alone application in a process plant or integrated in a process control system of a process plant.

[0134] In contrast, a device 100 shown in FIG. 6 for ascertaining fouling can be provided by a local or remote computer system (cloud), for example, to offer the ascertaining of fouling by a service provider as Software as a Service. Herein, the receiver facility 20 is located in situ in the process plant of the heat exchanger 1 and the evaluating facility 30 is located on a local or remote computer system (cloud). To this end, the receiver facility 20 stores the received measured values in a memory 21 and sends (for example, at regular time intervals, on an event-driven basis or upon request by the evaluating facility 30) the measured values M (or variables derived therefrom) via a sending facility 22, for example, via the internet or an intranet, to the evaluating facility 30.

[0135] The evaluating facility 30 comprises a processor 31, a memory 32 for storing the received measured data and a memory 33 in which a program 34 with instructions is stored which, when executed via the processor 31, cause the above-described method to be executed.

[0136] The processor 31 stores the measured values M received from the facility 20 via an interface 36 in the memory 32, and, if appropriate, for further input variables that are received via a separate interface 37. The values for the fouling resistance R.sub.f ascertained with the program 34 and/or a signal indicating the need for cleaning are output via an interface 38. Here, the interfaces 36, 37 and 38 can also be provided by a single common interface, for example, to the intranet or an intranet.

[0137] Virtually real-time acquisition of the measured values and calculation of the fouling resistance enable a continuous data-based fouling analysis and monitoring of the fouling to take place concurrently with the operation of the plant or the heat exchanger. However, an offline-fouling analysis with a time offset to the real operation of the plant is also possible.

[0138] FIG. 7 is a flowchart for ascertaining fouling in a heat exchanger 1 in which heat is transferred from a first medium S to a second medium P through a wall. The method comprises utilizing a function with at least one parameter, where the function describes the dependence of a first variable k influenced by the fouling on at least one of a flow rate and a temperature of at least one of the first medium S and the second medium P comprising a simultaneous influence of changes in flow rate and temperature on the first variable k, as indicated in step 710.

[0139] Next, a value for the at least one parameter is ascertained with the aid of measured values of at least one of the first mediums and the second medium, as indicated in step 720.

[0140] 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.