Method and Device for Determining Fouling in a Heat Exchanger

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.

Claims

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.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0070] The invention and further advantageous embodiments of the invention are explained in greater detail below in the figures using exemplary embodiments, in which:

[0071] 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

[0072] FIG. 2 shows a temporal progression of a standardized k value for an industrial heat exchanger in accordance with the prior art;

[0073] 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;

[0074] 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;

[0075] 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;

[0076] FIG. 6 shows an application of a linear regression using the example of the industrial heat exchanger in FIG. 2;

[0077] FIG. 7 shows a temporal progression of the fouling resistance R.sub.f for the industrial heat exchanger in FIG. 2 in a calculation in accordance with Method 2 of the invention;

[0078] FIG. 8 shows a temporal progression of the fouling resistance R.sub.f for the industrial heat exchanger in FIG. 2 in a calculation in accordance with Method 3 of the invention;

[0079] 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;

[0080] 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;

[0081] 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,

[0082] 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;

[0083] 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;

[0084] 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′

[0085] 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;

[0086] 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

[0087] FIG. 17 is a flowchart of the method in accordance with the invention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

[0088] 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.sub.P (or the flowrate or the volume flow) of the product medium and its temperature T.sub.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.sub.P, Out of the product medium P exiting from the heat exchanger 1.

[0089] 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.sub.S (or the flowrate or the volume flow) of the service medium and its temperature T.sub.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.sub.S, Out of the service medium S exiting from the heat exchanger 1.

[0090] To monitor the heat exchanger 1 for fouling, the flow 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 measured value F.sub.S, as well as the temperature measured values T.sub.S, In, T.sub.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.sub.P, In or T.sub.S, In, are established based on given basic conditions and hence can be assumed to be unchanging, they do not need to be measured.

[0091] The following applies for 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.ρ.sub.P.Math.F.sub.P.Math.(TP,.sub.out−T.sub.P, In)

[0092] and

{dot over (Q)}.sub.S=−c.sub.P, S.Math.ρ.sub.S.Math.F.sub.S.Math.(T.sub.S, Out−T.sub.S, In).

[0093] Where

[0094] c.sub.P, P thermal capacity of the product medium,

[0095] c.sub.P, S thermal capacity of the service medium,

[0096] ρ.sub.P density of the product medium,

[0097] ρ.sub.S density of the service medium.

[0098] 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)}.sub.P={dot over (Q)}.sub.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.Math.A.Math.ΔT.sub.m.

[0099] The following applies here:

[0100] k: thermal transmission coefficient (in W/m.sup.2K)

[0101] A: available surface for heat exchange (in m.sup.2)

[0102] ΔT.sub.m: mean logarithmic temperature difference

[0103] Q: heat flow.

[0104] The mean logarithmic temperature difference ΔT.sub.m is defined as:

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

[0105] where ΔT.sub.A stands for the temperature difference of the inlet side (from the perspective of the product medium) and ΔT.sub.B for that of the outlet side.

[0106] Thus, the transferred heat flow can be calculated in three variants, as:

[0107] a) heat flow dissipated by Medium 1

{dot over (Q)}.sub.P=−c.sub.P, Pρ.sub.PF.sub.P (T.sub.P, Out−T.sub.P, In)

[0108] b) heat flow passing through the heat exchanger 1

{dot over (Q)}=k.Math.A.Math.ΔT.sub.m

[0109] c) heat flow dissipated by Medium 2

{dot over (Q)}.sub.S=−c.sub.P, Sρ.sub.SF.sub.S(T.sub.S, Out−T.sub.S, In)

[0110] It follows from this that:

c.sub.P, Pρ.sub.PF.sub.P(T.sub.P, Out−T.sub.P, In)=k.Math.A.Math.ΔT.sub.m=−c.sub.P, Sρ.sub.SF.sub.S(T.sub.S, Out−T.sub.S, In).

[0111] 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.sub.actual and the thermal transmission resistance 1/k.sub.target that was determined in the clean state.

[00005]$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}$

[0112] Thus the k value can be calculated using the relationship:

[00006]$k=\stackrel{.}{Q}\frac{1}{A}\frac{\ln \left(\frac{\Delta T_A}{\Delta T_B}\right)}{\Delta T_A-\Delta T_B}$

[0113] where

ΔT.sub.A=T.sub.P, In−T.sub.S, Out and ΔT.sub.B=T.sub.P, Out−T.sub.S, In

[0114] in the case of a reverse current heat exchanger.

[0115] In the case of values for A, c.sub.P, P, c.sub.P, S, ρ.sub.P and ρ.sub.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.

[0116] 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 k.sub.0 present at the time t.sub.0=0 has been determined, and in FIG. 2 a value 1/k′ related to the initial value k.sub.0 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.

[0117] 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.

[0118] 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:

[00007]$k=\frac{1}{\frac{1}{\alpha 1}+\frac{s_w}{{\lambda }_w}+\frac{1}{{\alpha }_2}+R_f}$$\mathrm{or}$$\frac{1}{ k}=\frac{1}{\alpha 1}+\frac{s_w}{ {\lambda }_w}+\frac{1}{{\alpha }_2}+R_f$

[0119] where [0120] R.sub.f: fouling resistance (in m.sup.2K/W) [0121] s.sub.w: wall thickness (in m)) [0122] λ.sub.w: thermal conductivity of the wall (in W/mK) [0123] a.sub.1: thermal transmission coefficient from the first medium to the wall (in W/m.sup.2K) [0124] a2: thermal transmission coefficient from the second medium to the wall (in W/m.sup.2K).

[0125] 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.sub.1,2.

[0126] Where

[00008]$X=\frac{1}{{\alpha }_1}+\frac{1}{{\alpha }_2}+\frac{s_w}{{\lambda }_w}$

[0127] the following is produced:

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

[0128] The fouling resistance R.sub.f can then be calculated by:

R.sub.f=1/k−X.

[0129] In this case

[0130] R.sub.f: is a variable characterizing the fouling,

[0131] 1/k: is a first variable which is affected by the flow,

[0132] X: is a second variable which is not affected by the fouling.

[0133] 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.

[0134] 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.

[0135] Three methods for how the flow can be taken into account are now presented here based on FIGS. 3 to 10:

[0136] Method 1

[0137] In Method 1 the value for X is adjusted at each abrupt change in flow. Here, the following assumptions are made: [0138] the wall thickness and the thermal conductivity thereof (sw/λw=const.) do not change in operation, [0139] the properties of the media do not change, or only insignificantly, [0140] the fouling resistance does not significantly decrease or increase without a particular reason (for example cleaning) in normal operation.

[0141] In a learning phase, immediately after cleaning, an initial value for X is learned.

[0142] For a certain time interval after cleaning, it can be assumed that the fouling resistance is Rf=0.

[0143] In this range, the values for .sup.1/a.sub.1, 1/a.sub.2 and s.sub.w/λ.sub.w are learned (aggregated in the value X). Where R.sub.f=0 and X=1/a.sub.1+1/a.sub.2+s.sub.w/λ.sub.w, X.sub.0 for the initial interval (or after a cleaning interval) can now be determined using the previously calculated k value k.sub.0. X.sub.0=1/k.sub.0 applies here.

[0144] Case 1: The flows do not change

[0145] 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.sub.f=1/k−X. FIG. 3 to this end shows by way of example a progression of 1/k, X and R.sub.f over the time t. The value X is constant and results in a constant difference between 1/k and R.sub.f.

[0146] Case 2: A flow changes at the time t.sub.0

[0147] At the time t.sub.0, the fouling resistance R.sub.f(t.sub.0) is briefly kept constant and X.sub.new is calculated, for example, with X.sub.new=1/k−R.sub.f(t.sub.0).

[0148] For 1/k a mean value for an interval from t.sub.0 to t.sub.0+x can now be used. Alternatively, X.sub.new can also be calculated as follows:

X.sub.new=X.sub.old−(1/k.sub.old−1/k.sub.new).

[0149] 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.

[0150] In the subsequent progression, the fouling resistance is then calculated again using R.sub.f=1/k.sub.new−X.sub.new.

[0151] FIG. 4 to this end shows by way of example a progression of 1/k, X and R.sub.f over the time t. As is apparent, with this method the fouling resistance R.sub.f is continued steadily in the event of a change in the flow at the time t.sub.0, instead of resulting in a change in level.

[0152] If this method is now used to calculate the 1/k value, X and R.sub.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/k.sub.0 and X.sub.0 present at the time t.sub.0=0 have now been determined and values 1/k′ and X′ related to these initial values are represented in FIG. 5.

[0153] 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.sub.f are largely compensated for by changes in the X′ value.

[0154] 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.

[0155] Method 2

[0156] 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.

[0157] 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.sub.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.sub.p), where the function f is a product of the linear regression of F.sub.p and X.

[0158] If this method is now used to calculate the relative fouling resistance R.sub.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 X.sub.0 present at the time t.sub.0=0 has been determined here too and a value X′ related to this initial value is represented in FIG. 7.

[0159] As is apparent, this method also produces a satisfactory result in many ranges.

[0160] Perpendicular lines in this case again show the cleaning times.

[0161] 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.

[0162] Method 3

[0163] 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.

[0164] If this method is now used to calculate the relative fouling resistance R.sub.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/k.sub.0 and X0 present at the time t.sub.0=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.

[0165] 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.

[0166] 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.

[0167] 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.

[0168] In addition to the three methods, combinations and extensions can also be applied.

[0169] Combination of Methods 1 and 2

[0170] 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.

[0171] Method 4

[0172] 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 (ΔF.sub.1) and of the X value (ΔX.sub.1) 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 ΔF.sub.1 and ΔX.sub.1 is used. FIG. 9 to this end shows an assignment of values for X to the flow F over the time t.

[0173] 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.

[0174] Method 5

[0175] 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.

[0176] 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.

[0177] 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.

[0178] It is assumed that the reciprocal k value is composed of the sum of the fouling resistance and X:

[00009]$\frac{1}{k}=X+R_f,$

[0179] where X is composed of all further thermal resistances. The time derivation produces:

[00010]$\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,$

[0180] wherein

[00011]$\kappa \left(t\right)=\frac{d\frac{1}{k}}{\mathrm{dt}},\Phi \left(t\right)=\frac{\mathrm{dF}}{\mathrm{dt}},m=\frac{{\mathrm{dR}}_f}{\mathrm{dt}}.$

[0181] Thus, the following applies:

[00012]$\frac{\mathrm{dX}}{\mathrm{dF}}=\frac{\kappa \left(t\right)-m}{\Phi \left(t\right)}$

[0182] For Φ.sub.1(t)≠Φ.sub.2(t), the following applies:

[00013]$\frac{1}{{\Phi }_1-{\Phi }_2}\left({\Phi }_1\frac{dX}{dF}-{\Phi }_2\frac{dX}{dF}\right)=\frac{dX}{dF}$

[0183] At a point X.sub.0, F.sub.0 the unambiguous but unknown relationship

[00014]${\frac{\mathrm{dX}}{\mathrm{dF}}.Math.}_{X_0,F_0}$

[0184] applies, regardless of Φ(t) and κ(t).

[0185] Hence the following applies:

[00015]$\frac{dX}{dF}=\frac{1}{{\Phi }_1-{\Phi }_2}\left({\Phi }_1\frac{dX}{dF}-{\Phi }_2\frac{dX}{dF}\right)=\frac{1}{{\Phi }_1-{\Phi }_2}\left({\Phi }_1\frac{{\kappa }_1\left(t\right)-m}{{\Phi }_1\left(t\right)}-{\Phi }_2\frac{{\kappa }_2\left(t\right)-m}{{\Phi }_2\left(t\right)}\right)=\frac{1}{{\Phi }_1-{\Phi }_2}\left({\kappa }_1\left(t\right)-{\kappa }_2\left(t\right)\right)$

[0186] for all Φ.sub.1(t)≠Φ.sub.2(t).

[0187] It is therefore necessary to calculate the thus weighted difference in the

[00016]$\frac{1}{k}$

[0188] changes, tor two aiiierent changes in flow Φ.sub.1(t)≠Φ.sub.2(t).

[0189] To now therefore determine a characteristic curve, it is proposed successively to compile all data with

[00017]$\frac{\mathrm{dF}}{\mathrm{dt}}>c_F,$

[0190] for all F in the environment of an F.sub.0, and in each case to determine

[00018]$\frac{\mathrm{dX}}{\mathrm{dF}}$

[0191] for paired Φ.sub.1(t)≠Φ.sub.2(t). By integrating the derivation characteristic curve, the characteristic curve that is desired is then created.

[0192] In this case, the absolute value is advantageously irrelevant, so that an initial value need not be taken into account in the integration.

[0193] 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.

[0194] 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.

[0195] FIGS. 10 to 12 to this end show a simulation of an industrial heat exchanger with variation in a flow.

[0196] FIG. 10 in this case shows a temporal progression of (simulated) measured values of the flow F.sub.P of the product medium and of the flow F.sub.S of the service medium through the heat exchanger.

[0197] FIG. 11 shows the associated (simulated) measured values for the temperature T.sub.P, In of the product medium at the inlet and the temperature T.sub.P, Out of the product medium at the outlet of the heat exchanger. In addition, (simulated) measured values of the temperature T.sub.S, In of the service medium at the inlet and of the temperature T.sub.S, Out of the service medium at the outlet of the heat exchanger are shown.

[0198] FIG. 12 shows the associated calculated relative values for 1/k and the fouling resistance R.sub.f.

[0199] 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.

[0200] 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.

[0201] Method 6

[0202] 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.

[0203] 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.

[0204] In the case of a heat exchanger, the effects of both the characteristic curves X.sub.P=f.sub.P(F.sub.P) and X.sub.S=f.sub.S(F.sub.S) on the 1/k value overlap one another where

[00019]$\frac{1}{k}=X_P+X_S+R_f.$

[0205] The derivation of 1/k after the time produces

[00020]$\frac{d\frac{1}{k}}{\mathrm{dt}}=\frac{\mathrm{dX}}{{\mathrm{dF}}_p}\frac{{\mathrm{dF}}_p}{\mathrm{dt}}+\frac{dX}{d{F}_S}\frac{d{F}_S}{dt}+\frac{d{R}_f}{dt}$

[0206] where X=X.sub.P+X.sub.S.

[0207] n.sub.P interpolation points (dx.sub.pi, F.sub.pi) of the derivation characteristic curve

[00021]$\frac{{\mathrm{dX}}_P}{{\mathrm{dF}}_P}=\stackrel{-}{f_P}\left(F_P\right)$

[0208] and n.sub.S interpolation points (dx.sub.si, F.sub.si) of the derivation characteristic curve

[00022]$\frac{{\mathrm{dX}}_S}{{\mathrm{dF}}_S}=\overline{f_S}\left(F_S\right)$

[0209] are now sought.

[0210] To this end, for each time t for which

[00023]$\frac{{\mathrm{dF}}_P}{\mathrm{dt}}>\mathrm{dFpLimit}\mathrm{or}\frac{{\mathrm{dF}}_S}{\mathrm{dt}}>\mathrm{dFsLimit}$

[0211] applies, an equation with three unknowns (dx.sub.pi,dx.sub.si,m) is generated:

[00024]$\frac{d\frac{1}{k}}{\mathrm{dt}}=d{x}_{Pi}\frac{d{F}_P}{dt}+d{x}_{\mathrm{Si}}\frac{d{F}_S}{dt}+m$

[0212] n.sub.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:

[00025]$Ab=c$${{{{{b=[\frac{d{X}_P}{d{F}_P}.Math.}_{F_{P_1}},.Math.,\frac{d{X}_P}{d{F}_P}.Math.}_{F_{P_{n_p}}},\frac{d{X}_S}{d{F}_S}.Math.}_{F_{s_1}},.Math.,\frac{d{X}_S}{d{F}_S}.Math.}_{F_{s_{n_s}}},m]}^T$$c=\left[\kappa \left(t_1\right).Math.\kappa \left(t_m\right)\right]$$A\in R^{n_D\times \left(n_p+n_s+1\right)}$

[0213] For better understanding, a row of A is specified. At the corresponding time, it should be the case that F.sub.P≈F.sub.P5 and F.sub.S≈F.sub.S7, where n.sub.P=10 and n.sub.S=20. The row of A then corresponds to:

[00026]${{{[0,.Math.,0,\frac{d{X}_P}{d{F}_P}.Math.}_{F_{P5}},0,.Math.0,\frac{d{X}_S}{d{F}_S}.Math.}_{F_{S7}},0,.Math.,0,1]}^T$

[0214] where there are entries different from zero only in the 5.sup.th and 17.sup.th (=10+7) and last column.

[0215] 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.

[0216] The two derivation characteristic curves can then again be generated from the vector and integrating these produces the characteristic curves X.sub.P=f.sub.P(F.sub.P) and X.sub.S=f.sub.S(F.sub.S).

[0217] 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:

[00027]$R_f=\frac{1}{k}-X_P-X_S$

[0218] 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.

[0219] 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.

[0220] FIGS. 13-15 to this end show a simulation of an industrial heat exchanger with variation in the flows.

[0221] FIG. 13 in this case shows a temporal progression of (simulated) measured values of the flow F.sub.P of the product medium and of the flow F.sub.S of the service medium through the heat exchanger.

[0222] FIG. 14 shows the associated (simulated) measured values for the temperature T.sub.P, In of the product medium at the inlet and the temperature T.sub.P, Out of the product medium at the outlet of the heat exchanger. In addition, (simulated) measured values of the temperature T.sub.S, In of the service medium at the inlet and the temperature T.sub.S, Out of the service medium at the outlet of the heat exchanger are shown.

[0223] FIG. 15 shows the relative values calculated therefrom for 1/k and the fouling resistance R.sub.f.

[0224] 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.

[0225] 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.

[0226] 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.

[0227] 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.sub.P, F.sub.S, T.sub.P, In, T.sub.P, Out, T.sub.S, In, T.sub.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.

[0228] 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.

[0229] 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”.

[0230] 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.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 an evaluation device 30 which is configured to determine and output a value for the fouling resistance R.sub.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.

[0231] 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.

[0232] It is not necessary to detect further variables, such as c.sub.P, P, c.sub.P, S, ρ.sub.P, ρ.sub.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.

[0233] 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.

[0234] 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.

[0235] 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.

[0236] 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.sub.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.

[0237] 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.

[0238] 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.

[0239] 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.

[0240] 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.

[0241] 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.

[0242] 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.