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.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method and a device for ascertaining fouling in a heat exchanger.

2. Description of the Related Art

Heat exchangers, frequently also referred to as heat-transfer devices, are technical apparatuses used to heat or cool a medium. To this end, heat is transferred from a warmer first medium to a colder second medium. Depending upon their design, heat exchangers differ in their operating principle. The most frequent designs are classified into one of the following three functional groups: parallel-flow heat exchangers, counter-flow heat exchangers or cross-flow heat exchangers.

The medium to be heated or cooled is frequently also referred to as the “product medium” and the heating or cooling medium is frequently also referred to as the “service medium”. The service medium can, for example, be heating steam or cooling water. The service medium usually either flows through a conduit arrangement arranged within the product medium or flows around a conduit arrangement through which the product medium flows.

The first and the second media are conducted through the heat exchanger, where the two media usually flow past one another, separated by a wall, and herein the heat of the warmer medium is dissipated to the cooler 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 for the formation of such deposits can be of a physical, chemical or biological nature. In many cases, it is not possible to prevent them, such as due to the prevailing product-related boundary conditions. The coatings impede heat transfer between the media and thereby reduce the efficiency of the heat exchanger. Once a certain degree of contamination is reached, chemical or mechanical cleaning or possibly even replacement of the heat exchanger becomes necessary. This problem is particularly prevalent in large industrial heat exchangers used 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 usually designed for a heat transfer capacity of more than 100 kW.

From the outside, it is very difficult to determine the degree of contamination of the interior of the heat exchanger and so it is not possible to clean or replace the heat exchanger as required. A temperature control circuit can compensate for the effects of contamination to a certain degree and so the contamination is not immediately apparent from the initial temperature of the product medium. This lack of knowledge means it is frequently not possible to clean or replace the heat exchanger as required.

Therefore, to date, heat exchangers affected by contamination have been cleaned or replaced at regular intervals, i.e., without any knowledge of the actual state of contamination.

With this approach, maintenance intervals cannot be adapted in accordance with different degrees of fouling. As a result, it is, for example, possible for the heat exchanger to be cleaned or replaced prematurely even though there are only minor deposits at this stage. Although this would ensure efficient operation of the heat exchanger, it would be uneconomical because, not only are direct costs for the maintenance work incurred, but also indirect costs due to the additional adverse effect on the ongoing operation of the plant in which the heat exchanger is employed. If appropriate measures are taken too late, excessive deposits inside the heat exchanger result in significantly reduced heat transfer. The consequence is that, for the same heat flow to be transferred, a much greater flow rate of the service medium is required than is the case when the heat exchanger is in a clean state. This leads to increased energy consumption for the provision of the service medium, i.e., heating and pumping capacity, which likewise represents a cost factor. Furthermore, heavy deposit formation entails the risk of a deterioration in the quality of the product medium since, for example, temperature specifications are not adequately adhered to.

EP 2 128 551 A1 discloses a method for monitoring the effectiveness of a heat exchanger with regard 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, zero degree of contamination and maximum permissible degree of contamination, of the heat exchanger. The respective reference heat flow {dot over (Q)}_Ref is ascertained in dependence on the current operating point of the heat exchanger from a characteristic field previously created and stored with the aid of a simulation program for different operating points, where the operating point of the heat exchanger is determined by the flow rates F_P, F_S of both media and their temperatures T_P,in, T_S,in upon entry into the heat exchanger. The use of the simulation program enables the operating point dependency of the transferable quantity of heat to be precalculated, for example, at several hundred interpolation support points, without it being necessary 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 flow rates, inlet temperatures and outlet temperatures of the service and product medium represent process variables, where at least one process variable is variable on the product side, 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 rate 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 rate of the service medium is ascertained from the measured values obtained herein in a reference state of the heat exchanger and is stored. Here, 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 measure of the deviation of the current state of the heat exchanger from the reference state.

It is known from Zölzer K. et al. “Einsatz des Kessel-Diagnose-Systems KEDI im Kraftwerk Staudinger 5”, [“Use of the Boiler Diagnostic system KEDI in the Staudinger 5 Power Plant”] VGB Kraftwerkstechnik, Essen, DE, Vol. 75, No. 9, Sep. 1 1995, pp 755-762, DE 195 02 096 A1, U.S. Pat. No. 4,390,058 A or EP 0 470 676 A2 that the heat transfer coefficient or k-value can be taken into consideration when monitoring heat exchangers. The heat flow {dot over (Q)}=k·A·ΔT_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 heat transfer. Both the k-value and the logarithmic temperature difference each depend on the operating point of the heat exchanger and thus on the flow rates 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 DE 195 02 096 A1, a current k-value is ascertained for each heating surface from a calculated heat output, a logarithmic temperature difference and the size of the heating surface. A comparison of the current k-value with a stored reference k-value Kref for the “cleanest possible state” is used to calculate a cleaning state CF according to the relationship CF=K/Kref. The reference values Kref are stored in a memory in dependence on the load and possibly in dependence on the fuel. The reference values Kref can be corrected with correction factors in accordance with certain current state variables. Thus, for example, a correction is made according to the steam velocity. However, the way in which the reference values are obtained remains an open question.

In Zölzer's publication, a “heating surface factor FV” is defined as a measure for heating surface contamination. This is defined as the ratio of an actual evaluation factor factual to a base evaluation factor fBasis. The actual evaluation factor factual is the ratio of a “measured” heat transfer coefficient Kactual to a theoretical heat transfer coefficient KTheorie. The “measured” heat transfer coefficient Kactual is ascertained based on the temperatures of the media and the size of the heating surface. The theoretical heat transfer coefficient KTheorie is, inter alia, determined based on the geometry data, such as pipe dimension, and/or width and longitudinal separation, of the heating surface. The base evaluation factor fBasis is ascertained 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 feed-water parameters, live steam parameters and repeater parameters. However, precise details of the process data used are not disclosed.

DE 10 2016 225 528 A1 discloses a method for monitoring a state of contamination in a heat exchanger with the aid of an additional temperature sensor 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 any deviation between the correctively calculated operating wall temperature and a reference wall temperature is ascertained. 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, such as deviations in the fluid temperatures or in the volume flows of the fluids. The operating wall temperature and reference wall temperature are values that are measured at the same point and/or specified for the same point on the heat exchanger.

A current fouling resistance R_f can be calculated from the difference between a current heat-transfer resistance 1/k_actual and heat-transfer resistance 1/k_target, calculated when the heat exchanger is in clean state:

$R_f=\frac{1}{k_{\mathrm{actual}}}-\frac{1}{k_{\mathrm{target}}}$

However, as has been found, an evaluation of the fouling resistance on this basis is inaccurate. For example, short-term fluctuations or level jumps of the heat-transfer resistance occur without any apparent particular reason, as would, for example, be present during cleaning or replacement of the heat exchanger.

A method for ascertaining fouling in a heat exchanger is known from the applicant's published patent application PCT/EP2021/055563 in which a value for a variable characterizing the fouling is ascertained from a value for a first variable influenced by the fouling and a value of a second variable, where the second variable at least partially compensates a change in the first variable caused by a change in a flow rate of a first medium and/or a second medium through the heat exchanger. Here, the second variable, i.e., the compensation variable, is based on measured values of flow rates and temperatures of the media, i.e., without using data on material properties of the media, and on structural properties of the heat exchanger.

SUMMARY OF THE INVENTION

In view of the following, it is an object of the present invention to provide a method and a device with which fouling in a heat exchanger can be ascertained even more accurately.

This and other objects and advantages are achieved in accordance with the invention by a a device and a computer program and a method via which, in order to ascertain fouling in a heat exchanger in which heat is transferred from a first medium to a second medium through a wall, a function with at least one parameter is used that describes a dependence of a first variable influenced by the fouling on a flow rate and/or a temperature of the first medium and/or the second medium, in particular on a simultaneous influence of changes in flow rate and temperature on the first variable, and a value for the at least one parameter is ascertained with the aid of measured values of the first medium and/or the second medium.

The invention is based, on the one hand, on the knowledge that fluctuations, in particular level jumps, in the variable characterizing the fouling can frequently be explained by changes in the flow rate and/or temperature of the first and/or second medium. The reason for this is that changes in the flow rate and/or temperature can also change the flow velocity and the type of flow at the points of the heat transfer from the first medium to the second medium. However, depending upon the type of flow that is then established (for example, laminar flow, weakly turbulent flow, strongly turbulent flow) and flow velocity, there may then also be changes in the value of the first variable influenced by the fouling. Even within one type of flow, mixing and hence heat transfer can change in dependence on flow velocity. For example, even a turbulent flow forms laminar boundary layers at the edge regions, the size and thus influence of which depends, for example, on the flow rate or flow velocity. Therefore, in order to ascertain a value of the variable characterizing the fouling, it is necessary to take these changes into account.

On the other hand, the invention is based on the knowledge that thermodynamic models and simulation studies can be used to obtain functions that describe a dependence of a first variable influenced by the fouling on a flow rate and/or a temperature of the first medium and/or the second medium, in particular on a simultaneous influence of changes in flow rate and temperature on the first variable. The starting point for this can be what is known as white-box models of the heat exchanger with which the fouling can theoretically be calculated almost exactly. However, these models can only be used to a limited extent for practical applications, because this requires all geometric variables of the heat exchanger and also the temperature-dependent material variables of the media used to be known. However, these are often not known. In addition, these models require a high degree of parameterization. However, a function with one or more unknown parameters can be derived from these models with the aid of simulation studies and validated for various framework conditions. Measured values can then be used to ascertain (or estimate) the parameter or parameters from which a value of the first variable can be derived or corrected and hence ultimately to ascertain a more accurate value for a variable characterizing the fouling.

A variable characterizing the fouling is preferably heat-transfer resistance or heat-transfer conductivity. However, it can also be flow resistance.

The first variable is preferably ascertained from a heat balance of the heat exchanger. Therefore, the first variable influenced by the fouling is advantageously a heat-transfer resistance or heat-transfer conductivity (or a heat transfer coefficient, frequently also referred to as a “k-value”). The heat-transfer resistance or the heat-transfer conductivity (or the k-value) can be ascertained particularly easily with the aid of a heat balance from measured values of flow rates of the first and second medium through the heat exchanger and temperatures of the first medium and the second medium in each case at an inlet and at an outlet of the heat exchanger.

Preferably, 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 that compensates an influence of a dependence of the first variable on a flow rate and/or a temperature of the first medium and/or the second medium, in particular on a simultaneous influence of changes in flow rate and temperature on the first variable, where the value of the second variable is ascertained with the aid of the function with the at least one parameter.

If the heat is transferred from the first medium to the second medium through a wall, the k-value is, for example, theoretically composed as follows:

$k=\frac{1}{\frac{1}{\alpha 1}+\frac{s_w}{{\lambda }_w}+\frac{1}{{\alpha }_2}+R_f}\mathrm{or}\frac{1}{k}=\frac{1}{\alpha 1}+\frac{s_w}{{\lambda }_w}+\frac{1}{\alpha 2}+R_f$

where

• • R_f: is the fouling resistance (in m²K/W)
  • s_w: is the wall thickness (in m),
  • λ_w: is the thermal conductivity of the wall (in W/mK),
  • α₁: is the heat-transfer coefficient from the first medium to the wall (in W/m²K), and
  • α₂: is the heat-transfer coefficient from the second medium to the wall (in W/m²K)

Changes in the flow rate of the first and/or second medium through the heat exchanger can result in changes in the flow velocity and type of flow and hence in changes in the heat-transfer coefficient α_1,2.

Where

$\begin{array}{cc}X=\frac{1}{{\alpha }_1}+\frac{1}{{\alpha }_2}+\frac{s_w}{{\lambda }_w}& \mathrm{Eq}.4\end{array}$

produces

1/k=X+R_f   Eq. 5

The fouling resistance R_f can then be calculated by

R _f=1/k−X.   Eq. 6

Here,

• • R_f: is the variable characterizing the fouling,
  • 1/k: is the first variable, and
  • X: is the second variable.

Preferably, the second variable 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.

Alternatively, the first variable influenced by the fouling can be a flow resistance of the first or the second medium through the heat exchanger. A flow resistance can be ascertained particularly easily from measured values of pressures of the first medium and the second medium in each case at an inlet and at an outlet of the heat exchanger.

Preferably, the value of the at least one parameter is ascertained based on measured values of flow rates and temperatures of the first medium and/or the second medium. This can be measured very easily on a heat exchanger.

In accordance with a particularly advantageous embodiment, the function with the at least one parameter for at least one side of the wall, preferably for both sides of the wall, takes into account a dependence of a heat-transfer coefficient α of the respective side on the flow rate and/or the temperature of the first or second medium that are each conducted past the side of the wall. As has been found, the influence of flow rate dependencies and/or temperature dependencies can be taken into account particularly well on the basis of the heat-transfer coefficient or coefficients.

In accordance with a further advantageous embodiment, in the event of only flow rate changes being present, the dependence of the heat-transfer coefficient α on the flow rate of the medium conducted past the respective wall is described by the function α(F)=a·F(t)^b, where F is the flow rate of the medium at the respective side of the wall, t is the time and a, b are parameters. As validations have found, this method can obtain highly accurate results.

In accordance with a further advantageous embodiment, in the event of only temperature changes being present, the dependence of the heat-transfer coefficient α on the temperature of the medium conducted past the respective wall is in accordance with the relationship α(T)=a·(T(t)+b)^c, where T is the mean temperature of the medium at the respective side of the wall, t is the time and a, b, c are parameters. Here, once again, validations have shown that this method can achieved highly accurate results.

In accordance with a further particularly advantageous embodiment, the dependence of the heat-transfer coefficient α on the flow rate and temperature with simultaneous changes in the flow rate and temperature of the medium conducted past the respective wall is in accordance with the relationship α(F,T)=a·F^b·(T+c)^d, where F is the (time-dependent) flow rate and T is the (time-dependent) mean temperature of the medium at the respective side of the wall and a, b, c, d are parameters. As validations have found, this enables simultaneous changes in flow rate and temperature to be represented very accurately.

In accordance with a further particularly advantageous embodiment, the measured-value-based ascertaining of the at least one parameter comprises providing a target function based on the function with the at least one parameter, and ascertaining the value of the at least one parameter by optimizing the target function on the basis of measured values of flow rates and/or temperatures of the first and/or second medium with the aid of a parameter optimization algorithm.

Optimization can entail either minimization or maximization of the target function. If, for example, the target function describes an error, optimization consists of minimizing the error.

Preferably, the target function is obtained based on an at least first-order time derivative of the function with the at least one parameter. Since the dynamics of the fouling process have very slow dynamics, the time derivative enables the influence of fouling resistance on the ascertaining of parameters to be disregarded.

As has been found, very good parameter optimization results can be obtained when particle swarm optimization (PSO) or an evolution strategy algorithm is used as the parameter optimization algorithm.

In accordance with a particularly advantageous embodiment, a value of a variable characterizing the fouling or a value of the first variable and a value of the second variable is ascertained without using material data of the first and second medium or without using geometry data of the heat exchanger, preferably without using either the material data or the geometry data.

In accordance with a further particularly advantageous embodiment, a value of a variable characterizing the fouling or a value of the first variable and a value of the second variable is ascertained, preferably exclusively, from measured values of several of the following measured variables:

• • temperatures (T_P,Ein, T_P,Aus, T_S,Ein, T_S,Aus) of the first medium (S) and the second medium (P) at the inlet and outlet of the heat exchanger (1) and
  • flow rates (F_P, F_S) of the first medium (S) and the second medium (P) through the heat exchanger (1).

These measured variables and heat balance calculations enable very good results to be achieved when ascertaining the variable characterizing the fouling. Here, this can be attained using instrumentation often available in heat exchangers and does not require any special additional measuring instruments (for example, a temperature sensor on a heat exchanger wall).

Moreover, overdetermination of the heat balance equations also enables one of the measurements of flow rates and input/output temperatures of the media to be dispensed with, so that not even complete instrumentation is required.

If individual process variables of the product medium or service medium, such as the inlet temperature, are fixed due to given framework conditions and can, therefore, be assumed to be unchangeable, these likewise do not need to be measured.

There is no need to detect further variables, such as material properties of the two media or structural properties of the heat exchanger. On the contrary, it is preferably assumed that these are not known. Any constants can be assumed in the calculations for this purpose that, when seen in absolute terms, result in incorrect values for the first variable, the second variable and the variable characterizing the fouling, but ultimately the relative changes of these variables are sufficient for the mode of operation and the success of the method in practice. Therefore, preferably, only relative values are ascertained for the variable characterizing the fouling or for the first and the second variable.

Using the example of an industrial heat exchanger, the disclosed embodiments of the invention have been able to achieve a significantly better result when ascertaining fouling than that achieved with a conventional calculation. Thus, the results can help a plant operator to achieve a significantly better evaluation of the fouling resistance. Advantageously, the disclosed embodiments of the invention can be applied not only to heat balances, but also to the consideration of pressure differences and thus of flow resistances.

The objects and advantages are also achieved in accordance with the invention by a device for performing the method in accordance with the disclosed embodiments of the invention, where the device comprises 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 a flow rate and/or a temperature of the first medium and/or the second medium, in particular on a simultaneous influence of changes in flow rate and temperature on the first variable is stored, where the evaluating facility is configured to ascertain a value for the at least one parameter with the aid of the measured values or the variables derived therefrom of the first medium and/or the second medium.

The “derived variables” can, for example, be statistical variables such as mean values, minima, maxima of measured values.

The objects and advantages are achieved in accordance with the invention by a computer program comprising instructions that, when executed on a computer, cause the computer to execute the method in accordance with disclosed embodiments of the invention.

A corresponding computer program product comprises a storage medium on which a program with instructions is stored that, when executed on a computer, cause the computer to execute the method in accordance with disclosed embodiments of the invention.

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 according to features of the subclaims are explained below with reference to exemplary embodiments in the figures, in which:

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,

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;

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

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;

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;

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

FIG. 7 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 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_P (or the volume flow) of the product medium and its temperature T_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_P,out of the product medium P leaving 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 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_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_S,out of the service medium S leaving the heat exchanger 1.

To monitor the heat exchanger 1 with regard to fouling, the flow rate measured value F_P and the temperature measured values T_P,in, T_P,out of the product medium P and the flow rate measured value F_S and the temperature measured values T_S,in, T_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_P,in or T_S,in, are fixed due to given framework conditions and therefore can be assumed to be invariable, they do not need to be measured.

The following applies to 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·(T_P,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 is the thermal capacity of the product medium,
  • c_P,S is the thermal capacity of the service medium,
  • ρ_P is the density of the product medium, and
  • ρ_S is the density of the service medium.

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)}_P={dot over (Q)}_S={dot over (Q)}).

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·A·ΔT _m.

Herein:

• • k: is the heat transfer coefficient (in W/m²K),
  • A: is the available surface for heat exchange (in m²),
  • ΔT_m: is the mean logarithmic temperature difference, and
  • {dot over (Q)}: is the 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 is the temperature difference of the inlet side (from the perspective of the product medium) and ΔT_B is that of the outlet side.

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

• • c) heat flow dissipated by medium 1

{dot over (Q)} _P =c _P,Pρ_PF_P(T_P,Aus−T_P,Ein)

• • b) heat flow passing through the heat exchanger 1

{dot over (Q)}=k·A·ΔTm

• • c) heat flow dissipated by medium 2

{dot over (Q)} _S =−c _P,Sρ_SF_S(T_S,Aus−T_S,Ein)

As a result:

c _P,Pρ_PF_P(T_P,Aus−T_P,Ein)=k·A·ΔTm=−c_P,Sρ_SF_S(T_S,Aus−T_S,Ein).

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_ist and the heat transfer resistance 1/k_soll, that was ascertained in clean state.

$R_f=\frac{1}{k_{\mathrm{ist}}}-\frac{1}{k_{\mathrm{soll}}}k=\frac{1}{\frac{1}{\alpha s}+\frac{s_w}{{\lambda }_w}+\frac{1}{{\alpha }_P}+R_f}$

where

• • s_w: is the wall thickness (in m),
  • λ_w: is the thermal conductivity of the wall (in W/mK),
  • α_S: is the heat-transfer coefficient from the service medium to the wall (in W/m²K), and
  • α_P: is the heat transfer coefficient from the product medium to the wall (in W/m²K).

Hence, the k-value can be calculated with the relationship

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

where

ΔT_A=T_P,A−T_S,out and ΔT_B=T_P,Aus−T_S,Ein

for the case of a counterflow heat exchanger.

Hence, with values for A, c_P,P, c_P,S, ρ_P and ρ_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.

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.

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.

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.

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:

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

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 α_S,P.

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 α on the flow rate can be described for both sides of the wall by the structure function

α(F)=a·F(t)^b,   (3)

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

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 α on the temperature by the structure function

α(T)=a·(T(t)+b)^c,   (4)

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

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

α(F, T)=a·F^b·(T+c)^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 α on both the flow rate and temperature.

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.

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

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

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

$\begin{array}{cc}J=❘\frac{d\frac{1}{k}}{\mathrm{dt}}-\left(\frac{d\frac{1}{{\alpha }_P}}{\mathrm{dt}}+\frac{d\frac{1}{{\alpha }_S}}{\mathrm{dt}}\right)❘& \left(7\right)\end{array}$

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_P,Ein, T_P,Aus, T_S,Ein, T_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_P, F_S of the service medium S and the product medium P through the heat exchanger 1.

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

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

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

Preferably, only relative values or relative changes in the fouling resistance are taken into account. Therefore, in (2), the constant thermal resistance Rw=s_w/λ_w of the wall can be disregarded and the fouling resistance can then be calculated by

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

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_P,Ein, T_P,Aus, T_S,Ein, T_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_P, F_S of the service medium S and the product medium P through the heat exchanger 1.

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_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_f is very clearly apparent.

FIG. 5 shows a time profile of the normalized fouling resistance R_f in FIG. 4 ascertained with the method in accordance with the invention compared to normalized fouling resistance R_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.

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.

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

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.

In principle,

$X=\frac{1}{{\alpha }_S}+\frac{1}{{\alpha }_P}+\frac{s_w}{{\lambda }_w}\mathrm{and}1/k=X+R_f.$

enables the fouling resistance R_f to be calculated by

R _f=1/k−X.

Herein

• • R_f: is a variable characterizing the fouling,
  • 1/k: is a first variable that is influenced by the flow rate, and
  • X: is a second variable that is not influenced by the fouling.

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.

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.

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.

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.

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”.

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_P,in, T_P,out, T_S,in, T_S,out, F_P, F_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_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.

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.

Although it is possible to detect further variables, such as A, c_P,P, c_P,S, ρ_P, ρ_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.

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.

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.

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.

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_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.

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.

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.

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.

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

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; andascertaining 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: α(F)=a·F(t)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: α(T)=a·(T(t)+b)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: α(F, T)=a·Fb·(T+c)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; andan 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.