EP1743133B1 - Method and arrangement for determining the capacity of a heat exchanger - Google Patents

Description

The invention relates to a method and a device for determining the performance of a heat exchanger, by means of which the temperature of a product flowing through the heat exchanger, with the aid of an auxiliary medium, which serves as a cooling or heating means to be changed.

Such heat exchangers are often used in process engineering plants in addition to a variety of different plant components, such as machinery, containers, chemical reactors, steam generators, columns or pumps. A heat exchanger is in principle a tube through which a product flows, which is to be cooled or heated by the surrounding medium, which is referred to as an auxiliary medium. For the efficiency of the heat exchanger, among other things, the largest possible heat exchange surface and the largest possible heat transfer factor are crucial. Certain requirements for the heat exchanger arise from the materials used, for example, of what kind product and auxiliary medium, required cooling or heating capacity, cooling method used, structural conditions or legal requirements, for example with regard to cleaning. Due to the different requirements many different types of heat exchangers are common, for example stirred tank, DC and countercurrent heat exchanger, tube bundle heat exchanger or plate heat exchanger.

A major problem in the operation of heat exchangers is the so-called fouling. Fouling is a collective term for soiling of all kinds. Fouling changes the heat transfer factor between the auxiliary medium, which serves as a cooling or heating medium, and the product. This has the consequence that more coolant or heating medium as an auxiliary medium it is necessary that the operating costs increase and / or that in extreme cases, the desired temperature of the product can not be adjusted by the heat exchanger. If this extreme case occurs, this can cause an unscheduled shutdown of the process plant in which the heat exchanger is used. A common remedy is therefore a regular production stop for maintenance and cleaning of the heat exchanger. However, this increases the operating costs and limits the availability of the system. US 3,918,300 discloses a device that calculates the fouling of the heat exchanger.

The invention has for its object to provide a method and a device which make it possible to detect a decline in the performance of a heat exchanger early.

To solve this problem, the new method of the type mentioned in the features specified in claim 1 or the new device the features specified in claim 5. In the dependent claims developments of the invention are described.

The invention has the advantage that the effects of changed heat transfer factors on the operation of the heat exchanger are determined and displayed in such an illustrative manner that they can also be correctly interpreted by non-specialists. The determined and displayed outlet temperature of the product, which would be set at maximum flow of the auxiliary medium, represents a particularly illustrative size for the user, since here the heat exchanger is operated at its power limit. Namely, it becomes apparent how the fouling range available reduces the available setting range. For the user, it is thus easy to see whether and for how long the heat exchanger can set a desired temperature of a product and in a process-technical plant trouble-free can continue to operate. Unanticipated downtime of the system can thus be largely avoided.

The development of the method described in claim 2 has the advantage that the method for determining the resulting at maximum flow of the auxiliary medium outlet temperature of the product is computationally simple and easy for different types of heat exchangers applicable.

In the development according to claim 2, the arithmetic mean value of the values of the outlet temperature of the product in the subset of pairs of values can be calculated in an advantageous manner according to claim 3 as a statistical criterion for the selection of a value pair. This applies a particularly simple, reliable and intuitive method of selection.

A calculation and display of the standard deviation of the values of the outlet temperature of the product in the subset of value pairs has the advantage that a statement about the reliability of the result is obtained. The smaller the standard deviation, the greater the significance of the result in determining the efficiency of the heat exchanger.

Annex of the drawings, in which an embodiment of the invention is shown, the invention and refinements and advantages are explained in more detail below.

Show it:

FIG. 1

a schematic diagram of a heat exchanger and

FIG. 2

a display to illustrate the performance of a heat exchanger.

Depending on the application conditions, there are heat exchangers in a wide variety of designs. The basic structure of a heat exchanger is shown in FIG.
A heat exchanger 1 according to FIG. 1 consists of a container 2, in which a product flows through an inlet 3 and outflows through an outlet 4 again. The flow direction of the product is indicated by an arrow 6. In the container 2 is a coiled tube 7, which is flowed through by an auxiliary medium in the direction of an arrow 8. In the case of cooling the product through the heat exchanger 1, for example, cooling water flows through the pipe 7. In the heat exchanger 1, the auxiliary medium enters at an inlet 9 and at an outlet 10 again. The inlet temperature θ _{K, Ein of} the auxiliary medium is detected by a temperature transducer 11, the outlet temperature θ _{K, Aus} with a temperature transducer 12. Accordingly, the inlet temperature θ _{W, A of} the product with a temperature transducer 13 and the outlet temperature θ _{W, Aus are} measured with a temperature transducer 14. Furthermore, to determine the flow F _{K of} the auxiliary medium through the pipe 7 and the flow F _{W of} the product through the container 2 flow meter 15 and 16 are provided. With a control valve 17, the flow of the auxiliary medium can be adjusted such that the product sets a desired outlet temperature. A control signal is received by the control valve 17 from a control device 18, to which the measured values of the transducers 11... 16 are fed as input signals. In addition to its function of calculating the position of the control valve 17 as a function of the measured values of the measuring transducers 11... 16, the control device additionally has the function of an evaluation device which determines the output temperature of the heat exchanger 1 at maximum flow of the auxiliary medium Determined product. In a process engineering system, the control device 18 is realized, for example, by an automation device which has a data transmission network with the transducers 11 ... 16 and connected to the control valve 17. The display of the determined outlet temperature and other values that are useful for assessing the performance of the heat exchanger 1 by a user, then can be done using a faceplate 19, that is, through a display window for process visualization on an operating and monitoring station. If too great a decrease in the performance of the heat exchanger 1 is displayed, the user can initiate appropriate measures to eliminate the problem already at a time before a desired outlet temperature of the product can not be adjusted and thus before a correct sequence of the process in which the Heat exchanger is used, no longer guaranteed.

The following explains how the performance of the heat exchanger 1 is determined by the control device 18, which is also referred to as the evaluation device 18 due to its additional function.

• ϑ _K,Ein ··· ϑ_K,Aus,i ··· ϑ_W,Ein
• ϑ_K,Ein ··· ϑ_W,Aus,j ··· ϑ_W,Ein.

The outlet temperature θ _{W, out of} the product and the outlet temperature θ _{K, from} the auxiliary medium can only be within a certain range, which is limited by the inlet temperature θ _{W, Ein of} the product and the inlet temperature θ _{K, Ein of} the auxiliary medium. For example, if a product is to be cooled down, the outlet temperature θ _{W, out of} the product can not become smaller than the inlet temperature θ _{K, Ein of} the auxiliary medium. Likewise, the exit temperature θ _{K, out of} a coolant can not be greater than the inlet temperature θ _{W, Ein of} the product. The temperature range between the two inlet temperatures θ _{K, Ein} and θ _{W, Ein} , in which physically sensible values of the outlet temperatures θ _{K, Aus} and θ _{W, Aus} can be set, is used for the calculation with the outlet temperatures θ _{K, Aus} and θ _{W , From} the auxiliary medium and the product quasi scanned by the At the beginning, the two outlet temperatures are set to the inlet temperature θ _{K, Ein of} the auxiliary medium and then increased stepwise to the inlet temperature θ _{W, Ein of} the product. Expressed mathematically, for example, this corresponds to n values θ _{K, Aus, i} with i = 1 to n, where, θ _{K, Aus, i} = θ _{K, Ein} and θ _{K, Aus, n} = θ _{W, Ein} and m values _, respectively θ _{W, Aus, j} with j = 1 to m, where, θ _{W, Aus, l} = θ _{K, Ein} and θ _{W, Aus, m} = θ _{W, Ein} . Or in a different spelling:

• θ _{K, A} ··· θ _{K, Off, i} ··· θ _{W, On}
• θ _{K, A} ··· θ _{W, Off, j} ··· θ _{W, On} .

Furthermore, all value pairs (θ _{K, Aus, i} , θ _{W, Aus, j} ) of the two exit temperatures are formed, which are mathematically possible. In this way, a plurality of pairs of values, namely nxm at i = 1 to n and j = 1 to m, obtained, which are mathematically possible due to the above consideration. For these pairs of values, the transferred amounts of heat are calculated at maximum flow of the auxiliary medium. In the evaluation, it is considered that in the stationary state due to the balanced energy balance, a change Q̇ _{w of} the heat quantity of the product is equal to a change Q̇ _{K of} the amount of heat of the auxiliary medium and equal to the heat transferred through the heat exchanger Q̇. The amount of heat transferred is therefore calculated in three different ways.

The change Q̇ _{W of} the heat quantity of the product is calculated from the temperature difference between inlet temperature θ _W, inlet and outlet temperature θ _W, outlet _{, j of} the product, actual mass flow ṁ _{W, current} product and specific heat cp _{W of} the product: $${\dot{\mathrm{Q}}}_{\mathrm{W}}\mathrm{=}{\mathrm{cp}}_{\mathrm{W}}\mathrm{\cdot }{\dot{\mathrm{m}}}_{\mathrm{W}\mathrm{.}\mathrm{Current}}\mathrm{\cdot }\left({\mathit{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{One}}\mathrm{-}{\mathit{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{Out}\mathrm{.}\mathrm{j}}\right)\mathrm{,}$$

In this case, the mass flow ṁ _{W, Current can be determined} in a simple manner as the product of the flow F _W measured with the flow meter 16 and the density of the flowing product.

The change in Q _k of the heat quantity of the auxiliary medium is determined from the temperature difference between the inlet temperature θ _K, inlet _and outlet temperature θ _{K, Aus, i} of the auxiliary medium, the maximum possible mass flow ṁ _K.Max and specific heat cp _K of the auxiliary medium calculated: $${\dot{\mathrm{Q}}}_{\mathrm{K}}\mathrm{=}{\mathrm{cp}}_{\mathrm{K}}\mathrm{\cdot }{\dot{\mathrm{m}}}_{\mathrm{K}\mathrm{.}\mathrm{Max}}\mathrm{\cdot }\left({\mathit{\theta }}_{\mathrm{K}\mathrm{.}\mathrm{Out}\mathrm{.}\mathrm{i}}\mathrm{-}{\mathit{\theta }}_{\mathrm{K}\mathrm{.}\mathrm{One}}\right)\mathrm{,}$$

mit Δϑ_a = ϑ _W,Ein -ϑ_K,Aus und Δϑ _b = ϑ _W,Aus -ϑ _K,Ein.To calculate the amount of heat transferred, the currently effective heat transfer _factor k is _first determined on the basis of the current measured values of the transducers 11. The following equation applies to the example of a countercurrent heat exchanger: $${\mathrm{k}}_{\mathrm{becomes}}=\frac{{\mathrm{cp}}_{\mathrm{W}}\mathrm{\cdot }{\mathrm{\delta }}_{\mathrm{W}}\mathrm{\cdot }{\mathrm{F}}_{\mathrm{w}}\mathrm{\cdot }\mathrm{(}{\mathrm{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{One}}\mathrm{-}{\mathrm{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{Out}}\mathrm{)}}{\mathrm{A}\cdot \frac{{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{a}}-{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{b}}}{\ln \frac{{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{a}}}{{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{b}}}}}$$

with Δθ _a = θ _{W, a} -θ _{K, off} and Δ θ _b = θ _{W, off} -θ _{K, on} .

Therein, A denotes the effective exchange area of the heat exchanger and δ _W the specific density of the product.

This equation applies to the case that the quantities are not temperature-dependent or pressure-dependent. Otherwise, this can be taken into account in the calculation for increasing the accuracy.

wobei für die mittlere Temperaturdifferenz bei Gegenstrom eingesetzt wird: $${\mathrm{\Delta }\mathit{\vartheta }}_{\mathrm{a}}={\mathit{\vartheta }}_{\mathrm{W}\mathrm{,}\mathrm{Ein}}-{\mathit{\vartheta }}_{\mathrm{K}\mathrm{,}\mathrm{Aus}}\mathrm{und}{\mathrm{\Delta }\mathit{\vartheta }}_{\mathrm{b}}={\mathit{\vartheta }}_{\mathrm{W}\mathrm{,}\mathrm{Aus}}-{\mathit{\vartheta }}_{\mathrm{K}\mathrm{,}\mathrm{Ein}}$$

und für die mittlere Temperaturdifferenz bei einem Gleichstromwärmetauscher: $${\mathrm{\Delta }\mathit{\vartheta }}_{\mathrm{a}}={\mathit{\vartheta }}_{\mathrm{W}\mathrm{,}\mathrm{Ein}}-{\mathit{\vartheta }}_{\mathrm{K}\mathrm{,}\mathrm{Ein}}\mathrm{und}{\mathrm{\Delta }\mathit{\vartheta }}_{\mathrm{b}}={\mathit{\vartheta }}_{\mathrm{W}\mathrm{,}\mathrm{Aus}}-{\mathit{\vartheta }}_{\mathrm{K}\mathrm{,}\mathrm{Aus}}\mathrm{.}$$

The transmittable heat quantity Q̇ is calculated from the average temperature difference between product and auxiliary medium, the heat transfer _factor k _akt and the effective exchange area A according to the following equation: $$\dot{\mathrm{Q}}\mathrm{=}\mathrm{k}\mathrm{\cdot }\mathrm{A}\cdot {\mathrm{\Delta }\mathit{\theta }}_{\ln }\mathrm{With}{\mathrm{\Delta }\mathit{\theta }}_{\ln }=\frac{{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{a}}-{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{b}}}{\ln \frac{{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{a}}}{{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{b}}}}.$$

wherein for the mean temperature difference is used in countercurrent: $${\mathrm{\Delta }\mathit{\theta }}_{\mathrm{a}}={\mathit{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{One}}-{\mathit{\theta }}_{\mathrm{K}\mathrm{.}\mathrm{Out}}\mathrm{and}{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{b}}={\mathit{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{Out}}-{\mathit{\theta }}_{\mathrm{K}\mathrm{.}\mathrm{One}}$$

and for the mean temperature difference in a DC heat exchanger: $${\mathrm{\Delta }\mathit{\theta }}_{\mathrm{a}}={\mathit{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{One}}-{\mathit{\theta }}_{\mathrm{K}\mathrm{.}\mathrm{One}}\mathrm{and}{\mathrm{\Delta }\mathit{\theta }}_{\mathrm{b}}={\mathit{\theta }}_{\mathrm{W}\mathrm{.}\mathrm{Out}}-{\mathit{\theta }}_{\mathrm{K}\mathrm{.}\mathrm{Out}}\mathrm{,}$$

After the three transferred heat quantities Q̇ _W , Q̇ _K and Q̇ have been calculated for each of the value pairs, those value pairs are sorted out that are physically meaningful on the basis of a heat quantity comparison. In steady state, the three calculated amounts of energy must be the same size. That is for the case of cooling is that the change must Q _W of the heat quantity of the product by heat transfer Q Q _K cause a corresponding change of the heat quantity of the auxiliary medium. Due to measurement errors and simplifications For the calculation, a certain tolerance must be allowed for the calculated values: $${\dot{\mathrm{Q}}}_{\mathrm{K}}\mathrm{\approx }{\dot{\mathrm{Q}}}_{\mathrm{W}}\mathrm{\approx }\dot{\mathrm{Q}}\mathrm{,}$$

This equation can in principle be analytically resolved. However, it is easier and more easily applicable to different designs of heat exchangers to determine a subset of the multiplicity of value pairs on the basis of the calculated changes in heat quantity and the calculated value of the transferred heat quantity, in which the calculated values lie within a predefinable tolerance. The latter equation thus corresponds to a "filter" with which the physically meaningful value pairs can be sorted out as a subset of the multiplicity of mathematically possible value pairs.

Given a broad, predetermined tolerance, the subset of the value pairs is correspondingly larger, so that it is advantageous to use a statistical method to select a value pair that contains the probability that the maximum flow of the auxiliary medium will be established. As a particularly simple statistical method, the arithmetic mean of the values of the outlet temperatures of the product, which are contained in the value pairs of the subset, is calculated for this purpose. In order to assess the accuracy of this result, the standard deviation of the discharge temperature values of the product from this partial quantity as well as the minimum value and the maximum value of the outlet temperature of the product are also determined. If these values are larger, this indicates a comparatively inaccurate result. With a smaller standard deviation or closely related minimum and maximum values, a good accuracy of the result can be assumed.

To enable a particularly simple assessment of the results by a user, they can be displayed on a faceplate according to FIG. 2, for example on an operating and monitoring station of a process plant. A left bar B1 indicates by the height of a bar section B11 the currently measured actual value of the outlet temperature θ _{W, Off} , which in the example shown is approximately 60 ° C. The value range starts at 0 ° C at the lower end of the bar and ends at 100 ° C at the upper end. To the right of this bar B1 is a second bar B2, by means of which the user can easily judge the efficiency of the heat exchanger. The value range of the bar B2 corresponds to that of the bar B1. The height of a lower beam section B21 indicates the minimum possible exit temperature θ _{W, Off, New of} the product when the heat exchanger is new. This was calculated and stored when new, based on the measured at that time, effective heat transfer factor. In the example, this temperature is 31.5 ° C. An overlying bar section B22 indicates by its height the already occurred performance reduction of the heat exchanger by fouling. The currently calculated value of the minimum possible outlet temperature θ _{W, Aus, Min} in this example is 44.5 ° C and is thus due to the fouling already 13 ° C above the corresponding outlet temperature in new condition. Another bar section B23 indicates with its upper end the inlet temperature θ _{W, A of} the product, which is currently measured at 90 ° C. Thus, the beam portion B23 corresponds to the adjustment range of the heat exchanger. The height distance between the upper limit of the beam portion B11 and the upper limit of the beam portion B22, which in the example shown is 15.8 ° C, shows how large a remaining range is compared to the currently existing outlet temperature θ _{W, Off, current of} the product. This allows a user without special know how to judge how reliable the heat exchanger can be operated even further. Of course, in order to allow an accurate readability of the values on the faceplate, they will also be used in practice displayed numerically. These numerical displays are not shown in FIG. 2 for the sake of clarity. In order to allow an estimation of the accuracy of the calculations, the standard deviation determined in the manner described above and the minimum and maximum values, the number of pairs of values which have been used for the calculation as well as the number of value pairs in the subset for which the calculated heat quantity changes are within the specified tolerance band, are displayed numerically.

The heat quantity changes are calculated only for the stationary state of the heat exchanger. This has the advantage that only equations for mass and energy balances must be used in the balanced state. Thus, no further, much more complex physical models are needed to simulate the dynamic behavior of the process. This advantageously makes possible a comparatively simple calculation of the exit temperature θ _{W, Aus, Min of} the product which occurs at maximum flow of the auxiliary medium.

Claims (5)

1. Method for determining the capacity of a heat exchanger (1) comprising the following steps:

   - measurement of the inlet temperature and outlet temperature of the product, whose temperature is to be changed by the heat exchanger (1), and of the inlet temperature and outlet temperature of the auxiliary medium that serves as a cooling or heating medium during operation of the heat exchanger (1) in an at least approximately stationary condition,

   - calculation of the heat transfer coefficient of the heat exchanger as a function of the measured temperature values,

   - determination of the outlet temperature of the product set for maximum flow of the auxiliary medium as that at which the change in the heat content of the product is at least approximately the same as the change in the heat content of the auxiliary medium and the amount of heat which can be transmitted at the respective product flow by the heat exchanger (1) with the calculated heat transfer coefficient, and

   - display of the determined outlet temperature of the product set for maximum flow of the auxiliary medium.
2. Method according to claim 1, characterised in that, to determine the outlet temperature of the product set for maximum flow of the auxiliary medium, for a plurality of value pairs (ϑ_K,Aus,i, ϑ_W,Aus,j)
   where ϑ_K,Aus,i is a fictitious value of the outlet temperature of the auxiliary medium, which value lies between the measured inlet temperature of the auxiliary medium and the measured inlet temperature of the product, and
   ϑ_W,Aus,j is a fictitious value of the outlet temperature of the product, which value lies between the measured inlet temperature of the auxiliary medium and the measured inlet temperature of the product,
   the change Q̇_K in the heat content of the auxiliary medium, the change Q̇_W in the heat content of the product and the amount of heat Q̇ which can be transmitted by the heat exchanger (1) with the calculated heat transfer coefficient are calculated,
   in that from the plurality of value pairs a subset of value pairs is determined for which the two calculated values of the changes in heat content Q̇_K and Q̇_W and the calculated value of the quantity of heat Q̇ which can be transmitted differ by less than a predeterminable threshold value and
   in that, in accordance with a predeterminable statistical criterion, from the subset a value pair is selected having the value to be displayed of the set outlet temperature of the product.
3. Method according to claim 2, characterised in that, as a statistical criterion for the selection of a value pair, the arithmetic mean of the values of the outlet temperature of the product in the subset of value pairs is calculated.
4. Method according to claim 2 or claim 3, characterised in that the standard deviation of the values of the outlet temperature of the product in the subset of value pairs is calculated and displayed.
5. Device for determining the capacity of a heat exchanger (1)

   - comprising temperature measuring transducers (11 ... 14) for measuring the inlet temperature and outlet temperature of the product whose temperature is to be changed by the heat exchanger and the inlet temperature and outlet temperature of the auxiliary medium which serves as a cooling or heating medium during the operation of the heat exchanger (1) in an at least approximately stationary condition,

   - comprising an evaluation device (18) which is designed for calculating the heat transfer coefficient of the heat exchanger (1) as a function of the measured temperature values and for determining the outlet temperature of the product set for maximum flow of the auxiliary medium as that at which the change in the heat content of the product is at least approximately the same as the change in the heat content of the auxiliary medium and the amount of heat which can be transmitted by the heat exchanger (1) with the calculated heat transfer coefficient for the respective product flow, and

   - comprising a device (19) for displaying the determined outlet temperature of the product set for maximum flow of the auxiliary medium.

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