WO2013164472A1

WO2013164472A1 - Parallel heat exchanger control

Info

Publication number: WO2013164472A1
Application number: PCT/EP2013/059304
Authority: WO
Inventors: Johannes JÄSCHKE; Sigurd SKOGESTAD
Original assignee: Norwegian University Of Science And Technology (Ntnu)
Priority date: 2012-05-03
Filing date: 2013-05-03
Publication date: 2013-11-07
Also published as: GB201207770D0

Abstract

In a heat exchanger network having two or more heat exchangers in parallel flow paths i that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths i and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, a method of controlling the heat exchanger network comprises: determining a split ratio u for the parts of the common process flow being directed into the parallel paths i that hold the heat exchangers, wherein for each of the parallel flow paths i a temperature based parameter ΔJT_iis determined and the split ratio u is set by adjusting it such that the temperature based parameter ΔJT_iis equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter ΔJT_i is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature T_i from the first side of the heat exchanger in that flow path i and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hiof the second fluid that supplies the second side of the heat exchanger.

Description

PARALLEL HEAT EXCHANGER CONTROL

The invention relates to a method of controlling a heat exchanger network in which two or more heat exchangers are present in parallel.

Heat exchangers are used in various applications and often it is desirable to have a network of heat exchangers that are installed in parallel flow paths. In many industrial plants waste heat from one process is used to heat up feed streams for the same process or for another process. Examples include air pre-heating in a power plant and feed preheating in oil refining units. Cryogenic systems also use networks of heat exchangers. A common situation arises when a stream is split for heating or cooling in two or more parallel heat exchangers and then the flow is recombined. The goal is typically to maximise heat transfer and this is equivalent to maximising (or minimising) the end temperature after the split stream is recombined. It can also be desirable to adjust the flow to maximise the use of flow streams that are considered to be more efficient or to involve less of a penalty when they are used. For example there may be a financial or environmental cost associated with the use of certain flow streams that makes it more attractive to maximise the use of one flow stream compared to another. There is hence a need for a method that allows for optimising the heat exchanger network for increased heat transfer and/or of increasing the use of more desirable flow streams. In some cases the required result will be maximised heat transfer. In other cases there will be a trade-off between increasing heat transfer and also increasing the usage of some more desirable flow streams.

Figure 1 illustrates a simple scenario of this type. Two incoming hot process streams having temperatures T_h1 and T_h2 are placed in heat exchange relationship with two parallel parts of a third cool process stream having an initial incoming temperature T₀. After heat exchange has occurred the temperature in the first branch rises from T₀ to T-i and the temperature in the second branch rises from T₀ to T₂. In this example the initial temperature T₀ of the third process stream is colder than the temperatures T_hi and T_h2 of the first two process streams, and hence the aim is to maximise the outgoing temperature T_end- It will however be understood that the same control principles apply when the temperature relationship is reversed, with T₀ being the higher temperature and being cooled by the other two incoming streams. The aim in that situation is to minimise the outgoing temperature Tend - This maximising or minimising of T_end will occur with the maximum heat transfer in the two heat exchangers. It is important to understand that this will not necessarily occur when the two temperatures T-i and T₂ are the same. They will often be different.

The incoming process streams have inlet heat capacity rates w_h1 , w_h2 and w₀. The common process flow is split between two parallel paths in accordance with a ratio u = w-|/w₂ where w-i and w₂ are the heat capacity rates along the two parallel paths. The heat - -

exchanged in the two heat exchangers will vary depending on the temperatures and flow rates. The split ratio u can be controlled in order to maximise the heat transfer. This is not trivial, even in the simple system of Figure 1 , since in real world systems the temperatures and flow rates will not be constant. Changes can occur, for example, due to variations in the upstream processes and/or in the sources of the process fluids. Changes will also occur due to fouling in the heat exchangers that can build up over time.

In known control methods the control of the split u is done in one of several ways. The simplest method is to set the split u to some value, for example based on expected performance of the system, and leave it fixed at this value. More sophisticated systems allow the split u to be adjusted. Some systems do this by controlling one of the

temperatures to a constant value. Other systems involve a human operator adjusting the split based on some empirical or heuristic system, perhaps using experience to set a preferred ratio. The most complex and accurate known method uses a real time

optimisation (RTO) and simulation process to determine the optimal split based on measurement of process parameters such as flow rates and temperatures. An example of a product for performing this type of optimisation is "Aspen Real-Time Optimizer" as provided by Aspen Technology, Inc., of Burlington, Massachusetts, USA.

However, although it is theoretically accurate the RTO process is expensive and time consuming. The heat exchanger network is modelled and optimized periodically to solve for the split (u) with maximum heat exchange. One drawback with RTO is that it requires an accurate model and known parameters. Obtaining and maintaining accurate process models is one of the main obstacles for using RTO. Also, whenever the process parameters change the RTO must be repeated to identify the correct split ratio(s). Thus, input values need to be re-measured and the iterative calculation needs to be repeated. For a multi-branching heat exchanger network this calculation may take hours to complete with typical systems.

Moreover, since RTO is generally based on a steady state model, the optimization can only be performed when the plant has settled and steady state has been verified. As a result RTO, whilst theoretically optimal, will not be accurate at all times since there is a lag between the change in process parameters and the updated RTO values for split ratio(s). The cost is also a significant disadvantage and this is one reason why the less accurate empirical and heuristic methods are still used.

Viewed from a first aspect, the invention provides a method of controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths i that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths i and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the - -

second sides of the heat exchangers, the method comprising: determining a split ratio for the parts of the common process flow being directed into parallel paths i that hold the heat exchangers, wherein for each of the parallel flow paths i a temperature based parameter AJTi is determined and the split ratio is set by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature Tjfrom the first side of the heat exchanger in that flow path i and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger.

Thus, the invention requires that in the situation where there is a single heat exchanger in one of the parallel flow paths then the temperature based parameter AJT, is determined in the way detailed above. Refinements to the method may also optionally allow for multiple numbers of heat exchangers by providing alternative calculations for the temperature based parameter AJT, for the relevant flow paths, as discussed in more detail below. Surprisingly, the inventors have found that setting this temperature based parameter AJTi to be equal in each of the parallel flow paths i results in optimal or close to optimal operation of the heat exchanger. Using mathematical notation and taking the simple system of Figure 1 as an example the temperature based parameter for a single heat exchanger in a flow path i can be expressed as:

tsJT =

It will be understood that T₀-T_hi can be substituted for T_hi-T₀ and the result will be equivalent. It does not matter how this difference is calculated, as long it is the same for all lines. It will also be seen that the equation above illustrates the situation where AJT, is exactly the described ratio, rather than being proportional to this ratio.

In the situation where the temperature based parameter AJT, is proportional to the described ratio then this ratio may simply be multiplied by a constant p_x for the heat exchanger x in flow path i. The constant p_x allows for a weighting to be added to take account of the desirability or disadvantage of using one of the second process fluids compared to using another of the second process fluids. This weighting may for example be used to promote or reduce usage of the second process fluids involved in the heat transfer for economic or environmental reasons. Different sources or sinks for heat may have - -

different prices. Under economical considerations it may no longer be optimal to simply maximise the end temperature after heat exchange since this may imply uneconomic use of one or more of the second process fluids. The use of the constant p_x for one or more of the temperature based parameters AJT, allows the optimisation to reflect this. In addition, different sources or sinks for heat may have different environmental penalties or advantages associated with them. It can be desirable to promote the use of second process fluids that are considered to be more environmentally friendly. Hence, making the temperature based parameters AJT, proportional to the described ratio by use of a constant p_x allows the optimisation to take account of any cost (or benefit), for example financial and/or

environmental costs.

Preferably when a weighting constant p_x is used then such a constant p_x is incorporated into all of the temperature based parameters AJT,. However this is not essential since the absence of a constant is of course equivalent to a constant that is equal to one and therefore a weighting constant may optionally be applied only to the parallel flow paths with heat exchangers making use of selected second process fluids where it is desired to promote or reduce usage of the selected second process fluids.

For a simple case with two parallel paths i=1 , i=2 the method involves the split ratio being controlled so that the formula:

c = AJz; -AJr₂

is set so that c is equal to zero. The invention may comprise the use of these equations and other mathematical equivalents.

When the parallel flow paths are recombined, which is a preferred feature, the temperature of the recombined flow paths (i.e. temperature T_end in Figure 1 ) can be maximised (or minimised) using this method. As set out in further detail below in relation to the preferred embodiment of this invention, the results achieved by the use of this method closely follow the results of the current RTO systems, within the bounds of operational accuracy. The step of adjusting the split ratio to equalise the temperature based parameter AJT, can be considered as a non-obvious approximation to an analytical solution for the heat exchanger network, which surprisingly allows for flow rate measurements and other data to be disregarded in determining an optimised value for the split ratio.

The split ratio u may be a volumetric split ratio w-|/w₂ as above. The exact way that the split ratio is controlled can be selected based on convenience and/or on the control techniques available for a particular heat exchanger network. What is important for this method is that the amount of fluid flowing in two or more parallel paths can be controlled to thereby optimise it based on the temperature based parameter described above. Control - -

could be achieved by valves, pumps or other flow controllers, and these may be controlled by a controller such as a computer processor or similar.

This method hence provides a quick and straightforward calculation that can be used to replace RTO and the other known methods for optimisation of the split ratio. Only temperature measurements are required and so the system can be implemented cheaply. Appropriate temperature sensors will generally already be in place in the heat exchanger network. No other technical data is required, for example no flow rate measurements, no heat transfer data and so on. In addition, since the calculation is relatively simple it is completed quickly, and can be far quicker than equivalent RTO calculations. Thus, when conditions change the method above can provide an updated split ratio u more quickly than known RTO methods. This means that the lag between a change in conditions and an update to the flow rates is smaller (perhaps minutes rather than hours) and therefore the time period when control is not optimised is also made smaller. The method hence preferably involves recalculating the split ratio when the conditions in the heat exchanger network change.

It should be noted that the two heat exchangers in parallel flow paths may comprise, in the limiting case, one heat exchanger in each of two parallel flow paths. However, there may also be more than one heat exchanger on one or both of the parallel flow paths, in which case the calculation for the temperature based parameter AJT, may be refined as discussed below, by providing additional forms of the temperature based parameter AJT, allowing for multiple heat exchangers in one or more of the parallel flow paths. The method may involve a simple optimisation of flows between two parallel paths. It is however common for a heat exchanger network to include more than two paths. In this case the determination and equalisation of the temperature based parameter AJT, may be repeated for pairs of paths in a heat exchanger network with three or more parallel paths i. In this way the method can be extended to networks with any number of parallel paths i=1 to n.

It will be appreciated that the split ratios for multiple pairs of parallel paths i are interlinked and hence it is preferred for optimised values for these split ratios to be determined simultaneously, for example by proportional-integral control, proportional- integral-derivate control or a similar technique. Alternatively, a value for one flow rate can be set with the other two (or more) flow rates then being determined relative to that flow rate.

Preferred embodiments extend to the control of heat exchanger networks with multiple heat exchangers in series on one of the parallel flow paths i.

For example, there may be a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on both their first and second sides. This would hence have the common process flow passing through the first sides of two heat - -

exchangers in series along the flow path i and a second fluid passing through the second sides of both heat exchangers in series on an second fluid flow path . With this arrangement the temperature based parameter AJT, may be determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature from the first side of the final heat exchanger in that flow path i and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature of the second fluid that supplies the second side of the first heat exchanger in the flow path of the second fluid. Thus, the temperature based parameter AJT, uses incoming temperature T₀ along with the final temperature of the common process fluid after it has passed in series through both series connected heat exchangers and the initial temperature of the second fluid before it has passed through either heat exchanger. Advantageously, neither the temperature of the common process fluid between first sides of the two series heat exchanger, nor the temperature of the second process fluid between the second sides of the two series heat exchangers needs to be measured. The proportionality optionally encompassed by the temperature based parameter AJT, preferably comprises multiplication by a constant p_x for each second fluid, with the constant p_x being as discussed above

In another example, alternatively or in addition to the above, there may be a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides. This would hence have the common process flow passing through the first sides of two heat exchangers in series on the flow path i and two second fluids, one passing through each of the second sides of the two heat exchangers. With this arrangement the temperature based parameter AJT, must be adjusted to take account of the multiple second fluids and to do this the parameter AJT, includes the incoming temperatures of both of the second fluids prior to the respective second sides of the two series heat exchangers and also includes the temperature of the common process fluid at the outlets of both of the first sides of the two heat exchangers.

The temperature based parameter AJT, for this arrangement in the simplified scenario when there is no weighting (i.e. where all the constants p_x are absent or are set to be equal to one) is determined by in accordance with the formula below:

ΔΤ: = τ -τ_η

AT?(AT_h2 -AT₂) (A7 -Ar₂ ²)

t±JT_i ¾

ΔΤ^ΔΤ^ -ΔΤ;) (AT_h2— ΔΤ|) where

Δ7Ι - -

in which T-i , T_h1 and T₂, T_h2 are the temperatures relating to the first and second heat exchangers in series on the branch i of the heat exchanger network. Figure 3a shows an example of this type of arrangement where T₂, T_h2 and T₃, T_h3 are the temperatures relating to the first and second heat exchangers in series on the branch i of the network and this is explained in more detail below. Figure 3b shows a similar arrangement where Ti , T_h1 and T₂, T_h2 are the temperatures relating to the first and second heat exchangers. It will be appreciated that although the labelling and/or numbering used for the different heat exchangers and temperatures may vary this is merely a matter of notation and the same calculation is applied.

In the more complex situation when it is required to apply a weighting to the second process fluids using a constant p_x as described above then for a flow path i with two heat exchangers in series and different second process fluids being supplied to each of the two heat exchangers the temperature based parameter AJT, can be determined in accordance with the equation Pari below, where T-i , T_h1 and T₂, T_h2 are the temperatures relating to the first and second heat exchangers in series on the branch i of the heat exchanger network and p-ι and p₂ are constants defining a weighting for the respective second process fluids. To complete the example for a simple heat exchanger network as shown in Figure 3b where a second parallel flow path has a single heat exchanger with temperatures T₃, and T_h3 and a weighting constant p₃ one can use the equation Par2 below, in which the temperature based parameter AJT, is determined as described in the first aspect above.

AT

AT² - AT, - AT,)

AT, AT, ²

Pari = ρ

AT, Δ^ - ΔΤ;

Pari = p,——

AT,

Thus, AJT-i = Pari , and AJT₂ = Pari and the split ratio u in this example is adjusted so that the two temperature based parameters are equal in order to optimise the heat exchanger network based on the weighted usage of the second process fluids. It will be seen that when the constants p-ι and p₂ are set to be equal to one then Pari simplifies to the equation given above.

More complicated networks can also be dealt with in a similar fashion by using temperature based parameters AJT, as discussed in more detail below in relation to preferred embodiments. The method may optionally include calculation of such temperature based parameters AJT,. - -

The variations above provide building blocks for a method that can be adapted to determine optimal split ratios for a large number of parallel paths, including one or more paths with series heat exchangers in either or both of the configurations described above. The temperature based parameter is equalised for each path and the way that the flow must be split between the paths can be easily determined.

Viewed from a second aspect, the invention provides an apparatus for controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the apparatus comprising a controller arranged to: receive indications of temperatures of the incoming process fluids and of the parts of the common process fluid after it has passed through the heat exchangers; determine a split ratio for the parts of the common process flow being directed into parallel paths that hold respective ones of the heat exchangers, wherein the controller is arranged to determine a temperature based parameter AJT, for each of the parallel flow paths i and to set the split ratio by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature T, from the first side of the heat exchanger i in that flow path and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger i.

The controller may be programmed with the formulae set out above in relation to the method of the invention. The controller may comprise a computer device in which the function of the controller in calculating the temperature based parameter is implemented via software. Alternatively the controller may comprise a hardware device arranged to perform these calculations. In preferred embodiments, the controller is arranged to carry out the method of any of the preferred features of the first aspect described above.

The controller may control a device that adjusts the split ratio, for example one or more valves, pumps or other flow controllers. The controller may comprise or be a part of a broader control system for the heat exchange network. The controller may be a computer device, for example. The controller may supply setpoints for use by other controllers within the heat exchanger network. - -

In a further aspect the invention provides a heat exchanger network in which two or more heat exchangers are present in parallel flow paths that receive parts of a common process fluid at a temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, wherein the network further comprises an apparatus for controlling a heat exchanger network as described above.

The heat exchanger network may comprise multiple heat exchangers in series on one of the parallel flow paths i.

For example, there may be a flow path with two heat exchangers in series, with these two heat exchangers being connected in series on both their first and second sides. This would hence have the common process flow passing through the first sides of two heat exchangers in series and a second fluid passing through the second sides of both heat exchangers. With this arrangement the controller may be arranged so that the temperature based parameter AJT, is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature from the first side of the final heat exchanger in that flow path and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature of the second fluid that supplies the second side of the first heat exchanger in the flow path of the second fluid.

Alternatively or in addition to the above, the heat exchanger network may comprise a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides. This would hence have the common process flow passing through the first sides of two heat exchangers in series and two second fluids, one passing through each of the second sides of the two heat exchangers. In this case the controller may be arranged to determine the temperature based parameter AJT, using the formula set out above in connection with the preferred features of the first aspect of the invention.

In a still further aspect the invention provides a computer programme product comprising instructions that when executed on a data processing apparatus will configure the data processing apparatus to perform the method of the first aspect and optionally the preferred features thereof, as described above.

It will be appreciated that the use of proportionality in the temperature based parameter and the use of a temperature based parameter without this proportionality can be - -

expressed separately. The invention set out in the claims encompasses either alternative and these alternatives could also be expressed in separate independent claims.

Hence, in an alternative first aspect the invention provides a method of controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths i that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths i and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the method comprising: determining a split ratio for the parts of the common process flow being directed into parallel paths i that hold the heat exchangers, wherein for each of the parallel flow paths i a temperature based parameter AJT, is determined and the split ratio is set by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is determined by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature Tifrom the first side of the heat exchanger in that flow path i and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_h, of the second fluid that supplies the second side of the heat exchanger.

In another alternative first aspect the invention provides a method of controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths i that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths i and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the method comprising: determining a split ratio for the parts of the common process flow being directed into parallel paths i that hold the heat exchangers, wherein for each of the parallel flow paths i a temperature based parameter AJTi is determined and the split ratio is set by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature Tifrom the first side of the heat exchanger in that flow path i and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger. - -

Similarly, in one alternative second aspect the invention provides an apparatus for controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the apparatus comprising: a controller arranged to: receive indications of temperatures of the incoming process fluids and of the parts of the common process fluid after it has passed through the heat exchangers; determine a split ratio for the parts of the common process flow being directed into parallel paths i that hold respective ones of the heat exchangers, wherein the controller is arranged to determine a temperature based parameter AJT, for each of the parallel flow paths i and to set the split ratio by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is determined by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature T, from the first side of the heat exchanger i in that flow path and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger i.

In another alternative second aspect, the invention provides an apparatus for controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the apparatus comprising: a controller arranged to: receive indications of temperatures of the incoming process fluids and of the parts of the common process fluid after it has passed through the heat exchangers; determine a split ratio for the parts of the common process flow being directed into parallel paths i that hold respective ones of the heat exchangers, wherein the controller is arranged to determine a temperature based parameter AJT, for each of the parallel flow paths i and to set the split ratio by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is proportional to a value obtained by by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature T, from the first side of the heat exchanger i in that flow path - -

and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger i.

In each case the preferred features discussed above in relation to the first and the second aspect may be combined with the alternative aspects.

Certain preferred embodiments will now be described by way of example only and with reference to the accompanying drawings in which:

Figure 1 shows a simple heat exchanger network with two parallel paths;

Figure 2 shows a heat exchanger network where one parallel path includes multiple heat exchangers with their first and second sides both connected in series;

Figures 3a and 3b show heat exchanger networks where one parallel path includes multiple heat exchangers with their first sides connected in series and their second sides connected to separate incoming second process fluids;

Figure 4 illustrates a heat exchanger network with three parallel paths;

Figure 5 shows a larger heat exchanger network;

Figure 6 is a schematic diagram of a heat exchanger network for a crude oil fractionator system;

Figure 7 is a plot for the topology of Figure 1 showing variation of numerically calculated output temperature T_end and the equalisation of the temperature based parameter c=JT JT₂ as the split ratio u changes;

Figure 8 is a similar plot for the topology of Figure 3; and

Figure 9 shows contours for numerically calculated temperature along with a representation of the variation in the two split ratios for the topology of Figure 4.

The invention provides a method of control of a heat exchanger network with the aim of maximising heat transfer. The method is based on a determination of a temperature based parameter for each branch of the parallel flow paths. In this document this temperature based parameter is named the Jaschke temperature and given the notation AJT, for a branch i, which may be any branch of multiple branches 1 to n. The Jaschke temperature is calculated as set out below, in which ΔΤ_Χ denotes the difference between the temperature T_x of a stream x after heat exchange and the common inlet temperature T₀:

Τ_Χ = Τ_Χ -Τ₀

The same notation is used for the difference in temperature between the common inlet temperature T₀ and the temperature T_hi of the second process fluid that feeds the second side(s) of the heat exchangers. The Figures illustrate example topologies to which the method may be applied and the determination of the Jaschke temperature is explained below with reference to the Figures. In the example of Figure 1 , the parallel flow paths are - -

recombined and the temperature of the recombined flow paths (i.e. temperature T_end in Figure 1 ) can be maximised (or minimised) using this method.

For the most common situation of a single heat exchanger on each line, as in Figure 1 , the Jaschke temperature is determined as:

AJT.

T_hl -T₀ AT_hl

Optionally this ratio may be multiplied by a constant p_x for the heat exchangeras discussed above in order to apply a weighting to promote or reduce the use of certain second process fluids. The method for controlling the heat exchanger network requires the split ratio between the parallel paths to be controlled so that the Jaschke temperatures for all the flow paths are equal to a reference value AJT,. Generally the reference is recommended to be the Jaschke temperature of the stream with the largest flow rate, but it may also be some (weighted) mean of the Jaschke temperatures of all streams. For the simple example of Figure 1 with paths 1 , 2 the method involves the split ratio being controlled so that the formula:

c = AJT_l - AJT₂

is set so that c is equal to zero.

Figures 2, 3a and 3b show heat exchanger networks with multiple heat exchangers in series on one of the parallel flow paths.

In Figure 2 there is a flow path with two heat exchangers in series, with these two heat exchangers being connected in series on both their first and second sides. This would hence have the common process flow passing through the first sides of two heat exchangers in series and a second fluid passing through the second sides of both heat exchangers. With this arrangement the Jaschke temperatures are determined by the following

AT²

AJT, =— ^l- AT

formula: ^2

AJT =— ³- AT

As for the example above these ratios may optionlly be multiplied by a weighting constant p_x. The Jaschke temperature for the flow path with two heat exchangers in series thus uses the final temperature T₃ of the common process fluid after it has passed in series through both series connected heat exchangers and the initial temperature T_h2 of the second fluid before it has passed through either of the two series connected heat exchangers.

The same applies if there are any number of heat exchangers connected in series on both their hot sides and their cold sides and the basic formulation for the Jaschke

temperature does not change. The reason is that multiple heat exchangers which are fed in - -

series by one stream on both sides may be viewed as one single heat exchanger, even if the stream is split between the heat exchangers. Therefore the Jaschke temperature for any number of heat exchangers connected in this way is calculated the same way as for a single heat exchanger.

As for the simple example of Figure 1 , the split u between the flow paths is controlled so that the two Jaschke temperatures are equal in order to thereby maximise the heat exchanged in the network.

Figure 3a shows a flow path with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides. This would hence have the common process flow passing through the first sides of two heat exchangers in series and two second fluids, one passing through each of the second sides of the two heat

exchangers. This is considerably different to the situation in Figure 2, since the multiple heat exchangers are in separate flow paths and do not act has a single heat exchanger. The Jaschke temperatures for this arrangement, when no weighting is required, are determined in accordance with the formulae below:

AT

Δ/Jj

hi

The first flow path has a single heat exchanger and hence uses the basic Jaschke temperature formula. The second flow path has two heat exchangers each with their own separate feed and so it requires the adapted formula above. As for the earlier examples the split ratio u should be set so that the Jaschke temperatures are equal to thereby maximise heat exchange.

Figure 3b shows a similar heat exchanger network to that of Figure 3a and illustrates how different terminology may be used to describe the same basic network. By way of an example of an optimisation using a weighting constant p_x to promote or reduce the use of the different second process fluids the network of Figure 3b can be optimised by setting AJT-i = Pari , and AJT₂ = Pari , with equations Pari and Par2 as below.

P Pari 9 = p ^ΔΓ'

It is also possible to further adapt the Jaschke temperature formula so that it can be used for the situation where one branch of the parallel flow paths has three heat exchangers - -

each being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides. This is essentially the

arrangement of the second flow path of Figure 3a with the addition of a further heat exchanger. In this situation, when no weighting is required, the Jaschke temperature AJT, is given by the formula below:

In this formula T_x and T_hx take the same meaning as above, that is where the temperature T₀ has been subtracted, with T_x being the temperature of the common process fluid after a heat exchanger x minus T₀ and T_hx being the temperature of the incoming second process fluid for the heat exchanger x minus T₀. The three heat exchangers connected along the flow path are x = 1 , 2, 3.

A further adaptation allows for any number of series heat exchangers n along with the possibility of weighting constants p_x for each of the heat exchangers/second process fluids. In this case the general formula for the Jaschke temperature AJT, is given by the equation Par below:

N

Par =∑_PiJ_Ti

i=\

wit

Thereby allowing optimisation for networks including parallel flow paths having any number of series heat exchangers using different second process fluids.

Figure 4 shows the situation where the heat exchanger network comprises three heat exchangers in parallel with split ratios u-i and u₂ between a first parallel path and a second parallel path and between the second parallel path and a third parallel path, then the method comprises determining u-i and u₂ by adjusting the split ratios such that the parameters c-i and c₂ equal zero, wherein:

AT AT₃ ²

c_x = tsJT_x - AJT₃ -

- -

Optionally these ratios may incorporate multiplication by a weighting constant p_x as discussed above. Thus, the determination and equalisation of the Jaschke temperatures is repeated for pairs of paths in a heat exchanger network with three parallel paths.

This method can be extended to networks with any number of parallel paths, with the general formula being:

c^ A Tj - AJT

c₂ = AJT₂ - AJT_N c_t = MT_t - JT_N

Where for the case with a single heat exchanger on each line, without weighting, we have:

AT*

AJT_X AT'

AJT₂

AT hi

although of course the Jaschke temperature might be adapted in the case where a flow path i includes two or more heat exchangers and a weighting constant p_x may optionally be used as a multiplier. In this case the Jaschke temperature should be calculated as discussed above in relation to Figures 2 and 3. Instead of using the Jaschke Temperature of the N-th line as reference, as above, one could also use a (weighted) mean of all Jaschke temperatures as reference.

Figure 5 illustrates a more complex heat exchanger network along these lines. This network can be extended to include any number of parallel paths including paths with series heat exchangers as shown in Figures 3 and 4. The parallel flow paths each have an input temperature T₀ and the final output temperature is T,. The heat exchangers have first sides connected to these parallel paths, either alone or in some cases in series with further heat exchangers as in paths n and n-1 . The second sides of the heat exchangers are connected to multiple second process fluids with input temperatures T_hi , T_h2, and so on. The control - -

method can be extended to determine optimised flow values for networks of this type simply by equalising the Jaschke temperatures for pairs of parallel flow paths. Only temperature measurements are required, and for the most part the calculation for each flow path in the parallel flow paths only requires three temperatures to be known, being the common input temperature T₀, the second process fluid input temperature T_h and the output temperature T, for the common process fluid.

It will be understood that although the examples of Figures 1 to 5 all recombine the parallel flow paths to obtain a final temperature T_end this recombining is not an essential feature for the control method. The advantages of the control method also arise when the flow paths are not combined or when only some paths are combined. Optimising T_end is equivalent to maximising the sum of heat transferred in all heat exchangers.

An example of a 'real world' heat exchanger network is shown in Figure 6. It will be appreciated that this includes parallel flow paths with single heat exchangers as in Figures 1 and 2 and with series heat exchangers as in Figures 3 and 4. The method of the invention can be used to determine values for flow rates in the parallel paths. As a comparison of the current method with known systems operation of the heat exchanger network of Figure 6 was simulated to find optimal split ratios produced by optimization in Matlab and also based on split ratios calculated using the method described herein. For the sake of simplicity no weighting is applied in this example. The table below shows the output temperatures for the various process lines. The column marked "RTO" shows the temperatures on the real plant which is operated using RTO, the column marked Optimum" shows the optimal values from Matlab, and the column marked "Equal AJT" shows temperature values for the new method described herein.

As can easily be seen, the output temperatures are very close. Most importantly, the final recombined temperature T_end is practically identical. It is a small amount lower for the current method, but the difference is within the bounds of inaccuracy in temperature measurements and process noise. In any event, the advantages of the speed and reduced complexity/cost of the current method mean that a much higher difference in the final T_end value could be tolerated whilst still providing advantages over the RTO technique. - -

To further demonstrate the efficacy of the Jaschke temperature calculations described above the examples of Figures 1 , 3 and 4 were modelled using Matlab. The present self-optimising control method achieved by setting the Jaschke temperature values to be equal was compared with true optimal values determined numerically by Matlab. The results are shown in Figures 7, 8 and 9.

For the topology of Figure 1 the inlet temperature T₀ was set as 60°C. The table below shows the input temperatures T_h for the second fluids, the cold inlet heat capacity rates w_h and the heat exchanger UA values. c¾ [W/K] I h,in [" IJA [W/K]

HXl 30 120 50

HX2 50 140 80 Matlab calculated values for T_end using these input parameters. Figure 7 shows a plot of this calculated T_end against the split ratio u along with a plot of the c value against split ratio u, where:

c = UT_v - lJT₂

as above. The split ratio u is shown along the horizontal axis with the temperature and c on the vertical axis. As can be seen, when c=0 the temperature is maximised. For this set of input variables the numerical calculation shows a maximum temperature with a split ratio us of 0.35, whereas c is equal to zero at a split ratio of 0.34. Hence, the method of optimisation based on c=0 is very close to the true optimal value, and of course involves considerably less calculation as well as only requiring knowledge of temperatures. The w_h and UA values are required for the numeric calculation but do not need to be measured to perform optimisation based on the Jaschke temperature values.

A similar process was carried out for the topology of Figure 3. In this case a first parallel path includes the two series connected heat exchangers, which are denoted HX1 and HX1 1. A second parallel path has a further heat exchanger HX2. The input parameters are tabulated below: ω\_τ [W/K] Ί ΐι,ίη [° C] UA [W/K]

H 1 i 30 120 50

HXl 50 140 140

HX2 20 140 65

The results are shown in Figure 8. Once again the self-optimisation control method finds a split ratio that maximises T_end when c is set to zero. - -

For the topology of Figure 4 it becomes more complex to illustrate the variation of the split ratios since with three parallel flow paths there is an added dimension to consider. A similar process was carried out using Matlab with input parameters as tabulated below:

Variable Value Description

J o 130 Feed stream temperature [C]

w₀ 120 Heat capacity [kWj

UAi 130 Product of heat transfer coefficient 1 and heat exchange area 1 [kW/KJ

UA₂ 190 Product of heat transfer coefficient 2 and heat exchange area 2 [kW/'Kj

17 5.3 180 Product of heat transfer coefficient 3 and heat exchange area 3 [kW/Kj

T- h lin 300 Hot stream 1 temperature fCj

52 Hot stream 1 heat capacity [kW/^'Kj

-£ ft 2m Hot stream 2 temperature [Cj

^'»-¾2 40 Hot stream 2 heat capacity [kW/K]

J hd' in 250 Hot stream 3 temperature [Cj

^"«%3 30 Hot stream 3 heat capacity [kW/^' ] It will be understood that once two of the heat capacity rates for the parallel flow paths are known then the third is also known, since the total input w₀ is fixed. Solutions can hence be considered based on varying two out of the three flows and we select w-i and w₂ for this example. When w-i and w₂ are set then w₃ is known. To illustrate this solution space Figure 9 plots w-i against w₂ and shows contours of temperature values for T_end, as determined via the numerical calculation. The Matlab numerical solution finds a maximum T_end of 242.0182°C, corresponding to w-, = 51.04 kW/K and w₂ = 39.19 kW/K.

The Jaschke temperatures were determined as above and w-i and w₂ adjusted to set the three Jaschke temperatures (one for each parallel flow path) to be equal. Figure 9 shows lines of c=0 for two c values, which in this case use pairs of Jaschke temperatures for the first and second paths and for the first and third paths. The intersection of these two lines occurs when all of the Jaschke temperatures are equal. It will be seen that this is close to the maximum T_end. In fact, the optimisation using c=0 results in:

AJTi = AJT₂ = AJT₃ = 88.34 °C

and a maximum T_end of 242.0153°C whereas for comparison the numerical solution finds its peak temperature T_end of 242.0182°C at:

AJT_! = 88.83 °C

AJT₂ = 87.35 °C

AJT₃ = 88.91 °C

There is hence a very small difference between the true optimum and the split ratio determined by the presently proposed method. For most purposes, given the size of the differences as compared to measurement accuracy and noise the result can be considered to be identical. - -

As an example of the use of a weighting constant p_x, consider the situation where such a constant is used to reflect a cost such as a financial or environmental cost. A financial cost is easier to assign absolute values to, but it will be appreciated that an environmental cost could be determined in an analogous fashion. A cost function can be defined as p_x for a heat exchanger x where p_x = cost - benefit. In the financial example the cost might be expenses in the form of the monetary price for using a given second process fluid and the benefit can be an income value, which may be the value of the heat exchanged with the first process fluid. This income value could be calculated as the equivalent cost for heating with an outside source, for example heating by an oil fired boiler.

The method may advantageously be applied to heat exchanger networks including crude oil heat exchangers as illustrated in Figure 6 as well as other similar networks such as district heating networks, cryogenic plants, chemical plants, water cooling networks and so on. Significant increases in efficiency can be obtained with quicker calculations and lesser cost compared to prior art RTO techniques, whilst maintaining a high level of accuracy.

Claims

CLAIMS:

1. A method of controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths i that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths i and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the method comprising:

determining a split ratio u for the parts of the common process flow being directed into the parallel paths i that hold the heat exchangers,

wherein for each of the parallel flow paths i a temperature based parameter AJT, is determined and the split ratio u is set by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and

wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature Tifrom the first side of the heat exchanger in that flow path i and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger.

2. A method as claimed in claim 1 , wherein the determination and equalisation of the temperature based parameter AJT, is repeated for pairs of paths in a heat exchanger network with three or more parallel paths i to determine split ratios u for each of the pairs of paths.

3 A method as claimed in claim 2, wherein values for the multiple split ratios u are determined simultaneously, for example by proportional-integral control or proportional- integral-derivative control.

4. A method as claimed in claim 1 , 2 or 3, wherein the heat exchanger network comprises multiple heat exchangers in series on one or more of the parallel flow paths i.

5. A method as claimed in claim 4, wherein the heat exchanger network comprises a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on both their first and second sides and wherein the temperature based parameter AJT, for this flow path i is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature from the first side of the final heat exchanger in that flow path and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature of the second fluid that supplies the second side of the first heat exchanger in the flow path of the second fluid.

6. A method as claimed in claim 4 or 5 wherein the heat exchanger network comprises a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides and the method comprises determining the temperature based parameter AJT, in accordance with the formula below:

AT_X = Ά - - T

^_T AT?(AT_h2 - AT₂) (A - Aff ) Δ¾ = T_hl - T

' ΔΤ^Δ^ - ΔΤ;) (ΔΓ_Α2 - ΔΤ;) AT₂ = τ - - T

in which ΤΊ is the outgoing temperature of the common process fluid after a first heat exchanger on the flow path i that receives the common process fluid at temperature T₀, T_hi is the incoming temperature of the second fluid on the second side of this first heat exchanger, T₂ is the outgoing temperature of the common process fluid after a second heat exchanger that receives the common process fluid from the first heat exchanger at temperature ΤΊ, and T_h2 is the incoming temperature of the second fluid on the second side of this second heat exchanger.

7. A method as claimed in claim 4 or 5 wherein the heat exchanger network comprises a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides and the method comprises determining the temperature based parameter AJT, as AJT, = Pari in accordance with the formula below:

AT Λ7Ι hi ΔΤ T - T

Pari = i

AT.. AT - AT Δ¾

where AT T - T

AT hi ^L h2 in which T-i is the outgoing temperature of the common process fluid after a first heat exchanger on the flow path i that receives the common process fluid at temperature T₀, T_h1 is the incoming temperature of the second fluid on the second side of this first heat exchanger, T₂ is the outgoing temperature of the common process fluid after a second heat exchanger that receives the common process fluid from the first heat exchanger at temperature Ti, T_h2 is the incoming temperature of the second fluid on the second side of this second heat exchanger, p-ι is a constant reflecting a cost or benefit of using the first heat exchanger and p₂ is a constant reflecting a cost or benefit of using the second heat exchanger.

8. An apparatus for controlling a heat exchanger network in which two or more heat exchangers are present in parallel flow paths that receive parts of a common process fluid at an incoming temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, the apparatus comprising:

a controller arranged to:

receive indications of temperatures of the incoming process fluids and of the parts of the common process fluid after it has passed through the heat exchangers;

determine a split ratio for the parts of the common process flow being directed into parallel paths i that hold respective ones of the heat exchangers,

wherein the controller is arranged to determine a temperature based parameter AJT, for each of the parallel flow paths i and to set the split ratio by adjusting it such that the temperature based parameter AJT, is equal for each of the parallel flow paths i, and

wherein for a flow path i containing a single heat exchanger the temperature based parameter AJT, is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature T, from the first side of the heat exchanger i in that flow path and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature T_hi of the second fluid that supplies the second side of the heat exchanger i.

9. An apparatus as claimed in claim 8, wherein the controller is arranged to perform the method of any of claims 2 to 7.

10. An apparatus as claimed in claim 8 or 9 wherein the controller is arranged to control a device that adjusts the split ratio.

11. A heat exchanger network in which two or more heat exchangers are present in parallel flow paths i that receive parts of a common process fluid at a temperature T₀, a first side of each of the heat exchangers being connected to the parallel flow paths i and hence receiving the common process fluid and the heat exchangers being arranged for heat exchange between this common process fluid and a plurality of second process fluids on the second sides of the heat exchangers, wherein the network further comprises an apparatus for controlling a heat exchanger network as claimed in any of claims 8, 9 or 10.

12. A heat exchanger network as claimed in claim 1 1 , comprising multiple heat exchangers in series on one of the parallel flow paths i.

13. A heat exchanger network as claimed in claim 12, comprising a flow path i with two heat exchangers in series, wherein these two heat exchangers are connected in series on both their first and second sides and wherein the controller is arranged so that the temperature based parameter AJT, for this flow path i is determined by or is proportional to a value obtained by calculating the square of the difference between the incoming temperature T₀ of the common process fluid and the outgoing temperature from the first side of the final heat exchanger in that flow path and then dividing this squared value by the difference between the incoming temperature T₀ and the incoming temperature of the second fluid that supplies the second side of the first heat exchanger in the flow path of the second fluid.

14. A heat exchanger network as claimed in claim 12 or 13, comprising a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides, wherein the controller is arranged to determine the temperature based parameter AJT, in accordance with the formula below:

AT, - T

Δ7 ² (Δ7 ₂ - ΔΓ₂) (A -Aff ) Δ¾ = T_hl - T

— whprp

ΔΤ^Δ^ - ΔΤ;) (ΔΓ_Μ - Δ7;) AT₂ = τ - - T

= τ - T

in which ΤΊ is the outgoing temperature of the common process fluid after a first heat exchanger on the flow path i that receives the common process fluid at temperature T₀, T_hi is the incoming temperature of the second fluid on the second side of this first heat exchanger, T₂ is the outgoing temperature of the common process fluid after a second heat exchanger that receives the common process fluid from the first heat exchanger at temperature T-i , and T_h2 is the incoming temperature of the second fluid on the second side of this second heat exchanger.

15. A heat exchanger network as claimed in claim 12 or 13, comprising a flow path i with two heat exchangers in series, with these two heat exchangers being connected in series on their first sides to the common process fluid and being connected to different second fluids on their second sides, wherein the controller is arranged to determine the temperature based parameter AJT, as AJT, = Pari in accordance with the formula below:

in which T-i is the outgoing temperature of the common process fluid after a first heat exchanger on the flow path i that receives the common process fluid at temperature T₀, T_hi is the incoming temperature of the second fluid on the second side of this first heat exchanger, T₂ is the outgoing temperature of the common process fluid after a second heat exchanger that receives the common process fluid from the first heat exchanger at temperature ΤΊ, T_h2 is the incoming temperature of the second fluid on the second side of this second heat exchanger, is a constant reflecting a cost or benefit of using the first heat exchanger and p₂ is a constant reflecting a cost or benefit of using the second heat exchanger.

16. A computer programme product comprising instructions that when executed on a data processing apparatus will configure the data processing apparatus to perform the method of any of claims 1 to 7.

17. A method substantially as hereinbefore described with reference to the accompanying drawings.

18. A controller for a heat exchanger network, the controller being substantially as hereinbefore described with reference to the accompanying drawings.