**2. Mechanical characteristics**

A PHE consists of a pack of thin rectangular plates with portholes, through which two fluid streams flow, where heat transfer takes place. Other components are a frame plate (fixed plate),

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**Figure 1.** Typical plate heat exchangers [1].

a pressure plate (movable plate), upper and lower bars and screws for compressing the pack of plates (Figure 2). An individual plate heat exchanger can hold up to 700 plates. When the package of plates is compressed, the holes in the corners of the plates form continuous tunnels or manifolds through which fluids pass, traversing the plate pack and exiting the equipment. The spaces between the thin heat exchanger plates form narrow channels that are alternately traversed by hot and cold fluids, and provide little resistance to heat transfer.

#### **2.1. Thermal plates and gaskets**

The most important and most expensive part of a PHE is its thermal plates, which are made of metal, metal alloy, or even special graphite materials, depending on the application. Stainless steel, titanium, nickel, aluminum, incoloy, hastelloy, monel, and tantalum are some examples commonly found in industrial applications. The plates may be flat, but in most applications have corrugations that exert a strong influence on the thermal-hydraulic per‐ formance of the device. Some of the main types of plates are shown in Figure 3, although the majority of modern PHEs employ chevron plate types. The channels formed between adjacent plates impose a swirling motion to the fluids, as can be seen in Figure 4. The chevron angle is reversed in adjacent sheets, so that when the plates are tightened, the corrugations provide numerous points of contact that support the equipment. The sealing of the plates is achieved by gaskets fitted at their ends. The gaskets are typically molded elastomers, selected based on their fluid compatibility and conditions of temperature and pressure. Multi-pass arrangements can be implemented, depending on the arrangement of the gaskets between the plates. Butyl or nitrile rubbers are the materials generally used in the manufacture of the gaskets.

**Figure 2.** Exploded View of a Plate Heat Exchanger [2].

a pressure plate (movable plate), upper and lower bars and screws for compressing the pack of plates (Figure 2). An individual plate heat exchanger can hold up to 700 plates. When the package of plates is compressed, the holes in the corners of the plates form continuous tunnels or manifolds through which fluids pass, traversing the plate pack and exiting the equipment. The spaces between the thin heat exchanger plates form narrow channels that are alternately

The most important and most expensive part of a PHE is its thermal plates, which are made of metal, metal alloy, or even special graphite materials, depending on the application. Stainless steel, titanium, nickel, aluminum, incoloy, hastelloy, monel, and tantalum are some examples commonly found in industrial applications. The plates may be flat, but in most applications have corrugations that exert a strong influence on the thermal-hydraulic per‐ formance of the device. Some of the main types of plates are shown in Figure 3, although the majority of modern PHEs employ chevron plate types. The channels formed between adjacent plates impose a swirling motion to the fluids, as can be seen in Figure 4. The chevron angle is reversed in adjacent sheets, so that when the plates are tightened, the corrugations provide numerous points of contact that support the equipment. The sealing of the plates is achieved by gaskets fitted at their ends. The gaskets are typically molded elastomers, selected based on their fluid compatibility and conditions of temperature and pressure. Multi-pass arrangements can be implemented, depending on the arrangement of the gaskets between the plates. Butyl

or nitrile rubbers are the materials generally used in the manufacture of the gaskets.

traversed by hot and cold fluids, and provide little resistance to heat transfer.

**2.1. Thermal plates and gaskets**

**Figure 1.** Typical plate heat exchangers [1].

166 Heat Transfer Studies and Applications

**Figure 3.** Typical cathegories of plate corrugations. (a) washboard, (b) zigzag, (c) chevron or herringbone, (d) protru‐ sions and depressions (e) washboard with secondary corrugations, e (f) oblique washboard [3].

**Figure 4.** Turbulent flow in PHE channels [4].

#### **2.2. Design characteristics**

This section presents some of the main advantages and disadvantages of a PHE, compared to shell-and-tube heat exchangers.

#### **Advantages**

*Flexibility:* Simple disassembly enables the adaptation of PHEs to new process requirements by simply adding or removing plates, or rearranging the number of passes. Moreover, the variety of patterns of plate corrugations available, together with the possibility of using combinations of them in the same PHE, means that various conformations of the unit can be tested during optimization procedures.

*Good temperature control:* Due to the narrow channels formed between adjacent plates, only a small volume of fluid is contained in a PHE. The device therefore responds rapidly to changes in process conditions, with short lag times, so that the temperatures are readily controllable. This is important when high temperatures must be avoided. Furthermore, the shape of the channels reduces the possibility of stagnant zones (dead space) and areas of overheating.

*Low manufacturing cost:* As the plates are only pressed (or glued) together, rather than welded, PHE production can be relatively inexpensive. Special materials may be used to manufacture the plates in order to make them more resistant to corrosion and/or chemical reactions.

*Efficient heat transfer:* The corrugations of the plates and the small hydraulic diameter enhance the formation of turbulent flow, so that high rates of heat transfer can be obtained for the fluids. Consequently, up to 90% of the heat can be recovered, compared to only 50% in the case of shell-and-tube heat exchangers.

*Compactness:* The high thermal effectiveness of PHEs means that they have a very small footprint. For the same area of heat transfer, PHEs can often occupy 80% less floor space (sometimes 10 times less), compared to shell-and-tube heat exchangers (Figure 5).

**Figure 5.** Illustration of the typical size difference between a PHE and a shell-and-tube heat exchanger for a given heat load [5].

*Reduced fouling*: Reduced fouling results from the combination of high turbulence and a short fluid residence time. The scale factors for PHEs can be up to ten times lower than for shelland-tube heat exchangers.

*Ease of inspection and cleaning*: Since the PHE components can be separated, it is possible to clean and inspect all the parts that are exposed to fluids. This feature is essential in the food processing and pharmaceutical industries.

*Easy leak detection*: The gaskets have vents (Figure 6) that prevent fluids from mixing in the case of a failure, which also facilitate locating leaks.

**Figure 6.** Vents in gaskets to detect possible leaks [4].

**Figure 4.** Turbulent flow in PHE channels [4].

This section presents some of the main advantages and disadvantages of a PHE, compared to

*Flexibility:* Simple disassembly enables the adaptation of PHEs to new process requirements by simply adding or removing plates, or rearranging the number of passes. Moreover, the variety of patterns of plate corrugations available, together with the possibility of using combinations of them in the same PHE, means that various conformations of the unit can be

*Good temperature control:* Due to the narrow channels formed between adjacent plates, only a small volume of fluid is contained in a PHE. The device therefore responds rapidly to changes in process conditions, with short lag times, so that the temperatures are readily controllable. This is important when high temperatures must be avoided. Furthermore, the shape of the channels reduces the possibility of stagnant zones (dead space) and areas of overheating.

*Low manufacturing cost:* As the plates are only pressed (or glued) together, rather than welded, PHE production can be relatively inexpensive. Special materials may be used to manufacture the plates in order to make them more resistant to corrosion and/or chemical reactions.

*Efficient heat transfer:* The corrugations of the plates and the small hydraulic diameter enhance the formation of turbulent flow, so that high rates of heat transfer can be obtained for the fluids. Consequently, up to 90% of the heat can be recovered, compared to only 50% in the case of

*Compactness:* The high thermal effectiveness of PHEs means that they have a very small footprint. For the same area of heat transfer, PHEs can often occupy 80% less floor space

(sometimes 10 times less), compared to shell-and-tube heat exchangers (Figure 5).

**2.2. Design characteristics**

168 Heat Transfer Studies and Applications

**Advantages**

shell-and-tube heat exchangers.

tested during optimization procedures.

shell-and-tube heat exchangers.

#### **Drawbacks**

*Temperature and pressure limitations*: An important limitation of PHEs is related to the plate gaskets. Pressures and temperatures exceeding 25 atm and 160 °C, respectively, are not tolerated because they can cause the standard gaskets to leak. However, gaskets made of special materials can withstand temperatures up to 400 °C, and it is possible to weld or braze the plates to each other in order to operate under more severe conditions. This would have the additional advantages of increasing the operational limits, as well as the possibility of working with corrosive fluids, because it would eliminate the need for gaskets. However, the PHE would lose its major advantages of flexibility and ease of cleaning, and the equipment would become more expensive.

*High pressure drop*: Because of the corrugated plates and the small flow space between them, the pressure drop due to friction is high, which increases pumping costs. The pressure drop can be reduced by increasing the number of passages per pass and splitting the flow into a greater number of channels. This diminishes the flow velocity within the channel, hence reducing the friction factor. However, the convective heat transfer coefficient is also reduced, decreasing the effectiveness of the heat exchanger.

*Phase change*: In special cases, PHEs can be used in condensation or evaporation operations, but are not recommended for gases and vapors due to the limited space within the channels and pressure limitations.

*Types of fluids*: The processing of fluids that are highly viscous or contain fibrous material is not recommended because of the high associated pressure drop and flow distribution prob‐ lems within the PHE. Compatibility between the fluid and the gasket material should also be considered. Highly flammable or toxic fluids must be avoided due to the possibility of leakage.

*Leakage:* Friction between the metal plates can cause wear and the formation of small holes that are difficult to locate. As a precaution, it is advisable to pressurize the process fluid so that there is less risk of contamination in the event of leakage from a plate.

#### **2.3. Arrangement of a plate heat exchanger**

The simplest types of arrangements of plate heat exchangers are those in which both fluids make just one pass, so there is no change in direction of the streams. These are known as 1-1 single-pass arrangements, and there are two types: countercurrent and concurrent. A great advantage of the single-pass arrangement is that the fluid inlets and outlets can be installed in the fixed plate, making it easy to open the equipment for maintenance and cleaning, without disturbing the pipework. This is the most widely used single-pass design, known as the Uarrangement. There is also a single-pass Z-arrangement, where there is input and output of fluids through both end plates (Figure 7).

Countercurrent flow, where the streams flow in opposite directions, is usually preferred due the achievement of higher thermal efficiency, compared to concurrent flow, where the streams flow in the same direction. Multi-pass arrangements can also be employed to enhance the heat

**Figure 7.** Arrangements of a simple-pass PHE. (a) U-arrangement and (b) Z-arrangement.

transfer or flow velocity of the streams, and are usually required when there is a substantial difference between the flow rates of the streams (Figure 8).

**Figure 8.** Multi-pass PHE.

**Drawbacks**

become more expensive.

170 Heat Transfer Studies and Applications

and pressure limitations.

decreasing the effectiveness of the heat exchanger.

**2.3. Arrangement of a plate heat exchanger**

fluids through both end plates (Figure 7).

*Temperature and pressure limitations*: An important limitation of PHEs is related to the plate gaskets. Pressures and temperatures exceeding 25 atm and 160 °C, respectively, are not tolerated because they can cause the standard gaskets to leak. However, gaskets made of special materials can withstand temperatures up to 400 °C, and it is possible to weld or braze the plates to each other in order to operate under more severe conditions. This would have the additional advantages of increasing the operational limits, as well as the possibility of working with corrosive fluids, because it would eliminate the need for gaskets. However, the PHE would lose its major advantages of flexibility and ease of cleaning, and the equipment would

*High pressure drop*: Because of the corrugated plates and the small flow space between them, the pressure drop due to friction is high, which increases pumping costs. The pressure drop can be reduced by increasing the number of passages per pass and splitting the flow into a greater number of channels. This diminishes the flow velocity within the channel, hence reducing the friction factor. However, the convective heat transfer coefficient is also reduced,

*Phase change*: In special cases, PHEs can be used in condensation or evaporation operations, but are not recommended for gases and vapors due to the limited space within the channels

*Types of fluids*: The processing of fluids that are highly viscous or contain fibrous material is not recommended because of the high associated pressure drop and flow distribution prob‐ lems within the PHE. Compatibility between the fluid and the gasket material should also be considered. Highly flammable or toxic fluids must be avoided due to the possibility of leakage.

*Leakage:* Friction between the metal plates can cause wear and the formation of small holes that are difficult to locate. As a precaution, it is advisable to pressurize the process fluid so that

The simplest types of arrangements of plate heat exchangers are those in which both fluids make just one pass, so there is no change in direction of the streams. These are known as 1-1 single-pass arrangements, and there are two types: countercurrent and concurrent. A great advantage of the single-pass arrangement is that the fluid inlets and outlets can be installed in the fixed plate, making it easy to open the equipment for maintenance and cleaning, without disturbing the pipework. This is the most widely used single-pass design, known as the Uarrangement. There is also a single-pass Z-arrangement, where there is input and output of

Countercurrent flow, where the streams flow in opposite directions, is usually preferred due the achievement of higher thermal efficiency, compared to concurrent flow, where the streams flow in the same direction. Multi-pass arrangements can also be employed to enhance the heat

there is less risk of contamination in the event of leakage from a plate.

There are five parameters that can be used to characterize the PHE configuration [6]: *NC*, *<sup>P</sup> <sup>I</sup>* , *P II* , *ϕ*, *Yh* and *Yf* .

Number of channels (*NC*): The space between two adjacent plates is a channel. The end plates are not considered, so the number of channels of a PHE is the number of plates minus one. The odd-numbered channels belong to side I, and the even-numbered ones belong to side II (Figure 9). The number of channels in each side are *NC I* and *NC II* .

Number of passes (*P*): This is the number of changes of direction of a determined stream inside the plate pack, plus one. *P <sup>I</sup>* and *P II* are the number of passes in each side.

Hot fluid location (*Yh* ): It is a binary parameter that assigns the fluids to the PHE sides. If Yh = 1 the hot fluid occupies side I while if *Yh* = 0 the hot fluid occupies side II.

Feed connection (*ϕ*): Feed side I is arbitrarily set at *η* = 0 as presented in Figure 9. The parameter *ϕ* represents the relative position of side II. Figure 9 illustrates all possibilities of connection. The parameter *η* is defined as *η* = *x* / *L <sup>P</sup>*.

**Figure 9.** Feed connection of a PHE.

The plates of a PHE can provide vertical or diagonal flow, depending on the arrangement of the gaskets. For vertical flow, the inlet and outlet of a given stream are located on the same side of the heat exchanger, whereas for diagonal flow they are on opposite sides. Assembly of the plate pack involves alternating between the "A" and "B" plates for the respective flows. Mounting of the plate pack in vertical flow mode only requires an appropriate gasket config‐ uration, because the A and B arrangements are equivalent (they are rotated by 180°, as shown in Figure 10a). This is not possible in the case of diagonal flow, which requires both types of mounting plate (Figure 10b). To identify each type of flow, Gut (2003) considered the binary parameter *Yf* (*Yf* = 1 for diagonal flow and *Yf* = 0 for vertical flow). Poor flow distribution is more likely to occur in the array of vertical flow [7]. Figure 9. Feed connection of a PHE. The plates of a PHE can provide vertical or diagonal flow, depending on the arrangement of the gaskets. For vertical flow, the inlet and outlet of a given stream are located on the same side of the heat exchanger, whereas for diagonal flow they are on opposite sides. Assembly of the plate pack involves alternating between the "A" and "B" plates for the respective flows. Mounting of the plate pack in vertical flow mode only requires an appropriate gasket configuration, because the A and B arrangements are equivalent (they are rotated by 180°, as shown in Figure 10a). This is not possible in the case of diagonal flow, which requires both types of mounting plate (Figure 10b). To identify each type of flow, Gut (2003) considered the binary parameterܻ (ܻ = 1 for diagonal flow and ܻ = 0 for vertical flow). Poor flow

Due to the large number of plate types and pass arrangements, there are many possible configurations of a particular PHE design. As a result, a number of mathematical modeling approaches have been proposed for the calculation of

 A mathematical model was developed to simulate the general configuration of a PHE operating under steady state conditions, characterized using six different parameters [6]. In this model, the parameters considered are the number of channels, the number of passes for each side, the fluid locations, the feed connection locations, and the type of channel

The main flow is divided equally among the channels that make up each pass;

Figure 10a. Vertical flow plate [9]. Figure 10b. Diagonal flow plate [9]. **Figure 10.** (a). Vertical flow plate [9]. (b). Diagonal flow plate [9].

performance. Two different modeling approaches are described below.

The PHE operates at steady state;

Perfect mixture in the end of each pass;

The velocity profile in the channels is flat (plug flow);

**3. MATHEMATICAL MODELING**

flow. The following assumptions are made:

**3.1 Model 1**

distribution is more likely to occur in the array of vertical flow [7].
