Plate Heat Exchanger

The thermal model of IDAES Plate Heat Exchanger (PHE) as part of the MEA scrubbing process for post-combustion carbon capture (PCC) is based on the Effectiveness-Number of Transfer Units (e-NTU) approach. In amine-based PCC, the rich solvent leaving the absorber is pre-heated in the PHE using heat recovered from the lean solvent leaving the stripper to reduce the regeneration energy requirement. In the PHE unit, the series of plates stacked together form channels where hot and cold fluids flow alternatively as shown in Figure 1(A). Divider plates enable the partitioning of PHEs into different operating zones. The main dimensions of a gasket plate are shown in Figure 1(B). The PHE is a viable alternative to the conventional Shell and Tube Heat Exchanger specifically because of its lower approach temperature difference capability. For more information on the PHE model see Akula et al. (2019).

Figure 1(A). Z-configuration Plate Heat Exchanger with P passes

Figure 1(B). Basic details of a Chevron Plate

Degrees of Freedom

The Plate Heat Exchanger model has 3 design parameters and 7 design variables.

Design Parameters and Variables:

number of passes (mutable parameter),

channels per pass (mutable parameter),

number of divider plates (mutable parameter,

plate length,

plate width,

plate thickness,

port diameter,

plate thermal conductivity, and

total heat transfer area.

Model Structure

The Plate Heat Exchanger unit model builds off the core HeatExchangerNTU model <reference_guides/model_libraries/generic/unit_models/heat_exchanger_ntu:Heat Exchanger using the NTU Method>, and heat transfer is based on the Effectiveness-Number of Transfer Units (e-NTU method).

Parameters

The following parameters can be set via configuration arguments when instantiating the Plate Heat Exchanger model, or modified later.

Variable	Symbol	Index Sets	Doc
number_of_passes	N_passes	None	Number of passes in heat exchanger unit
channels_per_pass	N_channels	None	Number of channels per heat exchanger pass (assumed equal in all plates)
number_of_divider_plates	N_dividers	None	Number of divider plates in heat exchanger assembly

Variables

The following variables are declared in addition to those variables created by the HeatExchangerNTU class.

Variable	Symbol	Index Sets	Doc
plate_length	L	None	Length of a heat exchanger plate
plate_width	W	None	Width of a heat exchanger plate
plate_thickness	H	None	Thickness of a heat exchanger plate
plate_pact_length	L_pact	None	Compressed plate pact length
port_diameter	d_port	None	Diameter of fluid ports in each plate
plate_therm_cond	k_plate	None	Thermal conductivity of heat exchanger plates

Expressions

The following expressions are declared in addition to those created by the HeatExchangerNTU class.

Plate gap:

$$g_{plate} = \frac{L_{pact}}{N_{plates}} - H$$

where

N_plates = 2N_channelsN_passes − (1 + N_dividers)

Channel diameter:

$$d_{channel} = \frac{2LWg_{plate}}{A}$$

Hot and cold side heat transfer coefficients are calculated using the following correlation:

$$U_{side} = \frac{k_{fluid} \times A \times Re^B \times Pr^C}{d_{channel}}$$

where k_fluid is the thermal conductivity of the fluid, Re and Pr are the Reynolds and Prandlt number respectively and A, B and C are coefficients.

The friction factor for the pressure drop correlation is expressed as:

f = A + B × Re^C

where Re is the Reynolds and A, B and C are coefficients (different to those above).

Constraints

The Plate Heat Exchanger unit model writes additional Constraints beyond those written by the HeatExchangerNTU class.

The overall heat transfer coefficient is calculated using the following correlation:

$$U == \frac{1}{\frac{1}{U_{hot}} + \frac{g_{plate}}{k_{plate}} + \frac{1}{U_{cold}}}$$

For heat exchangers with an even number of passes, the following correlation is used for the effectiveness factor:

$$\epsilon = \frac{(1 - exp(-\frac{NTU}{{channels}} \times (1 - C_{ratio})))}{(1 - C_{ratio} \times exp(-\frac{NTU}{{channels}} \times (1 - C_{ratio})))}$$

For heat exchangers with an odd number of passes, the following correlation is used for the effectiveness factor:

$$\epsilon = \frac{(1 - exp(-\frac{NTU}{{channels}} \times (1 + C_{ratio})))}{(1 + C_{ratio})}$$

Pressure drop for both sides of the heat exchanger is calculated using the following correlation:

$$\Delta P = \frac{2fN_{passes}v^2\rho_{mass} \times (L_{plate} + d_{port})}{d_{channel}} + 0.7N_{passes}v^2\rho_{mass}g \times (L_{plate} + d_{port})$$

where f is the friction factor for the side and v is the velocity of the fluid at the port.