Pinch Analysis is an attractive solution for reduction of thermal energy costs in thermo-chemical industries. In this approach, maximum internally recoverable heat is determined and a heat exchange network is designed to meet the recovery targets. The thermal performance of a heat exchanger over its lifetime is however a concern to industries. Thermal performance of a heat exchanger is affected by many factors which include the physical properties of the shell and tube materials, and the chemical properties of the heat transfer fluid. In this study, thermal performance of shell and tube heat exchangers designed to meet heat recovery targets in a Pinch Analysis study is simulated. The aim of this paper is to present predictions of thermal performances of shell and tube heat exchangers with different heat transfer fluids and geometries as they undergo fouling degradation. Engineering approaches based on thermodynamic analysis, heat balance and Kern Design equations, as well as what-if simulation modeling are used in this work. Shell and tube heat exchangers were designed to meet internal heat recovery targets for three process plants, A, B and C. These targets were published in a separate paper. The effects of degradation of the tubes-due to incremental growth of fouling resistance - on thermal performance of the exchanger were simulated using Visual Basic Analysis (VBA). Overall, it was found that growth in fouling reduces thermal efficiency of shell and tube heat exchangers with an exponential relationship. An increase of 100% of fouling resistance leads to an average reduction of 0.37% heat transfer. Higher values of logarithmic mean temperature difference (LMTD) and higher ratios of external diameter to internal diameter of the exchanger tubes amplify the effect of fouling growth on thermal performance of the exchangers. The results of this work can be applied in pinch analysis, during design of heat exchangers to meet the internal heat recovery targets, especially in predicting how fouling growth can affect these targets. This can also be useful in helping operators of shell and tube heat exchangers to determine cleaning intervals of the exchangers to avoid heat transfer loss.

Symbol | Property | Units |
---|---|---|

Tci | Initial temperature of cold stream | °C |

Tco | Target temperature of cold stream | °C |

Thi | Initial temperature of hot stream | °C |

Tho | Target temperature of hot stream | °C |

t | Mass flow rate of the cold stream | kg/s |

s | Mass flow rate of the hot stream | kg/s |

Ρt | Density of the cold stream | kg/m^{3} |

Ρs | Density of the hot stream | kg/m^{3} |

Cpt | Specific heat capacity of the cold stream | kj/kg.°C |

Cps | Specific heat capacity of the hot stream | kj/kg.°C |

St | Specific gravity of cold stream | Dimensionless |

Ss | Specific gravity of hot stream | Dimensionless |

µt | Dynamic viscosity of cold stream | kg·m^{−1}·s^{−1} |

µs | Dynamic viscosity of hot stream | kg·m^{−1}·s^{−1} |

Uass | Assumed overall coefficient of heat transfer | kW/m^{2}.°C |

Ks | Thermal conductivity of shell side fluid | kW/m·°C |

Kt | Thermal conductivity of tube side fluid | kW/m·°C |

Kw | Thermal conductivity of tube material | kW/m·°C |

Rt | Tube side fouling factor | m^{2}.K/W |

Rs | Shell side fouling factor | m^{2}.K/W |

Costs of production of goods and services have been increasing, partly due to increase in the energy costs. The energy cost is associated both with the fuel and electricity purchase prices and the environmental degradation [

Pinch analysis was first used in 1978 [

Published work on design and simulation of heat recovery network, for example, Becker [

From the available published works in pinch analysis [

Some aspects of fouling growth and performance of heat exchangers have been investigated in studies unrelated to pinch analysis. They however have not centered on thermal performance of shell and tube heat exchanger and neither have such studies elaborated how tube thickness and temperature gradient contribute to the fouling resistance effects severity on thermal performance. In [^{2}.K/W resulted in decrease of the output power and thermal efficiency of the plant by 1.36% and 0.448%, respectively. Effects of fouling of fills in a cooling tower have been studied by [

This paper seeks to contribute to the research on fouling by assessing the effects of tube side fouling growth on thermal performance of shell and tube heat exchangers designed using Kern Design Equations. This assessment includes visual representation of the thermal performance curve and analysis of the effects of tube thickness and fluid temperature difference on the severity of fouling resistance in heat transfer. The assessment is based on selected 5 shell and tube heat exchangers for three plants, A, B and C. Pinch analysis was carried out in these plants and heat recovery targets were determined. The targets were published in a separate paper [

Pinch analysis is a heat integration approach used to internally recover heat in thermo-chemical process plants. The analysis involves heat balancing, where the total heating loads for each process stream are determined, using the First Law of Thermodynamics. The second stage involves determination of maximum possible internally recoverable heat, using the heat cascading method. A heat exchange network is then developed to meet the computed recovery targets. Detailed description of pinch analysis can be found in [

A heat exchange network is made up of heat exchangers which recover heat from hot streams to cold streams. Shell and tube heat exchangers are the common types of exchangers used in thermo-chemical industries. They are described in [

This study was executed in three stages:

Extraction of design from the previous pinch analysis study

Determination of shell and tube heat exchanger areas using Kern Design Equations

What-if simulation of effects of fouling on quantity of heat transferred

This work is a continuation of a pinch analysis study carried out on a sulphonation plant, a dairy processing plant and an alcohol distillery plant. The plants were named A, B and C, respectively, and they were described in [

Kern Design Equations were used to take into account all the variables attendant to shell and tube exchanger heat transfer process. The starting point in design of these exchangers is expressed by:

where U_{ass} is the estimated overall coefficient of heat transfer. Estimates of U have been published for different fluids.

LMTD is the logarithmic mean temperature difference between the medium exchanging heat, computed as:

Here,

T_{hi} is the inlet temperature of the hot fluid

T_{co} is the outlet temperature of the cold fluid

T_{ho} is the outlet temperature of the hot fluid

T_{ci} is the inlet temperature of the cold fluid

Q, the heat flux to be exchanged, is determined by the process streams variables. The hot or the cold stream can determine this value.

is the mass flow rate of the hot fluid

C_{p} is the specific heat capacity of the hot fluid

Even though _{ass}, and then impose some design constraints on the fluid velocity, the Reynold’s number and the pressure drops. They as well allow selection of discrete geometrical variables.

where U_{c} is the calculated overall coefficient of heat transfer and F_{t} is the geometric correction factor. This factor corrects for true counter flow characteristics and can be determined analytically or graphically. U_{c} is determined by:

In

h_{s} |
Shell side coefficient of heat transfer | A_{i} |
Tube internal area | R_{t} |
Tube side fouling factor |

h_{t} |
Tube side coefficient of heat transfer | d_{to} |
Tube external diameter | K_{m} |
Thermal conductivity of the tube material |

R_{s} |
Shell side fouling factor | d_{ti} |
Tube internal diameter | A_{o} |
Tube external area |

d_{to} and d_{ti} are discrete variables, determined by Tubular Exchanger Manufacturers Association (TEMA) standards [_{o} and A_{i} are derived. Thermal conductivity k_{m} is also fixed, according to the material used. Fouling factors R_{s} and R_{t} are ranges of values, provided in literature and the designer has the latitude of varying them. They are dependent of the heat transfer fluid under consideration, the surface of the tube and shell and the flow characteristics [

Tube side heat transfer coefficient h_{t} is determined by:

where k_{t} is the thermal conductivity of the tube side fluid and Nu_{t}, the tube side Nusselt number is computed using the Dittus-Boelter correlation:

Pr_{t}, the Prandtl number, is given by:

where k_{t} is thermal conductivity of the tube side fluid, C_{pc} is the constant pressure specific heat capacity of the tube side fluid and µ_{t} is the tube side dynamic viscosity.

The tube side Reynold’s number, Re_{t}, is:

Here, _{c} is the mass flow rate of the tube side fluid, n_{t} is the number of tubes and n_{p} is the number of shell passes. They are discrete too, determined by TEMA standards. Initial value of n_{t} can be determined using the formula:

L, the length of the exchange tubes, is discrete and obtained from the TEMA standards.

Re_{t} is a design constraint. For design to be acceptable, this value should be greater than 10000. Turbulent flow is desired for optimal convective transfer of heat [_{ti}, n_{p} and n_{t}. Once this condition is satisfied, the tube side coefficient of heat transfer is determined.

The shell side heat transfer coefficient, h_{s}, is determined by:

Here, k_{s} is the thermal conductivity of the shell side fluid and Nu_{s} is the shell side Nusselt number. Nu_{s} is determined by the Nusselt number equation for turbulent sensible flow:

Shell side Prandtl number Pr_{s} is calculated using:

where C_{ph} and µ_{h} are the isobaric specific heat capacity and the dynamic viscosity of the shell side fluid, in that order.

Shell side Reynold’s number is given by:

G_{s} is the shell side fluid ratio of mass flow rate. It is a function of _{h} the shell side mass flow rate and cross-sectional flow area a_{s}.

The cross-sectional flow area a_{s} is:

Here, d_{to} is the external diameter of the exchanger tubes.

The equivalent shell diameter D_{e}, for square pitch, is calculated using:

For each heat exchanger, tube side fluid fouling factors were gradually increased, from the maximum design recommended value, in incremental steps of 5%, to a maximum increase of 100%. The values were obtained from [

where A_{additional} is the difference between required area with designed maximum allowable resistance and the required area due to fouling resistance that exceeds design limit, and U_{cf} is the coefficient of heat transfer after fouling growth. Q_{loss} was plotted against the changes in fouling factor for each exchanger. At the maximum allowable design fouling factor, performance was assumed to be 100% (0 heat loss), because the exchanger meets the targets it was designed to recover. These equations were executed through VBA. Simulation was carried out on 5 heat exchangers. Selection of the exchangers was based on the type of the fluid on the tube side. The exchangers had air (Exchanger 1, Plant A), air (Exchanger 2, Plant A), water (Exchanger 3, Plant A), milk (Exchanger 1, Plant B) and wash (Exchanger 1, Plant C).

The fluid flow parameters and the Heat Exchanger Design for Plant C are presented in

Symbol | Exchanger | 1 | 2 | 3 |
---|---|---|---|---|

Shell | Ethanol Liquid | Ethanol Vapor | Ethanol Vapor | |

Tube | Wash | Wash | Wash | |

Tci | K | 333.15 | 301.15 | 334.15 |

Tco | K | 334.15 | 333.15 | 339.9 |

Thi | K | 383.15 | 384.15 | 384.15 |

Tho | K | 344.15 | 383.15 | 383.15 |

t | kg/s | 0.766 | 0.766 | 0.766 |

kg/s | 0.766 | 0.0986 | 0.766 | |

Pt | kg/m^{3} |
1000 | 1000 | 1000 |

Ρs | kg/m^{3} |
789 | 3.181 | 3.181 |

Cpt | kj/kg.°C | 586.69 | 3.514 | 3.514 |

Cps | kj/kg.°C | 2.43 | 837.85 | 837.85 |

St | NA | 1 | 1 | 1 |

Ss | NA | 0.789 | 2.49 | 2.49 |

µt | Pa.s | 0.00089 | 0.00089 | 0.00089 |

µs | Pa.s | 0.001095 | 0.0000124 | 0.0000124 |

Uass | kW/m^{2}.°C |
0.015 | 0.015 | 0.015 |

Ks | W/m.°C | 0.171 | 0.0144 | 0.0144 |

Kt | W/m.°C | 0.677 | 0.677 | 0.677 |

Kw | kW/m.°C | 111 | 111 | 111 |

Rt | m^{2}.K/W |
0.00003 | 0.00004 | 0.00004 |

Rs | m^{2}.K/W |
0.00012 | 0.00012 | 0.00012 |

In plant C, as is for A and B, the hot fluids were allocated the shell side and the cold fluids on the tube side. The parameters in

Design Variable | Heat Exchanger Number | ||
---|---|---|---|

1 | 2 | 3 | |

Quantity of Heat (kW) | 72.5938 | 86.135168 | 15.477413 |

Tube length (m) | 6.096 | 6.096 | 6.096 |

Tube outer diameter (m) | 0.012875 | 0.012875 | 0.012875 |

Tube inner diameter (m) | 0.000635 | 0.000635 | 0.000635 |

Birmingham Wire Gauge | 1 | 1 | 1 |

Tube thickness (m) | 0.00762 | 0.00762 | 0.00762 |

Selected number of tubes | 838 | 408 | 108 |

Number of tube passes | 8 | 8 | 8 |

Shell inside diameter (m) | 0.9398 | 0.38735 | 0.38735 |

Tube pitch (m) | 0.0254 | 0.0254 | 0.0254 |

Number of baffles | 20 | 20 | 20 |

The quantity of heat specified for each exchanger should be exchanged to meet the specified internal recoverable heat, in pinch analysis.

Two types of heat exchanger areas required, designed to meet the quantified heat recovery are presented in this section. One area has been designed using U_{ass}, the assumed value of coefficient of heat transfer, while the other area has been designed using Kern Equations. The results are shown in

For all the plants, the areas computed by assuming the value of overall coefficient of heat transfer are more than those computed using the one calculated using Kern Equations. The average percentage difference for the plants is 10.1%, 6.9% and 14.9% for A, B and C, respectively. The design approach that uses assumed value of overall coefficient of heat transfer does not consider the fouling factor. The U_{ass} value from the literature is assumed to cater for the fluid fouling factor. However, this assumption leads to overstating the required heat transfer area, thus overstating the cost of heat recovery, by these computed percentages. This confirms findings of a simulation study by [

The percentage heat transfer loss due to growth in fouling resistance for the 5 selected heat exchangers is presented in ^{2}.K/W, the heat exchanger will meet the targeted quantity of heat transfer. As fouling increases beyond the designed value, heat transfer reduces.

The heat loss has an exponential relationship with growth of fouling, for the five exchangers. The modelled average losses, for the 100% increase in fouling factors, was 0.37%. The findings of this study fortify the findings of the work by [

The modelled maximum fouling growth for Exchanger 3 for Plant A is almost half that of Exchangers 1 and 2 for Plant A, at 0.000351 m^{2}.K/W, compared to 0.00585 m^{2}.K/W. However, the percentage heat loss is 0.39%. Its LMTD is higher, at 52.8°C, compared to Exchanger 1, at, 28.51°C. Similarly, the ratio of the external to internal diameter of the tube for Exchanger 3 is higher compared to Exchanger 1, at 11.11 (Birmingham Wire Gage of 7.62 mm), compared to 3.03 (Birmingham Wire Gage of 4.572 mm). This is illustrated in the design data in the appendices. Fouling growth thus has a higher effect on exchangers with tubes that have more thickness than those that have lower thickness.

The modelled heat transfer losses for Exchanger 1 Plant B and Exchanger 1 Plant C are 0.28% and 0.19%, respectively. The same fouling growth notwithstanding, the two have different percentage losses. The LMTD for Exchanger 1, Plant B is 31.8°C while that of Exchanger 1 Plant C is 25.4°C. The tube thickness of the two is the same, with Birmingham Wire Gage of 7.62 mm. The effect of fouling growth on the heat loss in the heat exchangers was thus moderated by the LMTD of the two exchangers.

This paper has analyzed the effects of growth of fouling in shell and tube heat exchangers, by use of thermodynamic analysis, heat balance and Kern Design equations. This study has revealed that estimation of overall heat transfer coefficient, which uses an estimated fouling factor for design of heat exchangers, leads to an overestimate of the required shell and tube exchanger area. The overestimation was by an average of 10.1%, 6.9% and 14.9% for plants A, B and C, respectively, compared to computation of the same using Kern Design Equations. Increase in the design fouling factor by 100% leads to increase in heat losses by an average of 0.37%, for the three plants.

This work has led to four conclusions concerning heat exchanger design, fouling resistance and thermal performance of shell and tube heat exchanger. The relationship between increase in fouling resistance and heat transfer losses in shell and tube heat exchangers is exponential. In design problems that estimate the overall heat transfer coefficient, thus not factoring in the fouling factors unique to the heat transport fluid, the exchange areas are overestimated, thus overestimating the costs of heat recovery. The LMTD determines the severity of fouling resistance in shell and tube heat exchangers. Higher values of LMTD exacerbate the heat losses, compared to lower values, because of the exponential relationship between exchanger heat loss and fouling growth. Similarly, the ratio of external diameter to internal diameter of the exchanger tubes amplifies the effect of fouling growth on thermal performance of the exchangers. The higher the ratio, the higher the heat loss due to growth in fouling. There is need for more work to be carried out on the effect of fouling growth in shell and tube heat exchangers conveying different fluids, especially in prediction of fouling growth using computation fluid dynamics and linking the predicted growth to thermal performance.

I appreciate the efforts of Prof. Kinyua and Dr. Eng Ndiritu for helping me shape this work, which is a continuation of pinch analysis work I carried out on three process plants.

_{2}capture and compression using pinch analysis

_{3}fouling and the flow velocity in smooth tube

Symbol | Exchanger | 1 | 2 | 3 |
---|---|---|---|---|

Shell | SO_{3} |
Air | Air | |

Tube | Air | Air | H20 (l) | |

Tci | K | 389.15 | 388.15 | 373.15 |

Tco | K | 414.12 | 389.15 | 374.15 |

Thi | K | 476.15 | 474.15 | 418.18 |

Tho | K | 399.15 | 418.18 | 383.15 |

t | kg/s | 1.303 | 1.303 | 0.417 |

s | kg/s | 0.435 | 1.235 | 1.235 |

Ρt | kg/m^{3} |
1.274 | 1.274 | 1000 |

Ρs | kg/m^{3} |
3.37 | 1.225 | 1.225 |

Cpt | kj/kg.°C | 1.013 | 1.013 | 2260 |

Cps | kj/kg.°C | 0.9 | 1.013 | 1.013 |

St | 2 | 2 | 1 | |

Ss | 2.75 | 1 | 1 | |

µt | Pa.s | 2.26E-05 | 2.61E-5 | 89E-5 |

µs | Pa.s | 3.26E-05 | 2.61E-5 | 2.61E-5 |

U_{ass} |
kW/m^{2}.°C |
0.015 | 0.015 | 0.015 |

Ks | W/m.°C | 0.75 | 0.0262 | 0.0262 |

Kt | W/m.°C | 0.0262 | 0.0262 | 0.677 |

Kw | kW/m.°C | 0.111 | 0.111 | 0.111 |

Rt | m^{2}.K/W |
0.003 | 0.003 | 0.00018 |

Rs | m^{2}.K/W |
0.0012 | 0.0012 | 0.0012 |

Symbol | Exchanger | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

Shell | Milk | Milk | Milk | Milk | |

Tube | Milk | Water | Steam | Water | |

Tci | K | 298.15 | 298.15 | 374.15 | 373.15 |

Tco | K | 340.0 | 340.0 | 415.15 | 374.15 |

Thi | K | 358.15 | 349.1 | 420.15 | 418.02 |

Tho | K | 349.1 | 348.16 | 418.02 | 376.15 |

t | kg/s | 1.87 | 0.194 | 0.194 | 0.194 |

s | kg/s | 8.61 | 8.61 | 1.87 | 1.87 |

Ρt | kg/m^{3} |
1026 | 1000 | 0.6 | 1000 |

Ρs | kg/m^{3} |
1026 | 1026 | 1026 | 1026 |

Cpt | kj/kg.°C | 4.18 | 4.18 | 2.09 | 2260 |

Cps | kj/kg.°C | 4.18 | 4.18 | 4.18 | 4.18 |

St | 1.026 | 1 | 0.49 | 1 | |

Ss | 1.026 | 1.026 | 1.026 | 1.026 | |

µt | Pa.s | 0.003 | 0.00089 | 0.0000162 | 0.00089 |

µs | Pa.s | 0.003 | 0.003 | 0.003 | 0.003 |

U_{ass} |
kW/m^{2}.°C |
0.015 | 0.015 | 0.015 | 0.015 |

Ks | W/m.°C | 0.637 | 0.637 | 0.637 | 0.637 |

Kt | W/m.°C | 0.637 | 0.677 | 0.0288 | 0.677 |

Kw | kW/m.°C | 111 | 111 | 111 | 111 |

Rt | m^{2}.K/W |
0.00003 | 0.00003 | 0.00003 | 0.00003 |

Rs | m^{2}.K/W |
0.00009 | 0.00009 | 0.00009 | 0.00009 |

Design Variable | Heat Exchanger Number | ||
---|---|---|---|

1 | 2 | 3 | |

Quantity of Heat (kW) | 30.1455 | 70.02 | 70.02 |

Tube length (m) | 4.877 | 4.877 | 4.877 |

Tube outer diameter (m) | 0.00635 | 0.0127 | 0.0127 |

Tube inner diameter (m) | 0.002133 | 0.003556 | 0.001143 |

Birmingham Wire Gauge | 7 | 7 | 1 |

Tube thickness (m) | 0.004572 | 0.004572 | 0.00762 |

Selected number of tubes | 886 | 308 | 480 |

Number of tube passes | 4 | 4 | 4 |

Shell inside diameter (m) | 0.9398 | 0.59055 | 0.7366 |

Tube pitch (m) | 0.0254 | 0.0254 | 0.0254 |

Number of baffles | 20 | 20 | 20 |

Estimated Area (m^{2}) |
72.3305 | 88.4270 | 88.4270 |

Multi objective criteria-based Area (m^{2}) |
66.5392 | 84.0248 | 73.2285 |

Percentage (%) difference in Areas computed | 8 | 4.98 | 17.19 |

Design Variable | Heat Exchanger Number | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

Quantity of Heat (kW) | 33.830412 | 325.70769 | 16.649358 | 1506.893 |

Tube length (m) | 4.877 | 15.24 | 15.24 | 40 |

Tube outer diameter (m) | 0.015875 | 0.015875 | 0.015875 | 0.0127 |

Tube inner diameter (m) | 0.000635 | 0.000635 | 0.000635 | 0.0006096 |

Birmingham Wire Gauge | 1 | 10 | 10 | 4 |

Tube thickness (m) | 0.00762 | 0.0034036 | 0.0034036 | 0.0060452 |

Selected number of tubes | 346 | 948 | 116 | 948 |

Number of tube passes | 8 | 8 | 8 | 8 |

Shell inside diameter (m) | 0.635 | 0.9906 | 0.38735 | 0.9906 |

Tube pitch (m) | 0.0254 | 0.0254 | 0.0254 | 0.0254 |

Number of baffles | 20 | 15 | 15 | 20 |

Estimated Area (m^{2}) |
95.20459 | 685.5007 | 62.216 | 1499.932 |

Multi objective criteria-based Area (m^{2}) |
90.24414 | 659.8252 | 59.38413 | 1288.354 |

Percentage (%) difference in Areas computed | 5.21 | 3.74 | 4.55 | 14.12 |