Department Of Chemical Engineering

Published Date: 02 Nov 2017

IMPERIAL COLLEGE LONDON

SW7 2AZ

PEERHOSSAINI (Donia)

Literature Review

_________

CFD Modelling of heat exchanger equipment

Supervised by Professor Sandro Macchietto

A report presented to Imperial College London in partial fulfillment of the requirements for the degree of Master of Science in CHEMICAL ENGINEERING

February 2013

Table of contents

Introduction

Many experimental and modeling attempts have been carried out to analyze the effects of fouling on heat exchanger efficiency. So far, the research has been focused on the deposition of fouling elements on the tube inner side and its corresponding thermal-hydraulic effects. This project aims at investigating these aspects inside the tube but also on the shell side of a shell and tube heat exchanger by CFD simulations.

First, we will examine whether the deposition models established for the tube side can be applied to the heat exchanger shell side. Then we search in the literature for the existing shell side models. The next step starts with modeling of fouling in the inside and outside of a single tube, and then we refine and extend the model to more real cases by relaxing the limiting hypotheses. Finally, the numerical results for a shell and tube heat exchanger with a single tube will be compared with experimental data.

Chapter 1

Fouling in heat exchangers

This chapter describes the basics and science of fouling process. Different types of fouling and mechanisms that generate fouling are explained in this part.

Different types of fouling

The fouling refers to the deposits that appear in the heat exchangers surfaces. It can be found in different shapes: crystallization, sediments, biological residues, chemical reaction products, etc. These deposits have a thermal conductivity between 0.2 and 1 W.m-1.K-1 [4] that reduces the heat exchanger‘s performances and lead to an early ageing of the facilities.

The fouling process rolls out in five stages:

Initiation: the first stage is connected to the time before the first appearance of deposits in the facilities

The deposits transport until the wall

The deposit attachment: every particle does not necessary settle in the wall

Particle removal: some particles can be extracted from the deposit layer

Deposit ageing: the chemical layout or crystalline of deposit can change over time which reduces the particle bond and weaken the deposit.

Particulate fouling

Description

The heat exchangers are in contact with fluid that may contain airborne particles. These particles can settle in the heat exchanger’s walls and accumulate creating a deposit.

Particle deposit mechanisms in the walls

Many processes are involved in the transfer of the particles to the wall.

Transfer due to Brownian diffusion: the airborne particles are subjected to random motions.

Transfer due to gravity: particles are subjected to the gravitation field (P=mparticle.g). The gravity effect is significant in case of horizontal installations, with a slow fluid flow and regarding large particles (particles with a size superior to 1µm).

Transfer due to centrifugal force: the bond attraction is high -under the centrifugal force- in areas where the fluid flow re-circulates as shown in Figure 1.

recircualtion.png

Figure 1: Flow profile in a right angle bend [5]

Transfer due to thermal precipitation

When the fluid is subjected to a temperature gradient, particles move to the areas where the fluid is the coldest. In a heat exchanger, particles move to the areas with hot/cold interface. Consequently, when there is a considerable temperature difference between the two fluids of a heat exchanger, the bond to walls due to thermal precipitation is high.

Transfer due to electrical precipitation

Regarding small particles (size under 1µm), the electrical interaction is stronger than the gravity force and so affects the motion of these particles.

Transfer due to turbulence

The turbulence projects particles against the wall creating the deposit.

The Figure 2 summarizes these mechanisms that generate the deposit:

mecanisms deposit.png

Figure 2: Mechanisms creating deposit [5]

To conclude, the deposit is more likely to be generated from the gravitational and centrifugal forces in a heat exchanger that is horizontal and contains many bends. Besides, a high thermal gradient increases considerably the deposit. However, the deposit can be partly prevented by maintaining a high flow velocity.

Scaling [7]

Description

Scaling is a kind of fouling that appears in the presence of calcium (Ca2+), magnesium (Mg2+) and bicarbonate (HCO3) ions in water. This is exemplified by a limestone deposit (calcium carbonate CaCO3) on the walls, according to the following reaction: Ca2+ + CO32- ↔ CaCO3.

Risk factors

Water hardness, characterized by the presence of magnesium and calcium ions, is a significant scaling risk factor.

Another factor to bear in mind is the water temperature. Indeed, the increase of water temperature leads to the release of carbon gas which accelerates the previous reaction. That is why scaling is low on cold water pipes while it is common on hot water pipes such as water heaters.

A third risk factor is the presence of other ions in water such as iron Fe2+ ion that favors deposit. Conversely, when copper or zinc ions are present, the limestone does not attach the walls but stays airborne in water. The amount of these elements needed is very low such as 10-5 g.L-1 respectively. Therefore, copper pipes must be favored.

Scaling is a type of fouling that is most commonly found within aqueous environment. It is often combined to other fouling mechanism such as corrosion fouling.

Corrosion fouling

Description

Like scaling, corrosion fouling results from a chemical reaction. This reaction is an oxidation- reduction equation:

metal + n. H+ → metal ions + n/2 (H2)

Figure 3: Corrosion fouling mechanism [5]

Figure 3 presents the corrosion mechanism: it results from redox reactions that correspond to material migration and create cavities.

Biological fouling

Biological fouling is the result of the growth of micro- organisms that attach heat exchanger surfaces. Three types of micro- organisms are involved in this phenomenon: bacteria, algae and fungi.

Bacteria: the bacteria growth is due to nutrient such as hydrocarbons, ammonia, etc. The bacterial cell is a living cell capable of feeding, growing and multiplying in the environment in which it operates.

Algae: they are living organisms that grow in the presence of solar energy with photosynthesis. Green and brown algae are those commonly found in cooling system. It is of high importance to identify the presence of algae because it causes silica deposit which can create blockages.

Fungi: these plants have neither root nor stem or leaf. They grow thanks to nutrients, but mainly thanks to changes in their physical conditions such as pH, humidity and ambient temperature.

Chemical reaction fouling

This type of fouling occurs when a chemical reaction takes place next to a heat exchange surface and the solid products of the reaction attach the surface. Most of the time, it consists in a polymerization by auto- oxidation that spreads like a chain reaction with free radicals. Molecular oxygen plays a controlling role.

The reaction scheme is the following:

Initiation: RH + Z- → R- + HZ

Propagation: R¨ + O2 → ROO¨

ROO¨ + RH → ROOH + R¨

Stop: R¨ + R¨ → RR

ROO¨ + R¨ → ROOR

RH is a hydrocarbon molecule and Z¨ is a free radical originates from metal ions and nitrogen or sulfur compounds.

Chemical reaction rates depend on temperature, pressure, concentration and the presence of catalysts.

This type of fouling is mainly found in petrochemical and food industries, and heating circuits using an organic fluid.

Solidification fouling

This type fouling results from a pure liquid solidification in contact with an exchange surface sub cooled. This means that an ice layer is formatted inside the pipes. It can also refer to the deposit of an element in his high melting point within a liquid that is in contact with a cold surface exchange. Vapor may attach as well as a solid, without passing through the liquid state which corresponds to the frost formation.

Conclusions

Five major fouling categories exist: particulate fouling, crystallization fouling, corrosion fouling, chemical reaction fouling and biological fouling. Besides, installations can be subjected, at the same time, to several of these mechanisms that create a deposit.

The parameters that affect the fouling rate of exchange walls are various: temperature, pressure, the fluid nature and velocity, materials used… Consequently, fouling does not affect all exchangers in the same way because their configurations are dissimilar.

Impact of fouling

The main problems due to fouling are summarized by Coletti [3] by these four categories:

"Operating difficulties

Economic penalties

Environmental impact

Health and safety hazards while cleaning"

Operating difficulties

The fouling deposits have thermal conductivity that lead to the reduction of the heat transfer coefficient. Therefore, the energy efficiency is impacted as well and extra energy is required. For instance, Sikos and Klemes [41] have estimated that the energy consumed in crude distillations units because of fouling is between 10-20% higher than if it was cleaned.

Fouling also causes a reduction in cross- sectional area which creates pressure drops and consequently affects the hydraulic performances of the heat exchanger. At that point, additional pumping is required that is to say additional energy (electricity).

Economic penalties

Costs can increase because of several reasons. As explained previously, the extra energy consumption (like fuel) to counter the drops due to fouling leads to higher costs.

To reduce the fouling effects, cleaning actions are conducted but it induces the line activity to stop (for instance in a refinery) and consequently economic losses. Besides, these cleaning actions are complex and time- spending processes that required expense. However, they represent limited costs compared to the losses in the throughput and energy expenses.

Finally, to prevent these losses in heat transfer efficiency, some companies asked for the design of larger heat transfer surfaces or the use of anti- fouling chemicals which increase the capital costs. Particularly, these chemicals reduce considerably the fouling (65% reduction [3]) and the occurrence of cleaning actions but their implementations are costly.

Environmental impacts

The extra energy consumption caused by fouling is also responsible of environmental effects as it conducts to higher carbon dioxide emissions, for instance when more fuel is burnt in refineries. The second impact is as an ecological aspect due to the presence of "carbonaceous deposits" [3] that can be found in the exchangers surfaces affected by fouling.

Health and safety hazards

The cleaning actions require meticulous safety procedures and scheduling as lots of damages can occur during each process, especially while cleaning pressurized unit and in the oil industry.

Chapter 2

Description, fouling and caution of shell and tube heat exchangers

A great number of heat exchangers exist to meet the needs of the different industry sectors. The aim of this chapter is to present these different heat exchangers by specifying the fouling risks according to their design.

2.1 Shell and tube heat exchanger’s description

This is one of the most common heat exchanger. It is composed of a bundle of tubes in a shell. One of the fluids circulates inside the tubes while the other circulates outside the tubes, through the shell side.

Baffles are often added inside the shell and guide the fluid that circulates outside the tubes. They generate turbulence, possibly increase the fluid velocity and improve the heat transfer coefficient. However, they can create at the same time a resistance to the flow and damaging vibrations. There are also void regions at the corners that favor fouling and limit the heat exchange area. Consequently many studies on baffle types have been carried out involving CFD modeling [17]. For instance, we can find in the literature the following baffles that have been designed for shell and tube heat exchangers: rod [18- 19], orifice [20] and helical baffles [21- 22]. More recently, a numerical modeling of the shell side of a shell- and- tube heat exchanger with flower baffles [23] have been developed and validated by experimental data. The computation results with the flower baffles shows a better overall thermal hydraulic performance than the heat exchanger with the helical baffles. These latter were so far considered to have outstanding thermal hydraulic performance, low vibrations and less subject to fouling.

Figure ?: Shell and Tube heat exchanger [8]

The tubes are supported at their ends by tube sheets. These are the sensitive parts of the heat exchangers as they are easily subjected to corrosion fouling.

Two tubes configurations can be found: in square and triangular pitch. The square pitch gives access to all of the external part of the tubes while the triangular pitch is more compact as shown in Figure ?.

Figure ?: Square pitch (on the left), triangular pitch (on the right) [5]

2.2 Fouling risks and caution

If a very fouling fluid is being used, exchangers- type U should be avoided because they do not allow mechanical cleaning of the tubes inside. Besides, it is essential to circulate the more fouling fluid inside the tubes since tube side is easier to clean than the shell side. As explained previously, the square pitch is a better configuration for cleaning matters.

The baffle’s configuration should be considered regarding the flow in the shell. In order to have a uniform velocity and to avoid re-circulating flows that lead to deposit, it is essential to consider the following configuration:

To define a limited clearance between the baffles and the shell

To set a distance between the baffles slightly smaller than the shell diameter

Clearance between the baffles and the shell

ShellBaffles should define an opening of approximately 20% of the shell diameter

Distance between baffles

Baffles opening

Figure ?: Baffle’s configurations [5]

By implementing vents in the installation, the corrosive vapors can be released out of the exchanger. To avoid further fouling, preexisting micro cracks in the material should be minimized.

Chapter 3

CFD Modeling of heat exchangers undergoing chemical reaction fouling

Numerical modeling methods are sought increasingly to study the performance of heat exchangers. One of the main advantages of this method compared to the experimental method is economical. In addition, it allows visibility of some phenomena that are not necessarily possible experimentally and often saves time compared to experimental method. However, the modeling of loaded configurations is complex and often requires a simplification of the studied element and validation of computation results by comparison with experimental data.

3.1 Problem definition and objectives

The objective of this project is to study the influence of fouling in the shell side on the heat exchanger’s performances using CFD modeling. So far, most of the researches considered that the fouling in the tube side is often the dominant resistance to heat transfer [1]. Therefore and also because it presents more challenges, little research has been done in the shell side. It presents a rare and interesting area of investigation.

The idea is trying to apply to the shell side the numerical modelings developed for the tube side that can be found in the literature. For the sake of simplification for the CFD simulation, the modeling of a shell-and-tube heat exchanger is firstly reduced to a single tube model.

The evaluation of the influence in the overall heat transfer of the shell side fouling will be done by simulating the dynamic behavior and calculating thermo-hydraulic performances.

3.2 Mathematical modeling

This research project focuses in the chemical reaction type of fouling. As explained previously, the tubes located in each pass can be represented by one single tube model since we assume that they are subjected to similar thermal influences. The common method to assess the fouling dynamics is to calculate the fouling resistance that would be added to the mass transfer equations.

3.2.1 General heat transfer equations

The calculation of the fouling resistance is commonly used in modeling. We can find in literature two main methodologies to design heat exchanger that take into account fouling: the LMTD (log mean temperature difference) method [9] and the ε- NTU approach [10] [11].

The following figure shows the fouling phenomenon for a single tube heat exchanger and describes the nomenclature used in the mass transfer equations detailed below. This model is distributed axially (one dimension).

t

Figure ?: Fouling layer within the tube and the shell side [3]

LMTD methodology

First, the heat duty Q (W) is calculated for both (shell and tube) sides of the tube wall:

(3.1)

Where and (kg.s-1) are the mass flow rate of the hot and cold fluids, and (J.kg-1.K-1) the specific heat capacity, , and , (K) the inlet and outlet temperature of the two fluids.

The total heat transfer Q (W) in the exchanger can also been expressed by the Hausbrand formula:

Where U (W. m-2. K-1) is the overall heat transfer coefficient; S (m²) is the surface area of the exchanger, ΔTlm is the appropriate mean temperature difference between the hot and cold fluids. According to the configuration of the heat exchanger, the mean temperature is adjusted with a dimensionless coefficient ε departing from the counter- current flow so that:

ΔTlm = ε ΔT°lm (3.3)

where ΔT°lm is the mean temperature for a counter- current flow. [2]

The formula of the mean temperature is defined by:

(3.4)

The overall heat transfer coefficient U (W.m-2.K-1) is equal to the sum of the resistances including the tube- side and shell- side fouling resistances, Rf,t and Rf,s:

(3.5)

Where So (m²) and Si (m²) are the outer and inner heat transfer areas, , ht and hs are the tube- side and shell- side convective heat transfer coefficients, δw is the wall thickness, λw is the thermal conductivity  (W·m-1·K-1), Sm is the logarithmic mean area [3]:

(3.6)

Fouling resistance values to design heat exchangers can be found in the Tubular Heat Exchangers Manufacturers Association tables (TEMA) [24]. However, these tables are increasingly challenged [25- 28] as they do not take into account some parameter such as the dynamic nature of fouling and its dependence on process variables (fluid velocity, temperature and composition). Indeed, the calculation of the fouling resistance induced assumptions wearies up uncertainties as constant density and specific heat capacity. Other tables can be found in the literature and sometimes companies set up their tables based on their own calculations and experiments [1] [3].

3.2.2 Fouling model

Many correlations have been developed over the years for fouling model trying to take into account the variables affecting it (composition, temperature, pressure, velocity, shear stress and surface conditions) [3]. Epstein [29] has carried out a review of different existing fouling models. Many of them lead to a considerable difference between the simulation results and the experimental data. Indeed, these models can present limitations. The fouling threshold concept [32] has been evocated according to experiments, at some velocities, the fouling deposition does not occur. But this type of model like all lumped models, does not take into account the local variations such as in the heat transfer coefficient. [1]

Through these models, Schreier (1194) [30] established three criteria the model should take into account:

- "The rates of the processes lead to deposition

- The temperature distribution and deposit thickness profile

- The effect of flow on deposition and re-entrainment." [30]

Efforts should be put in establishing dynamic model of heat exchangers that takes into account the fouling properly. Roetze and Xuan [33] developed an extensive distributed model where the fouling is represented following a simple asymptotic model.

While there are a considerable number of numerical modeling studies to improve the performance of the tube side [12-16], there is little research on the shell side in the literature and even fewer studies considering fouling. This is due to the complexity of the velocity and temperature fields increased by the complicated geometry (baffles) of this side. Indeed, the pressure drop calculations usually used to calculate the flow patterns and the wall shear stress cannot be calculated on the shell side. Fryer and Slater [34] explored the shell side by developing a distributed mode that integrates milk fouling on the shell side but does not take into account the heat transfer through the tube wall. Besides, this model cannot be extended to multipass heat exchangers [1].

Aging process of the fouling must be considered as well. Indeed, over the time, the fouling deposit is subjected to chemical changes that alter its physical composition as mentioned by Coletti et al. [1]: "a soft, gel- like material to a harder, coke- like". The physical properties such as the viscosity, thermal conductivity, etc. can also be altered. Ishiyama et al. [37] and later Coletti et al. [38], have developed respectively aging lumped and distributed model to represent this process.

Computational Fluid Dynamics (CFD) appears to be an appropriate approach to overcome these limitations. One of the few CFD researches that can be found in the literature and investigates the shell side has been led by Clarke and Nicolas [35]. To simplify the configuration as a matter of computation load, they considered the shell side as a porous medium modeling the baffles influence. However the tube side model is limited to a linear temperature variation and with a constant heat transfer coefficient. Therefore, the interaction between the shell side and tube side is not taken into account in this simulation. That is one of the challenges of my research project.

In summary, we mostly find in the literature lumped models that do not take into account properly the dynamic, or distributed models that describe the dynamic but do not consider or otherwise simplistically fouling.

3.2.3 Retained approaches

According to the figure ? the system of our model is composed of five different domains that we will have to model: the shell side, the shell- side fouling layer, the tube wall, the tube- side fouling layer and the tube side.

3.2.3.1 A dynamic and distributed model of shell- and- tube heat exchangers undergoing fouling [1]

Coletti and Macchietto (2010) [1] have developed a distributed modeling that explore the tube- side fouling in shell- and tube- exchangers. The study results of this model are based on estimates of plant measurements such as temperature or flow rates rather than the calculation of derived fouling resistance. For each domain, the heat balance equation is defined neglecting the heat losses as shown below. As induced previously, this model does not explore the shell side fouling, so the scheme is composed of only four domains.

3.2.3.1.1 Thermal aspect

Shell side

For this domain, the heat balance equation is expressed in only one dimension that is to say in the axial coordinate (z axis):

Where ρS(z) is the shell side fluid density, cp,s(z) is its heat capacity, Ts(z) is the shell fluid temperature, λS is the thermal conductivity, As is the shell cross- section area, Np is the number of tube passes, Ps,n is the wetted perimeter, Tw,n is the wall temperature of the tube n. The second term of the equation (3.7) is negative if we are modeling a first tube pass in a counter- current arrangement. And where hs is the shell- side heat transfer coefficient defined by the Bell- Delaware method [36]:

Where hid is the heat transfer coefficient for an ideal cross- flow that depends on the space position regarding the z axis. are the simplified correction factors that includes "the segmental baffle window, the baffle leakage, the bypass tube bundle to shell, the laminar heat transfer and the no equal inlet/ outlet baffle spacing" [1].

Tube wall

The tube wall satisfies the standard conduction equation that is expressed in polar coordinate in both axial and radial directions:

Where ρw is the density, cp,w is the heat capacity of the metal wall and Tw,n(z,r) is the temperature.

Tube side fouling

This domain is defined for z comprised from 0 to L the tube length and between the tube’s inner radius Ri and the deposit interface of the fouling layer Rflow like:

Where δn is the deposit thickness with respect to the z axis. To determine δn, the fouling resistance Rf,n(z) needs to be calculated. The most common method to find the fouling resistance is given by the Ebert- Panchal [32] modeling. Coletti et al [1] has adjusted this model here to distributed model and according to local conditions. Hence, the thickness is calculated by:

The heat balance equation is expressed as a conduction phenomenon like for the tube wall:

Where ρL is the constant density of the deposit layer, cp,L is its constant heat capacity. λL,n is the thermal conductivity of the layer and TL,n the temperature. These latter depend on the spatial position (in respect with the axis z and the radial r).

To solve this partial differential equation, they introduced a dimensionless number defined by:

Consequently the equation (3.11) becomes for the domain defined by r* comprised beetween 0 (in case r is equal to Ri) and 1 (in cas r is equal to Rflow):

Fouling aging distributed model has been considered by Coletti [1] here as well and the details of the mathematical model can be found in Coletti et al. [38] previous publications.

Tube side

As for the tube side, like for the shell side, the heat balance equation is expressed considering one dimension:

Where ρn(z) is the tube side fluid density, cp,n(z) is its heat capacity, Tn(z) is the shell fluid temperature, λn is the thermal conductivity that depend on the local conditions. Unlike the shell side, the cross sectional area here varies in function of the flow radius Rflow,n as expressed in the equation:

3.2.3.1.2 Hydraulic aspects

These performances are measured by the velocities, pressure drop and the heat transfer coefficient that include the impact of the fouling inside the tube.

Velocity

The velocity variation is expressed by:

Where is the mass flowrate, Aflow,n is the flow area that depends on the flow radius Rflow,n varying according the fouling layer thickness.

Pressure drop

The pressure drop is expressed by:

Where Cf is the Fanning friction for rough tubes depending on the Reynold’s number and defined by Yeap et al. (2004) [39].

Heat transfer coefficient

The heat transfer coefficient is expressed by:

Where the pipe length is at least ten times greater than its diameter and the Nusselt number is defined by the Dittus- Boelter relationship:

With Re > 104 and 0.7 < Pr < 160.

3.2.3.1.3 Conclusions

These dynamic equations of the distributed model developed by Coletti et al. can then be implemented in the gPROMS modeling system [40] and used for the CFD. They required the following information in respect with the type of heat exchanger: number of passes, number of shells, number of tubes, diameters, fluid physical properties, fouling aging structure, etc.; and the following inputs: "inlet flow rates, temperatures, and pressure of the hot and cold steams"[1]. And finally, the boundary and initial conditions need to be set. Hence, this model can provide the outlet temperatures, the hydraulic variations (velocities, pressure drop) and information concerning the fouling structure, thickness and influence. These same information and outputs should be followed for the study of the shell- side fouling.