Comprehensive analysis of the thermohydraulic performance of cooling networks subject to fouling and undergoing retrofit projects

Abstract

The aim of this paper is to develop guidelines for the placing of new coolers in cooling systems subject to retrofit. The effects of the accumulation of scale on the flow system are considered. A methodology to assess the interconnected effect of local fluid velocity and fouling deposition is developed. The local average fluid velocity depends on the water flow rate distribution across the piping network. The methodology has four main calculation components: a) the determination of the flow rate distribution across the piping network, b) the prediction of fouling deposition, c) determination of the hydraulic changes and the effect on fouling brought about by the placing of new exchangers into an existing structure, and d) the calculation of the total cooling load and pressure drop of the system. The set of disturbances introduced to the system through fouling and the incorporation of new coolers, create network responses that eventually influence the cooling capacity and the pressure drop. In this work, these interactions are analysed using two case studies. The results indicate that, from the thermal point of view, the incorporation of new heat exchangers is recommended in series. The limit is the point where the increase of the total pressure drop causes a reduction in the overall volumetric flow rate. New coolers added in parallel create a reduction of pressure drop and an increase in the overall water flow rate; however, this increase is not enough to counteract the reduction of fluid velocity and heat capacity removal.

Keywords

Scale fouling water cooling networks flow distribution pumping power retrofit

Introduction

At industrial level, a cooling system is a type of cold utility whose purpose is the removal of low temperature heat and its rejection to ambient. If the cooling system employs water as a working fluid, power is used to force it to flow through the heat exchangers for heat removal. There is a direct relationship between pumping power consumption and heat removal because as the fluid is driven at higher velocities the rate of heat removal increases as well. The heat transfer surface area for heat removal varies in an inverse manner with power consumption, as higher fluid velocities leads to smaller surface areas for heat transfer. The main operating costs of a cooling system are the pumping power consumption and the costs associated to water treatment for the removal dissolved salts that constitute water hardness. If this chemical species are not properly removed, with time, the build-up of scaling reduces the heat transfer capacity of heat exchangers, increases the resistance to fluid flow and reduces the free flow area which cause the pressure drop to increase in the overall system. To counter these effects, more power is required causing the operating costs to rise.

There are design and operating reasons why the heat exchangers in cooling networks foul due to scaling. Some of them are, a) low fluid velocities in heat exchangers due to overdesign, b) high water return temperatures, and c) deficient cooling water chemical treatment. For decision making at the appropriate stage, accurate prediction of scaling is fundamental for the minimization of the fouling detrimental effects. In projects leading to the increase of the heat transfer area for increased cooling load, some of the important issues to consider are the prediction of how fouling deposits progress with time on a heat transfer surface, the prediction of the thermo-hydraulic effects on the heat exchangers and finally, how all these interact in a cooling system composed by cooling towers, coolers and the piping system.

In terms of the prediction of fouling, the choice of the right model is an important issue since most of the common flaws in existing predicting models are the over prediction of fouling rates or the lack of sensitivity to incorporate the effect of fluid velocity in the reduction of fouling.¹ The information that models provide can be used to determine the effect of fouling over time and consequently to plan cleaning strategies or to establish retrofit strategies. Research to understand the fundamentals of fouling has led to demonstrate the inverse effect that shear stress has on fouling, with higher shear tress leading to reduced fouling.² In practice, shear stress can be increased either by increasing the fluid velocity, using heat transfer enhancement techniques,³ or by the implementation of highly efficient surfaces like the ones employed in compact heat exchangers of the plate type. For the latter type of application, fouling models based on transport and chemical reaction models have been proposed.⁴ An important issue related to the consideration of fouling at the design stage of a heat exchanger, is the choice of the most appropriate fouling factor to use. An excessive value will inevitably lead to overdesign which in turn results in lower fluid velocities that enhance fouling. This situation evidences the need to approach heat exchanger design from a different perspective. For instance, to incorporate fouling as a design objective at the design stage.⁵

Cooling systems are complex structures with strong interactions between their principal components when disturbances are introduced into the system. Disturbances can be imposed from external sources⁶ or from internal sources such the build-up of scaling. From a thermo-hydraulic point of view, the most critical operating parameters that determine the performance of a cooling network are the volumetric water flow rate, the water return temperature and the pressure drop distribution in the network.

The relative position of coolers, either in series or parallel, has an important impact on the flow rate distribution and the fluid velocity across the coolers. From a thermal point of view, the series arrangement tends to be more favourable than the parallel arrangement as it exhibits higher velocities. The optimal operating parameters of a cooling system can be found either by finding the minimum operation costs due to pumping, or by fixing the maximum return temperature. An optimisation study considering these objectives was proposed by Ma et al.⁷ Moving one step ahead, Liu et al.,⁸ presented an optimisation study where the actual design of the coolers was incorporated as part of the approach. They used a mixed integer nonlinear programming (MINLP) incorporating pumping power, pipeline distance and network layout.

Other aspects in the design and operation of cooling systems are the ones related to debottlenecking,⁹ and the maximisation of the temperature difference between the supply and return temperature based on Life Cycle Costs analysis.¹⁰ Two other aspects that have been the focus of attention are the design for the reduction of the heat transfer area of coolers¹¹ and the reduction of operating costs due to pumping. On this last subject, studies have been conducted considering other working fluids such as air,¹² other type of cooling systems,¹³ and the optimisation of the pumping systems.¹⁴

The design approaches mentioned above have in common the consideration of point operating conditions. However, since cooling systems are often subject to changes in the external and internal conditions, its design must be approached considering a range of possible variation of conditions.¹⁵

The situations that arise in the case of retrofit of existing cooling systems have their own special features. Picon-Núñez¹⁶ analysed the effect of introducing new exchangers into existing networks and produced a methodology to study the thermohydraulic performance of the network by considering the incorporation of new units in a new parallel line, in series with existing units and in parallel with an existing exchanger. What is appreciated from this work is that the placing of new units modifies the water distribution across the network.

Souza and Costa¹⁷ acknowledged the importance of developing a complete simulation model to reproduce the thermohydraulic performance of cooling systems by linking all their components, namely cooling tower, coolers, pumps, the piping system and the effect of scaling as the most important type of fouling in the cooling system. Further work along these lines was reported by Lugo Granados et al.¹⁸ who analysed the change in pressure drop, flow rate re-distribution and the detrimental effects on the thermal performance of coolers due to the build-up of scaling.

The incorporation of new coolers into existing cooling networks must also be analysed from the operational point of view. This is the purpose of this work. The overall approach used is depicted on a block diagram in Figure 1. The introduction of new exchangers creates flow distribution adjustments in the system that alter the local fluid velocity. The changes in velocity cause thermal and hydraulic disturbances in the performance of heat exchangers. Among other variables, the rate of growth of fouling on a heat transfer surface is influenced by the fluid velocity, then, the changes in flow distribution and velocity result in the reduction of the heat removal capacity and the increase of pressure drop.

Figure 1.

Block diagram of the overall approach to determine the thermo-hydraulic performance of cooling networks subject to retrofit.

In this work cooling network retrofit guidelines are developed considering the interactions between fouling, fluid velocity, pressure drop, flow distribution and thermal performance. The paper is organised as follows: first, a model for the flow rate distribution across a piping network based on the volumetric flow rate that incorporates the pumping system is presented. Next, the estimation of the variation of fouling with time is discussed. Then two case studies are analysed to show the thermo-hydraulic effects of the incorporation of new coolers into existing networks. Finally, retrofit design recommendations are discussed.

Water flow rate distribution

The pressure drop across a cooling network can be determined by knowing the fluid velocity across the different branches and fittings present in the system. An important drawback of this approach is that the changes of pipe diameter, D (m) bring about changes in velocity. Since this is a common situation in water cooling networks, a convenient way to characterise the pressure drop is using the volumetric flow rate, V(m³/s). The pressure drop across a pipeline can conveniently be expressed as a function of the volumetric flow rate as:

Δ P = K V^{2}

(1)

Where K (Pa s/m⁶) is the flow resistance, V(m³/s) is the volumetric flow rate and ΔP (Pa) is the pressure drop due to friction. For the case of a network of heat exchangers arranged in series (Figure 2), the flow across all units is the same and the total pressure drop is the summation of the individual pressure drop per unit. This is expressed as:

Δ P = \sum_{i = 1}^{n} K_{i} (V^{2})

(2)

Figure 2.

Series arrangement of heat exchangers in a cooling system.

When the network configuration is in parallel, the pressure drop in each branch is the same and the flow rate across each branch is different (Figure 3); then, the total flow rate equals the summation of the flow rate across each branch. Equation (2) can be rearranged to obtain the total flow rate as:

V = V_{1} + V_{2} = \sqrt{\frac{Δ P}{K_{B 1}}} + \sqrt{\frac{Δ P}{K_{B 2}}}

(3)

Figure 3.

Parallel arrangement of heat exchangers in a cooling system.

Where V₁ and V₂ are the flow rates through branches 1 and 2 and K_B1 (Pa s/m⁶), and K_B2 (Pa s/m⁶), are the resistance to flow across branches 1 and 2 respectively. Combining equations (1) and (3) the expression for the combined resistance to flow, K (Pa s/m⁶), between two branches is:

K_{1 + 2} = \frac{Δ P}{V^{2}} = \frac{1}{{[{(\frac{1}{K_{B 1}})}^{0.5} + {(\frac{1}{K_{B 2}})}^{0.5}]}^{2}}

(4)

The total flow of the two branches is:

V_{1 + 2} = \sqrt{\frac{Δ P}{K_{1 + 2}}}

(5)

And the flow through branch 1 and of the fraction of the total flow is:

V_{1} = \sqrt{\frac{Δ P}{K_{B 1}}}

(6)

\frac{V_{1}}{V_{1 + 2}} = \sqrt{\frac{K_{1 + 2}}{K_{B 1}}}

(7)

Flow resistance through pipes and fittings

Pressure drop across a straight pipe is a function of the fluid velocity, u(m/s), the friction factor (f), the pipe length, L (m) and the pipe diameter D (m). Equation (8) represents this relationship:

Δ P = 2 f (\frac{L}{D}) ρ u^{2}

(8)

Expressing equation (8) as a function of the volumetric flow rate V (m³/s) gives:

Δ P = \frac{32}{π^{2}} \frac{L}{d^{5}} ρ f V^{2}

(9)

From equations (1) and (9), the expression for the flow resistance for a straight tube becomes:

K_{pipe} = \frac{32}{π^{2}} \frac{L}{d^{5}} ρ f

(10)

For slightly corroded tubes, the recommended expression to determine the friction factor is¹⁹

f = 0.007 + \frac{0.528}{{R e}^{0.42}}

(11)

In most systems, the hydraulic resistance across straight tubes can be considered small compared with the resistance across valves, fittings, and heat exchangers. In the case of other piping components, such as valves, elbows, tees and other fittings, the pressure drop is generally represented in terms of the velocity head:

Δ P = k_{f} \frac{ρ u^{2}}{2}

(12)

If the velocity term of equation (12) is replaced by the volumetric flow rate, the general term for the flow resistance in fittings can be expressed as:

K_{fitting} = \frac{8}{π^{2}} \frac{ρ}{d^{4}} k_{f}

(13)

Where K_fitting (Pa s/m⁶) is the flow resistance due to fittings and k_f is the resistance coefficient. The values of k_f have been calculated for most fittings and there are many tabulates values. For the purposes of this work, the tabulated data presented in²⁰ is used. The value of K for the whole system can be obtained from:

K = \sum K_{fitting} + \sum K_{pipe} + \sum K_{exch}

(14)

Where K_pipe (Pa s/m⁶) is the flow resistance through a pipe, and K_exch (Pa s/m⁶) is the flow resistance through a heat exchanger. In the case of the heat exchangers located in each branch of a cooling network, the hydraulic resistance can be calculated using equation (1):

K_{exch} = \frac{{Δ P}_{exch}}{V_{exch}^{2}}

(15)

The pressure drop due to friction across the core of a tubular heat exchanger is calculated form:

{Δ P}_{exch} = \frac{32 f L_{c} {N p}^{2} ρ}{π^{2} d^{5} {N t}^{2}} V^{2}

(16)

Where f is the friction factor, L_c (m) is the length of the tube, Np is the number of passes, ρ (kg/m³) is the fluid density, d (m) is the tube diameter, and N_t is the number of tubes. Under a condition of fouling, the diameter of the tube, d (m) reduces with time as the layer thickness increases. The expression to determine the thickness of the layer of fouling, X_f (m) with time is:

X_{f} = \frac{t {\dot{m}}_{d}}{ρ_{f}}

(17)

The term ${\dot{m}}_{d}$ (kg/m² s) is the rate of mass deposition, t (s) is the time and ρ_f (kg/m³) is the density of the deposited material. The calculation of the rate of mass deposition is presented in the Prediction of fouling with time section.

Pump performance

In a cooling system, there is a close relationship between volumetric flow rate, pressure drop and pumping power. With the accumulation of fouling, pressure drop increases due higher flow resistance on the tube walls and due to the reduction of the sectional area for fluid flow. The installed pumping system uses the power that consumes to overcome the whole pressure drop, therefore, with higher pressure drop, the delivered water flow rate tends to reduce. The overall consequence is that the heat removal capacity reduces due to two parallel effects: the reduction of the heat transfer coefficient and the increase of the fouling factor. To quantify all these thermo-hydraulic interactions, the reduction in volumetric flow rate must be calculated. This can be done by introducing a simple model of pump performance. In this section the hydraulic performance of reciprocal pumps is analysed.

The hydraulic performance of a pump is determined by its characteristic curve. The diagram shows the relationship that exists between volumetric flow rate, net positive suction head and efficiency (Figure 4). The pressure drop to overcome across the cooling network can also be plotted and the intersection between the characteristic curve and the process pressure drop represents the point of operation of the pump as shown by point A in Figure 4. Point B shows a case of lower process pressure drop. In this case, the same pump delivers less positive suction head but increases the volumetric flow rate.²¹

Figure 4.

Typical characteristic curve of a centrifugal pump.

A simple way to relate the pressure drop across the cooling network to the volumetric flow rate delivered by the pump is given by the following expression:

Δ P = a + b V - c V^{2}

(18)

The pressure drop of the cooling system is used to determine the variation of the total pressure drop versus the volumetric flow rate. If the network structure changes, for instance, when a new cooler is added, the pressure drop of the new system can be determined to generate the system curve. The intersection of the system curve and the characteristic curve gives the required volumetric flow rate.²²

Prediction of fouling with time

This section describes the model used to predict the variation of the fouling factor with time. The operating conditions that have a major effect on the formation of fouling are water temperature, concentration, velocity, and pH. Out of these variables, fluid velocity is a parameter that can be easily handled at an early stage in heat exchanger design to reduce the rate of fouling deposition. A model that gives a reasonable account of the effect of velocity on scaling was proposed by Lugo and Picón.¹ The model assumes that the ionic species flow through the laminar layer to reach the surface of the wall where they form the crystals. The process was modelled assuming that it could be represented by means of a chemical reaction. Such model is used in this work. Readers are referred to the original source for further details of the model.

For the case of tubular exchangers, a correction parameter to account for the inertial and frictional effects is considered. The constants involved in the correction parameter were obtained from experimental data published from various research groups as explained in.¹⁸

α = \frac{191}{f {R e}^{1.67}}

(19)

The expression to determine the rate of mass of scale deposition is:

{\dot{m}}_{d} = \frac{β}{2} (\frac{β}{α k_{r}} + (C_{1} + C_{2}) - \sqrt{\frac{{[β + (C_{1 +} C_{2}) α k_{r}]}^{2} + 4 α^{2} {k_{r}}^{2} (K_{s p} - [C_{1}] [C_{2}])}{α^{2} {k_{r}}^{2}}})

(20)

Where ${\dot{m}}_{d}$ is the mass deposition (kg/m²s); C₁ and C₂ are the concentration of Ca²⁺ and CO₃²⁻ (kg/m³) contained in the water; K_sp (kg²/m⁶) the solubility of calcium carbonate; k_r (m²/kg s) is the rate of reaction which is a function of temperature and is obtained from the Arrhenius equation, where the activation constant and frequency factor in the equation at a temperature range typical of the operation of cooling systems are: E_a = 113 kJ/mol and k₀ = 2.05x10¹⁵ m⁴/kg s.²³ β (m/s) is the mass transfer coefficient obtained from expression for turbulent flow (Re > 4000) in tubes:

\frac{d β}{D_{A B}} = 0.023 \bar{u} {Re}^{0.83} S c^{1 / 3}

(21)

Where d is the tube diameter (m); D_AB is the diffusivity of the chemical species (0.79 × 10−9 m²/s), $\bar{u}$ is the fluid average bulk velocity (m/s) and Sc is the Schmidt number (μ/ρ D_AB). In the next sections, the application of the thermo-hydraulic model of cooling networks that includes the prediction of fouling is analysed using two case studies.

Case studies

In this section, two case studies are analysed to demonstrate the application of the thermohydraulic analysis of cooling networks subject to fouling. Case study 1 considers the retrofit of an existing network and case study 2 looks at the grassroot design stage with the aim of making design decisions that minimise the detrimental effects of water distribution and fouling on the thermal and pressure drop performance of cooling systems.

Case study 1

This case study considers the retrofit of an existing cooling network structure (Figure 5). The heat exchangers are of the shell and tube type. For the calculations, a concentration of calcium carbonate of 300 ppm is assumed. The flow distribution across each branch of the system is analysed considering three scenarios: 1) all heat exchangers operate at clean conditions, 2) a fixed fouling factor is considered, 3) fouling changes with time. To have a deeper understanding of the way a cooling network performs, scenario 3 is further explored considering a change in the network structure by placing a new cooler. The new cooler is positioned in a new branch in parallel, and it is contrasted to the performance where the new unit is installed in series in an existing branch. Details of the network piping structure that includes pipe length, diameter and elevation are given in Table 1. For the heat exchangers, the k_f values and some geometrical and operating data are given in Table 2.

Figure 5.

Cooling network for case study 1.

Table 1.

Network piping data for case study 1.

Component	Diameter (m)	Length (m)	Elevation (m)
Feed	0.35	200	0
Brach A	0.25	120	5
Branch B	0.2	170	5
Branch C	0.2	180	5
Return pipe	0.35	200	0

Table 2.

Heat exchanger information for the thermo-hydraulic analysis of case study 1.

	H1-B	H2-B	H3-B	H4-A	H5-A	H6-C
k_f	9	9	9	9	9	9
No. Tubes	820	450	800	400	850	800
Tube pitch [m]	0.0254	0.0254	0.0254	0.0254	0.0254	0.0254
Tube arrangement	Triangular	Triangular	Triangular	Triangular	Triangular	Triangular
No. Passes	2	2	2	2	2	2
Cold fluid [kg/s]	85	85	85	85	85	85
Hot fluid [kg/s]	70	70	70	70	70	70
T_Ci [°C]	20	T_CO1	T_CO2	20	T_CO4	20
T_Hi [°C]	110	90	85	85	100	120
Tube length (L_C) [m]	6.1	6.1	6.1	6.1	6.1	6.1
Tube diameter (d) [m]	0.0148	0.0148	0.0148	0.0148	0.0148	0.0148
Shell diameter (D_i) [m]	0.83	0.63	0.83	0.63	0.83	0.83
R_S [m² °C/W]	0.0005	0.0005	0.0005	0.0005	0.0005	0.0005

The overall pressure drop of the cooling network due to friction, difference in elevation and pressure loss through heat exchangers can be obtained as a function of the volumetric flow rate. The overall pressure drop corresponds to the discharge pressure of the pump. The corresponding expression is:

Δ P = 421 + 2041 V - 6789 V^{2}

(22)

The adverse thermal effects of the deposition of scale are more evident than the hydraulic effects, which, apart from resulting in increased pressure losses, create flow rate redistribution which in turn, have secondary effects on the heat transfer coefficients and consequently, on the heat transfer performance. To visualize the hydraulic effects on cooling networks, the effect of flow rate distribution is analysed. Figure 6 shows two scenarios, the case where no fouling is considered, and the case where the fouling factor has a constant value. Under these conditions, Figure 6 demonstrates that the flow rate distribution remains constant with time. When variable fouling is considered, Figure 7 shows the way flow rate tends to redistribute with time. In the case of clean conditions, Figure 6(a) indicates that the largest fraction of the flow rate goes through branch A, followed by branch C and then branch B. The most important variables that determine such distribution are, elevation, number of heat exchangers per branch and pipe diameter. In this case, the three branches have the same elevation but different diameter. Branch A exhibits the bigger diameter; this factor seems to have a major impact despite the existence of two exchangers. Branch C comes next with a smaller tube diameter and one heat exchanger, and finally branch B with a smaller diameter and three heat exchangers.

Figure 6.

Water flow rate distribution: (a) No fouling, (b) Fixed fouling factor.

Figure 7.

Performance of the cooling network considering variable fouling factor: (a) water flow rate distribution, (b) variation of flow resistance (K) with time.

The scenario shown in Figure 6(b) could be interpreted as a situation in which the network exhibits a fixed fouling factor right from the beginning of the operation and the pressure drop is immediately affected. In this case, the distribution of the flow differs from the case of clean conditions. In this scenario the larger fraction of the flow circulates through branch C, followed by branch A and finally branch B. The presence of fouling affects directly the pressure drop across the heat exchangers, therefore, with the same elevation, the presence of more heat exchangers creates larger pressure drop.

When the variation of fouling with time is brought into the analysis, the effect on water flow rate distribution is as shown in Figure 7(a). At time zero, the flow rate distribution equals the one obtained in Figure 6(a). However, as time goes on, the increase of fouling causes a larger flow distribution effect on branches with more heat exchangers. Therefore, the flow rate through branch C tends to rise while that of branch A to decrease. Eventually it would be expected that the flow distribution will be identical to the values reported in Figure 6(b) once the fouling factor reaches a value of 5 × 10⁻⁴ m²°C/W (see Table 2).

Figure 7(b) shows the variations of the flow resistance (K) with time. The trend shows that the flow resistance for this network structure grows more rapidly for branch B where three heat exchangers are located, followed by branch A and branch C.

The cooling network is retrofitted to absorb a higher cooling load. Therefore, a new heat exchanger is added to the network. When a retrofit study identifies the need to integrate additional heat transfer area, a decision must be made about the most appropriate location for the placement of the new unit. New heat exchangers can be placed in series with existing exchangers in the same branch or in a new branch in parallel with the existing ones. The thermohydraulic performance of the network must be evaluated to determine the pros and cons of the two options. The effect of fouling with respect to time is considered. Figure 8(a) shows the placement of the new cooler in series with exchanger H6 in branch C and Figure 8(b) the placement of the new exchanger in a new branch (D) in parallel with the network.

Figure 8.

Retrofit of the existing cooling network: (a) The placement of a new exchanger in series, (b) the placement in a new parallel branch.

The overall flow rate of the system is altered when a new heat exchanger is introduced. Figure 9(a) compares the variation of overall volumetric flow rate for the three scenarios. From Figure 9(b) it can be observed that when a new heat exchanger is added in a new branch, the overall flow rate of the system increases with respect to the original structure. The existence of a new branch reduces the overall pressure drop as shown in Figure 9(b) and the result is the increase of the overall flow rate. However, as fouling accumulates, the rise of pressure drop in the system creates a reduction in the overall flow rate.

Figure 9.

Performance of the new structure with an additional heat exchanger and branch: (a) water flow rate distribution, (b) behaviour of the pressure drop with time.

Even though the overall flow rate of the system increases when a new exchanger in a new branch is added to the system, the flow rate per branch is reduced as further analysis reveals. This is observed by comparing the results shown in Figure 6(a) with those of Figure 10.

Figure 10.

Flow rate distribution per branch for the case of a new heat exchanger in a new branch.

The consequence of the reduction of the flow rate per branch is that the fluid velocity through the heat exchangers is also reduced. On the one hand, this velocity reduction has a detrimental effect on the heat transfer coefficient, and on the other , the reduction of the fluid velocity tends to accelerate the rate of fouling deposition which further reduces the thermal resistance to heat transfer. These two responses combine themselves to deteriorate the heat transfer removal capacity of the coolers. To make up for the reduction in flow rate, a new pump must be put in place. Figure 11 indicates that when the new branch is added, the overall flow rate increases due to the lower pressure drop of the system. However, as it was discussed, the flow rate per branch moves to lower values. To maintain the fluid velocity through the heat exchangers, the pump impeller could be replaced to operate at a higher flow rate (ω₃). The result is the delivery of a higher volumetric flow rate at but at practically the same pump pressure head.

Figure 11.

Pictorial representation of the options for the selection of a new pump to maintain the same operating conditions.

The placement of a new heat exchanger in series in an existing branch, results in the reduction of the water flow rate due the increase of the pressure drop of the system. In this situation, the use of a higher velocity impeller with higher pressure head to restore the volumetric flow rate might be necessary. The placing of new heat exchangers in series or in parallel, will require the replacement of the pumping system, however, of the two, the power consumption of the parallel option will be lower.

Case study 2

In this case study two grassroot design alternatives for the same problem are analysed and compared considering the variation of fouling with time. In design option 1 (Figure 12(a)), the system has a total of 6 exchangers distributed in two branches. In design 2 (Figure 12(b)) the system has 6 exchangers and three branches. Table 3 shows the pipe lengths, diameters and elevation of the various sections of the system and Table 4 shows the design and operating information of the six shell and tube heat exchangers.

Figure 12.

Cooling network for case study: (a) design 1 with two branches, (b) design 2 with three branches.

Table 3.

Network piping data for case study 2.

Component	Diameter (m)	Length (m)	Elevation (m)
Feed	0.3	200	0
Brach A	0.2	160	3
Branch B	0.25	120	3
Branch C	0.2	140	3
Branch D	0.2	80	3
Return pipe	0.3	200	0

Table 4.

Heat exchanger information for the thermo-hydraulic analysis of case study 2.

	H1	H2	H3	H4	H5	H6	H7*
k_f	0.5	0.5	0.5	0.5	0.5	0.5	0.5
No. Tubes	820	450	800	400	850	800	840
Tube pitch [m]	0.0254	0.0254	0.0254	0.0254	0.0254	0.0254	0.0254
Tube arrangement	Triangular	Triangular	Triangular	Triangular	Triangular	Triangular	Triangular
No. Passes	2	2	2	2	2	2	2
Hot fluid [kg/s]	70	70	70	70	70	40	70
T_Ci [°C]	33	T_CO1	T_CO2	33	T_CO4	33	33
T_Hi [°C]	75	70	85	85	70	85	85
Tube length (L_C)[m]	6.1	6.1	6.1	6.1	6.1	6.1	6.1
Tube diameter (d) [m]	0.0148	0.0148	0.0148	0.0148	0.0148	0.0148	0.0148
Shell diameter (D_i) [m]	0.83	0.63	0.83	0.63	0.83	0.63	0.83

(*) To be considered in the analysis of Figure 15.

Figure 13 shows the variation of the water flow distribution of the two design options with time. In the case of design 1 (Figure 13(a)), the flow rate on both branches reduces with time; however, for design 2, the flow rate on branch C increases, on branch B decreases and for branch A remains almost constant. In this case, if the characteristic of the pump is the same for the two designs, design 1 will operate with lower volumetric flow rate compared to design 2. Figure 14 shows the development of the resistance to flow for the two designs where we see that the K values increase with time.

Figure 13.

Volumetric flow distribution for: (a) design 1 with two branches and, (b) design 2 with three branches.

Figure 14.

Hydraulic resistance for: (a) design 1 with two branches and, (b) design 2 with three branches.

The network structures of Figure 12 are subject to retrofit to increase the heat load. Two options are analysed: a) the new exchanger is placed in branch C, b) the new heat exchanger is placed in a new added branch (D). Figure 15 depicts the two structures. The network and heat exchanger details are those presented in Tables 3 and 4.

Figure 15.

Retrofitted network structure: (a) a new heat exchanger is added into an existing branch, (b) a new heat exchanger is added in a new branch.

Figures 16 and 17 show the comparison of the two retrofitted options in terms of flow rate distribution and hydraulic resistance, respectively. A new branch in parallel tends to receive the largest fraction of the flow rate as it exhibits the slowest resistance to flow. The flow redistribution affects the thermal performance of the existing heat exchangers; this must be taken into consideration for decision making during the retrofit project. To further investigate the sensitivity of the model, the height of branch (D) is increased from 3 to 6 meters. Comparative results are given in Figure 18 (a) and (b) where the pressure drop through branch D increases because of the increased height, with less water flow rate circulating through it.

Figure 16.

Volumetric flow distribution for: (a) retrofit option 1 with the new heat exchanger added in series in an existing branch and, (b) retrofit option 2 with new heat exchanger added in a new parallel branch.

Figure 17.

Hydraulic resistance for: (a) retrofit option 1 with the new heat exchanger added in series in an existing branch and, (b) retrofit option 2 with new heat exchanger added in a new parallel branch.

Figure 18.

Effect of the change of height of branch D from (a) 3 m, (b) 6 m.

Figure 19 shows the evolution of the outlet temperatures (T_HO1, T_CO1) of exchanger H1 of the network structure of Figure 15(b) with time. The inlet temperatures (T_H1 = 75°C, T_C1 = 33.3 °C) are assumed to remain constant throughout the operation. As the flow rate through branch A decreases with time, this has a like effect on the heat transfer capacity of exchanger H1. The consequence is that less heat load is removed, and the hot outlet temperature increases while the outlet temperature of the cold stream decreases. Similar exercises can be carried out for all other exchangers and for different network configurations to have a wider view of the thermo-hydraulic effects of the retrofit project.

Figure 19.

Variation of the hot and cold outlet temperatures of exchanger H1 of network structure in Figure 15(b).

For the purposes of comparison, the network water return temperature and total heat load of the structures in Figures 12(a) and (b) (referred to as configurations 1 and 2) and Figure 15(a) and (b) (referred to as configurations 3 and 4), are plotted together in Figure 20. The results indicate that in a grassroot design or in a retrofit project, with time, the existence of more parallel lines results in a larger reduction of the return temperature and the total heat removal. This suggests that the adverse effects of water distribution and fouling on a cooling network is less detrimental when exchangers are placed in series.

Figure 20.

Variation of the overall network thermal performance with time for the four case studies of Figures 12 and 15: (a) water return temperature, (b) overall cooling load.

Discussion of results

Scale fouling plays an important role in the thermohydraulic performance of cooling networks. The dynamic nature of the build-up of scale on the surface of heat exchangers creates internal disturbances that give rise to increased pressure drop in the system. As the pressure drop increases, a series of thermal and hydraulic effects take place. The consequence is that the water flow distribution across the network changes with time. The consideration of fouling in the analysis of the thermo-hydraulic performance of cooling systems is of great significance in the accomplishment of retrofit projects. However, this analysis paves the way for other applications, for example, the exact planning of periods of heat exchanger cleaning. The overall thermal performance of a cooling network, plotted in Figure 20, gives an indication of the strategy to follow for establishing cleaning schedules. Examples of such strategies are the period elapsed until the thermal capacity of the coolers has dropped to a fixed percentage or the point where the overall pressure drop has reached a certain limiting value.

From the thermo-hydraulic point of view, Figure 20 also gives an indication of the decisions that must be made to improve operation. When new exchangers are placed in parallel, the overall thermal load reduces because of two phenomena, the increase of the fouling resistance and the reduction of the water flow velocity through the coolers. This behaviour can be explained as illustrated in Figure 11. New branches in parallel tend to reduce the pressure drop which in turn, causes the pumping system to deliver more flow rate which has to be distributed across additional branches. However, the increase in flow rate is not enough to maintain the same fluid velocity causing the reduction of the heat transfer coefficients. This means that the restoration of the original heat removal capacity can only be achieved through pump replacement. A different situation arises in the case of new exchangers placed in series where the fluid velocity is increased with more heat being removed at the expense of increased pressure drop.

The analysis carried out in this work was performed assuming constant calcium carbonate concentration. In this regard, the model enables the generation of thermal and hydraulic performance curves considering different concentrations. Additionally, further analysis consists in the consideration of the change of the foulant concentration with time. In practice, this is likely to be the case due to the scale deposition on surfaces, water evaporation, the replenishment of water in the system or the variations that take place in the water treatment plant with time. The dynamics of the system are complex but the consideration of the worst- and best-case scenarios can assist in this task.

Conclusions

The operation of a cooling system is subject to fouling created by the deposition of scale on the heat transfer surfaces. With time, this situation introduces disturbances that ultimately have thermal and hydraulic effects. The quantification of these effects is essential in the case of retrofit projects. This work has introduced a model to predict the thermohydraulic performance of cooling systems characterised by the pressure drop, flow rate distribution, and fouling factor. The main conclusions of this work are:

In the retrofit of an existing cooling network, the installation of new coolers causes redistribution of flow rate and changes in fouling deposition.

For the same pumping capacity, the heat removal capacity of new coolers in parallel is lower compared to the installation of new coolers in series.

The presence of fouling affects the thermohydraulic performance of cooling networks in a cyclic way. Fouling causes pressure drop to increase, in turn, higher pressure drops tend to cause flow rate reduction. As the flow rate reduces, fouling deposition increases again.

The use of fixed values of fouling factor conceals the true thermal and hydraulic behaviour of a heat exchanger in a cooling system. Therefore, it is essential that variable fouling be considered to analyse its detrimental effects with time.

The magnitude of the thermohydraulic effects of fouling on a cooling system, depends on the case under consideration.

The thermo-hydraulic analysis in this work was performed assuming that the foulant concentration remains constant with time. Further studies are necessary to assess the effect of the fluctuation of foulant concentration with time.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: H Lugo-Granados was supported since 2015 by a PhD grant from CONACYT (National Council of Science and Technology). The authors thank the authorities of the University of Guanajuato for the financial support for the presentation of the research paper at the PRES 2019 Conference that gave rise to this article. The authors received no financial support for the research.

ORCID iD

Martín Picón-Núñez

Hebert Lugo-Granados is a Mechanical Engineer from the Department of Mechanical Engineering. Got his MSc in 2012 and his PhD in 2014, both in Chemical Engineering, at the Natural and Exact Sciences Division, University of Guanajuato, Guanajuato, Mexico. He has worked on the energy integration of Stirling engines and in the development of scaling models for use in design and operation of cooling systems.

Lázaro Canizalez-Dávalos is a Chemical Engineer from the Autonomous University of Zacatecas in Mexico. Obtained the PhD in Mechanical Engineering from the University of Guanajuato in Mexico. His research interests are the use of CFD techniques for the design and analysis of heat exchangers and the design and analysis of utility systems. He is currently a lecturer at the Autonomous University of Zacatecas in Mexico.

Martín Picón-Núñez is a Chemical Engineer from the University of Guanajuato in Mexico. Obtained the MSc and the PhD from the University of Manchester, Institute of Science and Technology. He has acted as an industrial consultant in areas of heat recovery, heat transfer equipment design and debottlenecking for increased production for various companies in Mexico. His research interests are compact heat exchanger design, multi-stream heat exchangers, fouling in heat exchangers, design of cooling systems and industrial applications of solar energy. He is currently a professor at the Chemical Engineering Department of the University of Guanajuato in Mexico.

Nomenclature

References

Lugo-Granados

Picón-Núñez

Scaling growth in heat transfer surfaces and its thermohydraulic effect upon the performance of cooling systems. Chem Eng Tran 2017; 61: 799–804.

Crittenden

Yang

Dong

, et al. Crystallization fouling with enhanced heat transfer surfaces. J Heat Transfer Eng 2015; 36: 741–749.

Aubin

Tube inserts for heat exchangers for energy conservation. In: Proceedings of international conference on heat exchanger fouling and cleaning (eds MR Malayeri, H Müller-Steinhagen and AP Watkinson), Enfling (Dublin), Ireland, 7–12 June 2015, pp.413–417. Navasota, Texas: Heat Transfer Research, Inc.

Kapustenko

Klemeš

Matsegora

, et al. Accounting for local thermal and hydraulic parameters of water fouling development in plate heat exchanger. Energy 2019; 174: 1049–1059.

Lugo-Granados

Tamakloe

Picón-Núñez

Controlling scaling in heat exchangers through the use of fouling design curves. Process Integr Optim Sustain 2020; 4: 111–120.

Picón-Núñez

Nila-Gasca

Morales-Fuentes

Simplified model for the determination of the steady state response of cooling systems. App Thermal Eng 2007; 27: 1173–1181.

Liu

, et al. Optimization of circulating cooling water networks considering the constraint of return water temperature. J Clean Prod 2018; 199: 916–922.

Liu

Feng

, et al. Simultaneous integrated design for heat exchanger network and cooling water system. App Thermal Eng 2018; 128: 1510–1519.

Souza

JNM

Levy

ALL

Costa

ALH.

Optimization of cooling water system hydraulic debottlenecking. App Thermal Eng 2018; 128: 1531–1542.

10.

Liu

Zou

Liao

, et al. The optimization of large scale heating and cooling network. Appl Mech Mater 2014; 525: 616–620.

11.

Zhang

Feng

Wang

, et al. Optimization of cooler networks with different cooling types in series and parallel configuration. Ind Eng Chem Res 2019; 58: 6017–6025.

12.

Zhang

Feng

Wang

, et al. Optimization of cooler networks considering different types of cooling. Chem Eng Tran 2018; 70: 487–492.

13.

Zhang

Feng

Wang

, et al. Sequential optimization of cooler and pump networks with different types of cooling. Energy 2019; 179: 815–822.

14.

Sun

Feng

Wang

, et al. Pump network optimization for cooling water system. Energy 2014; 67: 506–512.

15.

Picón-Núñez

Polley

Canizalez-Dávalos

, et al. Short cut performance method for the design of flexible cooling systems. Energy 2011; 36: 4646–4653.

16.

Picón-Núñez

Polley

Canizalez-Dávalos

, et al. Design of coolers for use in an existing cooling water network. App Thermal Eng 2012; 43: 51–59.

17.

Souza

ARC

Costa

Modeling and simulation of cooling water systems subjected to fouling. Chem Eng Res Des 2019; 141: 15–31.

18.

Lugo-Granados

Canizalez-Dávalos

Picón-Núñez

Incorporating the use of a fouling model in the design and operation of cooling networks. Chem Eng Trans 2019; 76: 43–48.

19.

Saunders

Heat exchangers: selection, design & construction. Harlow: Longman Scientific & Technical/New York: J. Wiley, 1989.

20.

Chengqin

An analytical approach to the heat and mass transfer processes in counterflow cooling towers. J Heat Trans T ASME 2006; 128: 1142–1148.

21.

McCabe

Smith

Harriott

Unit operations of chemical engineering. 7th ed. New York: McGraw Hill Education Company Inc., 2004, pp.207–255.

22.

Hicks

TG.

Pump selection and applications. 1st ed. New York: McGraw-Hill Book Company Inc., 1988, pp.20–30.

23.

Agustin

Bonhet

Influence of the ratio of free hydrogen ions on crystallization fouling. Chem Eng Proc 1995; 34: 79–85.