1

Methodology for generic pipe model: Failure risks assessment for heating and

domestic hot water systems due to corrosion and bacterial growth

Qusay Mansour (1) *, Ivan Verhaert (1)

(1) University of Antwerp, Faculty of Applied EngineeringCampus Groenenborger, Groenenborgerlaan 171, 2020 Antwerp, Belgium

(*) Principal Author: qusay.masnour@uantwerpen.be

Abstract

Both water supply systems as district heating grids, drain or sewer systems exist out of complex networks of water

pipes and channels. Different types of threats or water pollution can be distinguished on system level, such as corrosion

and bacterial growth. These threats are often strongly linked to each other, as there is a clear correlation between some

threats regarding growth and propagation in networks.

This paper proposes a generic modelling approach to describe the growth and propagation of corrosion and bacterial

growth threats in water networks. The model is based on a two control volumes approach for each threat, namely a

flow conducting volume and a layer volume. The double control volume approach allows to include the specific

behavior in biofilm, convection layer, pipe surface, … with respect to growth, diffusion and decline of each threat.

This occurs at different speed compared to the main water volume. By including an exchange between both layers

within the water pipe model, the model can take this into account and still be easily incorporated in large system

assemblies. The result is a better understanding of the failures or a comprehensive base for data interpretation, which

is a first step adopting machine-learning techniques in this field for predictive maintenance.

1- Introduction

With civilization, transport of water through ducts and pipes has numerous applications. They show up in water

distribution networks supplying water for washing and hygienic purposes [1]. The lack of water is still one the main

problems resulting in poor living conditions, poverty and migration [2]. This illustrates the importance, despite its

common nature. Also in heating and cooling systems, the use of water pipes to transport heat from heater to radiator

within a building or throughout an entire city by a district heating network. Besides the provision of heat and water,

both for domestic as for industrial applications, water is often used as a carrier to remove waste or other materials

through sewers and other utilities. Because of the aforementioned reasons, the hydraulic behavior of water through

pipes is one of the oldest research domains within fluid dynamics, enabling proper design and control (Study [3] in

1995).

When exposed in aquatic environment, materials suffer from corrosion influenced by physical, chemical and biological

parameters. Among these, microbiologically influenced corrosion (MIC) has received much more attention these years

where it has been estimated to account for 20% of annual corrosion damage of metallic materials [4,5]. The corrosion

of pipes is not only responsible for the destruction of the pipe material, but also for the deterioration of water quality.

Corrosion scales formed by the accumulation of corrosion products can reduce the water transportation capacity and

offer habitation for pathogenic and opportunistic bacteria [6,7], red water or discolored water that caused by severe

corrosion product release are among the main reasons for consumer complaints. On the other hand, and as an example,

the drinking water systems can be considered as a large-scale biological environment that hosts a wide variety of

microorganisms both in bulk water and on the pipe surfaces (as biofilms), which could lead to high disinfectant demand

and dissolved oxygen (DO) consumption [8].

1.1. Literature review

On each aspect, different studies exist. In [9], the influence of oxygen and flow conditions on the iron deterioration

and formation of magnetite or other corrosion products have been investigated. In [10] and [11] the influence of water

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quality and presence of other dissolved gases on corrosion rate is studied, whereas other studies focus on the

improvement of corrosion resistance of the pipe material itself [12]. As the presence of oxygen influences corrosion,

the presence of air infiltration is strongly linked to corrosion phenomena. Typically, under pressure (below atmospheric

conditions) is a known trigger to increase the diffusion of air into the water pipe. In [13], the diffusion of air through

polypropylene pipes is investigated, whereas [14], [15] and [16] describe the transport of these gas (droplets) through

the pipes, not only locally, but also along with the flow of water. Similar remarks can be made for bacterial growth,

which can happen at different locations, but do influence each other as presented in [17] on a system level.

Van Kenhove on Legionella [18], presents a modelling approach that combines a hydraulic pipe model with the risk

on Legionella decontamination. The pipe model exists out of two control volumes, namely water and biomass. For

each control volume, empirical models describe Legionella growth/starvation. The model is bound to some

assumptions, that need more careful interpretation, and limit the applicability of the model.

1.2. Summary and problem statement

Bacteria and corrosion lead to failures or pollution in water networks. They cannot be treated separately, as there is a

clear correlation between them. To examine that, one should understand not only their origin, growth or decline, but

also how the products of these threats propagate through the network. For this reason, this paper proposes a

methodology for a generic pipe model, which can predict the different threats and to describe how their product is

transferred through the network.

2- Theory and Hypothesis

2.1. Theory

Water systems are composed of different components, such as pipes, heat sources, storage tanks, heat exchangers,

expansion vessels and taps. Therefore, system component models have to be updated with corrosion, bacteria and

correlative growth equations. Figure 1 illustrates the principle of implementation of mass transfer equations with

respect to assumed control volumes within a portion of pipe. In this way, the propagation of the corrosion products

and bacterial biofilm within the water system can be simulated, evaluated and consequently predicted.

Figure 1: Pipe portion with two control volumes, local layer and bulk. Implementation of mass transfer equations

2.2. Hypothesis

In literature, there are no previous attempts to model the correlation of bacterial growth and corrosion in pipes with

water as working fluid. The found literature focused on modelling the threats separately and with particular cases of

bacteria such as Legionella pneumophila in [18] and Iron corrosion in [19]. The authors supposed that found bacterial

growth and corrosion equations can be turned into generic equations fit with the bacteria types, corrosion products,

and pipe materials.

3- Methodology

As done in [18], different existing Modelica pipe models can be analyzed to select useful model that could be extended

with equations for simulation of bacterial growth and corrosion. After selecting useful pipe model, component models

are chosen to be the first to be adapted with the implementation of the threats, as growth and exchange take mainly

place in these components using Dymola. Figure 2 shows the proposed methodology and the expected results.

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The benefit of modelling the threats’ growth in an existing pipe component model is the ease of compiling simulation

models of different systems later by dragging and dropping different components (which already include bacterial

growth and corrosion equations) into the system model.

Figure 2: The proposed methodology and expected results

3.3. Pipe model selection

There are number of parameters necessary for modelling bacterial and corrosion growth. The parameters are divided

into three categories, namely the three conservation equations: Mass, Momentum and Energy.

- The mass conservation parameter (trace substances) indicates if the existing pipe component contains certain

flow equations that make it possible to add substances to water.

- Momentum conservation parameter (gravity) defines if the pipe can be used in all directions

(vertical/horizontal). A pipe model without inclusion of gravity can only be used horizontally, except if the

gravity equation is canceled by the pressure drop.

- Energy conservation parameters, for example the possibility to add a (heat source) and (insulation), are

meaningful parameters to take into account.

Existing pipe models can be compared based on the above parameters necessary for modelling bacterial and corrosion

growth and that may or may not have been considered in the conservation equations in the existing component models,

so by comparing these parameters, the existing pipe models that can be extended with equations for simulation of

threats growth in water system

3.2. Implementation of equations

3.2.1. Mass transfer equations of bacteria

Bacteria may grow across a wide range of temperatures, from very cold to very hot, while it grow to a fixed size and

then reproduce through binary fission [20]. Bacteria have a minimum, optimum, and maximum temperatures for

growth and can be divided into 3 groups based on their optimum growth temperature: Psychrophiles are cold-living

bacteria (-5 to 15°C). The Mesophiles are bacteria that grow best at moderate temperatures with optimum growth

temperature is between 25°C and 45°C and finally the Hyperthermophiles are bacteria that grow at very high

temperatures (70 to 110°C). In this paper, Mesophiles are represented as “the average bacteria” that can be modelled

due to the optimum temperature range that match with the average temperature range in the water network and storage

systems, and as mentioned in the hypothesis, the Legionella pneumophila is considered as the average mesophile.

Multiplication of L. pneumophila is dependent on water temperature, volume flow rate, flow frequency, followed by

Water-19, Paris, 22-24 July 2019 Pag. 71

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nutrient availability [21]. At temperatures below 20°C, the bacteria become dormant but remain viable for months.

The bacteria grow best at temperatures between 20°C and 45°C with an optimum around 35°C-41°C. Beyond 45°C,

pasteurization starts and higher temperatures will eventually kill the organisms [22].

To model L. pneumophila growth in water in a pipe, equations need to be added to the hydraulic model. Following

mass conservation equations, that predict L. pneumophila growth in water, need to be coupled to an existing pipe

component [18] (equations below).

𝑉𝑝.𝑑𝐶(𝑡)

𝑑𝑡 = 𝐶𝑖𝑛(𝑡).

𝑄𝑖𝑛(𝑡)

𝜌− 𝐶𝑜𝑢𝑡 (𝑡).

𝑄𝑜𝑢𝑡(𝑡)

𝜌+ 𝑔𝑟𝑜𝑤𝑡ℎ 𝑖𝑛 𝑤𝑎𝑡𝑒𝑟

+ 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑤𝑎𝑡𝑒𝑟 𝑎𝑛𝑑 𝑏𝑖𝑜𝑓𝑖𝑙𝑚

= 𝑉𝑝.𝑑𝐶(𝑡)

𝑑𝑡= 𝐶𝑖𝑛(𝑡). 𝐴𝑖𝑛. 𝑣𝑖𝑛(𝑡) − 𝐶𝑜𝑢𝑡(𝑡). 𝐴𝑜𝑢𝑡. 𝑣𝑜𝑢𝑡(𝑡) + 𝑉𝑝. �̇� (𝑡) + 𝑘𝑐 . 𝐴𝑏. (𝐶𝑏 (𝑡) − 𝐶(𝑡))

𝑄𝑖𝑛 (𝑡) = 𝑄𝑜𝑢𝑡 (𝑡)

�̇� (𝑡) = 𝐶 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 .ln(2)

𝑦 . 𝑒

ln(2) 𝑑𝑡𝑦

To model L. pneumophila growth in biofilm in a pipe, equations need to be added to the hydraulic model in a similar

way as for growth in water. Following mass conservation equations, that predict L. pneumophila growth in the biofilm,

need to be coupled to an existing pipe component.

𝑉𝑏.𝑑𝐶𝑏(𝑡)

𝑑𝑡 = 𝐶𝑏, 𝑖𝑛(𝑡).

𝑄𝑏, 𝑖𝑛(𝑡)

𝜌− 𝐶𝑏, 𝑜𝑢𝑡 (𝑡).

𝑄𝑏, 𝑜𝑢𝑡(𝑡)

𝜌+ 𝑔𝑟𝑜𝑤𝑡ℎ 𝑖𝑛 𝑏𝑖𝑜𝑓𝑖𝑙𝑚

+ 𝑚𝑎𝑠𝑠 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑤𝑎𝑡𝑒𝑟 𝑎𝑛𝑑 𝑏𝑖𝑜𝑓𝑖𝑙𝑚

= 𝑉𝑏.𝑑𝐶𝑏(𝑡)

𝑑𝑡= 𝐶𝑏, 𝑖𝑛(𝑡). 𝐴𝑏, 𝑖𝑛. 𝑣𝑏,𝑖𝑛(𝑡) − 𝐶𝑏, 𝑜𝑢𝑡(𝑡). 𝐴𝑏, 𝑜𝑢𝑡. 𝑣𝑏,𝑜𝑢𝑡(𝑡) + 𝑉𝑏. �̇�𝑏(𝑡)

+𝑘𝑐 . 𝐴𝑏. (𝐶 (𝑡) − 𝐶, 𝑏(𝑡))

𝑄𝑖𝑛 (𝑡) = 𝑄𝑜𝑢𝑡 (𝑡) = 0

�̇�𝑏 (𝑡) = 𝐶𝑏, 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 .ln(2)

𝑦𝑏 . 𝑒

ln(2) 𝑑𝑡𝑦𝑏

Where,

Parameter Unit Description

𝐴𝑏 [m²] Surface between water and biofilm

𝐶(𝑡)𝑎𝑛𝑑

𝐶𝑏(𝑡)

[cfu/m³] Concentration of L. pneumophila in water and biofilm respectively at time t

𝐶𝑖𝑛(𝑡) 𝑎𝑛𝑑

𝐶𝑜𝑢𝑡 (𝑡)

[cfu/m³] Concentration of L. pneumophila in water entering and leaving system

respectively

𝐶 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑎𝑛𝑑

𝐶𝑏, 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠

[cfu/m³] Concentration of L. pneumophila in water and biofilm respectively on

previous timestep.

𝑑𝐶(𝑡)

𝑑𝑡 𝑎𝑛𝑑

𝑑𝐶𝑏(𝑡)

𝑑𝑡

[cfu/m³·s] Changing concentration of L. pneumophila over time in water and biofilm

respectively

𝑘𝑐 [m/s] Mass transfer coefficient to calculate the mass transfer of

L. pneumophila between water and biofilm

�̇�(𝑡) 𝑎𝑛𝑑 �̇�𝑏(𝑡) [cfu/m³·s] Change in concentration of L. pneumophila in water and biofilm

respectively due to growth or

death

𝑄 𝑖𝑛(𝑡)𝑎𝑛𝑑 𝑄 𝑜𝑢𝑡(𝑡) [kg/s] Mass flow rate of water (containing L. pneumophila) entering and leaving

system respectively

Eq. 1

Eq. 2

Eq. 3

Eq. 4

Eq. 5

Eq. 6

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3.2.2. Mass transfer equations of corrosion

It has been previously suggested that, in the mathematical simulation of the corrosion of steels in neutral solutions, at

least six species in the solution must be taken into account [23]. These species are the metal “Me” (e.g. Fe or Cu) ions

from the dissolution process, sodium and chloride ions (for example), which are commonly included to control the

bulk conductivity, hydrogen and hydroxyl ions from the dissociation of water, and a metal hydrolysis product e.g. Fe

(OH)+. In their investigation, Engelhard et al. [24], assumed that dissolved oxygen is also present in the solution and,

accordingly, it is assumed that there are seven different species, Sj (j=1,2,3….7), inside and outside the cavity, so that

the followed approach will be adopted.

S1=Me2+ S2= Me(OH)+ S3= Na+ S4=Cl- S5=H+ S6=OH- S7=O2

With the volume-based concentrations being designated as, Cj (mol/cm3). If the rates of the chemical reactions are

sufficiently high, the concentrations of the species can be set equal to their equilibrium values with the equilibrium

constants K1, K2, and Kw being defined as:

K1= C2C5/C1 K2=C5/C2 Kw=C5C6

where the activity coefficients are assumed to be unity, as are the standard state concentrations. The boundary

conditions far from the crevice mouth at (𝑥 → −∞) are written as

C1=C2C5/K1 C2=C5/K2 C3=CNaCl,water C4=2C1+C2+C3+C5-C6 C5=10-pH,w -3 C6=Kwater/C5 C7=0=CO2,water 𝜑

pH water is the bulk value of the pH and CNaCl, water and C7 are the bulk concentrations of NaCl and O2, respectively.

Corrosion formation can be subdivided in five different processes: electrochemical reactions, chemical reactions, flux,

diffusion and electromigration. The main chemical reactions that occur include the hydrolysis of metal II ion,

precipitation of metal II hydroxide and water dissociation. Equations for these reactions are:

- Me2+ + H2O⇔ Me (OH)+ + H+

- Me(OH)+ + H2O⇔ Me(OH)2(S) + H+

- H2O⇔ H+ + OH−

Concentration variations at the interface, which are governed by the chemical reactions mentioned, must also meet the

mass conservation equation, which includes the transport of species. The general equation describing the transport of

species j, including the contribution of chemical reactions and the electrostatic potential is [19]:

𝜕𝑐𝑗

𝜕𝑡= 𝑤𝐷𝑗

𝑚𝜕

𝜕𝑥 (

𝜕𝐶𝑗

𝜕𝑥+

𝑛𝐹

𝑅𝑇 𝑐𝑗

𝜕𝜑

𝜕𝑥 ) + 𝑤

𝑑𝑐𝑅𝑗

𝑑𝑡|𝑐ℎ𝑒𝑚𝑖𝑐𝑎𝑙 𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛

T [K] Absolute temperature

t [s] Time

Δ𝑡 [s] Timestep

𝑉𝑝 𝑎𝑛𝑑 𝑉𝑏 [m³] Volume of water and biofilm in pipe

𝑣⃗(𝑡) [m/s] Mass-average velocity for multicomponent mixture

𝑦 𝑎𝑛𝑑 𝑦𝑏 [s] Multiplication time of L. pneumophila in water and biofilm respectively

dependent on temperature

ρ [kg/m³] Mass density of mixture

𝐶𝑏 (𝑡) [cfu/m³] Concentration of L. pneumophila in biofilm at time t

𝐶𝑏, 𝑖𝑛(𝑡) 𝑎𝑛𝑑

𝐶𝑏, 𝑜𝑢𝑡 (𝑡)

[cfu/m³] Concentration of L. pneumophila in biofilm entering and leaving biofilm

Segment

𝑄𝑏, 𝑖𝑛(𝑡)𝑎𝑛𝑑 𝑄𝑏, 𝑜𝑢𝑡(𝑡)

Eq. 4

[kg/s] Mass flow rate of water (containing L. pneumophila) entering and leaving

biofilm segment

𝑄𝑏, 𝑖𝑛(𝑡)𝑎𝑛𝑑 𝑄𝑏, 𝑜𝑢𝑡(𝑡)

Eq. 5

[kg/s] Mass flow rate of L. pneumophila entering and leaving biofilm

Water-19, Paris, 22-24 July 2019 Pag. 73

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where x is the spatial coordinate representing the distance from the edge of the crevice, w is the crevice width, 𝐷𝑗𝑚is

the molecular diffusion coefficient, 𝜑 is the electrostatic potential at the deep of the crack.

4- Conclusion and future recommendations

The different threats leading to failures or pollution in water networks cannot be treated separately, as there is a clear

correlation between them, so for the further steps, the correlation in the growth and death of corrosion and bacterial

growth can be studied. To examine the different kind of threats, one should understand not only their origin, growth

or decline but also how the result of these threats propagates through the network.

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