*Theory
Supporting Corrosion Model*

The
information presented below is primarily extracted from:

Bowker, Robert P.G., Smith, John M. and
Webster, Neil A. (1989) *“Odor and
Corrosion in Sanitary Sewerage Systems & Treatment Plants.”* Hemisphere Publishing Corporation.

This corrosion model has been
compiled by Biosol (using equations developed by Dr. Richard Pomeroy) to
demonstrate just one cost advantages to Sewage Catchment and Treatment Plant
(SC & STP) operators of implementing Biosol Technology. Corrosion is __one__ cost associated with
SC & STP operations. However due the
of nature corrosion, it is frequently “unseen” and its true cost is therefore
seldom adequately accounted for in budgets.
It is the intention of this model to assist in the quantification of
corrosion as a cost to any concrete, gravity sewage reticulation network.

The Model can be used with reasonable accuracy if appropriate generalisations are made about the given parameters. The model may be used for an entire sewage network (catchment) if averages are calculated for the mean pipe diameter, speed of flow etc. or a section of the sewage network (catchment) if inputs are entered for each individual single section and summed.

This model makes a number of key assumptions:

1. As
no oxygen (air) is available in force mains, the oxidation of H_{2}S to
H_{2}SO_{4} is assumed not to occur. Corrosion in force mains is therefore assumed
to be zero.

2. Gravity sewers are therefore the only pipes relevant to this model.

3. This model only considers corrosion in terms of the reaction rate with concrete. Only concrete sewers are therefore considered by this model.

4. A pipe is considered by this model to have reached the end of its useful life, when the average amount of material wear is back to the steel reinforcement of the pipe (See Figure 1).

Figure 1: Pipe wear

How concrete pipes actually wear |
How the model predicts wear |

Points to note:

· The calculated rate of penetration is an average. The maximum rate of penetration, which will be at the crown or the waterline, may be 50% greater than the average.

· The corrosion rate will be much greater (often ten times as fast) in the vicinity of point of much turbulence.

·
The pipe material is a very important
input. The use of calcareous aggregate
(limestone or dolomite) will increase the alkalinity of concrete and thus
prolong the life of structures subject to damage by sulfide conditions. The alkalinity of concrete made with granitic
or other acid resistant aggregate may range from about 0.16 up to 0.3. When calcareous aggregate is specified for
sewer construction, it is usually required that the alkalinity of the product
is equal to 80% or 90% CaCO_{3}.

·
Manholes, as well as sewer pipes, may be affected
by the acid produced from H_{2}S, but if
normal flow prevails through a manhole, the damage will be inconsequential
since the wall area is large relative to the water surface.

·
Manholes are sometimes the site of high turbulence.
Under these conditions the damage is likely to be severe if the sewage contains
sulfide.

The main bacteria that are responsible for the production of
sulphuric acid (H_{2}SO_{4}) are Thiobacillus bacteria. A number of conditions must be satisfied for
the formation and proliferation of these bacteria:

i.
There
must be a primary seeding of the concrete surface with the necessary bacteria,

ii.
The
concrete surface must be sufficiently moist,

iii.
The
necessary nutrients must be available for the proliferation of the various
bacterial species, and

iv.
The
temperature must be suitable.

These variables must therefore be carefully considered
before any predictive equations are established.

The following simplified reactions show that 32g of combined
sulphur is equivalent to 100g of cement products (represented by calcium
carbonate CaCO_{3})

_{}

(1)

If the overall mass transfer of hydrogen sulphide gas (as S)
from wastewater to the wall surface N_{s}, (g / m^{2}.h) and
the reaction is assumed to occur this way, the rate of cement material
destroyed can be estimated by dividing the gross CaCO_{3} equivalent
alkalinity of the cement (A).

ie. The rate of corrosion is therefore: (2)

This equation
makes the assumption that the aggregate itself is inert.

The volume rate of corrosion can be found by dividing by the
density of concrete (2400 kg/m^{3}).
This can then be used to express the results in terms of mm of
penetration per year (C).

(3)

Up to 50% of the acid formed may gravitate back in to the
wastewater without reacting and a factor, k (<1.0), is included to account
for this:

(4)

The useful life of a sewer pipe can be expressed as follows:

(5)

Where Z is the maximum allowable rate of penetration or the
“depth to the reinforcing steel”.

Combining equations (4) and (5) and rearranging,

(6)

The term Az is called the life factor and includes the
allowable penetration and the alkalinity.
Hence the life of the pipe can be prolonged by providing additional
sacrificial thickness or by using calcareous aggregates to increase the gross
alkalinity. k may vary from 1.0 for very
slow acid formation to 0.3 to 0.4 for very rapid acid formation. k however is best estimated in the
field.

It is assumed that all the hydrogen sulphide gas (mg / L)
released from the wastewater is absorbed onto the exposed area of pipe-wall and
that N_{S} is equal to the ratio of liquid surface area to exposed
pipe-wall area multiplied by the stream flux (f) which is the actual rate of
hydrogen sulphide emitted from the wastewater into the sewer atmosphere. The stream flux (g / m^{2}.h) is
typically 1-20% of the theoretical gas concentration and can be estimated by:

(7)

Where: S = slope of hydraulic gradient

V = wastewater
velocity (m/s)

[H_{2}S]aq
= molecular
hydrogen sulphide concentration in solution, (mg / L)

These equations are a guide only. They are not comprehensive as they overlook a
number of important environmental effects.

For example:

Aggregates in concrete are not completely inert to the
reaction with sulphuric acid, hence some of the acid reacts with the aggregate
and the overall depth of the corrosion of the concrete is lessened
accordingly. Some ventilation either is
provided for or occurs naturally and inevitably. Some of the H_{2}S in the sewer air
escapes via this ventilation without producing acid. To some extent also, ventilation commonly
reduces the moisture content of the sewer air, which in turn partly dries the
sewer walls and reduces the bacterial activity.

Computations are frequently based on dry whether conditions,
but in systems where periods of significant stormwater infiltration occur,
sulphide concentrations during such periods are much less than those for dry
whether conditions. In fact these
concentrations are reduced to practically zero in such conditions. Much more data, consequently must become
available before it will be feasible to correlate average rates of corrosion,
as computed by equation (4) with observed rates.

The steps required to calculate the useful sewer life can be
summarised as follows:

1.
Predict
the yearly average rate of sulphide generation in the wastewater.

2.
Determine
the concentration of soluble, molecular hydrogen sulphide.

3.
Calculate
the hydrogen sulphide stream flux (f) from molecular hydrogen sulphide
concentration in solution, slope of hydraulic gradient and wastewater velocity.

4.
Calculate
N_{S} from f, liquid surface width, B, and exposed pipewall perimeter,
P,

ie.

5.
Calculate
the corrosion, C, expressed as mm penetration per year. (Equation 3)

6.
Determine
the useful life of the sewer by making an allowance (k) for the acid, which
gravitates back into the wastewater without reacting and knowing the allowable
penetration. (Equation 6)

Assuming sewage characteristics:

pH = 7

j Factor @ pH 7 = 50%

Temperature = 20ºC

Dissolved Sulfide = 2 mg/L

Flow Rate = 0.9 m/s

Pipe volume = 50% full

Hydraulic
gradient = 0.0012

Equivalent
alkalinity cement = 0.2

k (assumed) = 0.5

Assuming network details of:

Total Km of sewage
network = 21 300 Km

Total Km of
concrete sewers = 11 000 Km

Value of sewage
network = $ 5 billion

Value of concrete
sewers = $ 3 billion

Average pipe
diameter = 600 mm

Average pipe wall
thickness = 90 mm

Average pipe
replacement at = 45 mm
Lost thickness

Step 1: Determine the molecular hydrogen sulphide in
solution

At pH 7:

[H_{2}S]aq = 0.5 x 2 mg / L

Step
2: Calculate the hydrogen sulphide stream flux f

_{}

g / m^{2}.h

Step
3: Calculate N_{S}

_{}

g / m^{2}.h

Step
4: Calculate the rate of corrosion

_{}

mm per year

Using the assumptions made above, the theoretical corrosion
rate is 0.98 mm / annum.

In one concrete sewer in