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.

Explanation supporting corrosion model

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 H2S to H2SO4 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% CaCO3.

·        Manholes, as well as sewer pipes, may be affected by the acid produced from H2S, 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.

Calculations within the model

The main bacteria that are responsible for the production of sulphuric acid (H2SO4) 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 CaCO3)

(1)

If the overall mass transfer of hydrogen sulphide gas (as S) from wastewater to the wall surface Ns, (g / m2.h) and the reaction is assumed to occur this way, the rate of cement material destroyed can be estimated by dividing the gross CaCO3 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/m3).  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 NS 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 / m2.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)

[H2S]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 H2S 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.

Steps in Calculating Useful Sewer Life

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 NS 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)

Using a prominent Australian Water Corporation as an Example:

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:

[H2S]aq = 0.5 x 2 mg / L

Step 2: Calculate the hydrogen sulphide stream flux f

g / m2.h

Step 3: Calculate NS

g / m2.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 Brisbane (Queensland, Australia), under severely aggressive conditions, the rate of corrosion was found to be as high as 25 mm / annum.