EPANET - Water Quality Analysis - Water Quality Reactions

Epanet water quality module can track the growth or decomposition of a substance by tailored reaction as it moves through a distribution system. To do this, he needs to know the rate at which the substance reacts and how that rate may depend on the concentration of the substance. Reactions can occur both within the mass and material flow along the pipe wall. Bulk fluid reactions can also occur inside tanks. EPANET allows a Constructor to use different reaction rates for the two reaction zones.

• Mass flow reaction rates
  Bulk flow reactions are reactions that occur in the main flow stream of a pipe or in a storage tank, unaffected by any processes that may involve the pipe wall.
  EPANET models these reactions using n-th order kinetics, where the instantaneous reaction rate (R ??in mass/volume/time) is considered concentration-dependent according to:
  R = Kb * C^n
  Where
  Kb = a mass rate coefficient,
  C = reagent concentration (mass / volume) and
  n = a reaction order. Kb has units of concentration raised to the power (1-n) divided by time.
  It is positive for growth reactions and negative for decay reactions.
  
  EPANET can also consider reactions where there is a threshold concentration in the ultimate growth or loss of the substance. In this case, the rate expression for a growth reaction becomes:
  R = Kb * (CL -C)*C^(n-1)
  Where
  CL = the threshold concentration. (For decay reactions (CL - C) is replaced by (C - CL).)
  
  Therefore, there are three parameters (Kb, CL and n) that are used to characterize bulk reaction rates.
  General values can be selected for these parameters that lead to several well-known kinetic models. These include:
  • Simple First Order Decay - (Kb < 0, CL = 0, n = 1)
    R = Kb * C
    The decomposition of many substances, such as chlorine, can be adequately modeled as a simple first-order reaction.
    Kb depends very much on the nature of the water being modeled and can range from less than -0.01/day to more than -1.0/day.
    It can be estimated by placing a water sample in a series of unreacted glass bottles and analyzing the contents of each bottle at different times.
    
    If the reaction is first order, plotting the natural log (Ct/Co) against time should yield a straight line, where Ct is the concentration at time t and Co is the concentration at time zero. Kb would then be estimated as the slope of this line.
  • First order saturation growth - (Kb> 0, CL> 0, n = 1)
    R = Kb * (Cl - C)
    This model can be applied to the growth of disinfection by-products such as trihalomethanes, where the final by-product (CL) formation is limited by the amount of reactive precursor present. Bottle tests can be used to estimate Kb if the test is run long enough to measure CL directly. (Kb is the slope of the graph of log [(CL - Ct) / Co] versus time, where Ct is the concentration after time t and Co is the concentration at time 0.)
  • Second-order two-component decay - (Kb < 0, CL ? 0, n = 2)
    R = Kb * C * (C - CL)
    This model assumes that substance A reacts with substance B in some unknown proportion to produce a product P. The rate of disappearance of A is proportional to the product of remaining A and B. CL can be positive or negative, depending on whether component A or B is in excess, respectively. This model sometimes shows improved fits for chlorine decay data that do not conform to the simple first-order decay model.
  • Michaelis-Menton kinetics - (Kb ? 0, CL > 0, n < 0)
    R = Kb * C / (Cl-C)
    As a special case, when a negative reaction of order n is specified, EPANET will use the Michaelis-Menton rate equation shown above for a decay reaction. (For growth reactions, the denominator becomes CL + C.) This rate equation is often used to describe enzyme-catalyzed reactions and microbial growth. It produces first-order behavior at low concentrations and zero-order behavior at high concentrations. Note that for decay reactions, CL must be set higher than the initial concentration present.
• Pipe wall reaction rates
  In addition to mass flow reactions, EPANET can model reactions that occur with material at or near the pipe wall. The rate of this reaction can be considered dependent on the concentration in the bulk stream using an expression of the form:
  R = (A / V) * Kw * C ^ n
  Where:
  Kw = a wall reaction rate coefficient and
  (A/V) = the surface area per unit volume within a pipe (equal to 4 divided by the diameter). The last term converts the reacting mass per unit area of the wall to a volume per unit basis. EPANET limits the wall reaction order (n) to 0 or 1, so the Kw units are either mass/area/time or length/time, respectively.
  
  The Kw parameter appearing in the rate expression above must be adjusted to account for any Mass transfer limitations on the movement of reactants and products between the bulk flow and the wall. EPANET does this automatically, Catchmentg the adjustment on the molecular diffusivity of the substance being modeled and the Reynolds number of the flow. (Setting molecular diffusivity to zero will cause mass transfer effects to be ignored.)
  
  The wall rate coefficient can be temperature dependent and can also be correlated to the age and material of the pipe.
  
  Note: EPANET requires water to be flowing in a pipe for a wall reaction to occur. No-flow pipes have no calculated wall reaction.
• Pipe wall reaction rates
  It is well known that as metal pipes age, their roughness tends to increase due to fouling and tuburculation of corrosion products on the walls of the pipes. This increase in roughness produces a lower Hazen-Williams C factor or a higher Darcy-Weisbach roughness coefficient, resulting in greater head loss due to friction in the flow through the pipe.
  
  There is some evidence to suggest that the same processes that increase the roughness of a pipe over time also tend to increase the reactivity of your wall with some chemical species, mainly chlorine and other disinfectants. EPANET can make each tube's wall reaction coefficient (Kw) a function of the coefficient used to describe its roughness. A different function applies depending on the formula used to calculate the head loss through the pipe:
  
  

  Head Loss formula	Wall reaction formula
  Hazen-Williams	Kw = F / C
  Darcy-Weisbach	Kw= -F / log (and / d)
  Chezy-Manning	Kw = F * n

  
  Where:
  C = Hazen-Williams C factor
  e = Darcy-Weisbach roughness
  d = pipe diameter
  n = Crew roughness coefficient
  F = wall reaction - pipe roughness coefficient
  
  The F coefficient must be developed from site-specific field measurements and will have a different meaning depending on which head loss equation is used. The advantage of using this approach is that it only requires a single parameter, F, to allow the wall reaction coefficients to vary across the network in a physically meaningful way