Calculating wall reaction rate coefficient

Hello everyone,

I am in need of help regarding the wall reaction rate coefficient.
Is it possible to calculate this coefficient?
I due have the pipe diameter DN500, the Kb is -1 and the distance between two samples of the FRC ist 2186 meters. Sample one shows a value of 0.79mg/l and sample two a value of 0.67mg/l.
Am I correct if this should be done with this formula?
R=(A/V)KwCn

I would really appreciate if someone could explain me how to proceed in this case!

Assuming steady flow, the change in concentration C between points 1 and 2 along a pipe is:

C2 = C1 exp(-K*t)

where K is the overall rate coefficient and t is the travel time between 1 and 2 equal to:

t = L / v = L * (PI * D^2) / 4 / Q 

where L is distance between 1 and 2, v is flow velocity, D is diameter and Q is flow rate. Since you didn’t specify a flow rate, let’s assume it produces a velocity of 1 m/sec. Therefore t is:

t = 2186 / 1 / 86400 = 0.025 days

so that K is:

K = ln(0.67/0.79) / 0.025 = -6.6 / day

K consists of both the bulk and wall reaction coefficients as follows:

K = Kb + (4/D)*Kw

where we assume that mass transfer is not rate-limiting. Since we know K, Kb and D we can solve for Kw:

Kw = (K - Kb) * (D/4) = (-6.6 - (-1)) * (0.5/4) = -0.7 m/day

Of course this all assumes a velocity of 1 m/s. To estimate the actual wall coefficient you must know the flow rate through the pipe when you took your concentration samples.

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Thank you so much for your help!!!

Am I correct if I assume that t in this case should be 0.025?

Yes, it should be 0.025. I’ve edited my earlier response to fix this mistake and one other (left out the factor of 4 in the formula for area).

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