2. Additional processes due to biotic and abiotic degra- dation contributing to source decay can be ac- counted for by a

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2 Additional Processes Due To Biotic And Abiotic Degra Dation Contributing To Source Decay Can Be Ac Counted For By A 1 (39.44 KiB) Viewed 37 times

2. Additional processes due to biotic and abiotic degra- dation contributing to source decay can be ac- counted for by adding a decay term to (3) that is proportional to m(t), m'(t) = -am - λm, (i) where is the associated decay rate constant. Find solutions of Eq. (i) using the initial condition m(0) = mo for the following cases: (i) y = 1, (ii) y # 1 and λ = 0, (iii) y # 1 and λ 0. Then find expressions for c, (t) using Eq. (2). Hint: Eq. (i) is a type of nonlinear equation known as a Bernoulli equation. 3. Show that when y≥ 1, the source has an infinite lifetime, but if 0 < y < 1, the source has a finite lifetime. In the latter case, find the time that the DNAPL source mass attains the value zero. Assume the following values for the parameters: mo = 1620 kg, co = 100 mg/L, 4 = 30 mỉ, Ud = 20 m/yr, λ = 0. Use the solutions obtained in Problem 2 to plot graphs of c.(t) for each of the following cases: (i) y = 0.5 for 0 ≤ t ≤tf, where cs(t) = 0, and (ii) y = 2 for 0 ≤ ≤ 100 years.