(60 points) As an extension of the in-class example, we will do another tracer test that only inject the tracer for the first 1/10 of the residence time. The rest of the time we will inject clean water into the column. Please note that in order to do this you will need to generate two input files with one inputfile having the keywords "restart", "save_restart", and "later_inputfile". Please read the relevant section in CrunchFlow manual for these keywords. The exercise 12 in the exercise folder has sample input files on using these key words.
1.1 Please plot the spatial profile of the tracer (concentration as a function of distance) at 1/10, 2/10, 4/10, and 8/10 of the residence time. Please plot all spatial profiles in one figure. Describe how the shapes of the Br concentration curve change over time. What causes that change?
1.2 Change the dispersvity $\alpha$ to 0.1 and 10.0 of the base value in example 6.1. Rerun these two additional simulations. And do the same plot as in question 1). Observe the difference in the shape of Br- concentration spatial profile with different $\alpha$ values. What are the effects of changing $\alpha$ values?
(optional) (60 bonus points) As an extension of the in class example with continuous injection of Br- from the inlet, we will do a sensitivity analysis to understand the effect of parameters on the breakthrough curves in the same 1D column, including flow velocity, dispersivity, molecular diffusion coefficient, and cementation factor. In each sub question below, only one parameter or condition is changed. For each condition, please
2.1 calculate the characteristic times (residence time and dispersion time) and Pe;
2.2 draw the Br breakthrough curves (as a function of residence time) by changing only the parameter discussed in each sub-question, with all other parameters remaining the same as those in example 1. Note that each middle number is the number used in example 6.1 so you do not need to run the simulation again.
flow velocity: 0.5, 1.0, and 2.0 of the flow velocity in example 6.1. Plot all three BTC in one figure and describe the effect of flow velocity on breakthrough curves (BTCs).
dispersvity $\alpha$ : 0.1, 1.0, and 10.0 of the base value in example 6.1. Plot all three BTCs in one figure and describe the effects of dispersivity on BTC.
Molecular diffusion D0: 0.1, 1.0, and 10.0 of the base value in example 6.1. Plot all three BTCs in one figure and describe the effect of D0 on BTC.
cementation factor m: 1.0, 3.0, 5.0 of the base value in example 6.1. Plot all three BTC in one figure and describe the effect of cementation factor on BTC.
compile all previous cases in 1) – 4) and make a table that lists values of residence time $\tau_a$, dispersion time $\tau_d$, De, Dm, Dh, v, and Pe. Plot all breakthrough curves together, label the Pe values for different cases in different ranges. What do you observe and why?
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