Simulation of Ion Exchange Resin with Finite Difference Methods

Round 1

Reviewer 1 Report

The authors presented a model to predict the operational cycle time of mixed bed resin for reducing unused resin discharge. The model was solved by finite difference method and the predictions are compared with experimental results. However, I ask the authors to clearly address the following comments.

Major comments:

Line 43. What are the few studies attempted to model ion exchange using finite difference method? Authors should list all of them and discuss the main difference and improvement compared with the presented model one by one here to show the novelty of this work. Also, what are the pros and cons of applying finite difference method over analytical methods? Authors should also explain it thoroughly. Line 54. There are studies discussing axial diffusion coefficient for nuclear reactors. Authors should reference models that made the same assumptions here for comparison. Same for other assumptions so that it is clear the model is not over simplified. Line 241. Unlike Cl^- and Mn²⁺, the predicted breakthrough point of K⁺ is a lot different compared with the experimental result. What is the main reason causing this problem? Is the model only applicable for some specific ions? Also, why are the numbers not agreeing with the results shown in Figs. 2 (~7e4 for Cl^-) and 3 (~1e5 for Mn²⁺)? Can author provide some comparison between the presented model and some most commonly used models in Figs. 2 & 3?

Minor comments:

There are some typos:

Line 75-77. Please align the equations with contents.

Line 86. Should be “[18]”.

Line 98-99. The detailed steps of derivation (such as linear algebra operation) should be listed in supplementary materials or appendixes, not in contents. Same for the whole section 2.2.

Line 276. “values that are too big or too small value”.

Line 288. “not good” is not a precise scientific term. It should be something like “not converged”.

Line 274. Convergence of the model should be shown before the results. One must first show the model is reliable then introduce the results. References should be listed in the order of year. For example, [5-9] should be cited in the correct order.

Author Response

Thanks for your comments, please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper uses numerical method (finite difference upwind method) to solve a model equation for ion exchange resin. Numerical result agrees with experiment.

Main concern:
* figure 6 shows that the method converges for dt=0.1 while diverges when dt=0.01. This is odd as the CFL condition usually determines the largest dt for stability. The authors should try a sequence of dt value smaller than 0.01, then one may find the largest dt to guarantee stability.
* the model equation is one dimensional, so it is not very expensive to try higher order method. For example, Lax-Wendroff method.

minor issues:
* there is a typo in equation (1), 'E' is missing.

Author Response

Thanks for the comments, please see the attachment

Author Response File: Author Response.docx