Step-by-step algorithm

[mostafa-razavi]

If I remember correctly, RAM was going to send his version of step-by-step ITIC algorithm

[ramess101]

@mostafa-razavi

I have attached the JCTC manuscript along with the supporting information. Be forewarned, the manuscript file takes a while to load.

The discussion is found in Section 2.2 (pages 7-10 of manuscript). The details are provided in Section SI.II (pages SI.9-SI.16 of the Supporting Information). This should give us a good starting point, but I think we will want to draft our own copy together.

Note that Section 4 (pages 36-37 of the manuscript) provides the PCFR-MBAR-ITIC algorithm. This is not that helpful because ITIC is only a portion of the overall algorithm, but it gives you an idea as to what I am envisioning.

JCTC_manuscript_accepted.pdf

Supporting_Information_JCTC_accepted.pdf

[ramess101]

@mostafa-razavi @jrelliottoh

Here is what I would put:

1. Perform NVT ensemble simulations for:

   a) 9 densities along the supercritical isotherm (points 1 to 9 in Fig 1.) b) 5 estimated saturation temperatures corresponding to the five most dense systems in Step 1a) (points 11, 13, 15, 17, and 19 in Fig 1.) c) 5 intermediate temperatures for each isochore in Step 1b) (points 10, 12, 14, 16, and 18 in Fig 1.) d) 3 low densities along the supercritical isotherm (green points in Fig 1.) e) 3 low densities for Tr = 0.9 (purple points in Fig 1.)

2. Obtain the average internal energy (Udep) and compressibility factor (Z) from simulation results in Step 1

3. Fit line to (Z-1)/rho with respect to rho to estimate B2 for T_IT (Step 1d) and T_0.9 (Step 1e)

4. Develop B2 temperature correlation using Equations 22, 24, and 25

5. Estimate Tsat from Z vs 1/T with Zliq = 0.01 as initial guess

6. Perform numerical integration (Eq 17 or 18) of (Z-1)/rho with respect to rho from rho=0 to rho=rho_IC along the supercritical isotherm using simulation results from Steps 1a) and 1d)

7. Perform numerical integration (Eq 17 or 18) of Udep with respect to 1/T from T_IT to Tsat (Step 3) along each of the isochore densities using simulation results from Steps 1b and 1e)

8. Compute Alig-Aig/RT from Eq 8 using results from Steps 5, 6, and 7

9. Solve Eq 15 for rhov using fixed-point iteration method and rholiq = rho_IC, Zliq = 0.01 for initial guess or from Step 11 for iterations, and Alig-Aig/RT from Step 8

10. Compute Pvap from Eq 16 with rhov from Step 9, B2 from Step 4, and B3 from Step ?

11. Recompute Zliq using Pvap from Step 10, Tsat from Step 5, rholiq = rho_IC

12. Iterate steps 5 through 11 with updated value of Zliq

13. Break loop when Zliq, rhov, Tsat, and Pvap have converged to within a desired tolerance

Note that MD or MC can be used for the simulations in steps 1a), 1b), and 1c). However, we recommend that MC be used for step 1d) and 1e) (see Section V). Also, note that ITIC solves for Tsat, rhov, and Pvap for a fixed value of rhol, whereas GEMC and GCMC solve for rhov, rhol, and Pvap for a fixed value of Tsat.

We probably need some more discussion or at least reference different sections to explain when B3 is needed and how integration is performed, etc. But this gives you an idea as to the level of detail I think we want to have.

[mostafa-razavi]

@ramess101 @jrelliottoh I thought a diagram would be more appealing, so I made one that explains the ITIC method from setting up the NVT simulations to obtaining VLE properties. I tried to retain most of the information in Rich's above comment. Let me know what you think.

[ramess101]

@mostafa-razavi

I like this a lot. I do think we want to modify the wording some though. For example:

• "Choose rho for green (T^IT)..." will be problematic for the color blind. I would just say "Choose rho for T^IT and T0.9" since these are referred to in Figure 1.

• Do we ever define T^(est)_sat? And since we use "sat" as a superscript for T^sat and T^sat_new, this should be T^sat_est.

• Do we really use Delta rho_vap to determine convergence, instead of Zliq, Tsat, Psat, or all four?

• Finally, I don't think we need to say "Pick an IC" and then "All IC's done?" not only because "Pick" and "all done?" are not very scientific/professional but also because it would be simpler just to say "For each IC:"