Multiscale Modeling of an Industrial Nylon-6 Leacher

This thesis presents a multiscale model of an industrial nylon-6 leacher. We develop several models at various spatial scales and implement them together in a simplistic, efficient way to develop an overall leacher model. We solve dynamic transport differential equations using the finite-volume method and method of lines in an in-house-developed FORTRAN program. We use the ODEPACK package of ordinary differential equation (ODE) solvers to solve our system of coupled ODEs. Our multiscale model performs transport, thermodynamic, physical property, and mass-transfer calculations at a finite-volume scale. We introduce two additional scales: a mesoscale, in which we perform computational fluid dynamic (CFD) simulations, and a molecular scale. Our CFD simulations solve for turbulent properties of fluid flowing over a packed bed. We incorporate the turbulent diffusivity of the fluid into our finite-volume leacher model. We perform molecular simulations and use the conductor-like screening model-segment activity coefficient (COSMO-SAC) model to generate solubility predictions of small, cyclic oligomers in water and ε-caprolactam. Additionally, we develop an extension of COSMO-SAC to model polymer species, which we refer to as Polymer-COSMO-SAC, and apply it to solve liquid-liquid equilibrium equations. We present a unique methodology to apply COSMO-based models to polymer species, which shows reasonable results for nylon-6. Because of the computational intensity of our Polymer-COSMO-SAC liquid-liquid equilibrium algorithm, we generate pre-computed tables of equilibrium predictions that we may import into our leacher model. Our integration of multiscale models maximizes efficiency and feasibility with accuracy.

We are able to use our multiscale models to estimate necessary parameters, but we need to fit two mass-transfer related parameters to industrial data. We validate our model against the plant data and find average-absolute errors in the final mass percent of ε-caprolactam and cyclic dimer in polymer chips of 25.0% and 54.7%, respectively. Several plant data sets are suspected outliers and we believe an unforeseen equilibrium limitation may cause this discrepancy. If we remove these outlying data sets, we then find average-absolute errors of 7.5% and 19.3% for ε-caprolactam and cyclic dimer, respectively. We then use our validated model to perform application and sensitivity studies to gain critical insight into the leacher's operating conditions.