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Advanced Modeling of Continuous Digesters: Insights from Doyle et al.'s Fundamental Approach

This document explores the complex fundamental continuous digester model proposed by Doyle et al. It integrates Purdue pulping kinetics, focusing on various components like lignin, cellulose, and carbohydrates, with an emphasis on high and low reactivity. The model divides the digester into multiple continuous stirred-tank reactors (CSTRs) and examines mass transfer, heat, and momentum balances. Key predictions include kappa numbers, chip pressure, and velocity profiles, which help optimize process control strategies and grade changes in digester operations.

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Advanced Modeling of Continuous Digesters: Insights from Doyle et al.'s Fundamental Approach

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  1. Fundamental continuous digester model – Doyle et al. • Very big & complex model

  2. Fundamental continuous digester model – Doyle et al. Use Purdue Pulping Kinetics • Lignin • High reactivity • Low reactivity • Cellulose • High • Low • Xylan • High • Low • Glucomannan • High • Low • Alkali • Sulfide Dissolved lignin Dissolved Carbohydrates Passive alkali Passive sulfide

  3. Tfl, vfl, pfl, ρfl ρei Tc, vc, pc, ρsi Free Liquor Entrapped Liquor Solid Lo reactive lignin Hi reactive lignin Cellulose Araboxylan Galactoglucoman Active EA Passive EA Active HS Passive HS Dissolved Lignin Dissolved Carb- ohydrate ε Δz Reaction Site η Mass Transfer Tfl, vfl, pfl, ρfl Tc, vc, pc, ρsi ρei Fundamental continuous digester model – Doyle et al. • Transport in and out of chip modeled with an overall mass transfer coefficient • All components are assumed to diffuse in and out of chip at the same rate.

  4. Fundamental continuous digester model – Doyle et al. • Digester is divided up into a series of CSTRs that chips and liquor flow into and out of. • 60 to >100 in a digester • Model assumes no radial gradients.

  5. Fundamental continuous digester model – Doyle et al. • Use Harkonen model to calculate chip pressure and compaction as a function of kappa number. • Use Harkonen model to calculate the pressure drop in the chip bed. • Mass balance - w/ kinetics • Heat Balance - w/ kinetics • Momentum balance Dynamic model of continuous digester to predict

  6. Model is complex with many variables

  7. Fundamental continuous digester model – Doyle et al. Model predictions • Kappa, [OH-], [HS-], dissolved solids, chip density (function of extent of cooking), void fraction of bed, chip velocities, liquor velocities, temperature profiles, chips & liquor, chip porosity • Model has been used to examine different control strategies and the effect of grade changes.

  8. Model predictions

  9. Fundamental continuous digester model – Doyle et al. Model results Comparison of predicted and measured blow line kappa number SW-HW (top) and HW-SW (bottom) transitions where solid line is nonlinear model prediction.

  10. Fundamental continuous digester model – Doyle et al. Model applications • Model has been used to examine different control strategies and the effect of grade changes.

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