Question 3 of 9: Batch-Scale Determination of Process Pressure and Gelation Time

Question 3: Batch-Scale Determination of Process Pressure and Gelation Time (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (i) — maximum pyrolysis-stage pressure. Because pyrolysis is a temperature-triggered chemical event (thermal decomposition releasing gas), it must be located first: run a small sealed sample through the same heating rate the full process uses in a thermogravimetric analyzer (TGA) or differential scanning calorimeter (DSC), and identify the onset temperature at which mass loss / an exotherm/endotherm associated with decomposition begins. That onset temperature marks the "given stage of processing" the question refers to. With the critical temperature identified, reproduce the full process's time–temperature heating profile (same heating rate, same headspace-to-product volume ratio as the real vessel, scaled down) in a small, instrumented sealed batch reactor fitted with a pressure transducer and a data logger, and record the transient pressure trace as the sample passes through the pyrolysis onset temperature; the peak of that trace is the maximum pressure developed at that stage. Because the batch cell is geometrically similar (same headspace ratio, same heating rate) to the full-scale vessel, the measured peak pressure scales directly (subject to a safety factor for scale-up uncertainty) to the full-scale process, and the batch test also identifies when in the process the pressure peak occurs so a pressure-relief device can be set correctly.

Part (ii) — cooking time for a target degree of gelation. Starch gelatinization is itself measurable as a viscosity rise: as granules absorb water and swell (and eventually rupture) under heat, the suspension's apparent viscosity climbs from a low initial value to a peak. A batch Rapid Visco Analyser (RVA) or Brabender viscoamylograph reproduces the recipe's target cook temperature and stirs a small batch sample while continuously recording torque (viscosity) versus time; the degree of gelation at any instant can be read directly from where the viscosity trace sits between its initial (ungela- tinized) and peak (fully gelatinized) values, so the time to reach a specified percentage of peak viscosity is read straight off the RVA trace at the process temperature. Where the target gelation degree must be predicted at a temperature other than the one tested, gelatinization is well described as a pseudo-first-order process, degree of gelation G(t) = 1 − exp(−k·t), with the rate constant following an Arrhenius temperature dependence k = k₀exp(−E_a/RT); running the RVA batch test at two or more temperatures gives k at each, an Arrhenius plot of ln k vs. 1/T gives E_a and k₀, and the cooking time for the target degree of gelation at any process temperature follows directly by solving G(t) for t.