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Development of a theoretical adsorption model under constant pressure condition and measurement of apparent solid-side mass diffusivity for a siica gel-water vapor adsorption system
本文針對多孔吸附體在非等溫條件下的吸附行為求得解析解，熱效應與氣體側質傳阻力對動態吸附曲線的影響皆考慮於數學模式之中。統御方程式以拉式轉換法獲得解答，研究結果發現α、β和γ三個參數主宰了吸附速率，前兩者與熱傳阻力有關，而後者則影響氣體側之質傳阻力。各種簡化模式的適用範圍亦詳細探討之。研究中並自行設計組裝一套動態吸附曲線量測系統，分別量測出3mm直徑之矽膠顆粒於5.1℃, 22.2℃、49.5℃、和79.6℃等四種溫度下吸附空氣中水分子之動態吸附曲線與等溫吸附線的實驗資料，配合理論模式中所發展出的解析解，獲得矽膠於不同溫度與含水量狀態下的固體側質傳擴散係數（apparent solid-side mass diffusivity），同時以數值分析的方法，比較矽膠顆粒在較大含水量變化下的動態吸附曲線與實驗量測數據的差異。研究中並組裝一套吸附式固定床除濕系統，以實驗量測與電腦模擬分析共同探討濕度容器（moisture capacitor）之阻尼效果，以本篇論文量測所得之矽膠的等溫吸附線與固體側質傳擴散係數用於電腦模擬分析時，此模擬分析所得之數據與實驗量測之結果極為吻合。
An analytical solution for mass diffusion in a spherical microporous particle experienced with a small step change of gaseous phase adsorbate concentration is obtained. Thermal effect and gas-side mass transfer resistance are considered. The governing equations are solved by using the Laplace transformation method. Three factors, α, β and γ are defined to govern the heat and mass transfer in the process. α and β are relevant to the thermal effect and γ dominates the gas-side mass transfer resistance. The effect of the external mass transfer resistance on the uptake rate is investigated. The applicable ranges of three simplified models are individually discussed. A measurement of the apparent solid-side mass diffusivity of water vapor adsorbed in a regular density silica gel is performed by using a constant pressure thermal gravimetric apparatus. The diameter of the silica gel particles is 3 mm. Four adsorption isotherms, individually correspond to 5.1, 22.2, 49.5 and 79.6℃, are measured. Using the model developed in this thesis, the measured uptake curves yield the data of apparent solid-side mass diffusivity. The measured uptake curve for a large step change of water vapor is compared to the computer simulation result obtained by using the measured apparent solid-side mass diffusivity. In this work, the damping characteristics of a moisture capacitor in a fixed-bed adsorption system are determined both by experimental measurement and by computer simulation. The obtained isotherms and apparent solid-side mass diffusivity are used in the computer simulation. The simulation results match well with the experimental data.
Keywords: adsorption, mass diffusivity, silica gel, isotherms
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