A two-phase reactor model has been developed using a system of ordinary differential equations in MATLAB to model the carbonation reaction and therefore determine the kinetics of calcium oxide in a pressurized fluidized bed reactor as part of the calcium looping cycle. The model assumes that the particulate and bubble phases are modeled as a CSTR and a PFR, respectively. The random pore model developed by Bhatia and Perlmutter1 is incorporated into the system of equations to predict the rate of carbonation for pressures up to 5 bara total, and CO₂ partial pressures up to 150 kPa. The surface rate constant and product layer diffusivity in the random pore model expression were obtained by fitting the model to experimental data for a range of pressures, CO₂ concentrations, and temperatures by minimization of the residual sum of squares. The surface rate constants were found to be between 3.05 and 12.9 × 10^–10 m⁴ mol^–1 s^–1 for a temperature range of 550 to 750 °C. The product layer diffusivities were found to be between 0.06 and 23.6 × 10^–13 m² s^–1 for the same temperature range. The surface rate constant and product layer diffusivity activation energy were calculated using the Arrhenius equation and was found to be approximately 48 ± 17 kJ mol^–1 and 196 ± 43 kJ mol^–1, respectively.

中文翻译：

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氧化钙加压碳化动力学的两相流化床模型

使用MATLAB中的常微分方程系统开发了两相反应器模型，以对碳酸化反应进行建模，因此确定了加压流化床反应器中氧化钙的动力学，将其作为钙循环回路的一部分。该模型假设将颗粒相和气泡相分别建模为CSTR和PFR。由Bhatia和Perlmutter1开发的随机孔模型被合并到方程组中，以预测总压力最高为5 bara的压力和150 kPa以下的CO ₂分压的碳化速率。通过将模型拟合到一系列压力，CO _2的实验数据，获得了随机孔模型表达式中的表面速率常数和产物层扩散率。通过最小化残差平方和来确定浓度和温度。发现在550至750°C的温度范围内，表面速率常数在3.05至12.9×10 ^–10 m ⁴ mol ^–1 s ^–1之间。在相同温度范围内，产品层的扩散率在0.06至23.6×10 ^–13 m ² s ^–1之间。使用Arrhenius方程计算表面速率常数和产物层扩散活化能，发现它们分别约为48±17 kJ mol ^–1和196±43 kJ mol ^–1。