Mathematical leach model for leaching behavior of solidification of incinerator fly ash
|關鍵字:||放射性溶出試驗;化學性溶出試驗;擴散模式;飛灰;固化;Isotope leaching test;chemical leaching test;diffusion model;lead;fly ash;solidification||公開日期:||2008||摘要:||近來天然資源缺乏，廢棄物廣泛用於土木工程取代掩埋，為保護環境更嚴謹評估廢棄物之溶出有其必要，半動態溶出試驗( semi-dynamic leaching test ) ，主要以擴散機制來評估廢棄物中毒性物質溶出之標準方式，這種方式限制於水泥固化物污染物之溶出量小於20%及溶出液固比為10。棄物固化體係一種非均勻(non-homogeneous)擴散行為，數學溶出擴散模式乃基於均勻性擴散及非均勻性溶出，可以用分離常數方法解析，杜哈梅定理(Duhamel’s theorem)係一種與時間相關可以用來解釋這種現象之理論，並且可提供量測溶出擴散係數及溶出速率常數方法之一，本研究之直立圓柱廢棄物固化體溶出試驗及數學模式源於杜哈梅定理。溶出以擴散為主，利用微分方程來解析溶出初始及周界條件，將物理及化學反應綜合成一種綜合性參數模式(lumped-parameter model)之廢棄物固化體溶出擴散模式。研究分別以放射性氧化鉛及化學氧化鉛添加於飛灰，並以水泥為固化劑，分別製成直徑1公分及高4公分之二類廢棄物固化體，其水泥添加量別為20%,40% 及11%,13%,22%水泥二類廢棄物固化體，廢棄物固化體經養生二星期後，放入圓形溶出容器，分別用pH 0.89磷酸及pH 2醋酸為溶出劑連續六小時，並每隔一小時將溶出液取樣方析，液固比7.5，溶出條件控制於酸性條件下，溶出物以金屬離子型態擴散為主，經以γ及ICP-MS 分別量測二類廢棄物固化體中放射性鉛及鉛溶出。用最小平方法，以第1、2、3、4小時鉛溶出量求出經驗擴散係數(empirical mass diffusivity) 及經驗溶出速率常數(empirical mass generation rate constant) ，加以用貝塞爾函數根(Roots of Bessel function)來建立率定擴散模式(Calibrated diffusion model)，貝塞爾函數根所建立直立圓柱廢棄物固化體擴散模式，其所預測廢棄物固化體重金屬溶出量與實驗值相近，本研究利用第五小時及第六小時之模擬溶出量，在第5小時及第6小時實驗值的一個標準偏差內，完成驗證擴散模式 (verified diffusion model) 。最適貝塞爾函數根與溶出劑及水泥添加量有關，含水泥添加量多之固化體溶出擴散模式更準確。本研究20%-40%水泥添加量飛灰固化體，以磷酸為溶出劑pH0.89之最適貝塞爾函數正解根11；11%-22%水泥添加量飛灰固化體，以醋酸為溶出劑pH 2之最適貝塞爾函數正解根2。含不同水泥加量之廢棄物固化體，以杜哈梅定理推導直立圓柱廢棄物固化體質量擴散、經驗擴散係數及經驗質量溶出速率常數係數，顯示模式之準確性，並由這些參數研判醋酸溶出劑較磷酸穩定適用。經驗擴散係數、經驗質量溶出速率常數及模擬溶出量所建立之溶出擴散模式，開發溶出指數列線圖形，而長期之溶出指數可以利用外插列線方式求得，長期廢棄物溶出，可利用溶出指數列線圖形及簡單數學運算而得，利用所發展溶出指數可發現潛在性可能溶出物之危害，本研究所開發直立圓柱廢棄物固化體溶出試驗之溶出指數，對廢棄物固化處理設計、廢棄物資源化，及行政管制標準訂定為一種有效之工具。
Natural resources are short recently. Waste has been widely use in civil engineering work instead of sending it to the landfill. From an environmental aspect, more accurate assessments of constituent leaching of solidified waste are necessary.ne semi-dynamic leaching test aimed at predominately evaluating the release of metals in diffusion-controlled environments. We are limited to adding 20% cement to solidified waste and the testing specimen volume to surface area ratio 10. he diffusion behavior of a solidified waste matrix is a non-homogeneous diffusion phenomenon, it can be divided into a set of simple problems, solved by using the separation of variables method. The mathematical diffusion model for the solidified waste matrix cylinder is set up with homogeneous diffusion and non-homogeneous generation rate. Accordingly, Duhamel’s theorem with the time-dependent boundary condition and/or time-dependent condition provides a convenient approach for mass diffusivity and mass generation rate constant measurements. The experimental set-up design and development of the cylindrical diffusion model in this study was based on Duhamel’s Theorem. The diffusion model is mainly controlled by diffusion. ifferential equations are used to solve this initial value and boundary value problem. In this study, the physical and chemical processes are combined into one lumped parameter that can be applied to a variety of disposal/reusable scenarios to predict the environmental impact. wo types of solidified waste forms (ratio of the cement to waste was 20%, 40% and 11%, 13%, 22%, respectively) including lead isotope and lead oxide added, were produced by solidifying the fly ash using cement as a binder, respectively. In this recipe, the solidified waste forms were molded into a cylindrical form with a diameter of 1 cm and a height of 4 cm. Before the solidified test specimen was subjected to the leach test, it was allowed to harden for two weeks. The molded solidified waste matrix was placed in a cylindrical container. Extensive leaching tests were applied to this study for six hour leaching using pH 0.89 phosphoric acid and pH 2 acetic acid as the leachant, respectively. The leachant volume to the specimen’s external geometric surface area (VL/S) ratio was maintained at 7.5 cm. A γ detector instrument and ICP-MS were applied to measure the lead isotope and lead leached out of the solidified waste matrix, respectively. he empirical mass diffusivity ( )and empirical mass generation rate constant( ) were obtained using the least square method for the first, second, third , and fourth leaching result intervals , and a range of Bessel function roots were used to establish the cylindrical diffusion model . An appropriated Bessel function root lead the simulated leaching results compare with the experiment. The lead released from the waste specimen in the fifth and sixth intervals of the mass diffusion model were used to verify the mass diffusion model .The diffusion model was verified with the extended simulated leaching results within one standard derivation of experiment. The best fitted Bessel function root in the diffusion model depends on the leachant, the amount of cement added to the waste. Increasing the solidified agent in the waste matrix acquired a more accurate diffusion model. In this study, the best fitted root of Bessel function for the diffusion model of the solidified of incinerator fly with 20% to 40% cement addition is 11 using phosphoric acid as leachant. The best fitted root of Bessel function for the diffusion model of the solidified of incinerator fly with 11% to 22% cement addition is 2 using acetic acid as leachant. The amount of cement added to the waste carried a very distinguished mass diffusivity and mass generation rate constant that demonstrated the effectiveness of the cylindrical diffusion model in this study. Using acetic acid as the leachant is more stable than phosphoric acid.he leachability index was derived from the verified diffusion model used simulated leaching values and lumped- parameters. The long-term leachability index can be obtained by extrapolating the leachability index profiles (straight line). Simulated leaching can be obtained only with a graph and simple mathematical calculation. Using the proposed leachability index, it is possible to estimate the incremental probability of some harm occurring. The leachability index derived from this cylindrical diffusion method for investigating the diffusion behavior developed in this study, can be used as an effective tool for establishing the design of the solidification facility, waste resources recovery, and regulatory standards.
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