砂岩型铀矿地浸溶质迁移分数阶数学模型与参数反演

The proposal devotes to the law of solute transport and parameters inversion concerning in-situ leaching of deep sandstone-type Uranium deposits. It would enrich the basic theory and practical technology in the field of Uranium leaching. By focusing on the Ordos Basin, we are dedicated to the following three aspects: Firstly, in terms of solute transport kinetics and seepage theory, employing fractional PDEs theory and numerical method, we will establish a mathematical model and well-posedness analysis with reference to solute transport in situ leaching of deep sandstone-type Uranium deposits; Further more, by virtue of the Schlogt molecular mechanism, the major chemical reactions in the process of Uranium leaching will be embedded into the fractional PDEs model, to obtain the mathematical model and its numerical solutions of sandstone type uranium leaching by invoking some modern high-resolution numerical method, such as finite difference method, finite element method, finite volume method and spectral method. At last, in the light of some significant parameters in process of in-situ leaching and the forward fractional mathematical model, we will yield an inverse problem and approximation relate to identification of parameters such as depth, permeability and the well-distance by taking advantage of Bayesian stochastic inverse theory and method, to improve the leaching efficiency of Uranium mining.

本项目针对深部砂岩型铀矿原地浸出的溶质迁移机理与参数反演展开研究，对于丰富地浸采铀基础理论和技术具有实际应用价值。课题组以鄂尔多斯盆地为研究背景开展三方面研究：从地浸采铀的溶质迁移动力学、渗流理论方面，利用分数阶偏微分方程理论与方法，建立砂岩型铀矿原地浸出采铀溶质迁移规律的分数阶数学模型并进行正问题适定性分析；结合采铀工艺中的主要化学反应，采用Schlogt分子化学动力机制，建立基于分子化学动力机制的分数阶砂岩型铀矿原地浸出数学模型，并使用有限差分、有限元、有限体积法、谱方法等高精度计算方法数值求解；针对影响地浸的重要工艺参数，结合正问题分数阶模型，提出铀矿原地浸出的参数反问题数学模型及其数值解法，依据实验数据，利用贝叶斯随机反演理论与方法，计算出矿层深度、渗透率、井距等铀矿原地浸出的关键参数，从而有效地提高采铀的浸出效率。

本项目针对深部砂岩型铀矿原地浸出的溶质迁移机理与参数反演展开研究，对于丰富地浸采铀基础理论和技术具有实际应用价值。主要研究内容有以下三个方面：（1）探索砂岩型铀矿原地浸出采铀溶质迁移规律的分数阶数学模型；（2）寻求合适的分数阶数学模型求解方法；（3）分数阶数学模型的参数反演。本项目分别探索了分数阶偏微分方程数学模型（见成果：期刊论文[1-2,4], 学术专著[2]）与整数阶偏微分方程（见成果：期刊论文[3,5-6]，学术专著[1]）及多种不同形式的参数反演问题（见成果：期刊论文[2-4,6-7] ，学术专著[1-2]），对相关问题进行了稳定性等理论分析并构造了相应的数值计算方法，同时采用了当前热门的智能算法尝试求解偏微分方程参数识别反问题并探索了正则化参数选取策略（见成果：期刊论文[6-9]），部分研究成果于2020年获江西省自然科学奖二等奖（见成果：科研奖励[1]）。