### 利用余补误差函数模拟土壤中铜老化微孔扩散过程模型的构建

1. a 中国农业科学院农业资源与农业区划研究所 北京 100081;
b 济南大学资源与环境学院 济南 250022
• 投稿日期:2015-08-10 发布日期:2015-10-29
• 通讯作者: 马义兵 E-mail:mayibing@caas.cn
• 基金资助:

### A Model Predicting the Diffusion Process of Aging of Copper in Soils Using Complementary Error Function

Zeng Saiqia, Li Jumeia, Wei Dongpua, Ma Yibingb,a

1. a Institute of Agricultural Resources and Regional Planning, CAAS, Beijing 100081;
b School of Resources and Environment, University of Jinan, Jinan 250022
• Received:2015-08-10 Published:2015-10-29
• Supported by:

Project supported by Ministry of Science and Technology of the People's Republic of China (No. 2015BAD05B01).

Aging of copper added to soils refers to the process by which the bioavailability and/or toxicity, isotopic exchangeability and extractability of added copper decline with time. This process also termed as natural attenuation or fixation. Although aging of extraneous copper added to soils is a key process in the risk assessment and soil restoration and management that need to be well-considered, it has not been studied in details yet. When water-soluble copper added to soils, the lability of copper decreases rapidly at first, especially in soil samples with relatively high pH value (pH>6 in this article), followed by further decreases at slower rate, and finally become stable. The cause of the rapid decrease of copper lability may be the precipitation/nucleation process, while the long-term decrease of copper lability is due to the diffusion of copper into the micropores/mesopores in soils and cavity entrapment. In previous studies, Ma et al. developed two semi-mechanistic models to predict the short-term and long-term aging of copper added to soils separately. In the short-term model, the diffusion process is linear related to square root of time and in the long-term model the diffusion process is linear related to natural logarithm of time. As those two models have different description of diffusion process, both of them fail to predict the short- and long-term aging continuously. By combining and analyzing two models developed by Ma et al. and study the duffusion equation in Crank's book, we found that both short- and long-term behaviors of diffusion process of aging can be well described using complementary error function. Thus, the new model we developed in this paper (erfc model) could predict the both short-term and long-term aging of added copper in soils continuously. In the erfc model, the precipitation/nucleation and diffusion processes were considered, as well as occlusion of Cu within organic matter. But the estimated results indicate that the occlusion process plays an insignificant role in aging and can be ignored. The erfc model we developed in this paper showed better results compared with Ma et al.'s previous models, and was validated by testing it against 19 soil samples from different European countries in Ma et al.'s previous paper with wide range of physiochemical properties, and was successfully predict the isotopic exchangeability of copper added to soils.

Key words: copper, aging, semi-mechanistic model, pH