Abstract A mathematical model for bioassimilation (BS) combined with bioaccumulation (BC) has been conducted to determine the removal and recovery of heavy metals (HMs) from wastewater using green algae. Response Surface and Box Benken Methodology (BBM) combined with best-fit simulation were used to determine ultimate uptakes. Results revealed that the percentages of HM removal (% RE r) and recovery (%HMc) are correlated with algal growth under the studied conditions. The developed mathematical model accurately predicts the % RE and HMc based on BS and BC mechanisms. Although the biosorption process exhibited higher metals uptakes than BS, the latter had a better affinity for the removal of different metals. The combined BS and BC mechanisms achieved 73 % and 69 % of Cu2+ and Pb2+removals, respectively, with the BC process is 6 folded higher than BS. Comparable percentage removal ∼ 74 % was observed for Cd2+, with 99 % of the removal was based on BC. The %HMc from aqueous and solid phases out of the hydrothermal liquefaction (HTL) process was estimated at 56.5 %. Mathematical modeling of the combined BS with BC processes provides an efficient and robust tool for predicting and forecasting the performance of HMs removals and recovery via algae process.

中文翻译：

---

利用藻类去除废水中重金属的生物同化和生物积累模型：新策略

摘要 为了确定使用绿藻去除和回收废水中的重金属 (HMs)，已经进行了生物同化 (BS) 与生物积累 (BC) 相结合的数学模型。响应面和 Box Benken 方法 (BBM) 结合最佳拟合模拟用于确定最终吸收量。结果表明，在研究条件下，HM 去除百分比 (% RE r) 和回收率 (%HMc) 与藻类生长相关。开发的数学模型基于 BS 和 BC 机制准确预测 % RE 和 HMc。虽然生物吸附过程表现出比 BS 更高的金属吸收，但后者对不同金属的去除具有更好的亲和力。结合 BS 和 BC 机制分别实现了 73% 和 69% 的 Cu2+ 和 Pb2+ 去除率，BC 工艺比 BS 高 6 倍。观察到 Cd2+ 的去除率约为 74%，其中 99% 的去除率基于 BC。来自水热液化 (HTL) 过程的水相和固相的 %HMc 估计为 56.5%。结合 BS 与 BC 过程的数学建模为预测和预测通过藻类过程去除和回收 HMs 的性能提供了一种有效和强大的工具。