A mathematical model for bioassimilation (B-S) combined with bioaccumulation (B-C) 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 (% REr) and recovery (%HMc) are correlated with algal growth under the studied conditions. The developed mathematical model accurately predicts the % RE and HMc based on B-S and B-C mechanisms. Although the biosorption process exhibited higher metals uptakes than B-S, the latter had a better affinity for the removal of different metals. The combined B-S and B(C )mechanisms achieved 73 % and 69 % of Cu2+ and Pb(2+)removals, respectively, with the B-C process is 6 folded higher than B-S. Comparable percentage removal similar to 74 % was observed for Cd2+, with 99 % of the removal was based on B-C. The %HM(c )from aqueous and solid phases out of the hydrothermal liquefaction (HTL) process was estimated at 56.5 %. Mathematical modeling of the combined B-S with B-C processes provides an efficient and robust tool for predicting and forecasting the performance of HMs removals and recovery via algae process. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.