A mechanistic mathematical model for the treatment of synthetic oil-field wastewater (produced water) by electrocoagulation process using aluminium electrodes

Produced water (PW) is the largest by-product that comes out of the oil wells during oil and gas (O&G) field exploration. PW contains high-salt concentration along with other organic and inorganic components; therefore, PW must be treated before disposal. Electrocoagulation (EC) is an effective treatment method to remove pollutants from PW which has been the focus of many experimental studies; however, a mathematical model specifically for PW treatment by EC has not been developed yet. In this work, a comprehensive mathematical model has been developed to elucidate the role of EC operating parameters on the PW treatment performance and determine the mechanism for COD (Chemical Oxygen Demand) removal. The present model considers and identifies the dominant Al-hydroxy complex species and their contribution to the COD removal from synthetic PW samples by estimating their rate constants and comparing their magnitudes and investigates multi-scale modelling of the EC reactor. The influence of working parameters such as current density, initial pH, interelectrode distance, mixing speed and solution volume of PW on Al coagulant production and COD removal was investigated and modelled. The study estimates the rate constants of the reactions taking place for COD removal by EC process and by comparing their magnitudes identifies the dominant reactions and coagulant species involved in the process. The mathematical model prediction of COD removal fits well with the experimental data at 10 mA cm⁻², 15 mA cm⁻² and 20 mA cm⁻² current density with R² value of 0.96, 0.97 and 0.92, respectively and for dissolved Al concentration R² value of 0.96, 0.99, and 0.97, respectively. The simulated results reproduced a good fit at initial pH of 6.1, 7.3 and 8.6 with R² value of 0.92, 0.96 and 0.98, respectively for COD removal. The mathematical model and the experimental results showed the role of dominant Al-hydroxy complex species such as \({{\text{Al}}\left({\text{OH}}\right)}^{2+}\) ${\text{Al}\left(\text{OH}\right)}^{2+}$ , \({{\text{Al}}{\left({\text{OH}}\right)}_{2}}^{+}\) ${\text{Al}{\left(\text{OH}\right)}_2}^{+}$ , \({\text{Al}}{\left({\text{OH}}\right)}_{3}\) $\text{Al}{\left(\text{OH}\right)}_3$ , \({{{\text{Al}}}_{2}{\left({\text{OH}}\right)}_{2}}^{+4}\) ${{\text{Al}}_2{\left(\text{OH}\right)}_2}^{+4}$ and \({{\text{Al}}{\left({\text{OH}}\right)}_{4}}^{-}\) ${\text{Al}{\left(\text{OH}\right)}_4}^{-}$ in controlling the COD removal process. Under different operating conditions considered in the study, the model also predicted the COD removal performance of the EC reactors at different reactor volumes with R² value of 0.96 for higher solution volume and larger reactor. The model presented and rate constants determined in the study will provide a theoretical basis for designing, scaling up and operating the EC reactor for oil-field PW treatment.