# Electrocoagulation Based Chromium Removal Efficiency Classification Using Logistic Regression
## 1 Introduction
### Understanding Electrocoagulation  
Electrocoagulation is one of the widely used methods in the field of water treatment, which helps to remove heavy metals from water discharges. The authors of [5] studied the possibility of eliminating 5 different heavy metals in synthetic wastewater by electrocoagulation. They studied the impact of the various parameters (initial pH of the solution, current density, and initial concentration of the metal) involved in electrocoagulation. Obtained results state that all used metals--except the manganese--gave excellent elimination in the majority of the samples. The best elimination is obtained at a very high pH of 9, a current density of 6.25 mA/cm\({}^{2}\) after 20 min for all the metal concentration. In the same topic, ref. [6] used principal component analysis (PCA) to evaluate the informational contribution of Electrocoagulation parameter to the removal efficiency. Authors--in [7]--analyzed the operating cost required to remove lead from industrial wastewater by studying the effect of the geometry of the electrodes. This study highlights, as a result, the effect of the geometry of the electrodes and their consumption as well as the energy consumption on the one hand and the value of the operating cost on the other hand. They found that the electric current supplied to the new electrode configuration. The duration of each experiment and the electrocoagulation treatment of the wastewater, has a direct effect on the cost of operation by adding to the other variables.  
Electrocoagulation is a process that allows coagulating the pollutants thanks to an electrolysis with a Aluminium or Iron consumable anode. The electrocoagulation process creates, in the water to be treated, metallic cations or streams of metallic hydroxides. When a direct current is imposed between the anode and the cathode, an electric field occurs and induces numerous reactions. The main reactions that take place with the electrodes are: At the anode: It is the oxidation of a metal **M** that will pass from the solid state to the ionic state according to the reaction: \(M=M^{n+}+ne^{-}\). This chemical reaction--as shown in Equation (1)-can be accompanied by the formation of oxygen by electrolysis of water at high current densities:  
\[2H_{2}O(I)=O_{2}(g)+4H^{+}(aq)+4e^{-} \tag{1}\]  
At the cathode, the following water reaction occurs as shown in Equation (2). Electro-flotation of the flocs may occur following the release of \(H_{2}\) and \(O_{2}\) gases at both electrodes.  
\[H_{2}O+e^{-}=\frac{1}{2}H_{2}+OH^{-} \tag{2}\]  
It is also possible to use other metals as the soluble anode. Nevertheless, aluminum and iron remain the most used metals because of their affordable price and their ionic form which has a high valence. The quantity of material produced or consumed during an electrochemical reaction is calculated by [PERSON]'s law. It is a function of the duration of the operation and the Intensity of Current I. The quantity of metal \(m\) is given by the Faraday law given by the equation \(m=\frac{I.I.M}{H.E}\), with \(m\) is the mass of the dissolved metal or formed gas (g) and \(I\) represents the intensity of the imposed current (A), while \(t\) is electrolysis time. \(M\) stands to the molecular weight of the element under consideration (g/mol). \(F\) refers [PERSON]'s constant (96,500 C/mol) and finally \(n\) is the number of electrons involved in the reaction considered. If the electrolysis model comprises \(p\) electrodes, and is powered by a liquid with a flow \(Q_{e}\), then: \(C=\frac{m(p-1)}{Q_{e}}\), with \(C\) is the mass flow of dissolved metal (kg h/m\({}^{3}\)). \(Q_{e}\) represents the flow rate of the cell (m\({}^{3}\)/h) and \(p\) is the number of electrodes. Finally \(m\) is the theoretical amount of dissolved metal (Kg). If other electrochemical reactions take place simultaneously, the electrolysis current will not be fully used by the oxidation reaction.