Materials
The two main pickling liquors used for industrial pickling are hydrochloric and sulfuric acids. However hydrochloric acid allows faster cleaning rates at lower temperatures and the concentration of the solution is lower than in the case of sulfuric acid [31]. Equations (1) to (3) show the normal evolution of the pickling process in the case of carbon steel and hydrochloric acid while Eq. (4) shows the over corrosion of the substrate [32].
$${Fe}_{3}{O}_{4}+8HCl \to {2FeCl}_{3}+{FeCl}_{2}+ {2H}_{2}O$$
1
$${Fe}_{2}{O}_{3}+6HCl \to {2FeCl}_{3}+{3H}_{2}O$$
2
$$FeO + 2HCl \to {FeCl}_{2}+{H}_{2}O$$
3
$${Fe + 2HCl\to FeCl}_{2}+{H}_{2 }\uparrow$$
4
The over corrosion phenomena is the main reason for material and economic losses. One of the methods used to control the corrosion is adding inhibitors to the pickling bath. Organic inhibitors containing heterocyclic compounds with polar functional groups (e.g., N, S, O and P) and conjugated double bonds with different aromatic systems, have been widely used and proven effective over the years [33].
Cetilpyridinium bromide is a surfactant that inhibits the corrosion phenomenon by adsorption on the electrode surface, in this case the carbon steel plate. The hydrophilic head of the inhibitor (the carbon chain) attaches to the surface while the hydrophobic part (the bromide group attached to the nitrogen) is subjected to the solution. The molecular structure of CPB is shown in Fig. 1 [34].
The CPB solution used during the experiments was acquired from local company. An IR analysis has been performed to confirm the structure of the corrosion inhibitor. As shown in Fig. 2 the structure is confirmed by the 3 visible peaks. The vibration associated with the ring structure is at around 3400 cm-1, also at around 3500 cm-1 there is a strong signal for the O-H stretching. The other 2 peaks are for the C = N stretching at 1650 cm-1 and the C-Br stretching at 600 cm-1.
The other materials used during the experiments are carbon steel plates (50x50x1 mm) and solution of HCl 37.5% and distilled water.
2.2 Experiments
Plates of carbon steel of similar shape (50x50x1 mm) and weight were degreased, washed, and initially pickled to be free of any contaminates before starting the experiments. They were put into 50ml hydrochloric acid solution of industrial making (H2O:HCl, 1:1) with different volumetric CPB inhibitor concentrations (referred along the paper as CI concentrations). For this experiment the CI concentrations are 8%, 9%, 10%, 11% and 12%. An additional blank solution that contained no inhibitor has been also employed for comparison purposes. It is important to remark here that two solutions containing 10% CPB have been used to illustrate the industrial pickling process mass loss experiments were conducted over the course of a 336h (for the first set of experiments), consisting in multiple pickling cycles. After each pickling cycle the plates were removed from the solution, washed with water, dried, and weighted with the help of an analytical balance.
The measured mass loss values have been used to estimate the corrosion rate (referred to along the paper as the experimental corrosion rate, V) with the widely used Eq. (5) [35].
$$V= \frac{\varDelta m}{tS} \left[\frac{g}{{m}^{2}h}\right]$$
5
The data from these experiments (8%, 9%, 10%, 11% and 12% CI) has been used for the development and calibration of the decision-making tool and for a first verification run (the additional 10% CI experiment).
2.3 Tool development
Taking into account the complexity of pickling and its dependence on a lot of parameters [36], our starting hypothesis is that, from a phenomenon point of view the widely used Equation. (5) could be improved in the form of Eq. (6) by adding additional parameters, to satisfy industrial needs.
$${V}_{c} = {X}_{1}lg\frac{{m}_{i}}{S} + {X}_{2}\frac{1}{lg t} + {X}_{3}{e}^{t/{t}_{max}} - {X}_{4}{e}^{CI}$$
6
The calculated corrosion rate (Vc [g/m2h], also referred to along the paper as the simulated corrosion rate or corrosion rate forecast) accounts for the presence of the inhibitor via the inhibitor concentration (CI, [%]); ensures the industrial need of using simple parameters for the prediction via the initial pickled mass (mi, [g]) and the metallic surface (S, [m2]); provides dynamic predictions via the batch timing along the entire pickling process (t, [h]) and the maximum time in which the pickling bath is going to be used (tmax, [h]). X1 − 4 are specific empirical coefficients ensuring the model’s accuracy and suitability for the case study.
Material losses are an important factor that needs to be prevented not only for its structural implications but for the economic ones as well. To keep track of this the decision-making tool provides the estimated mass loss vs the experimental mass loss graph
Further, the calculated mass loss (Δmc [g], also referred to along the paper as the simulated mass loss or mass loss forecast) is obtained with the help of Eq. (7) using the corrosion rate calculated with Eq. (6) using the already known metal surface and the time passes since the bath started being used.
$${\varDelta m}_{c} = {V}_{C}St$$
7
To determine the model empirical coefficients an optimization algorithm was developed in MATLAB. The starting point of the algorithm is the MATLAB build in function fmincon, which uses an objective function that calculates the difference between the two corrosion rates (estimated vs calculated) at the same point in time based on the correlation coefficient (R2) value as criteria for the prediction accuracy. A set of non-linear constraints have been specified in an additional function to eliminate the possibility of having negative unnatural estimated values of the corrosion rate. In the same order of ideas lower boundaries for the decision variables (X1 to X4) have been set to ensure a proper correlation between the input variables and the corrosion phenomena. The starting point for the decision variables (X1 to X4) has been set to zero.
Optimum values of the empirical coefficients were included in the model for calibration purposes and model has been further subjected to verification using an additional set of measurements (at 10% CI), not involved during model optimization.
The simulation tool results are visual representations of the forecasted corrosion rate and mass loss corresponding to each set of input variables (initial conditions) and comparative representations comprising results corresponding to multiple initial conditions.