(529c) Modeling Chromate Removal for Drinking Water Application Using the Method of Moments to Identify Key Parameters

Chromium-based compounds, such as Chromates and dichromates, are widely used in the plating industry to protect metals against corrosion. Unfortunately, chromium is a highly oxidizing metal that can be carcinogenic at low parts per billion concentrations. The European Union has restricted its use since 2002 while the EPA limited total chromium in water to 100 parts per billion (Directive 2002/95/EC of the European Parliament and the council) [1]. According to the USGS report, the EPA proposed in 2010 to "classify Cr (VI) as likely to cause cancer in humans when ingested over a lifetime” [2]. As the chromate ion is a negatively charged oxyanion that needs to be below 10 ppb in drinking water, a quaternary amine anion exchanger resin is the standard purification step used. In this work, the gel type strong anion exchanger, Purolite A600E, was evaluated for chromates removal from water containing an abundant amount of typical anions such as chlorides, sulfates, and bicarbonates to reflect real-life situations based on the hazardous nature of chromate and the necessity in removing it at concentrations below 20 ppb.

Objective:

As several fixed-bed sigmoidal models exist to predict the ion exchange process such as the Yoon-Nelson, the Clark, and the Thomas models [3], it is necessary to understand how process/operating conditions such as flow rates and inlet chromate concentrations affect resin capacity and therefore the performance of the ion exchange system. The objective of this work is to identify a working dynamic model where the system and resin characteristics are reflected in the model to improve the predictability of the chromate removal system. This is accomplished by the following objectives: (i) understanding the kinetics of chromate removal by identifying a suitable model [4], (ii) integrating the kinetics to the process operations via a detailed moment-based modeling approach, and (iii) optimizing the process operation using the models identified in objectives (i) and (ii).

Methodology:

Most existing models follow the general sigmoidal function, seen in (eq. 1) representing the ion exchange system is usually in the form seen in (eq. 1).

Normalized concentration = ψ = C/C₀ = 1/[1+exp (a-bt)] (1)

Where C – outlet concentration, C₀ – inlet concentration, ψ – normalized concentration, and t - time

Model discrimination was necessary to reflect process characteristics such as flow rates and inlet concentrations. Based on that necessity, the Thomas model was chosen for reflecting such characteristics as seen in (eq. 2).

Thomas model = ψ = C/C₀ = 1/[1+exp⁡(K_T q_mÏ„ - K_T C₀ t)] (2)

Where K_T - Thomas constant parameter, q_m – resin maximum capacity parameter, Ï„ – contact time (V/ν₀), V – volume of resin in column, and ν₀ – flow rate in column

The parameters in the model will be calculated by comparing the predicted calculated results to the experimental measurements by minimizing the residual sum of the squares error function (eq. 3).

Residual Sum of Square Error = ∑[(ψ_cal - ψ_exp)/ψ_cal ]² (3)

While the method of moments is limited in many publications to pulse data in chromatographic separations, the method was reformulated and used on the column and the resin systems. The moments were evaluated with respect to the amount of chromate in the effluent and on the resin respectively [4]. The moment equation used is seen in (eq. 3).

µ_i = ∫_t=1^∞ tⁱ C dt (4)

m_i =∫_t=1^∞ tⁱ q dt =∫_t=1^∞ tⁱ (C₀-C)ν₀ dt (5)

where μ_i – ith moment on the column system, m_i – ith moment on the resin system, and q – concentration on the resin system.

These moments will be used to calculate the parameters in the Thomas model and compared to the values obtained from minimizing the residual sum of square error.

Using the method of moments, different flow rates and chromate concentrations are used to confirm the accuracy of the moments in predicting the Thomas model representation of the chromate removal process.

Summary:

Due to the hazardous nature of chromates at low concentrations, it is important to use the appropriate modeling techniques to maximize the performance of the ion exchange purification step. The fixed-bed Thomas model was picked to predict the ion exchange process performance since it considers some important process characteristics such as inlet resin concentration and flow rates in its equation. To improve the control aspects of this process, the method of moments was used to display characteristics such as the maximum resin capacity (zeroth moment of the resin system) and longer processing time (first moment of the column system). The model was checked successfully for different inlet chromate concentrations and contact times.

Since the anion exchanger is typically used once due to the toxicity of chromium being removed, it is necessary to maximize the anion exchanger capacity. This is achieved by applying optimal control[6] on the system by maximizing the objective function associated with the resin loading capacity at a defined breakthrough point with the control variable being the flow rate into the resin process.

Keywords: Thomas Model simulation, model optimization, Chromate extraction, method of moments.

References:

1. "Directive 2002/95/ec of the European parliament and of the council" (PDF). Eur-lex.europa.eu. Retrieved 3 July 2015.
2. Gibbons, Catherine. “IRIS Toxicological Review of Hexavalent Chromium (2010 External Review Draft), IRIS US EPA” 2010, 4.
3. Nur, T., W. G. Shim, P. Loganathan, S. Vigneswaran, and J. Kandasamy. “Nitrate Removal Using Purolite A520E Ion Exchange Resin: Batch and Fixed-Bed Column Adsorption Modelling.” International Journal of Environmental Science and Technology 12, no. 4 (April 2015): 1311–20.
4. Li, Xue. “Meeting the New California MCL for Hexavalent Chromium with Strong Base Anion Exchange Resin”, ProQuest 10124393, University of California – Davis, 2016.
5. Goltz, Mark N., and Roberts, Paul V. “Using the Method of Moments to Analyze Three-Dimensional Diffusion-Limited Solute Transport from Temporal and Spatial Perspectives”. Water Resources Research, Vol 23, No 8, Pages 157
6. K. M. Yenkie and U. Diwekar, “Stochastic Optimal Control of Seeded Batch Crystallizer Applying the Ito Process,” Ind. Eng. Chem. Res., p. 120604103933002, Jun. 2012, doi: 10.1021/ie300491v.