Use of Surrogate Models In Water Network Synthesis

INTRODUCTION

The water is used in large quantities by the chemical industries, for being such a strategically resource it is the aim of severe restrictions imposed by environmental surveillance and control organisms, which should be followed strictly, causing a significant increase of its cost.

Several studies were developed with the aim of reducing water consumption through segregation and integration of wastewater streams. The water network problem was initially formulated by Takama et. al.(1980). After the initial problem formulation there were no major changes in the models for wastewater treatment processes synthesis. The research in this area focused mainly in the development of new methods for solving the NLP (nonlinear programming) or MINLP (mixer integer nonlinear programming) generated in the superstructure model formulated by Takama. Although it remained dormant, research in this area has raised up in the mid 90s, with the works of Alva-Argaéz (1998), Galan and Grossmann (1998), Huang et al. (1999), Bagajewicz (2000) and continues to increase steadily from 2000.

According to Jezówski (2010) "Just a few studies considered the most detailed treatment process models, however these approaches are often limited to a single technology for treating and of a fixed type." In Jezówskixs opinion "the crux involves the application of more rigorous processes models: water use units, as well as, effluent process treatment." However, the use of phenomenological models in superstructure process synthesis could be unfeasible due to its high computational time.

Oil refineries are large consumers of water, producing wastewater with high concentrations of H2S, oils and salts, because of the direct contact processes between water and oil (e.g., desalting, stream stripping and many washing operations) (Wang and Smith, 1994).

The most used process for such wastewater treatment is the steam stripper, where the volatile compounds are removed by distillation of the heavy component, water. The working temperature of this type of equipment is usually high, close to the water bubble point. Due to the temperature, the steam stripping allows the removal of compounds heavier than air stripping processes do.

The steam stripper is a device that consists of a column with previously heated wastewater feed at the top, and with a steam feed at the bottom. The phase contact takes place down the column while the wastewater becomes leaner and the steam more enriched with contaminants respect, Zygula T. M. (2008).

The objective of this contribution is the synthesis of a water treatment systems at petroleum refineries using a steam stripper surrogate model, for the. This surrogate model includes equipment construction variables (number of stages and steam flow) and process variables (feed conditions: flow, temperature and contaminant concentrations). The data for the adjustment of the surrogate model are generated from process simulations in, ASPEN PLUS.

METHODOLOGY

The mixture to be treated contains H₂S, oils and salts. As a simplifying assumption, we adopted the n-hexane to represent the oils and used NaCl as the contaminant salt of the process. The electrolytes dissociation equations in aqueous medium, where the equilibrium constants are temperature function, are considered.

There are several thermodynamic models capable of predicting the thermodynamic behavior of liquid vapor mixtures, but the mixture to be treated is formed by a combination of electrolytes, which generate non-idealities in the system, requiring a thermodynamic model that takes into account their behavior. The model selected for this system was the electrolyte-NRTL (Lee S. Y. et. al., 2004)

A stripper can use direct steam at  the plant boiler or a column bottom reboiler. Moreover, we can choose whether or not to use a condenser, to integrate energetically the feed and output streams and to preheat the feed stream. Fourteen equipment variations are considered for the simulations.

It is usual to use the treatment cost as the objective function in the wastewater treatment synthesis so, the fixed and operating equipment cost are calculated using cost graphics updated by the Marshall & Swift's cost index in the third quarter of 2010 (Peters, 2003). In the objective function, TAC (total annualized cost), the fixed cost is multiplied by an annualized factor, that divides the equipment fixed cost during its life cycle, taking into account the interest rate.

The data are obtained from process simulators with operating conditions varying. The input variables that are changed in the stripper operating ranges are the flow rate, the temperature and contaminants concentration in the feed stream, the number theoretical stages and the flow of steam. The data obtained from the simulations are normalized, and then used in the regression of a complete linear (with respect to the parameters) model  for the following output variables: TAC, contaminants concentrations, temperature and flow of output stream.

The regression is performed using the least squares method. This complete model is then reduced using the PCA method (principal component analysis). The validation of the surrogate model is made by cross-validation.

The model for the stripper is a MINLP composed by the mass balance of a mixer, stripper surrogate model and splitter.  Binary variables are used to represent decision variables for the stripper type and their sum is imposed to be 1.

CONCLUSIONS

A steam stripper surrogate model was formulated which decreases the number of variables of the system, reduces the great sensitivity to the initial guess and its complexity, without affecting much its prediction in the specific range. In comparison to the usage of a phenomenological model there is a large economy in computing time in the water network synthesis, appart of the simplicity of implementation in an optimization platform such as GAMS.

REFERENCES

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Bagajewicz M., “A review of recent design procedures for water networks in refineries and process plants*1”, Computers & Chemical Engineering 24, n. 9-10 (2000): 2093-2113.

Galan B. e Grossmann I. E., “Optimal Design of Distributed Wastewater Treatment Networks”, Industrial & Engineering Chemistry Research 37, n. 10 (1998): 4036-4048.

Huang C. H. et al., “A Mathematical Programming Model for Water Usage and Treatment Network Design”, Industrial & Engineering Chemistry Research 38, n. 7 (1999): 2666-2679.

Jeżowski J., “Review of Water Network Design Methods with Literature Annotations”, Industrial & Engineering Chemistry Research 49, n. 10 (2010): 4475-4516.

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