Mathematical modeling of the multiple effect evaporation (MEE) desalination process has been carried out to determine the effects of the important design and operating variables on the parameters controlling the cost of producing fresh water. The model assumes the practical case of constant heat transfer areas for both the evaporators and feed preheaters in all effects. In addition, the model considered the impact of the vapor leak in the venting system, the variation in thermodynamic losses from one effect to another, the dependence of the physical properties of water on salinity and temperature, and the influence of noncondensable gases on the heat transfer coefficients in the evaporators and the feed preheaters. The modified fixed-point iterative procedure is used to solve the large number of highly nonlinear equations describing the MEE desalting system. The algorithm consists of 10 calculation blocks and 6 logical blocks. The algorithm is implemented using L-A-S computer aided language. Results show that the heat transfer coefficients increase with the boiling temperature. Also, the heat transfer coefficient in the evaporator is always higher than that in the feed preheater at the same boiling temperature. The plant thermal performance ratio is nearly independent of the top brine temperature and strongly related to the number of effects. The specific heat transfer area increases by raising the number of effects and reducing the top brine temperature. The effect of the top brine temperature on the specific heat transfer area is more pronounced with a larger number of effects. The required specific heat transfer areas at a top brine temperature of 100°C are 30.3% and 26% of that required at 60°C when the number of effects are 6 and 12, respectively. The specific flow rate of cooling water is nearly constant at different values of top brine temperature and tapers off at a high rate as the number of effects is increased. Two correlations are developed to relate the heat transfer coefficients in the preheater and the evaporator to the boiling temperature. Design correlations are also developed to describe variations in the plant thermal performance, the specific heat transfer area, and the specific flow rate of cooling water in terms of the top brine temperature and the number of effects.

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Production planning in the petrochemical industry requires a model that can account for the different interactions, needs, and features and provide at the same time suitable mathematical representation. In this work, a model with an environmental objective is presented. The system is formulated as a mixed-integer linear programming model where new value-added products are produced from the basic feedstock chemicals. From the superstructure of the technology alternatives, the optimal set of processes is selected with the objective function of sustainability. The quest for pollution prevention and increased pressure and demand for environmental considerations makes sustainability an important objective function. In this study, sustainability is quantified by a health index of the chemicals and increasing profit represented by processadded value. The model is applied to the case study of planning the development of the Kuwait petrochemical industry. Results give an optimal structure for the development and prove that simple indicators can represent sustainability, giving good results in selecting environmentally friendly processes and at the same time being profitable.

The main objective of this work is to develop an optimization model for the supply chain of a petrochemical company operating under uncertain operating and economic conditions. First, a deterministic model is developed and tested, and then uncertainties in key parameters are introduced. The proposed objective function is based on optimizing the system resources by minimizing the total production costs and raw material procurement, as well as lost demand, backlog, transportation, and storage penalization. A stochastic formulation is then developed, which is based on the two-stage problem method with a finite number of realizations. The optimization model is tested on a typical petrochemical company, manufacturing different grades of polyethylene, operating at a single site and using two reactors. Uncertainties are introduced in demands, market prices, raw material costs, and production yields. The main conclusion of this study is that uncertainties have a dramatic effect on the planning decisions of the petrochemical supply chain. Market demand was found to be the most important parameter, exhibiting a strong impact on the production decisions, followed by the production yields. The stochastic approach was found to be quite effective in handling uncertainties, and the resulting production plans were found to have a rather low expected value of perfect information (EVPI).

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