An algorithmic approach to the optimization of process cogeneration

Abstract

In most industrial processes, there is a significant need for electric power and for heating. Process cogeneration is aimed at the simultaneous provision of combined heat and power. The net result is usually a reduction in the overall cost and emissions of greenhouse gases. Therefore, there is a significant need for the optimal design of process cogeneration systems. This objective of this paper is to introduce an algorithmic approach to the optimal design of process cogeneration systems. Focus is given to the interaction of the power cycle with the process heat requirements. Because of the need for explicit thermodynamic expressions, a new set of thermodynamic correlations of steam properties is developed for proper inclusion within a mathematical-programming approach. An optimization formulation is developed to provide a generally applicable tool for integrating the process and the power cycle and for identifying the optimum equipment size, operating parameters (such as boiler pressure, superheat temperature and steam load). The objective can be chosen as minimizing the cost, satisfying the heat requirement of the process, or producing the maximum possible of power. A case study is solved to illustrate the applicability of the devised approach and associated thermodynamic correlations.

Appendix: Expressions for isentropic efficiency of the turbine

For a given turbine, the isentropic efficiency is a function of the flow load and hardware parameters provided by the manufacturer. This expression is based on Willan’s line that correlates the load to the power output. The isentropic efficiency is expressed by Eq. 21 (Mavromatis and Kokossis 1998).

$$ \eta_{\text{is}} = \frac{6}{5B}\left( {1 - \frac{{3.41443 \times 10^{6} A}}{{\Updelta h_{\text{is}} M^{\max } }}} \right)\,\left( {1 - \frac{{M^{\max } }}{6M}} \right) $$

(21)

A and B are constants dependent on the turbine and are functions of the inlet saturation temperature and the flow rate is measured in lb/h. A good approximation, within 2%, is given by the following straight line segments (Mavromatis and Kokossis 1998; Varbanov et al. 2004):

$$ A = a_{0} + a_{1} T^{\text{sat}} $$

(22)

$$ B = a_{2} + a_{3} T^{\text{sat}} $$

(23)

Another expression of the isentropic efficiency developed by (Varbanov et al. 2004) is:

$$ \eta_{\text{is}} = \frac{{n.m - W_{\text{INT}} }}{{m.\eta_{\text{mech}} .\Updelta H_{\text{is}} }} $$

(24)

Whereas n and W _int are the slope and the intercept of the linear Willan’s line respectively and given by this equation:

$$ W_{\text{int}} = \frac{L}{b}(\Updelta H_{\text{is}} - \frac{a}{{m_{\max } }}) $$

(25)

$$ n = \frac{L + 1}{b}\left( {\Updelta H_{\text{is}} \,m_{\max } - a} \right) $$

(26)

With L is to be estimated by correlating the performance of each specific turbine. The parameters a and b depends on the type pf pressure, maximum power load and the saturation temperature differences as in the following table (Table 4; Smith 2005).

Table 4 The regression coefficients used in the isentropic efficiency equation

$$ a = a_{0} + a_{1} \,\Updelta T^{\text{sat}} $$

(27)

$$ b = a_{2} + {\text{a}}_{3} \Updelta T^{\text{sat}} $$

(28)