Page 125 - Sustainability in the Process Industry Integration and Optimization

102 Cha p te r F o u r

maximum shaft power) and to part-load performance; the shaft
power is modeled as a function of the steam mass flow that is known
as the Willan line. This model was extended to condensing steam
turbines by Shang (2000). All these works follow the same model
structure and employ the same equations; however, they use different
values for the turbine regression coefficients.
The intercept of the Willan line was mapped by Mavromatis and
Kokossis (1998) and by Shang (2000) as identical to the turbine energy
losses, also assuming a fixed loss rate. Varbanov, Doyle, and Smith
(2004) introduced improvements to those models by (1) recognizing
that the Willan line intercept has no direct physical meaning and is
simply the intercept of a linearization, and (2) accounting for both
inlet and outlet pressures of the steam turbines. These improved
steam turbine models have been incorporated into methodologies for
simulating and optimizing steam networks; they have also been
used to target heat and power cogeneration by assuming a single
large steam turbine for each expansion zone between two consecutive
steam headers.

4.6.5 Advanced Total Site Optimization and Analysis
A model for optimizing the utility system serves as a tool for reducing
site operating costs related to energy and for analyzing the
thermodynamic limitations of energy conversions. An advanced
approach to these concepts, known as top-level analysis, is one that
allows “scoping” which site processes to target for Heat Integration
improvement (Varbanov, Doyle, and Smith, 2004). Consider the utility
system shown in Figure 4.69 (Smith and Varbanov, 2005), whose
operating properties have been optimized for the given steam and
power demands.
Suppose it were possible to reduce the HP steam demand—for
example, by improving the energy efficiency within the processes
that use HP steam. What, then, would such a saving in steam actually
be worth? Reducing HP steam demand means that less steam needs
to be expanded from the VHP level, which could lead in turn to less
power cogeneration and increased import of power. As a support
tool for deciding how best to utilize the potential steam excess and
estimate the value of potential steam savings, Varbanov, Doyle, and
Smith (2004) introduced the concept of marginal steam price. This
characteristic captures the change in a utility system’s energy cost
per unit change in steam demand, and it is specific to a given
combination of steam header and operating conditions. By
optimizing the utility system at gradual successive reductions of
potential steam demand on the headers, it is possible to obtain a
curve of the marginal steam price versus the savings that could be
obtained. The marginal price curve for the utility system in