## Ln Kbj Aj Bj1Tj 1T

where T* is a reference temperature for the K value correlation. Outer loop variables, Aj and Bj, are generated for each stage from a reference KbjRef of a composite component:

ln KbjRef = X Wi ln Kji(actual)

where the wi are weight factors. The temperatures and compositions used to get the Kji(actual) are the latest from the inside loop. Simple relative volatilities are among the outside loop variables, and are used in the Kb method to calculate the temperatures and whenever K values are needed in the inside loop:

aji = Kji(actual)/KbjRef

These simple relative volatilities change little over the range of temperatures that is seen on a given stage and greatly simplify temperature and composition calculations in the inside loop. For nonideal mixtures, an activity coefficient for each component accounts for composition effects in the inside loop. This activity coefficient has a simple model, similar to the Kb model:

ln y* = aji + fyx where the new outer loop variables, ajl and j for each component are determined from the actual activity coefficient model at the current stage temperature and stage composition.

The simple K values used in the inside loop are easily determined from:

Simple models for the enthalpy of a phase are also used to reduce effects such as that caused by components moving past their critical conditions. Thus, the outside loop calculation consists of updating the terms of the simple K value, activity and enthalpy models which are updated after each inside loop solution using the latest temperatures and compositions from the inside loop.

The inside loop consists of the actual calculation of the MESH variables using the simple K value and enthalpy models. Boston initially used an inside loop solution method similar to a bubble point method and from that it may appear that the Boston method is most appropriate for narrow-boiling mixtures. However, the forcing style of the method also allows it to work well for wide-boiling mixtures. The Boston method works well for tall, high purity (superfrac-tionator) type columns, but has been extended to absorbers, to three-phase distillation, and to reactive distillation by using other arrangements of the MESH equations.

The Boston method includes a middle loop to allow for column specifications and constraints. The arrangement of equations in the inner loop, where the solution of the MESH variables occur, may allow for only a few control or specified variables, such as fixed reflux ratio and product rates. The middle loop adjusts the control variables to meet the specifications. The middle loop can be built as an optimization method with process specification equations and economic objectives and constraints.

Russell's (1983) method differs from Boston's in the inside loop by a solution method of the MESH equations that includes specifications for product quality, stage temperatures, internal flow rates, etc., without the use of a middle loop to solve these. Here, for each heat exchanger in the column, plus each additional side product, an additional specification and operating variable is added to the problem. Russell's method has been found to work well for refinery fractionators with side strippers and other similar columns.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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