Mixed Integer Optimization (MIO)

Powerful capabilities for process synthesis and equipment configuration decisions

There are many situations in chemical engineering where discrete decisions need to be considered. Typical examples are decisions on equipment configuration, selection of equipment or pipes from standard sizes, flow routing options, numbers of operating trains, or process synthesis decisions.

gPROMS’s industry-leading optimization capabilities allow integer or discrete decision variables – for example, the number of stages in a distillation column – to be included along with continuous variables such as column diameter.

The resulting Mixed Integer Optimization (MIO) problem is solved rapidly and robustly using specialised optimization solvers. MIO can be applied to both steady-state and dynamic gPROMS models.

Typical examples

MIO can be used to identify and create value virtually anywhere in chemical engineering. Some typical application areas are shown below.

Distillation column design

A typical MIO example is the steady-state design of a distillation column, where the number of trays and feed and side draw locations are key design decisions.

The MIO capability in gPROMS can be used to find the optimal configuration while simultaneously optimizing continuous variables such as column diameter and reflux ratio.

The objective function used in such an application is typically an economic one that includes both capital and operating cost.

Selection of optimal control schemes

The selection of the optimal control scheme for handling all anticipated disturbances to a system is another key decision in process engineering.

MIO can be used to select the best scheme while simultaneously providing optimal values for variables such as:

  • Controller tuning parameters
  • Key equipment design parameters such as column diameter
  • Optimal operating (for example, startup) policy.

Process synthesis

MIO can be used to determine the optimal process configuration from a number of proposed alternatives, taking into account

  • equipment and process constraints
  • product specification requirements
  • annualised capital and operating cost

The “separation options” in the diagram above can be different configurations of distillation columns, for example, or entirely different separation processes (for example flash units or membranes)

MIO – the economic benefits

MIO opens new opportunities in advanced areas such as the simultaneous design of processes and their control systems, potentially leading to significant economic benefits

This can be seen in the case study shown below, where optimal design of an coupled azeotropic distillation system results in some significant changes from the base design, and significant improvements in annualised operating profit.

  Existing design Design using MIO
Feed location 14 8
Draw location 22 18
Q column I (MW) 19.5 14.7
Q column II (MW) 0.87 2.45
Capital cost M$/year 0.63 0.56
Operating cost M$/year 4.37 3.56
Total cost M$/year 5.00 4.12

Types of integer decision in gPROMS optimization

The MIO facilities in gPROMS cater for the following discrete decision types:

  • Integer decisions – for example, the number of trays in a distillation column or the optimal number of reactors necessary to provide the required conversion and selectivity.
  • Binary decisions – for example, to determine whether an item of equipment needs to be included or not; or to obtain an optimal “bang-bang” profile for a time-varying on-off control.
  • Enumerated decisions – where the optimization chooses an item out of a given set – for example, selecting a batch reactor out of a set of standard “off-the-shelf” sizes; or obtaining an optimal control profile for a “staged” heater, i.e. one that can operate only in certain distinct modes, e.g. OFF, LOW, MEDIUM or HIGH.
  • “Special Ordered Set of type 1 (SOS1)” decisions, a set of binary decision variables from which only one may have a value of 1. An example is feed tray location in a distillation column, where a number of locations may be proposed but only one may be selected by the optimizer.