# Understanding optimizers

## Given the number of process variables interacting at most plants, finding the optimum mix to maximize profitability is likely beyond manual capabilities.

Optimization can mean different things to different people, so for purposes of this discussion we will concentrate on applying linear programming (LP) techniques, either online or offline, to determine the minimum cost solution, and therefore highest profitability for a set of targets or setpoints to drive a process. In order for LP to evaluate process conditions, it needs a process model to help it evaluate process conditions for a potential solution. In all cases the LP and model must respect all the constraints which exist in the process, including safety-related limits such as pressure, product quality specifications, and equipment constraints such as fluid handling or metallurgical limits.

**Why use optimization?**

In today’s operating environments with extensive heat integration, numerous process quality targets, and hundreds of constraints, the decision to drive a process in one direction or another or to push a constraint is anything but straightforward. Gasoline, for example, is a blend of as many as 12 or even more separate streams coming from refinery process units. These streams combine in a ratio control system to create a given gasoline grade. Each component has a cost, and the individual properties for that component will affect the properties of the final product.

For any given gasoline grade there are at least as many product specifications as there are properties, both minimum and maximum. Moreover, for each component used in the blend, there are also constraints related to availability, feedstock tank inventory, product tank inventory, rundown from the unit, and pumping constraints, to name only a few. Finding the one value of each component that delivers the final specification while honoring the constraints at the lowest cost requires evaluation of thousands of possible combinations. Optimizers can deliver this operating point faster and at significant savings over one that a traditional best practice might suggest. This can save a refinery several million dollars per year, while reducing product quality giveaway, eliminating rework, and improving overall production.

**Open vs. closed loop**

Closed-loop optimizers can be found in offsite product blending operations, process units, MPC (model predictive control) advanced controllers, planning and scheduling platforms, and raw material purchasing tools. These typically run on a minute-to-minute basis, but rigorous optimizers can run less frequently, from every few hours to once per day, with planning tools running on a weekly or monthly basis. In all these applications, optimizers are an integral part of the real-time system and therefore must have dynamic behavior and must incorporate best automation practices to make any online closed-loop control system robust and reliable.

On the other end of the spectrum, the planning department looks at the horizon measured in weeks and even months. In this case the optimizer is run in an offline mode to try out hundreds or even thousands of potential scenarios to get the best set of operating plans developed for the plant for the available raw materials to be purchased. LP is the main workhorse here, and hundreds of product qualities are considered along with a multitude of operating constraints. Optimizers are adapted to run in different scenarios with one of the most fundamental demarcation points being the online closed-loop service or the open-loop planning case. In the closed-loop case, such as in MPC, the LP is almost always used with a multivariate dynamic controller to decouple the interactions in the process and help drive the LP targets toward the optimum solution in a short amount of time and a stable manner. In these cases, the dynamic controller with the LP uses an empirical model of the process dynamics. This is just a fancy word for regressed models from process data that contain information on process dynamic behavior.

**Process models**

Earlier we mentioned that a model of the process was necessary for the optimizer to evaluate process conditions at the new operating point. For example, let’s ask, “If we increase the feed to the unit by 5%, what will the exit temperature from the reactor be, and does this violate any known constraints?” There are two broad classes of models, empirical and rigorous. Empirical models are derived from data which is usually processed through a tool that performs some sort of regression using techniques such as least squares or partial least squares. They are relatively quick to develop, are based on process conditions, and contain dynamic features of the process. However, they are limited in that they generally don’t predict very well outside of the range of data on which they are based.

Rigorous models result from first principle relations that do not depend on process data, although almost all rigorous models are validated with data from an actual process. They can predict process values over a much wider range and are better at predicting such things as nonlinear behavior in the steady state.

Although we have been discussing optimization tools in the LP context, many commercial offerings are capable of nonlinear programming (NLP) solutions. These are useful for certain types of applications like energy management, where major pieces of process equipment, such as a turbine, might not always be present when the solution is determined. These difficult situations call for another solver variant, the mixed-integer nonlinear program (MINLP). The common denominator for all these cases is that the tool will determine the best point or mode of operation as already discussed.