Process optimization involves the application of mathematical techniques & tools to find out the best possible solution from several available alternatives for the purpose of the maximum Return On Investment (ROI).

The main purposes of process optimization are:

- To increase the productivity with lowest applicable cost.
- To eliminate losses as much as possible.
- To utilize lower cost feed stock, energy with acceptable quality level.
- To maximize the operating capacity of process equipment.
- To design & operate the plant at the most optimum condition. To attain new or most efficient designs and to determine the most desirable operating conditions and safe operation.

So in a sentence all the above can be mentioned as **Process Optimization can increase production rate to its maximum with maximum profit and minimum waste generation and impact on environment**. By performing process optimization, we aim to obtain the best result under given circumstances.

In this article, we will understand the requirements for process optimization basics and techniques.

## Advantages of Process optimization

With process optimization we get improved plant performance like

- Increase Yield.
- Enhance Availability.
- Reduce energy consumption.
- Reduce maintenance cost.
- Reduce failure in equipment.
- Minimize the unplanned shutdown.

## Process Optimization Examples

The following paragraph lists down a few examples of Process optimization for maximizing profit:

- Design of HEX network (Heat Integration).
- Real time optimization of a distillation column.
- Model predictive control.
- Operations planning & scheduling.
- Pipeline sizing, Reactor sizing, Distillation column (CAPEX/OPEX).
- Predictive Maintenance (Machine Learning Applications) – Downtime Planning.

The objectives of refinery optimization (TARGET – Maximize Profit) include:

- Minimize crude OPEX at refinery.
- Optimize refinery crude mix.
- Optimize offspec generation and optimize overall product mix and dispatch.
- Minimize quality giveaway.
- Optimize fuel consumption, minimize losses.
- Optimize utilization of the assets.
- Optimize inventory management.
- Optimize capacity utilization and shutdown planning.
- Optimize unit operations maintaining highest standards of safety, catalyst life and activity, etc.

## Process Optimization Framework

- All optimization problems are stated in some standard form.
- One need to identify the essential elements of a given problem and translate them into a prescribed mathematical form.
- Requirements for application of optimization problem:
- The design variables.
- The constraints.
- The objective (Target) function (Max / Min).
- The process model.

### Process Optimization Framework-Design Variables

The engineers need to know the design variables that affect the system.

- Example: reactor temp, feed rate, No. of trays In column, reflux ratio, Batch time and reactor yield.
- A practical problem may involve many design variables.
- Some of these maybe highly sensitive and heavily influence the process being optimized. Choose these as design variables and others (not so sensitive variables) maybe kept constant.
- Note: If all the design variables are fixed, there is No scope for optimization.

Thus one or more variables must be relaxed so that the system becomes an Under Determined System which has at least principle infinite number of SOLUTIONS.

### Process Optimization Framework – Objective Function

A suitable objective function (cost function) is defined in terms of design variables and often prices parameters. The objective function may be technical or economic, which needs to be either maximum or minimum

#### Examples of economic objectives:-

- Maximum profit.
- Minimize cost of production.

#### Examples of technical objectives:-

- Maximize reactor yield.
- Minimize size of equipment.
- Minimize environmental impact.

Note:- technical objectives (Target) are ultimately related to economics

In practical process plant there would be multi objective functions to be optimized in one case only, therefore, there are more than one objective functions.

### Process Optimization Framework – Constraints

The constraints requests some additional relationships among the design variables and process parameters. The constraints originates because design variables must satisfy certain physical phenomena & certain resource limitation.

Example: Variable bounds: 0<x<1 (Don’t exceed the range at any direction) (Max / Min)

**Equality constraints:**Sum of mole fraction should be unity such as for component balance equation in distillation column.**In equality constraints:**In packed reactor, process temp should be less than the catalyst deactivation temp/acidic conditions PH<7, stress developed any where in a component should be less than the maximum allowable stress

### Process Optimization Framework – Process Model

- A process model (HYSYS) is required to describe the manner in which the design variables are related. The process model also tells us how the objective function is affected by the design variables.
- A model is a mathematical equation or is a collection of several equations that define how the design variables are related and the acceptable values these variables can take.
- Optimization studies are carried out using a simplified (but reasonably accurate) model of a real system.
- Note:- working with real system (life) is time consuming, expensive, risky & that’s why you need to work on a model rather than life case.

## Classification of Process Optimization Methods

**Based on the nature of equation involved, process optimization methods are classified as:-**

- Linear Programming (LP)
- Non – Linear Programming (NLP)
- Sequential Quadratic Programming (SQP)

**Based on the nature of design variables, process optimization methods are divided as:-**

- Continues optimization (Linear Programming)
- Integer programming (IP) (integer values)
- MILP mixed integer (Linear & Integer Programming)
- MINLP (Non-Linear & Integer Programming)

Based on number of object functions, process optimization methods are grouped as:-

- Single
- Multi

## Problem Formulation for Process Optimization

- In order to be able to perform optimization on any process, firstly you will need to formulate the optimization problem.
- In order to formulate a proper optimization problem, you will need to digest the following expressions:
- Process Models for optimization
- Degrees of freedom analysis
- Optimization problems in chemical engineering

### Process Models for Optimization

Optimization requires use of mathematical techniques for maximization or minimization of an objective function (Variable required to be approached – Target).

Note: With advent of computers, optimization have become part of computer-aided design.

• In order to use optimization algorithms on computers, we must have a quantitative model available to compute the responses of objective function.

**A process model is a set of equations that imitates reality and cannot incorporate all features the real process. However, a reasonably accurate model saves us time and money as we can avoid repetitive experience & measurements.**

#### Classification of process models:-

- Theoretical Models.
- Database Models (Practical).

#### Other classifications:-

- Linear vs non linear models
- Steady state vs non steady state

## Degrees of Freedom Analysis for Process Optimization

The degrees of freedom analysis gives us the number of design variables that can be changed during optimization process to obtain the optimal solution.

Degrees of freedom, DOF = No. of variables – No. of linear independent equations (As in Algebra)

- If DOF = 0, unique solution exists –
**NO optimization is possible** - If DOF> 0, under determined system – Infinite solution exist &
**optimization is possible** - DOF< 0, over determined system –
**No solution exists**

## Introduction to Linear Programming

Linear Programming is one of the most effective and widely used optimization techniques. A linear programming model seeks to Maximize or Minimize a linear function, subject to a set of linear constraints. The linear model consists of the following:

- A set of design variables
- An objective function which is a linear function of design variables
- A set of linear equality or inequality constraints

### How do the linear constraints arise?

**Design limitation:**For new established projects then limitation might arises from the design Codes / Standards / Specifications. For existing facilities, the design basis of the facility / asset will identify the limits which have to be respected.**Production limitation:**– equipment limitation, storage limits, market requirements.**Supply limitation:**Raw material / Feedstock limitation**HSE restriction:**– allowable operating ranges for temperature & pressure. Also respecting the environmental legislations with regards to the emissions and effluents generated from the process plant.**Physical property specification:**– product quality constraints when a blend property can be calculated as an average of pure component.

### How to formulate linear programming model:-

- Determine design variables
- Determine objective function/target
- Determine constraints

## Case Study: Hydrocarbon Pipeline Optimization using Simulation

**Objective:** Optimally determine the best suited pipeline size considering the material cost of the pipe, pump (CAPEX) and the associated running cost of pumping system (OPEX).

**Constraints:**

- Pipeline ANSI rating 300# and 600#.
- Pipeline Length 125 km.
- Diesel design flow of 725 m³/hr.
- Operational hours of 16 hrs.
- Potential pipe sizes (X), of 16”, 18” and 20”.
- ACCE (Aspen Capital Cost Estimator) for pipeline cost estimate.
- APEA (Aspen Process Economic Evaluation) for pump fixed and running cost

**Case 1- Base Case:** (Refer Fig. 1)

- Design Flow 725 m³/hr.
- ANSI rating 600#.
- Operational hours: 16 hrs.
- Pipe ID: 16”.

**Case 2:** Refer Fig. 2

- Design Flow 725 m³/hr.
- ANSI rating 300#.
- Operational hours: 16 hrs.
- Pipe ID: 18’’.

**Case 3:** Refer Fig. 3

- Design Flow 725 m³/hr.
- ANSI rating 300#.
- Operational hours: 16 hrs.
- Pipe ID: 20”.

**Key Results (Fig. 4):**

### Conclusions of the above case study

Case 2 can be disqualified where the shut off pressure of the transfer pump will exceed the design pressure of 47.7 barg.

- Case 1 and Case 3 are technically viable where them meet the Flow requirements and the design pressure of 300# and 600# respectively.
- Case 1 (16” pipeline – ANSI 600#) has reported a lower capex to Case 3 (20” – ANSI 300#), however the pump cost and electricity cost of Case 1 is higher.
- Although, Case 1 has reported lower pipeline capex, however, it Can be dismissed for the following reasons:
- Pump opex is nearly three times the value of case 3.
- Maximum operating pressure under case 1 is 2.8 times of case 3. As a Result, the expected peak surge and relieving volume would results in a Bigger srv size and more relieving volume.

### Recommendation

Considering previous technical discussion and outcomes From techno-economic analysis, it is recommended to: Case 3 is deemed more favourable and technically viable To cater for the operational requirements (design flow Rate and less surge demand) and more economic Compared to case 1 and case 2.

**Case Study: Tank Area Optimization Using MS. Excel Solver**

• **Objective**

You have to design an open storage tank made of Stainless Steel with a square base. The volume of the tank should be 50 m3.

Find the optimal dimensions of the tank that will require the least material and satisfy minimum cost.

**Problem Formation:**

Assume

- X: Length of base
- Y: Height of the tank

Quantity of material will depend on the total surface area of the tank

A = X^{2} + 4XY ————– This is the objective function

Volume is give as a Constraint in the problem statement = 50 m3

Since volume = Area of base * Height

50 = X^{2} * Y

Therefore,

Y=50 / X^{2}——————-equation i

Since Total Surface Area of tank = Area of square + Area of base

Area = 4XY + X^{2}, substitute using equation i

Therefore, Area = X^{2} + 4X (50/X^{2}) = X^{2} + 200/X

**There are two paths to proceed:**

- Short Path – Semi Quantitative Optimization.
- Proper Engineered Path – Quantitative Optimization.

**Semi-Quantitative Optimization**

o Since the equation relating Area to Length is ready, then you can assume various values for X, from 1 to 9, and then plot a curve for X versus Min Area.

o Trend will be as shown below:

o From the trend you can assume that the minimum area will be associated with a** length between 4 – 5 m.**

**2. Proper Engineered Path – Quantitative Optimization:**

o Use MS Excel Solver to get the accurate values of X & The associated Minimum Area.

o Following the steps of Solver discussed previously, you will get the below results:

Eventually, any engineer should utilize any optimization methodology either to produce an optimized design package or to optimize a running facility.

Always keep in mind that Optimization talks to few key words:

- Maximum Gain.
- Minimum Loss.
- Associated CAPEX.
- Associated OPEX.

Please Note that if there is shortfall or limitation of this document then it is because of me, while any success or correctness would be solely from the great and generous Allah.

Thank you for your patience and you are most welcome to contact me at the following email: professionalche@gmail.com / Ahmed Shafik | LinkedIn

Very useful article, easy ready for non process engineers.

Thanks for sharing.

Thank you for your kind words.

Excellent write up with relevant examples….article language is understood & can be picked up even by non technical personnel.

Keep up such good stuff in near future.

Much appreciated. Soon a new topic will be shared.