Basic Flowsheeting in Chemical Process Engineering PDF

Basic Flowsheeting in Chemical Process Members: CH160-2 GROUP 1 Cancio, Janae C. Cariño, Carl Sean Michael B. De Leon, Luke Raphael Dullon, Leinra Dane D. Oabel, Neil Rhoyd Oabel, Wincel Ong, Julienne C.  Table of Content...

Basic Flowsheeting in Chemical Process Members: CH160-2 GROUP 1 Cancio, Janae C. Cariño, Carl Sean Michael B. De Leon, Luke Raphael Dullon, Leinra Dane D. Oabel, Neil Rhoyd Oabel, Wincel Ong, Julienne C.  Table of Contents Definition of Flowsheeting in Chemical Engineering Importance of Flowsheeting in Chemical Engineering Importance of Flowsheeting in Process Design and Process Operation Challenges in Flowsheeting Core Components of a Flowsheet Steps in Developing a Flowsheet in Chemical Processes Applications of Flowsheeting in Industry Process Simulation Diagram Conclusion  What is Flowsheeting in Chemical Engineering? A detailed diagram representing the flow of materials and energy within a chemical process. Flowsheets can range from simple block diagrams to complex, detailed representations. Used for the design, analysis, and optimization of chemical processes.  Importance of Flowsheeting in Chemical Engineering Design and Synthesis: Visualization: Communication and Documentation: Used during the design phase to conceptualize Provides a clear, comprehensive visual Acts as a standardized communication tool and structure the chemical process. representation of the chemical process. among engineers, operators, and stakeholders. Determines the arrangement of equipment, Helps engineers and stakeholders grasp key Crucial for project planning, construction, and material flow, and integration of unit operations. components and interactions within the operational documentation. system. Analysis and Optimization: Safety and Compliance: Analysis and Optimization: Ensures process design adheres to safety Essential for performing heat and mass balance standards and regulatory requirements. calculations, sizing equipment, and cost estimation. Helps identify bottlenecks and optimize parameters Helps in identifying potential hazards and like temperature, pressure, and flow rates. implementing necessary safety measures.  Importance of Flowsheeting in Process Design Conceptual Process Cost, Value, & Clarity & Optimization & Feasibility Resource Risk Assessment Analysis Planning Flowsheets provide a Flowsheets allow for the Flowsheets serve as a clear visual identification of crucial source of representation of the inefficiencies and potential information for entire process, helping hazards early in the design understanding the engineers understand phase. This enables overall cost, value, and the sequence of engineers to optimize the economic viability of a operations and process for cost- process. They provide interactions between effectiveness and energy insights into potential different units. This efficiency while designing profitability, helping to clarity also aids in safer processes by determine if a project determining the types mitigating risks. should proceed to and quantities of raw detailed design and materials, utilities, and ensuring that equipment required, resources are not supporting accurate wasted on unprofitable budgeting and ventures. resource allocation. Importance of Flowsheeting in Process Operation Operational Guidance and Plant Start-up Regulatory Compliance Flowsheets provide a detailed roadmap for operators, guiding them through complex Flowsheets ensure that the process adheres to processes to ensure smooth execution, industry standards and regulatory especially during plant start-up and requirements, as they are often reviewed during subsequent operations. audits and inspections. Manual Preparation Process Control and Flowsheets are crucial for the preparation of Troubleshooting operating manuals, aiding in the consistent and By clearly depicting the placement of sensors, effective operation and maintenance of the control valves, and other instrumentation, plant. flowsheets enhance the ability to monitor and control the process. They also help operators quickly diagnose and resolve issues by tracing the flow of materials and energy through the system. Challenges in Flowsheeting: How to Overcome It: Complexity of Chemical Break down the process and use Processes hierarchical flowsheets. Inaccurate or incomplete Validate and manage data data effectively. Safety and Environmental Early integration of safety Concerns checks. Difficulties in communicating Standardize formats and use flowsheet details. clear documentation.  Process Units 01 These are the building blocks that represent the physical units of a flowsheet (Douglas, 1988). Core Components Streams 02 Streams are represented as arrows and include information about the properties of the process of a Flowsheet fluids (Towler & Sinnott, 2013). The core components of basic Material and Energy Balances flowsheeting help in modeling, stimulating, and optimizing a 03 These balances are fundamental calculations used to ensure that mass and energy are conserved chemical process. across each process unit and stream (Smith, 2005). Data and Models 04 Thermodynamic data and models are crucial for describing phase behavior, chemical equilibrium, and energy changes (Perry & Green, 2008). Core Components of a Flowsheet The core components of basic flowsheeting help in modeling, stimulating, and optimizing a chemical process.  Identify the purpose of making a 01 flowsheet Steps In Developing a 02 List each of the task in a step-by-step basis in order that they will be done Flowsheet In Chemical Processes 03 Create your title and the members included Make sure to enlist what type of To create a flowsheet, it is essential to 04 know what the process is supposed to process flowsheets. be used for, what each step is, the Design the Flowsheet to be used on details of each step, to keep the order 05 your work. of the steps, and to make it readable for the end user of the flowchart. (Tague 2005; Oriel Incorporated 2002), 06 Add Labels and Details 07 Review and Revise  APPLICATIONS OF FLOWSHEETING IN INDUSTRY Food and Water Chemical and Pharmaceutical Energy Sector Beverage Treatment Process Industry Industry Industry Industry Industry  Process Simulation Programs Process simulation programs are essential tools in chemical engineering for modeling, analyzing, and optimizing chemical processes. These programs allow engineers to create virtual models of processes, enabling the testing of different scenarios and conditions without the need for physical experimentation (Towler & Sinnott, 2008). Types of Process Simulation Programs Sequential-Modular Programs Simultaneous Programs 01 Each process unit operation is modeled and 02 Solve the entire process as a set of solved step-by-step. equations simultaneously rather than in a stepwise fashion. Iterative techniques are used to solve issues that arise from the recycling of information Although these programs demand more within the process. computing power, they are increasingly popular due to the capabilities of modern Traditionally favored due to its simplicity and computers. lower computational power requirements. Process Simulation Programs Conclusion The flowsheet is the key document in process design. It shows the arrangement of the equipment selected to carry out the process, the stream connections, stream flow rates and compositions, and the operating conditions. These diagrams range from simple block diagrams to complex, detailed representations for design, analysis, and optimization. Flowsheets are used for visualization, design, analysis, communication, and ensuring safety and regulatory compliance in chemical processes. Challenges in flowsheeting, such as complexity and data accuracy, can be addressed through hierarchical designs, careful data management, and standardized communication. Conclusion Key components of a flowsheet include process units, streams, material and energy balances, and thermodynamic models. Flowsheeting is widely used across industries like food and beverage, pharmaceuticals, water treatment, chemicals, and energy sector for process optimization and safety. Process simulation programs have two types: Sequential-Modular and Simultaneous or Equation-Oriented programs. Programs like Aspen Plus and HYSYS model and optimize chemical processes, supporting both steady-state and dynamic operations. THANK YOU!  BASIC FLOWSHEETING IN BIOLOGICAL PROCESS  PROJECT INTRODUCTION Basic flowsheeting, or process flow diagrams (PFDs), are essential tools in process engineering that provide a visual representation of the flow of processes and equipment within a plant. These diagrams focus on the relationships among major equipment, aiding in the understanding and optimization of processes, particularly in both chemical and biological engineering. In biological processes, flowsheeting incorporates additional considerations such as microbial kinetics, sterilization, and downstream processing, distinguishing it from traditional chemical processes. Reference: N. Metta et al., “Dynamic Flowsheet Model Development and Sensitivity Analysis of a Continuous Pharmaceutical Tablet Manufacturing Process Using the Wet Granulation Route,” Processes, vol. 7, no. 4, p. 234, Apr. 2019, doi: https://doi.org/10.3390/pr7040234. “Process Flow Sheet Generation & Design through a Group Contribution Approach d’Anterroches, Loïc.” Accessed: Aug. 27, 2024. [Online]. Available: https://backend.orbit.dtu.dk/ws/portalfiles/portal/5067161/PEC05-54.pdf OUTLINE FUNDAMENTALS APPLICATIONS TOOLS AND SOFTWARES  FUNDAMENTALS: FLOWSHEET A flowsheet is a graphical representation of a whole process, wherein its components are mainly the raw material, the energy and material balances that flow in and out of the varying process units, the final product, pipes, and the equipments carrying out those processes. Commonly found in the setting of an industrial scale operation, so it is important for the engineers involved to optimize such processes for efficiency.  FUNDAMENTALS: FLOWSHEET The key differences between biological process and chemical process. As for biological processes, they utilize living microbial organisms such as, bacterias, enzymes, and fungis. The reactions involved in processes are specific to certain parameters such as temperature, pressure, and the pH level. Lastly, their use of microbial organisms makes them relatively better for the environment compared to a chemical process. As for biological processes, they utilize living chemical reagents such as, acid and bases. The reactions involved in processes are less specific, or basically have a wider range of the certain parameters such as temperature, pressure, and the pH level. The wider range of those parameters has led to unwanted by-products at times. These unwanted by-products could potentially be harmful to the environment should they not be disposed of properly.  FUNDAMENTALS: FLOWSHEET Block Flow Diagrams (BFD) are the simplest form of flowsheet, wherein the simplicity allows for it to be an overview of a complex process. The blocks represent an equipment or a process. The energy and material flows are represented with an arrow, and that it starts with a raw material and ends with a product. This is a block flow diagram of the continuous extractive alcoholic fermentation, as a mixture of glucose and xylose was continually fed to a bioreactor containing Pichia stipitis as the microbial organism whose sole purpose is to ferment in order to produce bio-ethanol.  FUNDAMENTALS: FLOWSHEET Process Flow Diagrams (PFD) are the more detailed version of a Block Flow Diagram, generated by process simulation softwares such as ASPEN, and DWSIM. The process flow streams are basically numbered, while the equipments follow a certain nomenclature (Barghout and Qiao, 2020): First letter: equipment (P = pump) First number: plant section (1 = section 1 of plant) Last numbers: equipment number (01 = pump 1 in this section) Last letters: show duplicates/triplicates when two or more of the same equipment is used for the same stage of the process.  FUNDAMENTALS: COMPONENTS Equipments in the flowsheet are easily distinguished since they come in various forms  FUNDAMENTALS: COMPONENTS Heat Exchangers - transfers heat between two fluids separated by a series of pipes. In biological processes, it regulates the temperature within the bioreactor Reactors - it is an environment configured with the optimal parameters to allow for the biological reactions like fermentation, or the reactions of enzymes to take place. Pressure changers - it regulates the pressure as biological processes are particularly sensitive with that parameter  FUNDAMENTALS: COMPONENTS Distillation column - this exploits the difference of boiling point wherein the less volatile component is purified at the bottom, while the more volatile component is recovered at the top. Mixers - for biological processes, it ensures that the microbial organisms are well distributed throughout the process. Pipes - the most essential of them all, as it is an enclosed cylinder wherein the materials for processing are transported from one equipment to another.  FUNDAMENTALS: ROLE IN PROCESS DESIGN Biological processes are really complex processes or reactions that are often modelled or simplified by the understanding of kinetics Through the use of flowsheeting, production process design using biological systems can be optimized through the use of visuals and computer-aided calculations and simulations These optimizations and calculations are necessary to create feasible production processes of certain biological products such as food, liquor, pharmaceuticals, and others.  FUNDAMENTALS: ANALYSIS Material balances are based on the conservation of mass, stating that in steady-state MATERIAL BALANCES processes, mass entering a system equals mass leaving it. This principle helps calculate unknowns, like reactant needs and product yield and applies to atoms, molecules, and total mass. System and Process Types: Systems can be open (allowing mass exchange) or closed (no exchange). Processes include batch (closed), semi-batch (input or output allowed), fed-batch (input only), and continuous (both input and output). Steady State vs. Equilibrium: Steady-state maintains constant system properties over time, while equilibrium means no net change. Equilibrium is usually avoided in processing to keep materials transforming. Conservation of Mass: The mass balance equation tracks mass entering and leaving a system, accounting for any chemical reactions.  FUNDAMENTALS: ANALYSIS Energy balances help calculate necessary cooling or heating, essential for processes like ENERGY BALANCES steam sterilization. The principle of energy conservation is key to designing systems that maintain optimal process temperatures. The general energy-balance equation can be expressed as: Energy in through system boundaries−Energy out through system boundaries =Energy accumulated within the system For a process with one input and one output stream, the energy balance is: To simplify, the equation can be written using enthalpy (H), which is defined as: The specific enthalpy (h) is: The general energy-balance equation using enthalpy becomes:  FUNDAMENTALS: ANALYSIS SIZING AND COSTING OF EQUIPMENTS Graphical Estimation Equipment Cost Estimation Using Empirical Costs can also be estimated graphically, where the Equations equipment's capacity (e.g., flow rate in gallons per minute) is plotted against the purchase cost. This method provides a Equipment costs are often calculated using visual approximation but may be less accurate for outdated empirical equations, which generally follow the form: data. Importance of Current Data It is crucial to use up-to-date information for cost Here: estimation. Tools like Aspen, when kept current, can provide Fm​ is the material factor, which can be found in better approximations of equipment costs. However, older tables specific to the equipment type. versions of such tools may reflect outdated pricing, leading S is the sizing factor (e.g., flow rate, capacity). to inaccuracies. a, b, and c are equipment-specific coefficients. Cost Estimation for Other Equipment In the case of a centrifugal pump, the sizing factor S Similar empirical relationships exist for other types of might be defined as: equipment, such as fans and heat exchangers. For a fan, the sizing factor (S) might be simply the flow rate in cubic feet per minute (CFM), and the cost could be estimated using a similar empirical formula with equipment-specific coefficients.  FUNDAMENTALS: ANALYSIS ECONOMIC EVALUATION OPTIMIZATION The economic evaluation of bioprocesses involves the Optimization in the context of biological engineering systematic assessment of both capital investment costs refers to the process of improving the efficiency and (CapEx) and production costs (OpEx). Capital cost-effectiveness of bioprocesses. This involves the investment costs refer to the initial expenditures careful design and selection of unit operations, necessary to establish a bioprocessing facility, which equipment sizing, and cost analysis to reduce both includes acquiring, installing, and operationalizing capital investment and production costs. The goal is to equipment, as well as costs associated with building enhance the overall performance of enzymatic bio- infrastructure. conversions, microbial fermentations, and cell cultures by minimizing resource consumption (such as materials Production costs encompass the ongoing operational and energy) and maximizing output, ultimately leading to expenses required for the bioprocess, including more economical production processes. expenditures on raw materials, energy, labor, equipment usage, and maintenance. Conducting an economic evaluation is crucial for understanding the financial requirements, optimizing cost-efficiency, and ensuring the overall viability of bioprocess operations.  APPLICATIONS ENZYME EXTRACTION AND PURIFICATION PROCESS  APPLICATIONS THE RECOVERY OF CELLULASES FROM COFFEE HUSKS  APPLICATIONS PRODUCTION OF LACCASE AND OTHER ENZYMES FOR THE WOOD INDUSTRY TOOLS AND SOFTWARES MATLAB 01It enables - BRANDING users to perform dynamic modeling of biological systems, the simulation of biological processes, and evaluation of the obtained results through such tools as graphical representations and algorithms. Python One example is PySB, a Python-based modeling framework that generates reaction rules from a Python program. These rules can then be analyzed or used to create equations for simulation in which PySB employs a high-level, action-oriented vocabulary that aligns with the framework. (Lopez et al., 2013). SuperPro Designer It mainly deals with Chemical processes but it can be equally used to model and simulate the biological processes particularly those that involve biochemical reactions and unit operations. SuperPro can also carry out an accurate material and energy balance to keep track of process performance. PROCESS FLOW DIAGRAMS GROUP 3  DEFINITION A process flow diagram (PFD) is a IN THE CONTEXT OF CHEMICAL diagram commonly used in ENGINEERING AND OTHER chemical and process engineering to RELATED FIELDS indicate the general flow of plant processes and equipment. A process flow diagram (PFD) illustrates the arrangement of the equipment and accessories required to carry out the specific process; the stream connections; A. SHAH, N. R. BARAL, & stream flow rates and compositions; and A. MANANDHAR (2016) the operating conditions (Shah et al., 2016).  DEFINITION The process flow diagram (PFD) is a visual S. MORAN (2019) representation of the mass and energy balance. Process flow diagrams (PFD) are a graphical way of describing a B. ELAHI (2022) process, its constituent tasks, and their sequence.  HISTORICAL BACKGROUND EARLY BEGINNINGS Frank and Lillian Gilbreth introduce process charts to ASME, emphasizing 1921 the optimization of work processes (Gilbreth & Gilbreth, 1921). STANDARDIZATION BEGINS World War II accelerated the need 1940S - for standardized PFDs; ASME and 1950S AIChE developed standardized INTRODUCTION OF COMPUTER- symbols and guidelines. AIDED DESIGN CAD software is introduced, revolutionizing PFD creation with 1957 more detailed and accurate BRITISH STANDARD, BS 1553 representations (Beck, 2023). The British Standard BS 1553 for graphical symbols in engineering is 1977 published, gaining widespread use in the UK and Commonwealth countries (Towler & Sinnott, 2021).  INCORPORATION IN PROCESS SIMULATION SOFTWARE PFDs are integrated into process simulation software like ASPEN and HYSYS, allowing 1980S dynamic simulations and process optimization (Seider et al., 2016; ISO 10628:1997 AspenTech, n.d.). ISO 10628, "Flow Diagrams for Process Plants – General Rules," was 1997 established and widely adopted in DIGITALIZATION AND European countries (Towler & Sinnott, ADVANCED MODELING 2021). The digital revolution introduced real-time data integration, digital twins, AI, and 2000S - machine learning, making PFDs more PRESENT interactive and informative (Seider et al., UPDATES TO ISO 10628 2016; Theisen et al., 2023). ISO 10628-2:2012 and ISO 10628-1:2014 are published, providing updated standards 2012 & for graphical symbols and diagram 2014 specifications for the chemical and petrochemical industries (ISO, 2012; ISO, 2014).  CONTENTS 1. DESIGN BASIS 2. MATERIAL BALANCE For batch processes Composition and quantity of materials for each ◦Batch capacity unit operation and important pipeline ◦Batch cycle time For batch processes For continuous processes ◦ Equipment capacity ◦Design production rate ◦Pipeline flow per batch basis For continuous processes ◦Mass or volumetric flow rates per unit of time REFERENCE: PANJA, 2024  CONTENTS 3. ENERGY BALANCE 4. PHYSICAL DATA Heat balance or heat Operating pressure and temperature transfer data for Specific gravity each unit operation Molecular weight Viscosity Specific heat Other essential physical data REFERENCE: PANJA, 2024  CONTENTS 5. EQUIPMENT INFORMATION 6. PIPING INFORMATION All unit operations involved in the process Major process lines with proper Proper arrangement and correct relative position directions Proper name, tag number, and capacity of each Other significant piping items (e.g., equipment item sampling point) Important features of equipment (e.g., agitators, Control valves trays, and jacket coils) Major service or utility line When necessary: Spare equipment, duplicate parallel lines, and bypass lines REFERENCE: PANJA, 2024  CONTENTS 7. INSTRUMENT INFORMATION 8. SIZE AND SCALE All critical instruments involved in Draw using the standard scale ratio set the control loop (e.g., mass flow by project standards. meter, temperature transmitter, Arrange the flow for trimming to 11” or etc.) 22” height. Instruments in the control scheme If an absolute scale is not used: Show the relative size and elevation of the components. REFERENCE: PANJA, 2024  CONTENTS 9. DRAWING INSTRUCTIONS 10. FLOW SUMMARY The standard symbol of the equipment, sketch, A summary of the etc. in the legend sheet process flow data and Applicable data for each unit operation and conditions process line Steam numbers of each process line and operating condition Proper arrow showing the correct process flow Process lines carrying the two-phase flow REFERENCE: PANJA, 2024  TERMS IN PFD(S) FEED The raw materials or input streams entering a PRODUCT process The final output streams or materials exiting the process A portion of the condensed A stream diverted vapor returned to the around a particular distillation column to process unit improve separation BYPASS REFLUX RECYCLE A stream returned to a previous stage of the process for further processing  PURGE SPLIT/SEPARATION The removal of a small A stream divided into portion of a stream to prevent two or more paths the accumulation of impurities within the process or unwanted components STREAM Represents the flow of materials (liquid, gas, or solid) between different process units  ELEMENTS IN PFD(S) REACTORS HEAT EXCHANGER DISTILLATION COLUMN PUMPS VALVES REBOILER PIPING MIXERS SEPARATORS CONDENSER ABSORBER SOFTWARE Made by ASPEN Tech from Advanced System for Process Engineering (ASPEN) project in Massachusetts Institute of Technology (MIT). Primarily used for for fine chemistry or general chemical processes. Along with ASPEN Plus, ASPEN HYSYS is created by ASPEN Tech in MIT. ASPEN HYSYS on the other hand focuses more on petrochemicals and crude oil refining or liquified natural gas. Created back in 1968 in University of Houston. Otherwise known as the Chemical Engineering Simulation System (CHESS) back in the 1983 until it was renamed to CHEMCad in 1985. Great for general applications and modelling for both steady state and dynamic systems. Before becoming AVEVE Process Simulation, it was known as SimSci PRO/II before it the merger between The Schneider Electric and AVEVA occurred. AVEVA Process Simulation was primarily focused on refining oil, gas, and energy optimization. Created in 2004 and based on Excel VBA macros and an open-source application made by Daniel Wagner Oliveira de Medeiros. Since it is a free software, it is usually used for academic use or in small-scale industries. ProSim Plus owned by ProSim SA and launched on the early 2000's an was hailed as the leader of energy-efficient process simulation. ProSim Plus is solely focused on steady state systems and on environmental modeling MAKING PROCESS 1 2 3 CLICK “NEW” AND CHOOSE A CLICK “SIMULATION” “USER” PREFERRED UNIT TAB MAKING PROCESS 4 5 6 CLICK ON A COMPONENT & CLICK ON MATERIAL DOUBLE CLICK ON DRAGGING IT TO STREAMS & COMPONENT TO WORK AREA TO CONNECT TO EDIT CREATE DIAGRAM INLET/OUTLET  EXAMPLES PROCESS FLOW DIAGRAM (PFD)  EXAMPLES PROCESS FLOW DIAGRAM (PFD) FOR THE PRODUCTION OF BENZENE VIA HYDRODEALKYLATION OF TOLUENE  STANDARDS ISO 15519: SPECIFICATION FOR DIAGRAMS FOR PROCESS INDUSTRY Specifies the preparation of different types of diagrams and the use of graphical symbols, letter codes, and reference designation in diagrams Deals with all process industry fields, such as chemical, petrochemical, power, pharmaceutical, foodstuff, pulp, and paper  STANDARDS ISO 15519-1:2010(EN) ISO 15519-2:2015(EN) PART 1: GENERAL RULES PART 2: MEASUREMENT AND CONTROL Tackles the rules for the preparation of diagrams and associated documents Addresses the representation and data for the process industry of measurement, actuation, Indicates rules and recommendations and control in process for the application of associated diagrams standards in diagrams REFERENCE: INTERNATIONAL ORGANIZATION REFERENCE: INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, 2010 FOR STANDARDIZATION, 2015  ISO 10628: DIAGRAMS FOR THE CHEMICAL AND PETROCHEMICAL INDUSTRY ISO 10628-1:2014(EN) ISO 10628-2:2012(EN) PART 1: SPECIFICATION PART 2: GRAPHICAL SYMBOLS OF DIAGRAMS Defines graphical symbols for the Provides the classification, content, and preparation of diagrams for the representation of flow diagrams chemical and petrochemical industry Dictates drafting rules for flow diagrams Does not apply to graphical symbols in the chemical and petrochemical for electrotechnical diagrams industry Does not apply to electrical engineering diagrams REFERENCE: INTERNATIONAL ORGANIZATION REFERENCE: INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, 2014 FOR STANDARDIZATION, 2012 Preliminary set of standard symbols formulated ANSI Y32.11: GRAPHICAL for use in basic process flow diagrams to represent the major items of equipment items in SYMBOLS FOR PROCESS the petroleum and chemical industries FLOW DIAGRAMS IN No longer an American National Standard or an THE PETROLEUM AND ASME-approved standard CHEMICAL INDUSTRIES Withdrawn in 2003 REFERENCE: AMERICAN SOCIETY OF MECHANICAL ENGINEERS, 1961 Available for historical reference only SAA AS 1109: GRAPHICAL SYMBOLS Offers graphical symbols FOR PROCESS FLOW DIAGRAMS for PFDs specifically for the FOR THE FOOD INDUSTRY food industry REFERENCE: STANDARDS ASSOCIATION OF AUSTRALIA, 1981  LIMITATIONS 1. SIMPLIFICATION 2. LACK OF DETAILED OF PROCESSES OPERATIONAL DATA PFDs give a high-level overview PFDs do not typically include and usually simplify the actual specific operational data (e.g., processes. temperatures, pressures, and They omit minor equipment and flow rates). detailed piping. REFERENCE: TOWLER & SINNOTT, 2013 REFERENCE: TURTON ET AL., 2018  LIMITATIONS 3. ABSENCE OF CONTROL 4. STATIC REPRESENTATION AND SAFETY SYSTEMS PFDs illustrate the process at a PFDs generally exclude information on particular point in time, usually under control systems, instrumentation, and normal operating conditions. safety interlocks. They do not show how the process They are insufficient for understanding might function during start-up, how the process is managed under shutdown, or emergencies. various conditions. REFERENCE: PETERS ET AL., 2003 REFERENCE: TOWLER & SINNOTT, 2013  LIMITATIONS 5. NO DYNAMIC PROCESS 6. POTENTIAL FOR INFORMATION MISINTERPRETATION PFDs do not capture the dynamic PFDs can be misinterpreted, aspects of processes (e.g., how especially if used without different components interact over additional detailed documentation time or respond to changes in or by individuals unfamiliar with operating conditions). the specific process. REFERENCE: TURTON ET AL., 2018 REFERENCE: PETERS ET AL., 2003  LIMITATIONS 7. UNSUITABILITY FOR DETAILED DESIGN PFDs are not detailed enough for engineering design purposes, which require more comprehensive diagrams. REFERENCE: TOWLER & SINNOTT, 2013  USERS PROCESS ENGINEERS SAFETY ENGINEERS The primary users of PFDs Use PFDs to identify and assess Utilize these diagrams during the design, potential hazards in a process optimization, and troubleshooting of Rely on these diagrams to develop processes safety protocols and emergency PFDs help them ensure that the process response plans, ensuring that the meets the desired specifications and process complies with safety regulations operates efficiently and safely. and standards  USERS CONTROL ENGINEERS OPERATORS & TECHNICIANS Utilize PFDs to design and implement Use PFDs to understand the overall control systems that automate and process flow and their specific roles regulate process operations within it Can determine the optimal placement These diagrams are crucial during of sensors, actuators, and controllers daily operations, maintenance to maintain process stability by activities, and troubleshooting efforts. analyzing the PFD  USERS PROJECT MANAGERS & STAKEHOLDERS Use PFDs to gain an overview of the process, understand the scope of the project, and communicate with engineers and other team members PFDs help them make informed decisions regarding project timelines, budgets, and resource allocation.  USES PROCESS DESIGN AND PROCESS OPTIMIZATION DEVELOPMENT PFDs are instrumental in the conceptual phase of PFDs allow engineers to analyze existing processes process design. They help engineers visualize the to identify inefficiencies, energy losses, or process layout, understand the sequence of opportunities for improvement. By comparing operations, and identify key equipment and different PFDs representing various design control points. By providing a clear overview, PFDs alternatives, engineers can optimize processes for assist in the selection of appropriate technologies better performance, reduced environmental and the development of efficient, safe, and cost- impact, and lower operational costs. effective processes.  USES PROCESS DESIGN AND PROCESS OPTIMIZATION DEVELOPMENT PFDs are instrumental in the conceptual phase of PFDs allow engineers to analyze existing processes process design. They help engineers visualize the to identify inefficiencies, energy losses, or process layout, understand the sequence of opportunities for improvement. By comparing operations, and identify key equipment and different PFDs representing various design control points. By providing a clear overview, PFDs alternatives, engineers can optimize processes for assist in the selection of appropriate technologies better performance, reduced environmental and the development of efficient, safe, and cost- impact, and lower operational costs. effective processes.  USES SAFETY AND HAZARD PROCESS CONTROL AND ANALYSIS AUTOMATION In chemical and biological engineering, safety is a PFDs are essential in designing control strategies priority. PFDs are used in hazard identification and for automated processes. They provide the risk assessment processes such as HAZOP (Hazard foundational layout for developing control loops and Operability Study). They help in understanding and integrating instrumentation and control the flow of hazardous materials, identifying systems. This ensures that the process operates potential risks, and developing mitigation within the desired parameters, maintaining strategies to ensure safe operations. product quality and operational efficiency.  USES TRAINING AND EDUCATION PFDs serve as educational tools for training engineers, operators, and other personnel involved in process industries. They provide a simplified yet comprehensive view of complex processes, making it easier for learners to understand the flow of materials and energy and the interaction between different process units.  APPLICATIONS Communication & Process Design Systematic Process Synthesis Energy Integration PFDs convey process information PFDs enable systematic PFDs optimize energy use in and are crucial for designing and generation and optimization of processes like heat-integrated optimizing processes, ensuring process flowsheets, breaking distillation, reducing costs. safety and compliance. down complex tasks. Digitization & Integration with AI & Machine Learning Evolutionary Process Modification Digital Tools PFDs provide data for AI-driven PFDs support iterative design Digitized PFDs integrate with IoT and process improvement, fault improvements, enhancing digital twins, improving real-time detection, and maintenance. performance and cost- monitoring and data management. effectiveness. SIGNIFICANCE & IMPACT Significance Documentation for better understanding, quality control, employee training, and operation foundation (Wallace, 2014), (Lucidchart, n.d.) Outlines processes (Wallace, 2014) Standardization for efficiency and repeatability (Lucidchart, n.d.) Efficiency and improvement (Lucidchart, n.d.) Communication and demonstration of the rationale behind design decisions (American Society for Quality, 2019), (Kolko, 2011) Impact Define parameters for design (Arnold, et al., 2005) Performance prediction (Theisen, et al., 2023)  REFERENCES American Society for Quality. (2019). What is a flowchart? Process flow diagrams & maps. ASQ. https://asq.org/quality-resources/flowchart American Society of Mechanical Engineers. (1961). ASME - ANSI Y32.11: Graphical symbols for process flow diagrams in the petroleum and chemical industries. GlobalSpec. https://standards.globalspec.com/std/7864/ansi-y32-11 Arnold, K. E., Karsan, D. I., & Chakrabarti, S. (2005). Topside facilities layout development. Handbook of Offshore Engineering, 861–889. https://doi.org/10.1016/b978-0-08-044381-2.50017-5 AspenTech. (n.d.). AspenTech: Over 40 years of innovation. https://www.aspentech.com/en/about- aspentech/history Beck, A. (2023, November 2). 60 years of CAD infographic: The history of CAD since 1957. CADENAS PARTsolutions. https://partsolutions.com/60-years-of-cad-infographic-the-history-of-cad-since- 1957/ Chiyoda Corporation. (n.d.). FEED (Front End Engineering Design). https://www.chiyodacorp.com/en/service/ple/feed/ Elahi, B. (2022). Risk analysis techniques. Safety Risk Management for Medical Devices (Second Edition), 89–153. https://doi.org/10.1016/B978-0-323-85755-0.00014-X  REFERENCES Gilbreth, F. B., & Gilbreth, L. M. (1921). Process charts: First steps in finding the one best way to do work. Transactions of the American Society of Mechanical Engineers, 43, 1029–1043. https://doi.org/10.1115/1.4058133 International Organization for Standardization. (1997). ISO 10628:1997: Flow diagrams for process plants – General rules. ISO. https://www.iso.org/standard/18721.html International Organization for Standardization. (2010). ISO 15519-1:2010(en): Specification for diagrams for process industry — Part 1: General rules. ISO. Add a little bit of body text International Organization for Standardization. (2012). ISO 10628-2:2012(en): Diagrams for the chemical and petrochemical industry — Part 2: Graphical symbols. ISO. https://www.iso.org/obp/ui/#iso:std:iso:10628:-2:ed-1:v1:en International Organization for Standardization. (2014). ISO 10628-1:2014(en): Diagrams for the chemical and petrochemical industry — Part 1: Specification of diagrams. ISO. https://www.iso.org/obp/ui/#iso:std:iso:10628:-1:ed-1:v1:en International Organization for Standardization. (2015). ISO 15519-2:2015(en): Specifications for diagrams for process industry — Part 2: Measurement and control. ISO. https://www.iso.org/obp/ui/#iso:std:iso:15519:-2:ed-1:v1:en  REFERENCES Kolko, J. (2011). Managing complexity. Thoughts on Interaction Design (Second Edition), 40–51. https://doi.org/10.1016/b978-0-12-380930-8.50002-4 Moran, S. (2019). Process plant design deliverables. An Applied Guide to Process and Plant Design (Second Edition), 39–62. https://doi.org/10.1016/B978-0-12-814860-0.00004-5 Panja, P. P. (2024, March 7). What is process flow diagram (PFD)? Purpose, symbols, examples, & development of process flow diagram. What Is Piping. https://whatispiping.com/process-flow- diagram-pfd/ Peters, M. S., Timmerhaus, K. D., & West, R. E. (2003). Plant design and economics for chemical engineers (5th ed.). McGraw-Hill. Seider, W. D., Lewin, D. R., Seader, J. D., Widagdo, S., Gani, R., & Ng, K. M. (2016). Product and process design principles: Synthesis, analysis and evaluation (4th ed.). Wiley. http://ci.nii.ac.jp/ncid/BB0059445X Shah, A., Baral, N. R., & Manandhar, A. (2016). Technoeconomic analysis and life cycle assessment of bioenergy systems. Advances in Bioenergy, 1, 189–247. https://doi.org/10.1016/bs.aibe.2016.09.004 Standards Association of Australia. (1981). SAA AS 1109: Graphical symbols for process flow diagrams for the food industry.  REFERENCES Theisen, M. F., Flores, K. N., Schulze Balhorn, L., & Schweidtmann, A. M. (2023). Digitization of chemical process flow diagrams using deep convolutional neural networks. Digital Chemical Engineering, 6, Article 100072. https://doi.org/10.1016/j.dche.2022.100072 Towler, G., & Sinnott, R. (2013). Chemical engineering design: Principles, practice and economics of plant and process design (2nd ed.). Butterworth-Heinemann. Towler, G., & Sinnott, R. (2021). Chemical engineering design: Principles, practice and economics of plant and process design (3rd ed.). Butterworth-Heinemann. Turton, R. A., Shaeiwitz, J. A., Bhattacharyya, D., & Whiting, W. B. (2018). Analysis, synthesis, and design of chemical processes (5th ed.). Prentice Hall. University of Toronto Scarborough. (n.d.). Reflux. UTSC. https://www.utsc.utoronto.ca/webapps/chemistryonline/production/reflux.php Wallace, C. A. (2014). Food safety assurance systems: Hazard analysis and critical control point system (HACCP): Principles and practice. Encyclopedia of Food Safety, 4, 226–239. https://doi.org/10.1016/b978-0-12-378612-8.00358-9 What is a process flow diagram. (n.d.). Lucidchart. https://www.lucidchart.com/pages/process-flow- diagrams THANK YOU Piping and Instrumentation Diagram Presented by : Group 4  Definition A Piping & Instrumentation Diagram (P&ID) is a schematic layout of a plant showing the units, pipes, sensors, and control valves used in the process.  History of Piping and Instrumentation Diagram Installers typically use a Piping and Instrumentation Diagram generated during the process flow design phase as a guide while setting up a plant. P&ID is followed by another graphic known as the Process Flow Diagram, or PFD. The schematic of the intended workflow, or how the fully operational equipment will operate after installation, is displayed in a process flow diagram. PFDs need more specifics like numbers, statistics, and data on the exact measurement.  History of Piping and Instrumentation Diagram After a PFD is created, it serves as reference material for the drawing of a P&ID, which includes workflow details such as the motors, pipeline system, and other crucial components. Nonetheless, it is crucial to remember that a P&ID shouldn't be overly detailed because its main function is to highlight the crucial pipelines and equipment. A separate chart must be made for each segment of a Piping and Instrumentation Diagram that requires additional explanation. During the design phase, P&IDs are first created using a combination of data from process flow sheets, mechanical process equipment designs, and instrumentation engineering designs. The diagram serves as the foundation for the creation of system control schemes throughout the design phase, enabling additional safety and operational research, including a Hazard and operability study (HAZOP).  Function and purpose P&IDS are essential to the upkeep and adjustment of the process that it visually depicts. The Hazard and Operability Study (HAZOP) and other system control methods are developed throughout the design phase using the diagram as a foundation. Function and purpose It's a visual depiction of processing facilities: Important information about the instruments and pipes Regulation and cessation plans Regulations and safety standards Fundamental facts about startup and operation Function and purpose P&IDs perform several vital tasks, such as: Process Representation: They offer a thorough overview of the actual arrangement of devices and systems, demonstrating how these systems communicate and work as a unit. Details like pipes, valves, instruments, and control interlocks are included in this. Design Foundation: P&IDs play a crucial role in a project's design phase, providing the framework for safety evaluations like Hazard and Operability Studies (HAZOP) and system control systems. Maintenance and Modification: For the continuous upkeep and alterations of process systems, these diagrams are essential. They facilitate safe modifications and upgrades by assisting engineers and personnel in understanding the plant's present setup.  Uses of diagram Field technicians, engineers, and operators utilize P&IDs to gain a deeper understanding of the process and the interconnectivity of the instruments. They can help provide contractors and employees with training.  Uses of diagram Few applications for a P&ID: Design and Development: Process systems, which are designed and developed using a P&ID. It assists engineers in planning and visualizing the architecture of the system, guaranteeing that it is appropriately engineered and meets all requirements. Process Control: A P&ID offers a thorough illustration of the apparatus, sensors, and transmitters that monitor and manage the process inside the process control system. Troubleshooting: It supports technicians in troubleshooting, component finding, and corrective action implementation. Maintenance: It makes it easier for maintenance staff to locate parts, make sure they have the right equipment and supplies and finish jobs quickly. Training: It gives trainees a visual depiction of the system’s work, making it easier to comprehend its design, features, and functioning.  Uses of diagram Commissioning: A P&ID ensures that every component is placed correctly and operating as intended throughout the commissioning procedure. Documentation: A P&ID acts as an all-inclusive process system document, offering a permanent record of the system's installation, design, and functioning. Compliance: A P&ID can be used to show that safety, environmental protection, and quality control regulations, among others, are being complied with. Project Management: To guarantee that every component is installed and configured correctly, a P&ID is utilized throughout project planning and management.  Uses of diagram Plant Layout: The pipework, equipment, and other components of the plant floor may be precisely mapped out using a P&ID. Scheduling: Maintenance tasks, repairs, and replacements can be planned to use a P&ID. Estimating: The expenses of the supplies, labor, and machinery required for a project may be calculated using a P&ID. Bidding: By offering a thorough depiction of the process system, a P&ID may be used to submit a bid on a project. As-Built Documentation: A P&ID can serve as a record of the final installation when utilized to build as-built documentation for a process system.  Importance of P&ID When designing, building, and running process systems, a P&ID is a crucial tool. All project participants, including engineers, technicians, and operators, can use it as a reference point.  Importance of P&ID Shared knowledge of the processing system is provided by the P&ID, which helps in: Ascertain that the system has been implemented and planned correctly. Determine possible difficulties and sort out problems. Give a detailed explanation of the features and functioning of the system. Encourage communication between interested parties. Cut down on mistakes and boost security. Advantages and Disadvanges of P&ID There are several benefits to using a P&ID, such as: Enhanced communication: A P&ID gives all project stakeholders a single language to use. Error reduction: A P&ID guarantees that the system is installed and configured correctly, and it also aids in identifying possible problems. Increased safety: A P&ID guarantees that the system is constructed and designed with safety in mind, as well as aids in the identification of any dangers. Minimized downtime: A P&ID guarantees that the system is correctly maintained and operated and aids in the identification of any problems. Enhanced efficiency: A P&ID aids in lowering energy usage and improving system performance. Advantages and Disadvanges of P&ID A P&ID provides some benefits, but it also has certain drawbacks, such as: High cost: It takes a lot of time and resources to create a P&ID. Complexity: A P&ID can be complicated and challenging to comprehend, particularly for people who are not familiar with process design. Limited adaptability: Because a P&ID is a static depiction of the process system, it may not be easy to adapt to changes or alterations. Obsolescence: As a process system changes over time, a P&ID may become antiquated.  Components of a P&IDs The following elements are commonly seen in a P&ID: Pipes: shown as lines with arrows pointing in the direction of the flow. Valves: Shown by icons or symbols that denote the type of valve (e.g., ball valve, gate valve). Instruments: shown as icons or symbols that correspond to the type of instrument (temperature transmitter, pressure gauge, etc.).  Components of a P&IDs The following elements are commonly seen in a P&ID: Equipment: Depicted by icons or symbols that denote the kind of apparatus (such as a pump or tank). Fittings: Denoted by icons or symbols that represent the different types of fittings (e.g., elbow, tee). Instruments: Depicted by icons or symbols that denote the sort of instrument (such as a temperature transmitter or pressure gauge).  Best Practices for Creating a P&ID To generate a P&ID that works, adhere to the following recommended practices: Make use of standardized symbols and graphics. Make use of a constant orientation and scale. To make a distinction between various components, use color coding. To make sure the P&ID is accurate and comprehensive, review and edit it frequently. By adhering to these recommended procedures and comprehending the significance, benefits, and drawbacks of a P&ID, we may produce a diagram that effectively contributes to the successful planning, building, and functioning of the processing system.  Characteristics of a P&ID Categorized according to their functions and industrial uses. The major categories are piping, instrumentation, pumps, valves, vessels, heat exchangers, compressors, and equipment.  Characteristics of a P&ID Piping - Equipment that transports fluid substances. Types can be simple, multi-line, separators, connectors, end cops, flanges and coupling. Characteristics of a P&ID Pumps - Essential part of the majority of industrial plants that need pumps, it can be used for suction, compression, moving fluid, and for pressure control. Characteristics of a P&ID Valves - It is for control flow. There are actuators and self-regulated relief valves. Characteristics of a P&ID Vessels - Used to show containers to store fluids. Larger vessel group includes tanks, cylinders, columns, bags, and others.  Characteristics of a P&ID Instrumentation - Standardized to ensure consistent control and automation. Helps in the identification of the part and broad base understanding of the process. Characteristics of a P&ID Heat exchangers - Transfer heat between different surfaces, fluids, mediums, or areas. (Such as boilers, condensers, and other heat exchanging devices. )  Characteristics of a P&ID Compressors - Along with the blower it moves air or gas through an operational process. Operates at a high pressure-to-volume ratio, blowers operate at a lower- pressure ratio.  Instruments in P&ID An instrument is a tool that is used to regulate and analyze various factors including flow, temperature, angle or pressure. This broad category comprises of indicators, transmitters, recordings, controllers, alarms, sensors and on elements.  Instruments in P&ID Alarms - A device that alerts plant operators about an upset condition of the process variable. Consists of sound and light outputs. Controllers - Device that receives data from a measurement instrument, compares data to a programmed set point, and signals a control element to take corrective action. (Responsible for the control of the process variable.) Indicators - A human-readable device that displays information about the process. (Modifies basic instrumentation variables such as flow level, pressure, and temperature.)  Instruments in P&ID Sensors - Devices that measure the value of the process variable. (Ex. Thermocouples and Orifice meters) Recorders - Device that records the output of a measurement device. ( List of readings and times of reading taken; chart or graph of the readings) Transmitter - Device that converts a reading from a sensor or transducer into a standard signal and transmits to a monitor or controller. (Pressure, flow, temperature, level, and analytical). Instruments in P&ID Instruments in P&ID How to read P&IDs The symbols contained in P&IDs represent the equipment in the process such as actuators, sensors, and controllers. Process equipment such as valves, instruments, and pipelines are identified by codes and symbols. As well as devices and pipelines, a P&ID will commonly contain information on vents, drains, and sampling lines as well as flow directions, control I/O and Interconnection References. P&ID Code Format The Instrumentation codes listed in P&IDs follow a standard format. The first letter of the code identifies the parameters that are being controlled or monitored for example Flow, Temperature, Level or Pressure. The next letter is used to define the type of control device being used, for example, Transmitter, Valve or Controller. The number refers to the logical numerator. P&ID drawing symbols, circles, and lines are used to represent instruments and to show how they are connected to the rest of the system Standard Abbreviations Used in P&ID Standard Abbreviations Used in P&ID P&ID Instruments Location The presence or absence of a line in the circle determines the location of the physical device. No line: A simple circle indicates that the device is in the field and is a locally mounted instrument. The device is observable in the field and is accessed by the operator. Solid Line: A solid line in the center signifies that the instrument is placed in a primary location in the control room. The instrument is visible on the front of the panel or video display. Dotted Line: The dashed line specifies that the instrument is in a secondary position in the control room and inaccessible to the operator. It is not visible on the front of the panel or video display. P&ID Instruments Location The presence or absence of a line in the circle determines the location of the physical device. Double Solid Line: A double solid line tells that it is in a primary position in the local control center and is operator accessible at the panel front or console. Double Dashed Line: A double dashed line describes that the instrument is in a secondary position in the local control center and is not operator accessible. The device is located in the field cabinet and is not visible on the front of the panel or the video display. P&ID Piping and Connections The connections between elements help engineers identify a particular pipe in a standardized way. Different colors indicate different pipes to avoid confusion. P&ID Piping and Connections The piping or connection lines on the P&ID also tell us about the instrument, for example, a solid line would indicate the interconnection is via pipework whereas a dotted line would indicate an electrical connection. Primary Line Types Used Knowing the symbols is essential to understanding the P&ID charts correctly. Here are the primary line types used to connect different devices. References Basic Functions of Instruments in a P&ID. (n.d.). Learning Instrumentation And Control Engineering. How to Read a P&ID? (2020, January 27). RealPars. How to Read Piping and Instrumentation Diagram (P&ID) | EdrawMax. (n.d.). Edrawsoft. P&ID Symbols and Meanings. (n.d.). EdrawMax. Piping & Instrumentation Diagrams (P&ID) Guide. (n.d.). Lucidchart. What is a Piping and Instrumentation Diagram (P&ID). (n.d.). Edrawsoft. What is Piping and Instrumentation Diagram (P&ID) ? (n.d.). Inst Tools. Members: AL AL AY, ANTONIO, KA L IVIN GSTON , C ZAR AD R IAS , GOTIS , JOHN CAS SANDR A TR INA MAE IN E KIRSTE N R E N ALY N HE N RY JANE POSADAS ,YAS MU L AWIN, JOS E R AMIR EZ ,YV ROC AFORT, ME N CLAIRE VIC TOR E T TE M AIC AH Optimization Algorithm  Topics Covered 01 02 03 04 05 06 O F A B S P U P V E O P N R L E N F C O I R E T C T C A V F W I E T I I A I O S E T R O N S W S E N S S Optimization Algorithm An optimization algorithm is a mathematical method used to find the best possible solution to a problem, often by maximizing or minimizing a specific objective function. These algorithms iteratively adjust variables within a defined set of constraints to reach an optimal or near-optimal solution, and they are widely applied in fields such as engineering, economics, machine learning, and operations research.  Types of Optimization Problems Linear Optimization Integer Optimization involves optimizing a linear objective focuses on optimization problems function subject to linear equality and where some or all variables are inequality constraints. Examples include constrained to be integers, often used maximizing profits in business in scenarios like scheduling, resource operations or minimizing costs in allocation, and logistics. production. Non-Linear Optimization Combinatorial Optimization deals with optimizing an objective consists of finding an optimal object from a function that is non-linear, often with finite set of objects, where the set of feasible non-linear constraints, and is solutions is discrete or can be reduced to a commonly used in engineering design and financial modeling. discrete set.  Functions of Optimization Algorithms IMPORTANCE Optimization algorithms are essential in various fields such as data science, engineering, and economics, helping solve problems by finding the best possible solution within given constraints. They play a key role in tasks ranging from improving machine learning models to enhancing production processes. Below are three major functions of optimization algorithms: OBJECTIVE FUNCTION CONSTRAINT HANDLING EFFICIENT SEARCH AND 01 OPTIMIZATION 02 Ensure that solutions 03 CONVERGENCE Maximize or minimize an meet constraints whether Efficiently explore search objective function to find linear or nonlinear, while spaces to quickly converge the best possible solution. optimizing the objective on solutions while avoiding function local minima.  Process Optimization Software help support organizations in several ways. From streamlining operations to identifying and remedying flaws in current processes, process optimization software is a cutting-edge tool that industrial enterprises can use to enhance performance and maximize throughput. Benefits of Process Optimization Software ENHANCED PROCESS COST EFFICIENCY REDUCTION Process optimization Employing optimization techniques like linear algorithms significantly programming or mixed-integer enhance process efficiency nonlinear programming, in chemical engineering by companies can minimize raw identifying the most material usage, energy effective operating consumption, and waste conditions. production. Benefits of process optimization software IMPROVED PROCESS ENVIRONMENTAL CONTROL AND SAFETY SUSTAINABILITY Process optimization Process optimization algorithms can be used to algorithms contribute to minimize the environmental improved process control impact of chemical and safety by allowing for processes by reducing more precise and reliable emissions, waste, and control strategies. energy consumption. Software for Optimization Processes MATLAB Has Optimization Toolbox for problems in LP, NLP, QP, MIP, and Multi-objective Optimization Used by engineers to find the best design parameters for structures, equipments, etc. Used for process optimization and control system tuning ASPEN PLUS/ HYSYS Aspen Plus and HYSYS optimize chemical processes, energy use, environmental impact, and supply chains to enhance efficiency, reduce costs, and minimize environmental harm. Aspen Plus employs gradient-based and non-gradient-based optimization methods. HYSYS excels in dynamic simulation and optimization for time-dependent processes. Software for Optimization Processes PYTHON With its extensive library support, it enables engineers and data scientists to model, solve, and analyze optimization problems efficiently. Key libraries: SciPy, NumPy, PuLP, Pyomo, and CVXPY support various optimization algorithms Applications span across machine learning, supply chain management, financial portfolio optimization, and process engineering. ALTAIR Offers integrated, multiphysics optimization for seamless and robust design processes. Tools like OptiStruct, Inspire, and HyperStudy support topology, shape, and size optimization. Topology optimization creates lightweight, efficient designs by optimizing material layout. Altair's tools are used in automotive, aerospace, consumer products, and energy industries for performance and material efficiency. Optimization algorithms are used in engineering to enhance design efficiency, reduce costs, and improve performance in manufacturing processes. Examples include optimizing material usage in structures and fine-tuning parameters in control systems. In economics, optimization is Optimization algorithms are Operations research leverages crucial for resource allocation, central to training machine optimization to solve complex helping to maximize utility, learning models, where they decision-making problems in minimize loss functions to logistics, supply chain profits, or economic output improve model accuracy and management, and scheduling, under given constraints. It is aiming to enhance efficiency and widely used in economic performance. Techniques like reduce costs. It is essential for gradient descent are commonly modeling to simulate markets optimizing routes, inventory levels, used to optimize parameters in and policy impacts. and production schedules. neural networks.  Thank You GROUP 5 Baladad┃Dejan┃Gagarin┃Hortillosa┃Olar┃Refuerzo┃Ursolino  GROUP 6 Methods in Differential Equation Bulosan-Espinosa-Gotanco-Judilla Plange-San Pedro -Virtucio First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods First-Order Differential Equations A first order differential equation is an equation of the form F(t,y,y′)=0. A solution of a first order differential equation is a function f(t) that makes F(t,f(t),f′(t))=0 for every value of t. (Simon Fraser University, 2022) First-Order Differential Equations Separable Equations A first order differential equation is separable if it can be written in one of the following forms: First-Order Differential Equations Separable Equations 1 For an equation in the form: 3. which can be integrated directly: 2. multiplying both sides by h(y)dx 4. This will yield a solution for y(x). gives: First-Order Differential Equations Linear Equations A first order differential equation is linear when it can be made to look like this: First-Order Differential Equations Linear Equations Where P(x) and Q(x) are functions of x. To solve: We invent two new functions of x, call them u and v, and say that y=uv. We then solve to find u, and then find v, and tidy up and we are done! And we also use the derivative of y=uv First-Order Differential Equations Exact Equations Exact equation, type of differential equation that can be solved directly without the use of any of the special techniques in the subject. A first-order differential equation (of one variable) is called exact, or an exact differential, if it is the result of a simple differentiation. The equation: or in the equivalent alternate notation is exact if First-Order Differential Equations Integrating Factors Suppose we have the first order differential equation where P and Q are functions involving x only. For example We multiply both sides of the differential equation by the integrating factor I which is defined as First-Order Differential Equations Integrating Factors General Solution Multiplying our original differential equation by I we get that When is it used in Chemical Engineering? First-order differential equations are widely used in chemical engineering to model various processes where the rate of change of a variable is proportional to the variable itself or another factor. Here are some key applications: Reaction Kinetics Heat Transfer Mass Transfer Fluid Dynamics Process Control Population Balances and Mixing Radioactive Decay and Catalysis First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods Second-Order Differential Equations General Form Second order differential equation is a wherein, specific type of differential equation that consists of a derivative of a function of y’’ = is a second order 2 and no other higher-order derivative of y with derivative of the function appears in the respect to x equation. It includes terms like y'', d2y/dx2, y’ = first derivative a,b, and c = constant y''(x), etc g(x) = is a function of x  Second-Order Differential Equations Homogenous Equation Form: wherein General Solution: y1 & y2 are linearly independent solutions and C1 & C2 are arbitrary constants Auxiliary Equation: From the roots, we can determine the solution type: Real and Distinct: Complex Roots: Repeated Roots:  Second-Order Differential Equations Non-Homogenous Equation Form: where Yh​is the solution to the General Solution: corresponding homogeneous equation and Yp is a particular solution. Methods to Find the Particular Soln: Methods of Undetermine Coefficient Variation of Parameters  Second-Order Differential Equations Methods of Undetermine Coefficient When to use: The method of undetermined coefficients is most effective when the non-homogeneous term g(x): A polynomial An exponential function A sine or cosine function This method works well when g(x) has forms that allow for systematic guessing of the particular solution. Guide:  Second-Order Differential Equations Variation of Parameters When to use: This method is ideal for more complex non-homogeneous differential equations where the Method of Undetermined Coefficients is not applicable. Specifically, it’s useful when the non- homogeneous term g(x) is not a simple polynomial, exponential, or trigonometric function. Process: Identify the given second order differential equation and solve for General Solution To solve for particular solution or Yp apply the Wroskian Equation:  Application in Chemical Engineering Mass Transfer in Packed Beds and Membranes: When analyzing diffusion and mass transfer in packed bed reactors or membranes, second-order differential equations (like Fick’s second law of diffusion) describe how the concentration of a solute changes with respect to space and time. Axial Dispersion: Second-order PDEs model dispersion and diffusion of species in flow reactors and other similar systems. Fluid Mechanics: The Navier-Stokes equations, which govern fluid flow, often simplify to second-order differential equations for special cases like laminar flow in pipes. In the analysis of laminar flow (e.g., Hagen–Poiseuille flow), second-order ODEs describe velocity profiles and pressure drops in pipes. First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods Higher-Order Differential General form of the nth order differential equation Equations wherein, involves derivatives of an unknown function with respect to one variable and has derivatives of order greater than one. Higher-order Differential Equation Linear vs. Nonlinear DE If the equation involves only linear combinations of the function and its derivatives (no products or powers of y or y'), then it's linear. where are coefficient functions, and f(x) is the homogenous term (if zero). Higher-order Differential Equation Linear vs. Nonlinear DE On the other hand, if the equation involves nonlinear terms, such as powers or products of y and its derivatives, it is nonlinear. Nonlinear DE can be solved by reduction of order. Example: Get the integral of both sides insert dy/dx back Higher-order Differential Equation Linear vs. Nonlinear DE Get the integral of both sides of using First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods Systems of Differential Equations A finite set of differential equations. It What to expect: can either be linear or nonlinear. Also, Linear Systems such systems can either be a system of Ordinary Differential Equations (ODE) or Nonlinear Systems a system of Partial Differential Phase Plane Analysis Equations (PDE).  Linear Systems We are going to be looking at first order, linear systems of differential equations. The largest derivative anywhere in the system will be a first derivative and all unknown functions and their derivatives will only occur to the first power and will not be multiplied by other unknown functions. We call this kind of system a coupled system since knowledge of x2 is required in order to find x1 and likewise knowledge of x1 is required to find x2.  Linear Systems When we finally get around to solving these we will see that we generally don’t solve systems in the form that we were given. Systems of differential equations can be converted to matrix form and this is the form that we usually use in solving systems of differential equation  Linear Systems Converting the system to matrix form step-by-step.  Linear Systems Occasionally for “large” systems, we write the system as, Example: This time we’ll need define 4 new functions.  Linear Systems The system along with the initial conditions is then, Converting to matrix form. We need to be careful with the t2 in the last equation. We’ll start by writing the system as a vector again and then break it up into two vectors, one vector that contains the unknown functions and the other that contains any known functions.  Linear Systems Now, the first vector can now be written as a matrix multiplication and we’ll leave the second vector alone. where, We say that the system is homogeneous if g(t) = 0 and we say the system is nonhomogeneous if g(t) ≠ 0.  Nonlinear Systems A non-linear differential equation is one in which the unknown function and its derivatives don’t have a straight line when plotted in a graph. Problems involving nonlinear differential equations are extremely diverse, and methods of solution or analysis are problem dependent. Examples of nonlinear differential equations are the Navier–Stokes equations in fluid dynamics and the Lotka–Volterra equations in biology. Nonlinear Systems  Nonlinear Systems These equations describe how the velocity, pressure, temperature, and density of a moving fluid are related. The equations were derived independently by G.G. Stokes, in England, and M. Navier, in France, in the early 1800's. The equations are extensions of the Euler Equations and include the effects of viscosity on the flow.  Nonlinear Systems The Lotka–Volterra equations, also known as the Lotka–Volterra predator– prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact.  Phase Plane Analysis It is quite common now for phase planes to be readily determined and vividly displayed on any screen using software such as Matlab, Scilab, Mathematica, or MAPLE. These programs solve the system of differential equations numerically subject to given initial conditions. It is then easy for the program to take the numerical time-dependent solutions for x(t) and y(t) and use them directly to graph the phase plane (x, y). The time dependent solutiosn of the differential equation are the parametric description of the curve shown on your screen which we call the phase plane.  Phase Plane Analysis Here are a few more phase portraits so you can see some more possible examples.  Phase Plane Analysis Notice the difference between stable and asymptotically stable. In an asymptotically stable node or spiral all the trajectories will move in towards the equilibrium point as t increases, whereas a center (which is always stable) trajectory will just move around the equilibrium point but never actually move in towards it. First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods  Laplace Transforms Definition: The Laplace Transform is a mathematical tool used to make complex problems, like solving differential equations, simpler. It converts a function that depends on time like a signal or a system's response into a new function that depends on a different variable, usually called “s”. This new function is easier to work with because it turns difficult calculus problems into easier algebra problems. In chemical engineering, the Laplace Transform is very helpful for analyzing how systems behave over time, such as how heat flows through materials or how chemical reactions progress. Reference: Kreyszig, E. (2011). Advanced engineering mathematics (10th ed.). Wiley. Properties of Laplace Transform The Laplace Transform has certain properties that make it really useful in solving problems: Linearity: If you have two functions, you can transform them together, and the result will just be a combination of the two separate transforms. Time Shifting: If a process starts later (not at zero time), you can account for this shift easily in the transform. Differentiation and Integration: Instead of solving complicated derivatives or integrals directly, you can transform them, solve the simpler equations, and then transform back. These properties help engineers quickly solve problems that would take much longer using other methods. Properties of Laplace Transform The Inverse Laplace Transform is the opposite of the Laplace Transform. Once you've solved a problem in the “s”-domain (the transformed version), you use the inverse transform to convert it back to the original time-domain. Think of it as translating a problem into a different language to make it easier to solve, and then translating it back into the original language once you've found the answer. This is especially useful for finding out how a system behaves over time, like how a reactor’s temperature changes or how fast a chemical reaction reaches equilibrium. Solving Differential Equations with Laplace Transform: One of the biggest advantages of the Laplace Transform is how it simplifies solving differential equations. Here’s how: 1. Convert the equation: Use the Laplace Transform to change the differential equation into a simpler algebraic equation. 2. Solve the simpler equation: The transformed equation is much easier to solve because it’s just algebra. 3. Convert back: Use the Inverse Laplace Transform to get the solution back in the original form. This is especially useful in chemical engineering for analyzing dynamic systems—things that change over time, like temperature, pressure, or chemical concentrations. Applications in Chemical Engineering: In chemical engineering, the Laplace Transform is used in many areas: Process Control: Engineers use it to design systems that can automatically control processes like maintaining the temperature in a reactor or the flow rate in a pipe. Reaction Kinetics: It helps in modeling how fast chemical reactions happen and how reactants turn into products over time. Heat and Mass Transfer: It can be used to analyze how heat moves through materials or how chemicals diffuse in a mixture. These applications are critical for designing safe, efficient, and reliable chemical processes. First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods Fourier Series and Fourier transform is a tool for Transforms converting a function of time into a function of frequency. And it can also be applied not only to periodic functions but also nonperiodic functions. Fourier Series represents a periodic function as a sum of sines and cosines. It's particularly useful in analyzing periodic signals and functions. Fourier Series General Form If the function f(x) is on interval [-π,π], where Fourier Series Coefficient formulas Fourier Series General Form If f(x) has an interval of [-L, L], we change the following: so the form will be: Fourier Series Common functions One of the most common functions usually analyzed by this technique is the square wave. The Fourier series for a few common functions are summarized in the table below. Fourier Series Common functions If a function is even so that f(x) = f(-x), then f(x) sin(nx) is odd. Similarly, if a function is odd so that f(x) = -f(-x), then f(x) cos(nx) is odd. In simpler terms: even functions f(x), when multiplied by sin, produce odd results odd functions f(x), when multiplied by cosine, also produce odd results. Fourier Transform General Form The forward Fourier transform is a mathematical method used to convert a signal from the time domain into its frequency domain. It is denoted as F(k). The formula for forward Fourier transform is given as where, F(k) is the Fourier transform, which is a function of frequency k f(x) is the original function; a function of time e^-2πikx is the complex exponential; i is an imaginary unit Fourier Transform General Form The inverse Fourier transform transforms a signal from its frequency- domain representation back to its time-domain form. It is the reverse operation of the forward Fourier transform. The inverse Fourier transform is denoted by f(x) and is defined as: Fourier Transform General Form The inverse Fourier transform transforms a signal from its frequency- domain representation back to its time-domain form. It is the reverse operation of the forward Fourier transform. The inverse Fourier transform is denoted by f(x) and is defined as: Fourier Transform Properties 1. Linearity - if you have a linear combination of functions, the Fourier transform of that combination is the same linear combination of the Fourier transforms of the individual functions. where, a = time scaling constant b = time shifting constant g(x) = time-domain function G(k) = Fourier transform of g(x); frequency- domain of the function 2. Time-Shifting - A shift in time domain that corresponds to a phase shift in the frequency domain. where, i = sqrt. of -1 x0 = f(x) shifted in the time domain Fourier Transform Properties 3. Frequency Shifting - a modulation in the time domain. where, F (k-k0) = shifted F(k) in the domain k0 = frequency shift 4. Scaling - how scaling a function in the time domain affects its Fourier transform in the frequency domain. if |a| > 1, then f(ax) gets compressed in time and F(k) is stretched in freq. where, if |a| < 1, then f(ax) gets stretched and F(k) f(ax) = time-domain function scaled by factor a gets compressed 1/|a| = normalization factor; to adjust amplitude Fourier Transform Properties 5. Convolution - convolution operation in the time domain corresponds to multiplication in the frequency domain. 6. Conjugate Symmetry - if a function f(x) is real, its Fourier transform F(k) will have conjugate symmetry. Fourier Transform Properties 7. Duality - also known as time-frequency duality; states that the Fourier transform of a time-domain signal and the Fourier transform of its frequency-domain signal are related. First-Order Differential Equations Second-Order Differential Equations Higher-Order Differential Equations Systems of Differential Equations Laplace Transforms Fourier Series and Transforms Partial Differential Equations Numerical Methods Partial Differential Equations Partial Differential Equations (PDEs) are mathematical equations that describe the behavior of a function with respect to multiple independent variables. PDEs involve partial derivatives with respect to two or more variables. PDEs are essential tools for modeling continuous ph