Mô hình hóa, mô phỏng và tối ưu hóa các quá trình hóa học - Hoàng Ngọc Hà

Mụ hỡnh húa, mụ phỏng và tối ưu húa cỏc quỏ trỡnh húa học Modeling, simulation and optimization for chemical process Instructor: Hoang Ngoc Ha Email: ha.hoang@hcmut.edu.vn Bộ mụn QT&TB Curriculum/syllabi Seminar group CuuDuongThanCong.com https://fb.com/tailieudientucntt Outline • General introduction – Structure and operation of chemical engineering systems – What is a chemical process? – Motivation examples • Part I: Process modeling • Part II: Computer simulation • Part III: Optimization of chemical processes CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction • Structure of chemical engineering system (Copyright â by Prof. Paul Sides at CMU, USA) CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction • Conservation laws: – Give some balance equations such as mass balance (or the molar number by species), energy balance and momentum equation of the system under consideration • Equilibrium thermodynamics – The extensive variables/intensive variables – The laws of thermodynamics • Reaction engineering – Reaction mechanism – The rate of a chemical reaction • Transport processes – How materials and energy move from one position to another (heat conductivity, diffusion and convection) • Biological processes – Transform material from one form to another (enzyme process) or remove pollutants (environmental engineering) CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction • References (complements) : 1. Sandler S. I. (1999). Chemical and Engineering Thermodynamics. Wiley and Sons, 3rd edition. 2. H.B. Callen. Thermodynamics and an introduction to thermostatics. JohnWiley & Sons Inc, 2nd ed. New York, 1985. 3. De Groot S. R. and P. Mazur (1962) Non-equilibrium thermodynamics. Dover Pub. Inc., Amsterdam. 4. Vũ Bỏ Minh. (tập 4) Kỹ thuật phản ứng. NXB ĐHQG Tp. Hồ Chớ Minh, 2004 5. Nguyễn Bin, (tập 5) Cỏc quỏ trỡnh húa học. NXB Khoa học và Kỹ thuật, 2008 CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction • Conservation laws: – Give some balance equations such as mass balance (or the molar number by species), energy balance and momentum equation of the system under consideration • Equilibrium thermodynamics – The extensive variables/intensive variables – The laws of thermodynamics • Reaction engineering – Reaction mechanism – The rate of a chemical reaction • Transport processes – How materials and energy move from one position to another (heat conductivity, diffusion and convection) • Biological processes – Transform material from one form to another (enzyme process) or remove pollutants (environmental engineering) CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction „ Operation of a chemical engineering plant Copyright â by T. Marlin (Σ) Dynamical behavior CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction „ Oil and gas production plant CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction „ The system may be ‰ Isolated: There is no transfer of mass or energy with the environment ∑ ∑‰ Closed: There may be transfer ofmechanical energy and heat ‰ Open: There is mass transfer with the environment ∑ CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction Gas BA, JQ . BA BA υυ → Question: determinate physical volume of the following systems? CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction „ What is a chemical process? ‰ Process: A set of actions performed intentionally in order to reach some result (Longmans Dictionary of Contemporary English) ‰ Processes that involve energy conversion, reaction, separation and transport are called chemical processes (Prof. Erik Ydstie at CMU, USA) ‰ Definition: Chemical processes are a special subclass of processes since their behavior is constrained by a range of laws and principles which may not apply in other circumstances (mechanical/electrical systems) ‰ Properties: „ Highly nonlinear „ Complex network „ May be distributed CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction „ Chemical processes ‰ Thermal conductivity process ‰ Transport (reaction) process ‰ CuuDuongThanCong.com https://fb.com/tailieudientucntt General introduction „ Why we need informations about dynamical behavior? ‰ Research and development ‰ Process design ‰ Process control ‰ Plant operation ‰ Process modeling, computer simulation and optimization (Σ) Ordinary Differential Equations (ODEs) or Partial Differential Equations (PDEs) or Differential and Algebraic Equations (DAEs) CuuDuongThanCong.com https://fb.com/tailieudientucntt Motivation examples „ Example 1: Gravity-flow tank The higher the flow rate F¯ , the higher h¯ will be h F0 F F F0 = F0(t), h = h(t) and F = F (t) F¯0, h¯ and F¯ : steadystate values Overshoot How to understand dynamical behavior to design the system avoiding ô Overshoot ằ? CuuDuongThanCong.com https://fb.com/tailieudientucntt Motivation examples „ Example 2: Heat exchanger Thermocouple Temperature transmitter Temperature controller Final control element CuuDuongThanCong.com https://fb.com/tailieudientucntt Motivation examples „ Example 3: Typical chemical plant and control system ắTwo liquids feeds are pumped into a reactor ắThey react to form products ắReactor effluent is pumped through a preheater into a distillation To specify the various pieces of equipment: •Fluid mechanics •Heat transfer •Chemical kinetics •Thermodynamics and mass transfer CuuDuongThanCong.com https://fb.com/tailieudientucntt Motivation examples „ Example 4: Optimization of a silicon process The silicon reactor CuuDuongThanCong.com https://fb.com/tailieudientucntt Motivation examples „ Example 4: Optimization of a silicon process CuuDuongThanCong.com https://fb.com/tailieudientucntt Outline „ General introduction ‰ Structure and operation of chemical engineering systems ‰ What is a chemical process? ‰ Motivation examples „ Part I: Process modeling „ Part II: Computer simulation „ Part III: Optimization of chemical processes CuuDuongThanCong.com https://fb.com/tailieudientucntt Process modeling „ Introduction „ Fundamental laws ‰ Continuity equations ‰ Energy equation ‰ Equations of motion CuuDuongThanCong.com https://fb.com/tailieudientucntt Introduction „ Uses of mathematical models ‰ Can be useful in all phases of chemical engineering, from research and development to plant operations, and even in business and economic studies „ Research and development: ‰ Determinating chemical kinetic mechanisms and parameters from lab. or pilot-plant reaction data ‰ Exploring the effects of different operating conditions ‰ Adding in scale-up calculations „ Design ‰ Exploring the sizing and arrangement of processing equipment ‰ Studying the interactions of various parts „ Plant operation ‰ Cheaper, safer and faster ‰ Troubleshooting and processing problems CuuDuongThanCong.com https://fb.com/tailieudientucntt Introduction „ Scope of course ‰ A deterministic system is a system in which no randomness is involved in the evolution of states of the system ∑ Random effects such as noise ‰ A stochastic system is non-deterministic system CuuDuongThanCong.com https://fb.com/tailieudientucntt Introduction „ Principles of formulation ‰ Basis „ Fundamental physical and chemical laws such as laws of conservation of mass, energy and momentum ‰ Assumptions „ Impose limitations ô reasonable ằ on the model ‰ Mathematical consistency of model „ Number of variables equals the number of equations (degrees of freedom) „ Units of all terms in all equations are consistent CuuDuongThanCong.com https://fb.com/tailieudientucntt Introduction ‰ Solution of the model equations „ Initial and/or boundary conditions „ Available numerical solution techniques and tools „ Solutions are physically acceptable? ‰ Verification „ The mathematical model is proving that the model describes the “real-world” situation ‰ Real challenge CuuDuongThanCong.com https://fb.com/tailieudientucntt Fundamental laws „ Continuity equations ‰ Total continuity equations (total mass balance) EXERCISE ? ‰ Component continuity equations (component balance) CuuDuongThanCong.com https://fb.com/tailieudientucntt Fundamental laws „ Energy balance EXERCISE ? CuuDuongThanCong.com https://fb.com/tailieudientucntt Fundamental laws „ Equations of motion „ Pushing in the i direction (i=x,y,z) −→ F = d ³ M−→v ´ dt Where −→v = velocity, −→F = total force and M = mass Fi = d ³ Mvi ´ dt EXERCISE ? CuuDuongThanCong.com https://fb.com/tailieudientucntt Fundamental laws „ Consider a system with n components ‰ Number of equations obtained from the fundamental laws „ n balance equations by species „ 1 total mass balance equation „ 1 energy balance equation „ 3 equations of motion (if the system is under movement) ⎭⎬ ⎫ Not independent ⇒ n+ 1 + (3) equations CuuDuongThanCong.com https://fb.com/tailieudientucntt Constitutive equations Reaction kinetics of (bio)chemical reaction Transport equations k = k(T,C) CuuDuongThanCong.com https://fb.com/tailieudientucntt Other equations „ As we saw, we need equations that tell us how the physical properties, primarily density and enthalpy, change with temperature, pressure, and composition to rewrite alternative mathematical models ‰ Equations of state CuuDuongThanCong.com https://fb.com/tailieudientucntt Other equations (cont.) „ In some cases, simplification can be made without sacrificing much overall accuracy „ Or more complex, Cp is considered as a function of temperature H = CpT (liquid) H = CpT + λv (vapor) H = R T Tref Cp(T )dT CuuDuongThanCong.com https://fb.com/tailieudientucntt Other equations (cont.) „ A polynomial in T is used for Cp „ We obtain Cp(T ) = A1 +A2T H = h A1T +A2 T 2 2 iT Tref = A1(T − T0) + A22 (T 2 − T 20 ) CuuDuongThanCong.com https://fb.com/tailieudientucntt Other equations (cont.) „ If the mixture is composed of components (which we know the pure-component enthalpies) then the total enthalpy can be averaged H = PN j=1 xjhjMjP N j=1 xjMj xj Mj hj - mole fraction of jth component - molecular weight of jth component - pure-component enthalpy of jth component (energy per unit mass) CuuDuongThanCong.com https://fb.com/tailieudientucntt Other equations (cont.) „ Liquid densities can be assumed constant in many systems „ Vapor densities usually cannot be considered invariant in many systems and the PVT relationship is almost always required. ‰ The simplest and most often used case is the perfect gas law PV = nRT ⇒ ρv = nMV = PMRT CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process (Distributed) Transport reaction systems De Groot S. R. and P. Mazur (1962) Non-equilibrium thermodynamics. Dover Pub. Inc., Amsterdam. CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process „ Distributed reaction systems (reactor tubular for example) n chemical species Inlet material and/or energetic flux Outlet material and/or energetic flux V,Ω P k νkSk = 0 (Σ) dV CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process „ Mass conservation by species dmk dt = d dt R V ρkdV = R V ∂ρk ∂t dVR V νkMkrvdV ⇒ ∂ρk∂t = −div(Jk) + νkMkrv = − R V div(Jk)dV Gauss theorem Jk = vkρk − R Ω Jk ã dΩ Total m aterial flux CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process ρ = P k ρk v = P k Jk ρ Jdk = ρk(vk − v) Jck = ρkv ⇒ Jk = Jdk + Jck ∂( P k ρk) ∂t = −div( P k Jk) ∂ρ ∂t = −div(vρ) v = ρ−1 ∂v ∂t + v ã −→∇v = vdiv(v) Dv Dt CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process J0q = ρ (u+ pv)| {z } =h v + JqJu = ρuv + pv+ Jq ∂ρu ∂t = −divJu = − R Ω Ju ã dΩ P k hkJ c k P k hkJ d k dU dt = R V ∂ρu ∂t dV CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process „ Seminar: ‰ Nonisothermal CSTR ‰ Batch reactor ‰ pH systems ‰ Distillation column CuuDuongThanCong.com https://fb.com/tailieudientucntt Examples of mathematical modeling of chemical process „ Seminar: ‰ Nonisothermal CSTR ‰ Batch reactor ‰ pH systems ‰ Distillation column CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng „ Sự vận chuyển trong thiết bị phản ứng của hỗn hợp phản ứng, bao gồm: ‰ Dũng vật liệu (khối lượng/nồng độ) ‰ Dũng nhiệt năng (năng lượng) ‰ Dũng động lượng (xung) „ Cú dũng đối lưu, dũng dẫn, dũng cấp và dũng phỏt sinh ‰ Dũng đối lưu hoặc dũng dẫn cú thể tồn tại độc lập hoặc đồng thời nhưng chỉ trong một pha ‰ Sự võn chuyển xảy ra qua lớp biờn của hai pha là dũng cấp (lượng/thể tớch) Được đặc trưng bởi mật độ dũngΓ⇒ CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng „ Cỏc quỏ trỡnh vận chuyển trong thiết bị ‰ Dũng đối lưu „ Sự thay đổi vị trớ trong khụng gian của mật độ dũng được gọi là đối lưu (dũng vận chuyển vĩ mụ) „ Mật độ dũng đối lưu được biểu thị ‰ Dũng dẫn (khuếch tỏn) „ Chuyển động phõn tử trong lũng pha khớ hoặc pha lỏng là chuyển động vi mụ tạo thành dũng dẫn −→ j c = Γ −→v (lượng/thời gian/diện tớch) (lượng/thời gian/diện tớch) −→ j d = −D −−→ gradC CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng „ Cỏc quỏ trỡnh vận chuyển trong thiết bị (tt) ‰ Dũng cấp „ Sự vận chuyển của đại lượng đặc trưng từ pha này sang pha khỏc gọi là sự cấp „ Cỏc quỏ trỡnh xảy ra giữa cỏc pha thường được mụ tả bằng cỏc đại lượng quảng tớnh (lượng/thời gian/diện tớch) - hệ số cấp, ² - bề mặt riờng (xột trờn một đơn vị thể tớch)f −→ j = ²f∆Γ ∆Γ- động lực CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng ‰ Dũng phỏt sinh „ Dũng phỏt sinh vật chất do phản ứng húa học G = −−→ gradP Gj = Pm i=1 νjiri Gi = (−∆Hi)ri „ Dũng phỏt sinh cuả nhiệt năng do phản ứng húa học „ Dũng phỏt sinh của động lượng do chờnh lệch ỏp suất ‰ Được hỡnh thành do sự thay đổi của ỏp suất trong hệ, tức là cú tỏc dụng của xung lực „ Cỏc quỏ trỡnh vận chuyển trong thiết bị (tt) CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng „ Xột trường hợp hệ tổng quỏt (đồng thể hay dị thể) cú phản ứng húa học n chemical species Inlet material and/or energetic flux Outlet material and/or energetic flux dVP j νijSj = 0 CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng ‰ Phương trỡnh cõn bằng tổng quỏt cú dạng của phương trỡnh vi phần riờng phần được Damkửhler thiết lập (1936) −→ j c −→ j d Dũng cấp Dũng phỏt sinh ∂Γ ∂t = −div(−→v Γ) + div(δ −−→ gradΓ)− ²f∆Γ+G Γ = ρ Cj ρCpT ρ −→v CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng „ Viết lại cỏc phương trỡnh cõn bằng ∂Γ ∂t = −div(−→v Γ) + div(δ −−→ gradΓ)− ²f∆Γ+G ∂ρ ∂t = −div(−→v ρ) + div(D? −−→ gradρ)− β?f∆ρ+G ∂ρ−→v ∂t = −div(−→v ◦ ρ−→v ) + div(ν −−→ gradρ−→v ) −γf∆(ρ−→v ) +G ∂ρCpT ∂t = −div(−→v ρCpT ) + div(αT −−→ gradρCpT ) −α?f∆ρCpT +G ∂Cj ∂t = −div(−→v Cj) + div(D −−→ gradCj) −βjf∆Cj +Gj CuuDuongThanCong.com https://fb.com/tailieudientucntt Phương trỡnh dũng „ Example: xem chương 5, tập 5 (sỏch Cỏc quỏ trỡnh, thiết bị TRONG CễNG NGHỆ HểA CHẤT VÀ THỰC PHẨM, Nguyễn Bin) ‰ Mụ hỡnh toỏn cho hệ khuấy lý tưởng ‰ Chuỗi thiết bị khuấy lý tưởng ‰ Thiết bị khuấy giỏn đoạn ‰ Thiết bị đẩy lý tưởng ‰ Cỏc bài toỏn thực tế ∂Γ ∂t = −div(−→v Γ) + div(δ −−→ gradΓ)− ²f∆Γ+G CuuDuongThanCong.com https://fb.com/tailieudientucntt Outline „ General introduction ‰ Structure and operation of chemical engineering systems ‰ What is a chemical process? ‰ Motivation examples „ Part I: Process modeling „ Part II: Computer simulation „ Part III: Optimization of chemical processes Ref.: Burden R. L. and Faires J. D. Numerical analysis. CuuDuongThanCong.com https://fb.com/tailieudientucntt