1. introduction; equations, variables & units

1/28

Processteknikens grunder (”PTG”)Introduction to Process Engineering

course # 424101.0 v. 2014

Ron ZevenhovenÅbo Akademi University

Thermal and flow engineering (Värme- och strömningsteknik: VST) *tel. 3223 ; [email protected]

1. Introduction; Equations, variables & units

* until August 2009: Heat engineering laboratory (Värmeteknik, VT)

Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland

2/28

1.1 Process engineering; This course

2014: weeks 36-44: 1 Sept. – 31 Oct.Mon + Tue + Thu 1-3 pm


3/28

Contents of course 2014 (lecture hours +/-)

Introduction; Equations, variables and units (2)

System boundaries; Mass balances; Other balances (2)

Energy balances (1st Law of Thermodynamics), Energy efficiency(2nd Law of Thermodynamics), Equilibrium (10-12)

Heat exchangers and Heat (steam) cycles (6-7)

Heat transfer (conduction, convection, radiation) (10-12)

Fluid flow and Tube flow (8-10)

Exercises / Old exams (10)

Additional material (not part of exam !) on– Mass transfer; Separation processes– Particle technology; Multi-phase systems– Process equipment– Process control

For those for whom this course will be the first and last engineering course : take a look......

4/28

What is a process?

”A process occurs whenever some property of a system changes or if there is an energy or mass flow across the boundary of a system”(source: KJ05)


5/28

What is process engineering ?

“Process engineering is often a synonym for chemical engineering and focuses on the design, operation and maintenance of chemical and material manufacturing processes” (source: wikipedia)


6/28

A typical process: CO2 stripping

Picture: SA05

Natural gas + CO2

Liquid solventfor example

alkanol amine

Natural gas

Liquid solvent+ CO2

7/28

Chemical process engineering

ThermodynamicsHeat transfer Fluids engineering

Separationprocesses

Process equipmentand plant design

Mass transfer

Process control andautomation

This course: a lot This course: a bit

”THERMAL SCIENCES”

Process economics and legislation

Chemical reaction engineering

Product, waste andby-product handling

Process safety and maintenance

Raw material pre-processing


8/28

1.2 Process calculations; Equations, variables and units


9/28

Process calculations /1

Engineering calculations often start with balance equations (mass balance, energy balance, element balances, etc.) – see #2

Dynamics equations are often ordinary or partial differential equations with time as onevariable. Very important are boundaryconditions and starting conditions.

! Always respect the Laws of Physics ! Always check whether the result of a

calculation makes sense and is possible.for example: 0 ≤ reactor mass < mass of earth,

temperature ≥ 0 K, pressure ≥ 0 Pa


10/28


Back-of-the-envelope calculation may be morepowerful than a computer !

The results of good models may be close to reality but nonetheless will be incorrect.

Analytical solutions are often more useful(as a result of a wider range of applicability)

than numerical solutions. ! Too many decimals make no sense ! Engineering calculation results will be adjusted

and rounded-off to shop specifications: for example: calculated tube diameter 2.93 m 3 m


11/28


Some basic rules for variable symbols: – don’t use one symbol for two different things– try to use one character per variable– choose symbols ”logically”: time t, volume V, ...

for example: pressure p, temperature T, etc.– use indices/subscripts if one symbol is needed

for several things, use vectors x1, x2, x3, ...– use supercripts 2, 3 etc. for square x2, cube x3, ..– vector notation can make equations compact

for example v = (vx, vy, vz) in x,y,z coordinates

Always remember: READ IT AS PHYSICS.Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland

12/28

Prefix symbols for scales of 10

be careful with decimal . or ,

use scales of 10: 1 Gg = 109 g = 106 kg;1 nm = 0.001 µm = 10-6 mm = 10-9 m;etc.

Engineers usuallystick to powers of 3:103, 10-6, 109, etc.

Table: KJ05


13/28

Variables and units /1

A property or quantity (sv: storhet) of an object, substance or material can be defined as a characteristic that can be measured or calculated.

The value of a property or quantity)(sv: storhetvärde) is a combination of a numericalamount (sv: mätetal) and a unit (sv: måttenhet)

for example: length = 6.5 mquantity value unit

speed = 50 km/s

Without a unit the information of a value is of limited use or even useless !

Picture: KJ05


14/28

Most engineering calculations are based on physicalquantities that can be expressed as combinations of seven base quantities (sv: grundstorheter)

In the SI system (Système Internationale) these have the following base units (sv: grundenheter):

Base quantity Base unit name Base unit symbol (SI)

Length meter m

Mass kilogram kg

Time second s

Temperature Kelvin K

Amount of substance mole mol

Electric current Ampère A

Luminous intensity candela cd


Mostrelevant

forprocess

technology

15/28

Derived units (sv: härledda enheter) are based on combinations of basic units. Some examples of the ~ fifteen derived units:Quantity (symbol) Unit name, symbol Definition

Force (F) Newton, N kg m s-2

Pressure (p) Pascal, Pa kg m-1 s-2 = N m-2

Energy (E) Joule, J kg m2 s-2 = N m

Power (P) Watt, W kg m2 s-3 = J s-1

Frequency (f) Herz, Hz s-1

Electric charge (q) Coulomb, C A s

Catalytic activity katal, kat mol s-1

• Other units can always be rewritten as basic units:for example for dynamic viscosity: unit Pa·s = kg m-1 s-1


16/28

Variables and units /4 Different sets of base units can be used,

for example 1 mil (in Sweden) = 10 km.

Most important are the Anglo-Saxon or US ConventionalSystem (USCS) units: 1” = 1 inch = 2.54 cm ;1 foot = 1 ft = 12” = 30.48 cm; 1 yard = 1 yd = 3 ft1 ounce = 1 oz = 28.35 g;1 pound = 1 lb = 16 oz = 0.454 kg ;1 pound per square inch = 1 psi = 6894.8 Pa; 1 bar = 105 Pa = 14.504 psi;1 gallon US = 3.7854 liter; 1 gallon UK = 4.5461 liter1 barrel US = 158.9873 liter

Temperature as °C or °F or K (see slide 24)1 British thermal unit = 1 BTU = 1055 J

one ounce of gold


17/28


Calculatingnon-SI units ↔ SI unitsshould be a routine thing !

Use conversion tables.

Examples of some very important units:1 torr = 1 mm Hg (at 0°C)= 133.32 Pa; 1 atm = 101325 Pa1 t = 1 metric ton = 1000 kg; (viscosity: ) 1 centipoise = 1 cP = 0.001 Pa· s 1 kWh = 3.6 MJ; 1 calorie = 1 cal = 4.184 J; 1 Å = 0.1 nm

Picture: KJ05


18/28

A property is a characteristic of a system (see #2), which is related to a mass or a subtance, or to energy: for example: temperature, mass, volume, pressure, viscosity

An extensive property depends on the mass in the system for example volume, energy, ...

An intensive property is independent of the amount of material for example temperature, pressure, density...

Picture: CB98

Properties, state properties /1

19/28

Properties, state properties /2

A specific property is an extensive property per unitmass (resulting in an intensive property) for example specific volume = volume / mass = 1/density; unit: m3/kg ; specific energy = energy / mass; unit : J/kg

A set of state properties (sv: tillståndstorheter) defines the state of a system; the other properties are related to changes

The properties that depend on the present state of a system, independent of the way howthis state was prepared, are also calledstate functions

The properties that depend on how the present state was reached or how a system is affectedby a change are called path functions (for which the path must be specified !) (source: A83)

Sou

rce:

http

://im

ages

.flat

wor

ldkn

owle

dge.

com

/ave

rillfw

k/av

erill

fwk-

fig05

_006

.jpg


Two ways for the same result

20/28

Equations /1

All elements of an equation must have the same dimension.

Sometimes a constant is needed whenvariables with a different dimension are related in an expression,

for example heat transfer by

radiation (see #5): Q” = σ ·T4, with heat flux Q” (W/m2) and

temperature T (K) gives

Stefan-Boltzmann constant

σ = 5.67×10-8 W/(m2·K4) Picture: KJ05


21/28

Relations between quantities or variables non-specific to the unit system (sv: storhetsekvationer)

for example : for mass flow m of a fluid with density ρ, flowing at velocity v through a tube with radius r.

Relations between quantities or variables specific to the unit system (sv: kvotekvationer)

for example :

for the density of an ideal gas as function of pressure p, temperature T and molar mass M.

vrm 2

m

kg

)K(T

kmol/kgM

kPap

.ρ

.

Equations /2

22/28

Alternatively, but not recommended, equations are based on quantities and amounts (sv: mätetalsekvationer). The same unit system as the equation is based on must then be used.for examplefor the tube mass flow mentioned above, with r in mm, v in m/s, m in kg/h and ρ in kg/m3. Using other units will require a conversion and giveanother value for the constant.

vr.m 201130

.

Equations /3

23/28

Mass, weight, moles

”Weight” is a force equal to Mass × Gravity. (sv: tyngd,vikt, massa; fi: kuorma, kuormitus, paino)

Mass = Molar mass × Number of molesnote: Molar mass as g/mol = kg/kmol = 10-3 kg/mol (!!!)

for example 1 mole O2 = 32×10-3 kg/mol


24/28

Temperature scales

T(°F) = 1.8·T(°C) + 32 T(°C) = ( T(°F) – 32 )/1.8

T(K) = T(°C) + 273.15 T(°C) = T(K) - 273.15

T (R) = T(°F) + 459.67 T(R) = 1.8·T(K) Picture: SEHB06

for exampleuse symbols

T for T(K)and

θ for θ(°C)

Kelvin

Celsius

Fahrenheit

Rankine

25/28

Dimensionless variables /1 The requirement of dimension-correctness of an

equation can also be used to determine physicalrelations between quantities.for example: velocity v = f ( time t, distance x)

test function: v = tα· xβ

unit left-hand-side: m+1· s-1; unit right-hand-side: sα· mβ

gives for time: α = -1; for length β = +1 → v = x / t


26/28

Dimensionless variables /2 This method is very powerful and is used as so-called

dimension analysis in process engineering, combiningquantities in dimensionless groups. Very powerful for scale-up!

for example: pressure drop ∆p for flow of a fluid with density ρand dynamic viscosity η at velocity v in a pipe with diameter d and length L: ∆p = f(ρ,η,v,d,L) with 6 quantities and 3 basicunits (kg, m, s) requires 6 - 3 = 3 dimensionless groups. The result:

More on this method in VST course 424302 (7 sp)Massöverföring & separationsteknik / Mass transfer and separation technology

)Ld

()ηρvd

(Avρp∆

example for )Ld

,ηρvd

(fvρp∆ CB

27/28

A few examples Calculate the diameter of a tube, in m, for a mass flow of 380 kg/s

water at 98°C, with density 960 kg/m3, at 3 m/s (ÖS96-1.1a)

answer:

For the ideal gas law p·V = n·R·T with pressure p (Pa), volume V (m3), number of moles (mol) and temperature T (K), show that the unit for the universal gas constant R is J / (mol· K)answer:

What temperature in K and in °C corresponds to 2000 °R ?answer: 2000°R = 2000/1.8 = 1111.11 K = 837.96 °C

m .v

m2 r2d

d diameter for gives vrm equation

4103960

3802

2

Kmol

J

Kmol

mN

Kmol

m)m/N(

Kmol

mPa R of unit

323

28/28

Sources #1 A83: P.W. Atkins ”Physical chemistry”, 2nd ed., Oxford Univ. Press

(1983) CB98: Y.A. Çengel, M.A. Boles “Thermodynamics. An Engineering

Approach”, McGraw-Hill (1998) KJ05: D. Kaminski, M. Jensen ”Introduction to Thermal and

Fluids Engineering”, Wiley (2005) SA05: Socolow, R.H. ”Can we bury global warming” Scientific

American, July 2005, 49-55 SEHB06: P.S. Schmidt, O. Ezekoye, J. R.

Howell, D. Baker “Thermodynamics: An Integrated Learning System” (Text + Web) Wiley (2006)

ÖS96: G. Öhman, H. Saxén ”Värmeteknikensgrunder”, Åbo Akademi University (1996)


1. introduction; equations, variables & units

Documents