Exam 2

Matter is conserved, neither created nor destroyed

To calculate unknown quantities using the mass balance principle

Usually, it is impractical to measure the masses and compositions of all streams/materials entering and leaving a system

Given the masses of some input and output streams, calculate the masses of others

What is the concentration of carbon dioxide in the fermenter off-gas?

How much reactant is needed to produce x grams of product?

How much oxygen must be provided for this fermentation to proceed?

No mass enters or leaves the system

Mass exchanged across boundary

Variables do not change over time

Variables do change with time

Humidified oxygen-enriched air is generated for a gluconic acid fermentation process. This is achieved within a specialized humidification chamber. Liquid water is introduced into the chamber at a rate of 1.5 liters per hour, concurrently with dry air and a flow of 15 mol/min of dry oxygen gas. All supplied water is vaporized during the process. Upon exiting the chamber, the gas is observed to contain 1% (w/w) water content

1. Batch fermentation

2. Fed-batch fermentation

3. Semi-batch fermentation

4. Continuous fermentation

All materials added to the system at the start of the process

The system is then closed

The products are removed only when the process is complete

Operates in a closed system

Allows input of materials to the system but not output

Open systems

The total mass of the system is changing with time

Allows either input or output of mass

Allows matter to flow in and out of the system

Reactants are continuously fed into the reactor

Products are continuously collected.

Open system

Continuous processes may be either steady-state or transient

Continuous processes can be run as close to steady state.

Raw material continuously transforms into the desired product.

No accumulation

The system is at steady state: all properties of the system, including its mass, must be unchanging with time ( dm/dt = 0) (no leaking)

The accumulation is zero

Mass flow rates do not change with time.

The system under investigation does not leak

Mass in = Mass consumed

Mass in = Mass consumed + Mass out

Mass produced = Mass out

Mass out = Mass produced + Mass in

Mass in = Mass out

1. Draw a clear process flow diagram showing all relevant information

   • Identify mass streams

   • List all given values

   • Select system unit

2. Create a mass balance table

3. Preform mass balance calculations

the solid material that accumulates on the surface of a filter medium during a filtration process

Mass In = Mass Consumed + Mass Out

We separate the streams of gases from solids and liquids

Gas is used: fermenter off-gas in Mole %

Water is always part of Feed-in stream, and Product stream

We use kg for mass and kg/kmol for molar mass

Molar mass: kg/kmol is equivalent to g/mol

By wieght:

23.3% O2

76.7% N2

By mole:

21% O2

79% N2

At steady state, all properties of the system, including its mass, must be unchanging with time

dm/dt = 0

mass in = mass out

1. A batch Fermentation

2. A fed-batch Fermentation

3. A semi-batch Fermentation

4. A continuous Fermentation

Batch, fed-batch, and semi-batch processes: Unsteady State

Continuous processes: May be either steady-state or transient

System properties vary with time

Goal: determine the rate of change of system parameters

Rate of change of mass/concentration of materials in the system

Cells in the fermenter consume glucose at a given rate

A feed stream containing glucose enters a at a constant flow rate (F)

integration

requires knowledge of boundary condition

• Boundary conditions contain extra information about the system

• The number of boundary conditions required depends on the order of the differential equation

• One boundary condition is required to solve a first-order differential equation (dx/dt)

1. Determine which of the 3 equations we should use.

2. Determine which of the variables in the equation is zero, constant, or changes as a function of time

   Example: Volume, density, etc.

3. Determine appropriate initial conditions or boundary conditions