MATERIALS AND ENERGY BALANCES

Synthetic Gas Upgrading Process: Material and Energy Balances

Reprinted by permission from Materials and Energy Balances by Ray E. Desrosiers, Chemical Engineering Department, Texas Tech University. Copyright © 1998. All rights reserved.

Define

Stream indices

Species indices (in the order listed for products):

Reaction indices

Water split fraction in separator

Data

Thermodynamic Data for Gas-Phase Species

Heat Capacities
(average)

Molecular
Weights

CO
H₂
CO₂
CH₄
H₂O

Standard Heats
of Formation

Water Properties

Liquid-phase heat capacity

Heat of vaporization at 90 F:

Heat of formation:

Density:

Stream Temperatures

Initialize array:

Fixed temperatures and constants:

Feed

Cooler exit

Product stream

Condensate stream

Separator overhead

Water split fraction

Methane-free composition of feed:

CO
H₂
CO₂
CH₄
H₂O

Initialize compositions and flowrates:

Product composition:

CO
H₂
CO₂
CH₄
H₂O

Reaction stoichiometry:

CO + 3 H₂ = CH4 + H₂O (1)
CO + H₂O = CO₂ + H₂ (2)

Basis
Select the flowrate of the product stream

The product composition is given:

Overall Balances
For the performance of these balances only, let us envision that the feed actually consists of two streams: a methane-free stream and a stream of pure methane. If we perform three element balances, we can solve for the three unknown flowrates.

Estimate:

C balance:

O balance:

H balance:

Solve:

External Stream Flowrates

Feed:

Condensate:

Separator Balances

The flowrate of the condensate stream is known from the overall balances. This stream represents a given fraction of the water in stream 7, whose composition is known, so the component flowrates in this stream can be determined.

Splitter stream composition is known:

The water recovery fixes the flowrate:

The material balance characterizes the separator overhead stream:

The energy balance fixes the cooling duty on the separator. Reference state is the gaseous species at T_r.

Splitter constraint:

Enthalpy of liquid water stream:

Splitter Balances

Now that stream 7 is fully characterized, the flowrate and temperature of stream five can be determined.

Material balance:

Adiabatic-splitter:

Heat Exchanger II Balances

The flow rates of streams 4 and 10 are the same as those of streams 5 and 9 respectively. An energy balance yields the temperature of stream 10.

Material balances:

( 415 F)

Mixer Balances

The material and energy balances can be done sequentially.

Material balance:

Energy balance:

Reactor Balances

The composition of the stream leaving the reactor is known. Only the temperature needs to be determined. But to be safe, let’s first check the reaction rates, and check for consistency.

Heat exchanger constraint:

The rates of the two reactions can be determined most easily by using the stoichiometric relations for species that occur in only one reaction. Methane and carbon dioxide qualify.

Methane balance:

Carbon dioxide balance:

Check for consistency:

Reactor Energy Balance

For the reactor balance, we use reference states consisting of the elements.

Estimate:

Objective function:

Solve:

Cooler Energy Balance:

Convert to Mass Units:

Avg stream molec wts:

Total mass flow rates:

Component mass flow rates:

Mass fractions:

Get temps in def F:

Table 4. Material and Energy Balance Summary

Material Balance Checks