Often engineers are tasked with communicating equipment specifications with suppliers, where process data needs to be exchanged for engineering quotations & orders. Any dearth of data would need to be computed for which process related queries are sometimes sent back to the process engineer’s desk for the requested data. The following tutorial is a refresher for non-process engineers such as project engineers, Piping, Instrumentation, Static & Rotating Equipment engineers to conduct basic process calculations related to estimation of mass %, volume %, mass flow, actual & standard volumetric flow, gas density, parts per million (ppm) by weight & by volume.

1. Page 1 of 5
Chemical Process Calculations – Short Tutorial
Jayanthi Vijay Sarathy, M.E, CEng, MIChemE, Chartered Chemical Engineer, IChemE, UK
Often engineers are tasked with
communicating equipment specifications
with suppliers, where process data needs to
be exchanged for engineering quotations &
orders. Any dearth of data would need to be
computed for which process related queries
are sometimes sent back to the process
engineer’s desk for the requested data.
The following tutorial is a refresher for non-
process engineers such as project engineers,
Piping, Instrumentation, Static & Rotating
Equipment engineers to conduct basic
process calculations related to estimation of
mass %, volume %, mass flow, actual &
standard volumetric flow, gas density, parts
per million (ppm) by weight & by volume.
Problem Statement
A vendor requests the project engineer to
provide certain natural gas process data for
evaluation. The gas composition is as follows,
Table 1. Natural Gas Composition & Properties
Component MW Mol%
- kg/kmol %
Methane 16.04 76.23
Ethane 30.07 10.00
Propane 44.01 5.00
i-Butane 58.12 1.00
n-Butane 58.12 1.00
i-Pentane 72.15 0.30
n-Pentane 72.15 0.10
n-Hexane 86.18 0.05
H2O 18.02 0.25
CO2 44.01 3.00
H2S 34.08 0.07
N2 28.01 3.00
The process conditions are 40 bara, 500C &
1,000 kmol/h of natural gas. The process data
requested by the vendor is as follows,
1. Natural Gas Molecular Weight & Density
2. Component & Total Mass flow
3. Component & Total Actual Volume flow
4. Component & Total Standard Volume flow
5. Component mass %
6. Component Volume %
7. Component Parts per million (ppm) by
weight.
8. Component Parts per million (ppm) by
volume.
Component Molar Flow [M]
To estimate the component molar flow, the
mixture molecular weight [MW] is evaluated
first by using Kay’s mixing rule as follows,
𝑀𝑊 = ∑ 𝑦𝑖 𝑀𝑊𝑖, Where, i = 1 to n (1)
Where,
yi = Mole fraction of each component, -
MWi = Component MW, kg/kmol
The component molar flow rate is computed
as,
𝑀𝑖 = 𝑦𝑖 × 𝑀, Where, i = 1 to n (2)
Where,
Mi = Component Molar Flow, kmol/h
M = Total Molar Flow, kmol/h
Component & Total Mass Flow
To estimate the component mass flow [mi] &
total mass flow [m], the relationships are,
𝑚𝑖 = 𝑀𝑖 × 𝑀𝑊𝑖, Where, i = 1 to n (3)
𝑚 = ∑ 𝑚𝑖, Where, i = 1 to n (4)
Where,
mi = Component Mass Flow, kg/h
m = Total Mass Flow, kg/h

2. Page 2 of 5
Component & Total Volume Flow
To estimate the component volume flow &
total volume flow, the relationship is based on
the principle that 1 kmol of ideal gas occupies
22.414 m3 at 00C [273.15 K]. In order to
estimate the volume flow of each component,
the volume occupied by a gas at standard
pressure & temperature [STP], i.e., 1 atm &
150C, the relationship is corrected to,
𝑄𝑖 = 𝑀𝑖 ×
22.414
273.15
× [ 𝑇[℃] + 273.15] (5)
The total volume flow rate is,
𝑄𝑠𝑡𝑑 = ∑ 𝑄𝑖, Where, i = 1 to n (6)
Where,
Qi = Component Volume Flow [Sm3/h]
Q = Total Volume Flow [Sm3/h]
Component Mass %
The component mass % is calculated as,
𝑚𝑖% =
𝑚𝑖
𝑚
, Where, i = 1 to n (7)
Component Volume %
The component volume % is calculated as,
𝑄𝑖% =
𝑄 𝑖
𝑄 𝑠𝑡𝑑
, Where, i = 1 to n (8)
Actual Volumetric Flow Rate [Qact]
The actual volumetric flow is computed as,
𝑄 𝑎𝑐𝑡 =
𝑚
𝜌 𝑁𝐺
(9)
Where, the density of the natural gas [NG] is
computed from the expression that takes into
account the gas compressibility factor, Z as,
𝜌 𝑁𝐺 =
𝑃 𝑎𝑐𝑡×𝑀𝑊
𝑍 𝑎𝑐𝑡×𝑅×𝑇𝑎𝑐𝑡
𝑘𝑔/𝑚3
(10)
R = 0.0831447 m3.bar/kmol.K
The gas compressibility factor, Z of natural
gas can be computed based on the DAK
Equation of State [EOS] as described in
Appendix A. Alternatively the standard
volumetric flow rate can also be computed as,
𝑄𝑠𝑡𝑑 = ∑ 𝑄𝑖 = [
𝑃 𝑎𝑐𝑡×𝑄 𝑎𝑐𝑡
𝑍 𝑎𝑐𝑡×𝑇𝑎𝑐𝑡
] × [
𝑍 𝑠𝑡𝑑×𝑇 𝑠𝑡𝑑
𝑃 𝑠𝑡𝑑
] 𝑆𝑚3
/ℎ (11)
Where, Zstd is taken to be 1.0
Component PPM by Weight, ppm(w)
The component PPM by weight, ppm(w) is
computed as,
[𝑤𝑡 %]𝑖 × 10,000 = [𝑝𝑝𝑚(𝑤)]𝑖 (12)
Component PPM by Volume, ppm(v)
The component PPM by volume, ppm(v) is
computed as,
[𝑣𝑜𝑙 %]𝑖 × 10,000 = [𝑝𝑝𝑚(𝑣)]𝑖 (13)
Results
Based on the steps provided, the estimated
results of mass %, volume %, mass flow,
actual & standard volumetric flow rates, parts
per million (ppm) by weight & by volume is
shown in Appendix B & Appendix C.
Appendix A: Gas Compressibility
Factor, Z for Natural Gas Estimation
To assess the properties of natural gas,
calculations can be begun by estimating the
properties using Kay’s Mixing Rule as follows,
Mixture molecular weight [MW], kg/kmol
𝑀𝑊 = ∑ 𝑦𝑖 𝑀𝑊𝑖 (14)
Mixture Pseudo Critical Pressure [Pc], psia
𝑃𝑐 = ∑ 𝑦𝑖 𝑃𝑐,𝑖 (15)
Mixture Pseudo Critical Temperature [Tc], 0R
𝑇𝑐 = ∑ 𝑦𝑖 𝑇𝑐,𝑖 (16)
Gas Specific Gravity [g], [-]
𝛾𝑔 =
𝑀𝑊𝑔
𝑀𝑊 𝑎𝑖𝑟
; MWair = 28.96 kg/kmol (17)
From the above, Kay’s Mixing Rule does not
give accurate pseudocritical properties for
higher molecular weight mixtures
(particularly C7+ mixtures) of hydrocarbon
gases when estimating gas compressibility
factors [Z] and deviations can be as high as
15%. Therefore, to account for these
differences, Sutton’s correlations based on
gas specific gravity can be utilized as follows,
𝑃𝑝𝑐 = 756.8 − 131.07𝛾𝑔 − 3.6𝛾𝑔
2
(18)
𝑇𝑝𝑐 = 169.2 − 349.5𝛾𝑔 − 74.0𝛾𝑔
2
(19)

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The above equations are valid for the gas
specific gravities range of 0.57 < g < 1.68.
Using the Sutton correlations, the reduced
properties are calculated as,
𝑃𝑟 =
𝑃
𝑃 𝑝𝑐
(20)
𝑇𝑟 =
𝑇
𝑇𝑝𝑐
(21)
However the pseudocritical properties are
not the actual mixture critical temperature
and pressure but represent the values that
must be used for the purpose of comparing
corresponding states of different gases on
the Z-chart, as shown below in the Standing &
Katz, 1959 chart for natural gases.
Figure 1. Natural Gas deviation factor chart
(Standing & Katz, 1959)
Due to the graphical method of Standing &
Katz chart, the Z factor can be estimated using
Dranchuk and Abou-Kassem Equation of State
[DAK-EoS] which is based on the data of
Standing & Katz, 1959 and is expressed as,
𝑍 = 1 + [𝐴1 +
𝐴2
𝑇𝑟
+
𝐴3
𝑇𝑟
3 +
𝐴4
𝑇𝑟
4 +
𝐴5
𝑇𝑟
5] 𝜌𝑟 +
[𝐴6 +
𝐴7
𝑇𝑟
+
𝐴8
𝑇𝑟
2] 𝜌𝑟
2
− 𝐴9 [
𝐴7
𝑇𝑟
+
𝐴8
𝑇𝑟
2] 𝜌𝑟
5
+
+𝐴10(1 + 𝐴11 𝜌𝑟
2) (
𝜌 𝑟
2
𝑇𝑟
3) 𝑒−𝐴11 𝜌 𝑟
2
(22)
Where,
𝜌𝑟 =
0.27𝑃𝑟
𝑍𝑇𝑟
(23)
r = Pseudo-Reduced Density [-]
Tr = Pseudo-Reduced Temperature [-]
The constants A1 to A11, are as follows,
Table 2. DAK EoS A1 to A11 Constants
A1 0.3265 A7 –0.7361
A2 –1.0700 A8 0.1844
A3 –0.5339 A9 0.1056
A4 0.01569 A10 0.6134
A5 –0.05165 A11 0.7210
A6 0.5475
DAK-EoS has an average absolute error of
0.486% in its equation, with a standard
deviation of 0.00747 over ranges of pseudo-
reduced pressure and temperature of 0.2 <
Ppr < 30; 1.0 < Tpr < 3.0 and for Ppr < 1.0 with
0.7 < Tpr < 1.0. However DAK-EoS gives
unacceptable results near the critical
temperature for Tpr = 1.0 and Ppr >1.0, and
DAK EoS is not recommended in this range.
DAK EoS for NG Mixtures with Acid Gases
Natural Gas is expected to contain acid gas
fractions, such as CO2 and H2S, & applying the
Standing & Katz Z-factor chart & Sutton’s
pseudocritical properties calculation methods
would yield inaccuracies, since they are only
valid for hydrocarbon mixtures. To account
for these inaccuracies, the Wichert & Aziz
correlations can be applied to mixtures
containing CO2 < 54.4 mol% & H2S < 73.8
mol% by estimating a deviation parameter
[], which is used to modify the pseudocritical
pressure & temperatures. The deviation
parameter [] whose units are in 0R, is,
𝜀 = 120[𝐴0.9
− 𝐴1.6] + 15[𝐵0.5
− 𝐵4] (24)
Where,
A = YCO2 + YH2S in Gas mix [Y = mole fraction]
B = YH2S in Gas mixture [Y = mole fraction]

4. Page 4 of 5
Applying [], the modified pseudocritical
pressure & temperature is,
𝑇𝑝𝑐
′
= 𝑇𝑝𝑐 − 𝜀 (25)
𝑃𝑝𝑐
′
=
𝑃 𝑝𝑐 𝑇𝑝𝑐
′
𝑇𝑝𝑐−𝐵[1−𝐵]𝜀
(26)
Where, T’pc & P’pc are valid only in 0R and psia.
Based on the calculated modified
pseudocritical pressure [P’pc] and
temperature [T’pc], the pseudo-reduced
pressure [Pr] & temperature [Tr] is,
𝑃𝑝𝑟 =
𝑃 [𝑝𝑠𝑖𝑎]
𝑃 𝑝𝑐
′ [𝑝𝑠𝑖𝑎]
(27)
𝑇𝑝𝑟 =
𝑇 [° 𝑅]
𝑇𝑝𝑐
′ [° 𝑅]
(28)
𝜌 𝑝𝑟 =
0.27𝑃 𝑝𝑟
𝑍𝑇𝑝𝑟
(29)
Using the calculated values of Ppr Tpr & pr,
compressibility factor, Z is determined by
using DAK EoS. Owing to the value of ‘Z’ being
an implicit parameter in calculating pr as
well as in DAK-EoS, an iterative approach,
whereby Z value is guessed & iteratively
solved to satisfy both modified pseudo-
reduced density [pr] & DAK EoS.
References
1. “Handbook of Natural Gas Engineering”,
Katz, D.L., 1959, McGraw-Hill Higher
Education, New York
2. “Gases and Vapors At High Temperature
and Pressure - Density of Hydrocarbon”, Kay
W, 1936 Ind. Eng. Chem. 28 (9): 1014-1019
(http://dx.doi.org/10.1021/ie50321a008)
3. “Density of Natural Gases”, Standing, M.B.
and Katz, D.L. 1942 In Transactions of the
American Institute of Mining and
Metallurgical Engineers, No. 142, SPE-
942140-G, 140–149, New York
4. “Compressibility Factors for High-
Molecular-Weight Reservoir Gases”, Sutton,
R.P. 1985. SPE Annual Technical
Conference & Exhibition, Las Vegas,
Nevada, USA, 22-26 Sep, SPE-14265-MS
(http://dx.doi.org/10.2118/14265-MS)
5. “Calculation of Z Factors For Natural Gases
Using Equations of State”, Dranchuk, P.M.
and Abou-Kassem, H. 1975, J Can Pet
Technol 14 (3): 34. PETSOC-75-03-
03 (http://dx.doi.org/10.2118/75-03-03)
6. https://petrowiki.org/Real_gases
7. “Compressibility Factors for Naturally
Occurring Petroleum Gases, Piper, L.D.,
McCain Jr., W.D., and Corredor, J.H., SPE
Annual Technical Conference & Exhibition,
Houston, 3–6 October 1993, SPE-26668-
MS (http://dx.doi.org/10.2118/26668-MS)

5. Page 5 of 5
Appendix B: Natural Gas Composition Results
Appendix C: Natural Gas Process Data