Hydrocarbon Processing - January 2021 - 44

Process
Optimization
J. COLANNINO, Contributing Editor,
San Diego, California

Optimize processes with a spreadsheet
Hydrocarbon processing industry
(HPI)/continuous process improvement
(CPI) processes are often characterized
by complicated kinetics and simultaneous heat and mass transfer. Often, a significant amount of simulation science has
gone into setting operating conditions
with process control loops tuned for best
results. However, natural feedstocks have
inherent variability and even ambient
conditions, such as temperature, humid-

FIG. 1. Hypothetical response surface in two
factors. Although depicted here for illustration,
this function is not usually known, but can
only be observed after contamination
with random error (see FIG. 2).

FIG. 2. Observed response surface in two
factors, y(x1 , x2 ). This is the function of
FIG. 1 after contamination with significant
random process noise (i.e., random error).

44 JANUARY 2021 | HydrocarbonProcessing.com

ity and barometric pressure, can affect
product results. Moreover, start-of-run
to end-of-run conditions often require
process adjustments. Once initial process
conditions have been set, can one hope
to wring out additional improvement?
The answer is almost always, " Yes, "
but operators know that they must always
produce on-spec product. One method
of achieving process improvement under
these constraints is known as evolutionary
operation (EVOP)1,2, which makes small
adjustments to known process variables
to keep the process in-spec, while gathering information to move toward their
optimal combination. These principles
have wide applicability to virtually any
process, including optimizing pollution
control equipment or the production of
chemical or hydrocarbon products. This
article will show how to enable EVOP using a spreadsheet program, such as Excel.
The use of approximating functions. FIG. 1 shows a generic response

surface derived from a highly non-linear

FIG. 3. Regressed response surface in two
factors, ŷ(x1 , x2 ). This is the empirical surface
fitted by Eq. 1 to the data comprising FIG. 2.
The fitted surface is a good approximation
to the true surface (FIG. 1), despite significant
process noise.

expression as a function of two factors
for illustrative purposes. However, in
principle, any number of responses of
interest and as many factors are possible. Multiple response factors may be
assessed individually or combined in a
weighted model to create a single process score, which then functions as the
response surface to be optimized.
Nonlinear equations-or even systems of them-are typical for many processes. Rather than attempt to elucidate
the true function, statistical experimental
design (SED) fits a mathematical approximating function (ŷ), such as Eq. 1:
ŷ = c 0 + c 1x1 + c 2 x2 + c 11 x12 +
c 12 x1 x2 + c 22 x22(1)
Here, c 0-c 22 are regressed coefficients.
The observed responses we measure ( y)
will then be given by Eq. 2:
y = ŷ + ε(2)
where ε is the error between Eq. 1 and the
observed response. The error (ε) cumulates all other variation from the sources
that we cannot control (or that we may
not even know about), but which nonetheless affect the response in some way.
Despite this, the regression can recover a
good approximation to the true function.
FIG. 2 depicts actual observations, including random error. Despite significant
noise, the regressed approximating function (FIG. 3) is nearly indistinguishable
from the true function of FIG. 1. Considering how contaminated the original data
were, the approximation is remarkable.
The method of steepest ascent. The

genius of EVOP is that we do not need
a full picture of the response surface to


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Hydrocarbon Processing - January 2021

Table of Contents for the Digital Edition of Hydrocarbon Processing - January 2021

Contents
Hydrocarbon Processing - January 2021 - Intro
Hydrocarbon Processing - January 2021 - Cover1
Hydrocarbon Processing - January 2021 - Cover2
Hydrocarbon Processing - January 2021 - Contents
Hydrocarbon Processing - January 2021 - 4
Hydrocarbon Processing - January 2021 - 5
Hydrocarbon Processing - January 2021 - 6
Hydrocarbon Processing - January 2021 - 7
Hydrocarbon Processing - January 2021 - 8
Hydrocarbon Processing - January 2021 - 9
Hydrocarbon Processing - January 2021 - 10
Hydrocarbon Processing - January 2021 - 11
Hydrocarbon Processing - January 2021 - 12
Hydrocarbon Processing - January 2021 - 13
Hydrocarbon Processing - January 2021 - 14
Hydrocarbon Processing - January 2021 - 15
Hydrocarbon Processing - January 2021 - 16
Hydrocarbon Processing - January 2021 - 17
Hydrocarbon Processing - January 2021 - 18
Hydrocarbon Processing - January 2021 - 19
Hydrocarbon Processing - January 2021 - 20
Hydrocarbon Processing - January 2021 - 21
Hydrocarbon Processing - January 2021 - 22
Hydrocarbon Processing - January 2021 - 23
Hydrocarbon Processing - January 2021 - 24
Hydrocarbon Processing - January 2021 - 25
Hydrocarbon Processing - January 2021 - 26
Hydrocarbon Processing - January 2021 - 27
Hydrocarbon Processing - January 2021 - 28
Hydrocarbon Processing - January 2021 - 29
Hydrocarbon Processing - January 2021 - 30
Hydrocarbon Processing - January 2021 - 31
Hydrocarbon Processing - January 2021 - 32
Hydrocarbon Processing - January 2021 - 33
Hydrocarbon Processing - January 2021 - 34
Hydrocarbon Processing - January 2021 - 35
Hydrocarbon Processing - January 2021 - 36
Hydrocarbon Processing - January 2021 - 37
Hydrocarbon Processing - January 2021 - 38
Hydrocarbon Processing - January 2021 - 39
Hydrocarbon Processing - January 2021 - 40
Hydrocarbon Processing - January 2021 - 41
Hydrocarbon Processing - January 2021 - 42
Hydrocarbon Processing - January 2021 - 43
Hydrocarbon Processing - January 2021 - 44
Hydrocarbon Processing - January 2021 - 45
Hydrocarbon Processing - January 2021 - 46
Hydrocarbon Processing - January 2021 - 47
Hydrocarbon Processing - January 2021 - 48
Hydrocarbon Processing - January 2021 - 49
Hydrocarbon Processing - January 2021 - 50
Hydrocarbon Processing - January 2021 - 51
Hydrocarbon Processing - January 2021 - 52
Hydrocarbon Processing - January 2021 - 53
Hydrocarbon Processing - January 2021 - 54
Hydrocarbon Processing - January 2021 - 55
Hydrocarbon Processing - January 2021 - 56
Hydrocarbon Processing - January 2021 - 57
Hydrocarbon Processing - January 2021 - 58
Hydrocarbon Processing - January 2021 - 59
Hydrocarbon Processing - January 2021 - 60
Hydrocarbon Processing - January 2021 - 61
Hydrocarbon Processing - January 2021 - 62
Hydrocarbon Processing - January 2021 - 63
Hydrocarbon Processing - January 2021 - 64
Hydrocarbon Processing - January 2021 - 65
Hydrocarbon Processing - January 2021 - 66
Hydrocarbon Processing - January 2021 - 67
Hydrocarbon Processing - January 2021 - 68
Hydrocarbon Processing - January 2021 - 69
Hydrocarbon Processing - January 2021 - 70
Hydrocarbon Processing - January 2021 - 71
Hydrocarbon Processing - January 2021 - 72
Hydrocarbon Processing - January 2021 - 73
Hydrocarbon Processing - January 2021 - 74
Hydrocarbon Processing - January 2021 - 75
Hydrocarbon Processing - January 2021 - 76
Hydrocarbon Processing - January 2021 - 77
Hydrocarbon Processing - January 2021 - 78
Hydrocarbon Processing - January 2021 - 79
Hydrocarbon Processing - January 2021 - 80
Hydrocarbon Processing - January 2021 - 81
Hydrocarbon Processing - January 2021 - 82
Hydrocarbon Processing - January 2021 - Cover3
Hydrocarbon Processing - January 2021 - Cover4
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https://www.nxtbook.com/nxtbooks/gulfpub/petrochemical_2018_v2
https://www.nxtbook.com/nxtbooks/gulfpub/petrochemical_2018
https://www.nxtbook.com/nxtbooks/gulfpub/hp_201812
https://www.nxtbook.com/nxtbooks/gulfpub/hpimarket_2019_v2
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