Hydrocarbon Processing - January 2021 - 51

Heat Transfer
Nusselt number and heat transfer
coefficient. The Nusselt number (Nu)

and the heat transfer coefficients (h) are
based on the Dittus and Boelter equation.6
Since d and 0.023 are constant for all of the
hot oils, Eq. 7 is rearranged to Eq. 8 and is
defined as the modified heat transfer coefficient, H. The net change in modified
heat transfer coefficient (ΔH) is also defined to compare the heat transfer performance of the new hot oils with the proprietary oil.a The required heat exchange area
decreases as H and ΔH increase, because
the heat transfer coefficient is inversely
proportional to the surface area (Eq. 9):
h×d
Nu =
= 0.023 × Re0.8 × Pr 0.4
(7)
k
h×d
= k × Re0.8 × Pr 0.4 = H
(8)
0.023
⎛ heat transfer coefficient ⎞
⎜ of hot oil-heat
⎟
⎜ transfer coefficient
⎟
⎜ of 100 N
⎟
⎟ × 100
ΔH = ⎜
⎜ heat transfer coefficient ⎟
⎜
⎟
⎜ of 100 N
⎟
(9)
⎜
⎟
⎝
⎠
Frictional factor and pressure drop.
The friction factor ( f ) and line pressure
drop (ΔP) are estimated per approximations of the Colebrook equation.7 These
parameters are used for estimating the hydraulic horsepower requirement and associated cost, as shown in Eqs. 10 and 11:

f =

0.25
⎡
⎢
⎢ log
⎢
⎢⎣

(10)

⎞ ⎤
⎛
ε
5.74 ⎟ ⎥
⎜
⎜
inch × 1 ft + Re0.9 ⎟ ⎥
⎟⎠ ⎥
⎜⎝ 3.7 × d
12 inches
⎦⎥
2

where ε is the pipe roughness factor of
0.0005 ft:
ft ⎞ 2
f × L ( ft ) × V 2 ⎛
×
⎝ sec ⎠
lb
ρ ⎛ 3⎞
⎝ ft ⎠
ΔP ( Psi ) =
(11)
inch × 1 ft ⎞
d⎛
×2×
⎝ 12 inch ⎠
ft
g ⎛ 2 ⎞ × 144
⎝ sec ⎠

where g is acceleration due to gravity (32.17
ft/sec2). ∆P per 100 ft of pipe (ΔP/100 ft)
is estimated by substituting 100 ft for pipe
length (L) in Eq. 11. ΔP per 2,000 ft of pipe
is also estimated by using 2,000 ft for L.

Horsepower. Equivalent hydraulic horse-

power (HH) and the actual horsepower
(AH) for the calculated line pressure loss
are estimated using pump Eqs. 12 and 13:

VF ( gpm ) × ΔP ( Psi )
(12)
HH(hp) =
1,714
Assuming a pump efficiency of 60%:
Actual horsepower (AH , hp) =
HH(hp)
HH(hp)
(13)
=
0.6
Pump efficiency
Cost of horsepower. The cost of horse-

power is estimated based on the cost of industrial electricity in the client's location,
and with the assumption of 8,000 hr of operation. The estimated costs are compared
for the different hot oils: 1 hp = 0.7457
kw; cost of industrial electricity in client's
location, U.S. = $0.617/kwh;8 industrial
hours in a year = 8,000 hr (Eq. 14):
Cost = 0.7457 × 6.17 × AH ×
(14)
8,000 × 0.01 = USD
Cost of thermic fluid. The cost of proprietary heat transfer fluidsb,c,d products
are very high ($1,600/bbl). The wax-free
oila and ULSD are normally less than
$100/bbl (more like $70 /bbl on average).

RESULTS AND DISCUSSIONS
As seen in TABLE 1, the proprietary base
oila has the lowest vapor pressure at 680°F,
but is not suitable at the operating temperature. The base oil degrades rapidly above
600°F, which causes fouling issues within
the pumps and exchangers. ULSD has
the highest vapor pressure, which means
the system pressures need to be higher
to avoid two-phase conditions within the
system. The proprietary heat transfer fluidc has the lowest vapor pressure at both
680°F and 551°F, second only to the base
oil. As shown in TABLE 1, the viscosities for
all of the hot oils are relatively low when
compared to water (1 cP). A lower viscosity leads to lower energy requirements for
circulation within the system.
TABLES 2 and 3 show the hydraulic performance of different hot oils. The frictional factors for all of the hot oils are close
to each other. ULSD requires the lowest
mass flowrate. The base oila requires the
lowest volumetric flowrate, but is not
selected for use due to known fouling issues. One of the proprietary heat transfer
fluidsc requires the lowest volumetric rate.

That fluid also is lower in ΔP/100 ft, line
pressure losses and hydraulic horsepower
requirement compared to the other hot
oils. The lowest cost found for that fluid
shows that approximately $13,435/yr is
needed, which is about 16% lower than
ULSD and about 39% lower than both
other heat transfer fluidsb,d. The lowest
pumping cost for the heat transfer fluidc
is due to the lowest volumetric flowrate
compared with other hot oils.
As shown in TABLE 4, one thermic fluidc has a higher heat transfer coefficient
than both ULSD and the base oila, but is
still slightly lower than the second thermic fluidb. The third thermic fluid has a
slightly higher heat transfer coefficient
than both the first and second fluidsb,c.
The higher the heat transfer coefficient,
the lower the required area. The capital
cost related to equipment could be lower
due to the reduced area requirement,
but the operating cost (pumping) would
still be much higher for the third thermic
fluidd, as shown in TABLE 3. The first and
third thermic fluids discussed hereb,d have
higher ΔH values than the second fluidc,
but that fluid has a lower operating cost
and lower volumetric rates.
Every hot oil system requires a certain
amount of hot oil volume in the system,
and frequent refill is required to account
for losses and thermal degradation. The
aforementioned thermic fluidsb,c,d are
about 23 times more expensive compared
with ULSD and the base oila, but they
provide higher operating temperature required for the process.
Takeaway. Fluid properties and cost
data of hot oils can be used to determine
their suitability. Properties-temperature range, density, thermal conductivity,
heat capacity, vapor pressure, viscosity,
etc.-are used to estimate the hydraulic
and thermal performance of a hot oil. The
pressure drop through a line and the heat
transfer coefficient are essential for the
selection of a hot oil. The original hot oila
was not selected due to its poor fluid properties and degradation at a temperature
above 600°F. The low vapor pressure of
the termic fluidc is needed at a high operating temperature of 680°F to keep the hot
oil in the liquid phase. Other hot oils with
a higher vapor pressure like the first and
third fluidsb,d and ULSD require a higher
system operating pressure, which increases the operating costs of pumping. The
Hydrocarbon Processing | JANUARY 2021 51

Hydrocarbon Processing - January 2021

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