Sop calculation method

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03/02/2015
Anders Andreasen
Jacob Gram Iskov Eriksen
Carsten Stegelmann
Hasse Lynggaard
Ramboll Oil & Gas
Esbjerg, Denmark
Settle-out calculations in natural gas systems need to be sufficiently rigorous accurately
to predict settle-out under various operating conditions without being so conservative
as to increase costs.
This article proposes a particular rigorous calculation usable as an alternative to a
process simulator. The varied contributions of many subvolumes to the final settle-out
calculation complicate the process and can produce inaccuracies during use of a non-
rigorous method. The simple method, however, is easy to implement and requires no
thermodynamic package or calculation tool.
The simple method proposed in this article is also preferable to both Tn and Tm
methods due to its greater simplicity. The proposed simple method may be applied with
only minor calculation inaccuracy when:
• Based on an evaluation of settle-out calculations for installed equipment, the
inaccuracy created by use of one of the simpler methods presented is in the range ±2%
and the highest pressure in any of the subvolumes before settle-out is less than 150
barg.
• Parameter variation studies show that keeping the maximum pressure less than 100
bar or three times the lowest system pressure, whichever is the lowest, and at the
same time keeping the molecular weight less than 26 kg/kmol should limit calculation
inaccuracy to a maximum ±2% at temperature.
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Method improves high-pressure
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19.06.2015http://www.ogj.com/articles/print/volume-113/issue-3/transportation/method-improve...

Relative calculation inaccuracy should of course be compared with actual settle-out
pressure. The simple method also generally seems to overvalue settle-out pressure at
high pressure, which is conservative and safe but may lead to over-design if used in
extreme cases.
We recommend that liquid content be excluded in the calculation to prevent an
undervaluation of the settle-out pressure. The liquid should be considered an inert
spectator not exchanging mass or energy with the gas. The volume occupied by the
liquid should be subtracted from the system volume.
Settle-out calculations
Settle-out calculations represent an important step in several key engineering activities,
both in initial design and when updating operating conditions, alarm levels, and during
design modification projects, especially for compressor loops. Settle-out calculations
help:
• Decide upon design pressure of the low-pressure part of the settle-out system.
• Determine starting pressure and temperature for blow-down calculations.
• Calculate compressor restart conditions after a compressor trip.
Fig. 1 shows a typical system considered for settle-out calculations; a two-stage
compressor train including suction scrubbers, discharge coolers, and recycle lines. For
purposes of settle-out calculations, the system is segmented into subvolumes differing
either in pressure or temperature. Equipment data sheets and isometric piping
drawings provide the basis for estimating each part's volume.
Design pressure
The design pressure of suction side equipment-scrubber, cooler, etc.-shall be high
enough to provide sufficient margin when settling-out occurs. The suction side will
usually include a pressure safety valve (PSV) for fire protection of the scrubber.1
Providing a margin between settle-out pressure and design pressure can prevent
unnecessary flaring. API 521 says design pressure shall be a minimum 1.05 times
settle-out pressure at maximum pressure drop, calculated assuming the suction side is
operated at normal operating pressure and compressor discharge pressure is set to the
maximum achievable.2
It does not, however, specifically mention how maximum
discharge pressure should be determined.
Compressor performance, pressure alarm high-high (PAHH) on the discharge side, or
ultimately PSV-set pressure can limit maximum discharge pressure. NORSOK P-001
says maximum operating pressure should be determined as the settle-out pressure
occurring at coincident PAHH on both the suction side and the discharge side, adding a
10% margin for determining design pressure or PSV set pressure.3
API 521 therefore
seems less conservative than NORSOK P-001, as the settle-out pressure is calculated
from higher initial pressures and a higher margin is applied.
Blowdown, restart
Conducting a compressor system blowdown requires determining the initial
temperature and pressure, as well as composition of the system's contents.
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Temperature and pressure are defined as the settle-out pressure and temperature.4
Blowdown calculations, however, can be performed for a number of scenarios. Cold
blowdown simulations check for low temperatures, below the material design
temperature, which can cause brittle fractures.5
Fire cases are simulated where
ruptures due to high temperature, which can weaken the material, are a risk.6 7
For the
former we perform settle-out calculations from normal operating conditions and for the
latter settle-out calculations from coincident PAHH trips.
The settle-out pressure calculation is also of interest in estimating the required torque
in case of a compressor trip and a subsequent fast restart without intermediate
depressurization-blowdown.8 9
The higher the settle-out pressure the higher the
required torque. Restart torque is key information in appropriately specifying the
compressor driver.
Rigorous method
A key characteristic of the settle-out process is that it occurs at constant volume.
Assuming pressure equalization between subvolumes occurs quickly enough for heat
transfer to be negligible allows reduction of the first law of thermodynamics to
ΔU=Q+W=0, where ΔU is the change in internal energy, Q is heat, and W is work. The
thermodynamic problem to be solved, therefore, has a constant volume and constant
internal energy: a UV-problem.
The solution method proposed in this article is based on a constant-temperature and
constant-pressure flash calculation employing the Peng-Robinson equation of state
(EoS). Calculation of density and real gas corrections to all thermodynamic properties
(U, H, and S) are based on the EoS.
The solution procedure is to calculate the internal energy of all subvolumes, Vi, and
from these find the total internal energy, Utot, at the starting conditions for each
subvolume, Ti and Pi. The content in all subvolumes is added. An initial estimate of the
settle-out pressure is made with a simple method. Internal energy and fluid volume of
the total mass is calculated at the initial guess for T and P. Subsequently changing
pressure and temperature values ensures ΔV and ΔU are zero. The pressure and
temperature that satisfy a constant volume and a constant internal energy are the
settle-out pressure and temperature.
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Simple method
The simple method for calculating the initial guess in the UV-method described
previously considers each subvolume as separated by invisible walls that can move as
each element expands or is compressed during pressure equalization. For a single
subvolume, work occurs as if the volume is not constant. Assuming the process is
reversible and adiabatic (ΔQ=0) and that the fluid trapped follows the ideal gas law, the
work for each subvolume can be expressed as shown in Equation 1.10
Using this information, adding the work for all subvolumes, and assuming net work is
zero yields settle-out pressure (Equation 2). Equation 3 shows the calculation if an
initial guess for the settle-out pressure is calculated from an ideal gas mole balance,
which reduces to Equation 4. Investigating the simple method used for calculating initial
guesses as compared with the rigorous solution method allows quantifying the extent to
which the simple method can be used as an alternative to the rigorous method.
Tn-, Tm-methods
The Tn-method of calculating settle-out conditions applies a compressibility factor to
the ideal gas. It assumes that the temperature-mole term, n∙T, is constant and additive
for each volume. Equations 5-13 describe how to calculate settle-out conditions under
these assumptions for any arbitrary number of volumes.
Equation 5 determines the number of moles for each volume, with Equation 6 showing
the number of moles contained in the entire volume, i.e., the number of moles at settle-
out conditions, and Equation 7 the entire volume at settle-out conditions.

The normal volume of each volume-segment is calculated with normal conditions
(Equation 8); Pi,n=1.01325 bar and Ti,n=273.15 K., with Equation 9 determining normal
volume for settle-out conditions. Simply applying the ideal gas equation including the
compressibility factor then yields temperature-mole term for each volume (Equation
10).
Under the assumptions made for this simple approach, the temperature-mole term for
the settle-out conditions will be the total sum of each temperature-mole term (Equation
11). Equation 12 estimates the subsequent settle-out temperature. Applying the
concept of volume under normal conditions, as previously determined, yields estimated
settle-out pressure (Equation 13).
The Tn method of calculating settle-out conditions did not include the molar masses of
each individual volume. This omission, however, is negligible when molar masses are
more or less equal. The Tm method incorporates molar mass by using a temperature-
mass term, replacing the previously used temperature-mole term.
Equation 14 provides the relationship between the number of moles, molar mass, and
mass. Similar equations and assumptions as presented for the Tn-method can
determine settle-out conditions with the Tm method by applying the temperature-mass
term, m∙T.
Results
We applied the methods described for calculating settle-out pressure to a number of
real cases (Table 1). They cover settle-out in existing equipment installed offshore in
the Danish sector of the North Sea and include several compressor loops, both single-
compressor and two compressors in series, including scrubbers and coolers. Further
cases include connected vessels-piping operated at different pressures, where settle-
out will occur if the unit trips.

Each settle-out case pairs the number of distinct subvolumes-each differing in pressure
or temperature-with the lowest and highest pressure before settle-out occurs. Each
case calculates settle-out pressure with the rigorous, simple Tn and Tm methods and
lists calculation inaccuracy relative to the rigorous method (Table 2, Fig. 2).
Fig. 3 displays the inaccuracy caused by applying the non-rigorous methods, depicting
calculation inaccuracy as a function of the highest pressure in the system before settle-
out. Other descriptors could have been chosen as well, although it is difficult to find a
single good descriptor for the calculation while also accounting for the varying
complexity with different numbers of subvolumes. The maximum pressure is chosen,
since the largest deviations from the ideal gas law will occur in this part of the system.
The effect on the final result also depends on the high-pressure volume and gas
composition-molecular weight.
Settle-out calculation inaccuracy is less than 2% in most cases, and for the remaining
cases an inaccuracy of up to slightly above 4% is observed. Except for three cases,
absolute inaccuracy is less than 2 bar.
Fig. 2 shows non-rigorous methods usually generate similar results, especially for
systems in which the subvolume's maximum pressure is less than 150 barg. At
greather than this, some discrepancy is observed between the different methods. There
is a general tendency for the calculation inaccuracy to be highest for systems with the
highest maximum pressure. At lower maximum pressure settle-out pressure is in most
cases undervalued, while at the higher maximum pressures settle-out pressure is
overvalued.

Parameter variation
We studied the suitability of the simple method for settle-out calculations by performing
a number of parameter variation studies investigating the effects of pressure,
temperature, and molecular weight on the calculation inaccuracy for settling-out
between two equal volumes. Calculation inaccuracy is estimated by comparison with
the rigorous method.
Fig. 3 shows the effect of pressure and temperature for two different gas molecular
weights as well as the general trend that the largest inaccuracy is found at high
pressure differences when the temperature difference is small and at high temperature
differences when the pressure difference is small. A diagonal from the lower left to the
upper right of Fig. 3 has relatively low inaccuracy, with increasing molecular weight
generally seeming to increase the inaccuracy in settling-out pressure estimated by the
simple method.
Considering settling-out between one volume fixed at 50 bar and the other varied up to
200 bar extends the analysis to higher pressures. Fig. 4 shows the results for two
different molecular weights, illustrating the inaccuracy in the simple method changing
from being generally less than zero at lower pressure (~80-100 barg, depending on the
molecular weight) to being positive at higher pressure. Where the undervaluation of the
simple method is relatively moderate at lower pressure (Fig. 4), the overvaluation at
higher pressure becomes more severe and increasing molecular weight again amplifies
any inaccuracies.
Testing confirmed the effect of increasing molecular weight on the calculation
inaccuracy (Fig. 5): increased molecular weight leads to increased calculation
inaccuracy when using the simple method.
Handling liquid content
When performing settle-out calculations for compressor systems, the process engineer
must handle liquid content in the system in terms of calculation. Including liquid in the
calculations, however, will generate a lower settle-out pressure, regardless of whether
the rigorous or simple calculation method is used. Handling liquid complicates the
calculation by requiring more input (a liquid phase) and creates less conservative

results, leading us to exclude liquid content in the calculation when using either the
rigorous method or simple calculation methods.
Process simulator
A proprietary code for rigorous multiphase thermodynamic calculations performed the
calculations presented in this article. A tailor-made tool, however, may not be available
to everyone. In these cases a general-purpose steady-state process simulation tool can
be used, with a variety of commercial-proprietary, free-closed, and open-source options
available. Examples of commercial process simulators include AspenTech HYSYS,
Honeywell Unisim, Prosim, gProms, and Prode Properties (free for non-commercial
usage). DWSIM and COCO are examples of free process-simulation tools.11
Methods using a process simulator rely on constant volume with a constant enthalpy
flash. One must first define a stream representing each of the subvolumes constituting
the system under consideration. Pressure and temperature are assigned for each
stream composition, as well as an appropriate fluid package-equation of state, usually
the Peng-Robinson or Soave-Redlich-Kwong. Connecting each stream to an automatic
adjuster shifts the mole or mass per unit time until the actual volumetric per unit time
matches the volume of the particular subvolume. The chosen time unit is not important,
though it is important to use the same time unit consistently for all streams.
A mixer operation combines all streams representing the settle-out system subvolumes
into a single stream. The combined stream passes through a valve operation (constant
enthalpy operation), and the outlet stream represents the system after settle-out.
Connecting another adjuster shifts the pressure until the volume of the settle-out
stream is equal to the sum of all the subvolumes for a generic flow-sheet
implementation of settle-out calculation in a process simulator (Fig. 6).
The composition available from an overall plant process simulation can generate a
multiphase fluid when flashed at the temperature and pressure of any of the inlet
streams. Inserting a two-phase separation operation downstream of the inlet streams
and routing the separator gas outlet to the mixer operation can overcome this problem.
The volumetric flow given as feedback to the adjuster should be the gas volume, not
the total volume including liquid. When discarding the liquid, operators should verify
that the fluid is actually two-phase hydrocarbon liquid and gas and not in the dense-
phase region (P > Pc). The process simulator in some cases may map the dense
phase to a liquid state. In this instance, during insertion of a separator, no contribution
will be made to the settle-out calculation for that particular stream. To avoid this do not
insert a separator for streams with a pressure exceeding critical pressure.
We compared settle-out calculations performed with a process simulator (HYSYS) to
both the rigorous method and the simple method outlined previously. All cases
considered two equally sized volumes with the low-pressure part being 50 bar and 40°
C. for all cases. The high-pressure part is 60° C. for all cases and the settle-out
pressure is calculated for a total of five cases with a high pressure of 60, 90, 120, and
180 bar. Fig. 7 summarizes the results.

Results for the three different methods are very similar for the 60 and 90 bar cases. At
120 bar the settle-out pressure calculated with the simple method begins to deviate,
becoming more severe at 180 bar. Except for the 180 bar case, the rigorous method
and process simulation method are almost identical. It is generally observed that the
simple method gives higher settle-out pressure than the two others at elevated
pressure.
References
1. API RP 14C, "Recommended Practice for Analysis, Design, Installation, and Testing
of Basic Surface Safety Systems for Offshore Production Platforms," American
Petroleum Institute, 2007.
2. API STD 521, "Pressure-relieving and Depressuring Systems," 6th ed., American
Petroleum Institute, 2014.
3. NORSOK P-001, "Process Design," 5th ed., Standards Norway, 2006.
4. Hekkelstrand, B., and Skulstad, P., "Guidelines for the protection of pressurized
systems exposed to fire," Scandpower Risk Management AS, Mar. 31, 2004.
5. Sims, J.R., "Improve evaluation of brittle-fracture resistance for vessels,"
Hydrocarbon Processing, Vol. 92, No. 1, January 2013, pp. 59-62.
6. Mahgerefteh, H., Falope, B.O., and Oke, A.O., "Modelling Blowdown of Cylindrical
Vessels Under Fire Attack," AIChE Journal, Vol. 48, No. 2, February, 2002, pp. 401-
410.
7. Per Salater, T., Overaa, S.J., and Kjensjord, E., "Size Depressurization and Relief
Devices for Pressurized Segments Exposed To Fire," CEP Magazine, September
2002, pp. 38-45.
8. Samurin, N.A., and Talabisco, G.C., "System Design Study Using Dynamic
Simulation of a Propylene Refrigeration Process Compression Train," Dresser Rand
Insights, No. 1, Winter 2008, pp. 8-14.
9. Bhattacharya, D., Chittibabu, H., Mumm, J., and Valappil, J., "Dynamic simulation: a
tool for engineering problems," Digital Refining, Petroleum Technology Quarterly, Q4,
October 2012.
10. Smith, J.M., Van Ness, H.C., and Abbott M.M., "Introduction to Chemical
Engineering Thermodynamics," 5th ed., New York: McGraw-Hill, 1996.
11. Van Baten, J.M., Kooijman, H., and Taylor, R., "Flowsheeting for free with COCO,"
CACHE News, Winter 2007.

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The authors
Anders Andreasen (anra@ramboll.com) is chief consultant within process
engineering in the department of offshore field development and studies at
Ramboll Oil & Gas, Esbjerg, Denmark. He has also served as senior
research engineer at MAN Diesel & Turbo working with large two-stroke
diesel engine combustion optimization and emission reduction technologies. He holds
an MS in chemical engineering from Aalborg University, Esbjerg, and a PhD from the
Technical University of Denmark, Lyngby, also in chemical engineering. He is a
member of the Society of Petroleum Engineers.
Jacob Gram Iskov Eriksen (jgie@ramboll.com) is a student intern at
Ramboll. He holds a BS in energy engineering with specialization in thermal
processes and is pursuing his MS in process engineering and combustion
technology at Aalborg University, Esbjerg.
Carsten Stegelmann (cts@ramboll.com) is chief consultant within process
and technical safety engineering in the department of technical safety at
Ramboll. He holds an MS and a PhD in chemical engineering, both from
Aalborg University, Esbjerg, and is a certified functional safety expert
(CFSE).
Hasse Lynggaard (hsl@ramboll.com) is chief consultant within process and
technical safety engineering in the department of technical safety at
Ramboll. He holds an MS and a PhD in chemical engineering, both from
Aalborg University.
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