Design and Implementation of Sliding Mode Controller using Coefficient Diagra...
Final Report 4_22_15
1. The Pennsylvania State University
College of Earth and Mineral Sciences
Department of Energy and Mineral Engineering
Petroleum and Natural Gas Engineering Program
PNG 480-Production Process Engineering
Final Term Project: Design of a Surface Production Facility
Instructor: Dr. Luis F. Ayala H.
Teaching Assistants: Thomas Stumpf and Lina Da
Group 6
Michael Silver
Chad DiStanislao
Christopher Efstathion
David Hughes
2. 2
TABLE OF CONTENTS
Section 1 Project Introduction ....................................................................................4
Section 2 Description of Process Model.....................................................................6
Section 3 Reservoir Characterization and Feed Rate Calculation ..............................9
Section 4 Determination of Separator Operating Pressures........................................12
Section 5 Sizing of Separator Vessels ........................................................................15
Section 6 Sizing of Dehydrator System......................................................................30
Appendix A MATLAB Code......................................................................................41
Appendix C Module Results.......................................................................................54
Appendix C Viscosity Calculation..............................................................................58
3. 4
Section 1
Project Introduction
The goal of this project is to provide the basic design for a surface production facility that
will process the hydrocarbon stream produced from a single-phase natural gas reservoir. The
project design basis includes a 3-stage condensate stabilization train, a glycol dehydration unit,
and a hydrate prevention system. The reservoir of interest is being drained by 18 wells that will
feed the designed facility through a production manifold. A previous reservoir simulation has
provided a hydrocarbon production capacity of 11,750 RCF/D per well. The following natural
gas reservoir composition has been provided in order to develop a process model. The model will
be presented in detail in the following chapters.
Table 1. Natural Gas Reservoir Composition.
Component Molar Fraction
P1 0.662200
P2 0.119400
P3 0.100452
P4 0.045966
P5 0.050000
P6 0.011041
P7 0.010941
The goal of the model is to perform detailed and accurate calculation of properties like
compositional Z-factors, volatility ratios, split factors, fluid densities, and molecular weights.
These properties are essential for the design of the surface production facility. Based on these
4. 5
data, the model can be used to optimize the design of the separation train. The scope of this
design project includes selecting the appropriate operating pressure, size, and orientation of the
separator vessels in the stabilization train. The goal of the stabilization train is to meet
condensate vapor pressure specifications while maximizing liquids recovery at a minimum cost.
Next, a preliminary sizing of the glycol dehydration system has been completed based on the
composition and properties of the gas streams from the stabilization train. The purpose of this
system is to meet the water content specification of the gas stream, which is based on contract
agreements for the sale of the gas as well as process safety requirements to minimize the risk of
free water or hydrate formation in the gas pipeline. If the dehydration system goes offline, a
hydrate inhibition program using methanol (MeOH) or monoethylene glycol (MEG) can be used
based on the specifications in this report.
5. 6
Section 2
Description of Process Model
To calculate how the components in the wellstream react to changes in pressure and
temperature, we built a process model in MATLAB based on the Soave-Redlich-Kwong (SRK)
equation of state. The purpose of this model is to calculate molar split factors and compositions
of liquid and vapor streams for separators under various operating conditions.
The first step of the model was to write a MATLAB code that could output the Z factor
of a mixture based on pressure, temperature, composition, and thermodynamic parameters. For
the initial test in Module A, these inputs were hard-coded in the MATLAB file, but this code was
quickly revamped into a MATLAB function file (“ZFactor_Final.m”) which would output
minimum and maximum Z factor values if given inputs of composition, pressure, temperature as
well as component critical temperatures & pressures, acentric factors, omega factors, and
interaction parameters. The Z factor function used the following equations to solve the SRK
cubic equation.
Cubic equation to solve: 𝑍3
− 𝑍2
+ (𝐴 − 𝐵 − 𝐵2)𝑍 − 𝐴𝐵 = 0
[𝑎𝛼]𝑖 = Ω 𝑎𝑖
𝑅2 𝑇𝑐𝑖
2
𝑃 𝑐𝑖
[1 + 𝑓(𝜔𝑖)(1 − 𝑇𝑟𝑖
0.5
)]2
for i=1…nc
𝑏𝑖 = Ω 𝑏𝑖
𝑅𝑇 𝑐𝑖
𝑃 𝑐𝑖
for i=1…nc
Pitzer function: 𝑓(𝜔𝑖) = 0.48 + 1.574𝜔𝑖 − 0.176𝜔𝑖
2
[𝑎𝛼] 𝑚 = ∑ ∑ 𝑐𝑖
𝑛 𝑐
𝑗
𝑛 𝑐
𝑖
𝑐𝑗√(𝑎𝛼)𝑖(𝑎𝛼) 𝑗(1 − 𝛿𝑖𝑗)
6. 7
𝑏 𝑚 = ∑ 𝑐𝑖 𝑏𝑖
𝑛 𝑐
𝑖
Attraction parameter: 𝐴 =
(𝑎𝛼) 𝑚 𝑃
𝑅2 𝑇2
; Co-volume parameter: 𝐵 =
𝑏 𝑚 𝑃
𝑅𝑇
Next, we wrote a code file (“splitFunction_Final.m”) that is able to calculate the
volatility ratios of each component and molar split factor of a separator with a given pressure,
temperature, and feed composition. This code was based on the principle that at equilibrium, the
fugacities of each component in both the liquid and vapor phases must be equal. The function
worked by using Wilson’s correlation as an initial guess for the volatility ratios and then
iteratively updating the volatility ratios until the fugacities of all components in all phases
converged. Wilson’s correlation for estimating the volatility ratios is given by:
𝐾𝑖 =
𝑃𝑐𝑖
𝑃
𝐸𝑋𝑃[5.37(1 + 𝜔𝑖) (1 −
𝑇𝑐𝑖
𝑇
)]
The SRK equation was used to calculate the fugacity coefficients. The fugacity coefficients, φi,
and fugacity, fi, are defined by the following two relationships.
ln(Φ 𝑖) = (𝐵𝐵)𝑖(𝑍 − 1) − ln(Z − B) −
𝐴
𝐵
[(𝐴𝐴)𝑖 − (𝐵𝐵)𝑖]ln[
𝑍 + 𝐵
𝑍
]
where: (𝐵𝐵)𝑖 =
𝑏 𝑖
𝑏 𝑚
and (𝐴𝐴)𝑖 =
2
(𝑎𝛼) 𝑚
[(𝑎𝛼)𝑖
0.5
∑ 𝑐𝑗(𝑎𝛼) 𝑗
0.5
(1 − 𝛿𝑖𝑗)]
𝑛 𝑐
𝑗
𝑓𝑖 = 𝑐𝑖Φ 𝑖 𝑝
Initially, we used a two-component mixture such that the Rachford-Rice equation could
be simplified to the Warren-Adewumi equation and the split factor αg could be found explicitly.
The Rachford-Rice equation and Warren-Adewumi equation are as follows:
Rachford-Rice equation: 𝑔(𝛼 𝑔) = ∑
𝑐 𝑖(𝐾 𝑖−1)
1+𝛼 𝑔(𝐾 𝑖−1)
𝑛 𝑐
𝑖=1
7. 8
Warren-Adewumi: 𝛼 𝑔 = −[
𝑐1
𝐾2−1
+
𝑐2
𝐾1−1
]; 𝛼 𝐿 = 1 − 𝛼 𝑔
Finally, to calculate the volatility ratios and molar split factor of a separator with a stream
containing more than two components, we replaced the Warren-Adewumi equation in the
previous function with a function that calculates the molar split factor using the Newton-
Raphson method to solve the Rachford-Rice equation implicitly for the split factor if given the
composition and component volatility ratios (“alphaFunction_Final.m”). The Newton-Raphson
method for calculating the molar split factor utilizes an iterating process that updates αg until the
the specified convergence is achieved.
Using these three functions, we were able to calculate all of the operational and
thermodynamic parameters that are required for the design of the surface production facility.
8. 9
Input Given Data and Input Mixfile
Data
Check reservoir fluid phase to see if it is
single or two phase
Calculate split factor
Plug in values of α=0 and α=1 and if g(αg)
returns two positives it is single phase gas,
two negatives is single phase liquid and a
positive and negative indicates 2-phase
reservoir
Z-Factor Calculation of Reservoir Fluids
Calculate Molar Flow Rate to Separation
Train
Calculate Split Factor for First Separation
Train using the split factor function and z
factor function
Calculate Split Factor for Stock Tank using the
split factor function and z factor function
Calculate End Train Parameters
liquid MW, liquid density, liquid SG, API gravity,
liquid flow rate, gas flow rate, total split factor,
GOR, glycol tower gas composition, MW and z-
factor
Pressure loop which inputs pressures
ranging from 14.7:10:834.7 to find
optimum operating pressure
Lowest GOR and
Highest API?
Yes No
Done Iterations
9. 10
Section 3
Reservoir Characterization and Feed Rate Calculation
The reservoir has been described as a single phase natural gas reservoir at conditions of
7500 psia and 375°F. We began by performing Rachford-Rice calculations to prove that the
reservoir is a single phase gas reservoir. The Rachford-Rice equation is given by:
[1]
Under equilibrium conditions, g(αg) = 0 due to conservation of mass. To determine the phase of
the reservoir, the Rachford Rice equation was solved under two cases: g(αg=0) and g(αg=1) using
the reservoir composition and volatility ratios given by fugacity calculations with the SRK
equation of state (See code in the Appendix). In case 1, g(αg=0) = 0.01384 and in case 2,
g(αg=1) = 0.00051. Since both of these values are positive and the Rachford-Rice function is
monotonically decreasing over this range, it indicates that the true value of αg is greater than one.
This means that the reservoir is in fact a single phase gas reservoir at the given temperature,
pressure, and composition.
To calculate the molar feed rate entering the surface production facility from the
production manifold, the reservoir flow rate was converted to a molar flow rate using the
following equations:
𝑞𝑡𝑜𝑡𝑎𝑙 = 𝑞 𝑤𝑒𝑙𝑙 ∗ 18 [2]
𝑛𝑓𝑒𝑒𝑑 =
𝑞 𝑡𝑜𝑡𝑎𝑙 ∗ 𝑃 𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟
𝑍 𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟 ∗ 𝑅∗ 𝑇 𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟
[3]
The reservoir Z factor (Zreservoir = 1.2444) was calculated using the SRK equation of state for the
reservoir composition at the given reservoir conditions (See code in Appendix). Based on this
10. 11
calculation, the molar feed rate of hydrocarbons to the surface production facility is
approximately 14,200 lb-mol/d.
11. 12
Section 4
Determination of Separator Operating Pressures
As stated before, the goal of the stabilization train is to meet condensate vapor pressure
specifications while maximizing liquids recovery at a minimum cost. The stabilization train in
this case consists of a high pressure separator, a low pressure separator, and a stock tank. All
equipment is assumed to operate at 60°F. The high pressure separator is a three phase separator
(free water knockout) that removes all incoming liquid water. This separator must operate
between 820 and 1350 psig due to constraints from the production manifold and the need to
minimize recompression costs. The second separator operates at a pressure between the high
pressure separator and atmospheric, and the stock tank operates at atmospheric pressure (14.7
psia). To determine the optimum operating pressures for the two separators, the separation train
code was used with a double loop which tested pressures between 835-1365 psia for the first
separator and 20-830 psia for the second separator at 10 psi increments. 10 psi was chosen as an
increment because it was assumed that the pressure of a separator can be reasonably controlled to
within +/- 5 psi. For each pressure, the facility GOR and API gravity of the stock tank oil was
entered in the resulting 54x81 matrix. All of the pairs of operating conditions were analyzed to
determine which pair gave the lowest GOR and highest API gravity. These results can be seen in
the figures below.
12. 13
Figure 1: Determination of Separator Pressures by Minimizing GOR
Based on Figure 1, the minimum GOR of 4373 SCF/bbl occurs at a HP separator pressure
of 835 psia and a LP separator pressure of 60 psia.
4300
4400
4500
4600
4700
4800
0 50 100 150 200 250 300 350 400 450 500
GOR(SCF/bbl)
LP Separator Operating Pressure, psia
GOR vs. LP Separator Operating Pressure
for Various HP Separator Operating Pressures
835 psia
935 psia
1035 psia
1135 psia
1235 psia
1335 psia
13. 14
Figure 2: Determination of Separator Pressures by Maximizing API Gravity
Based on Figure 2, a maximum API gravity of the stock tank oil also occurs at a HP
separator pressure of 835 psia and a LP separator pressure of 60 psia. This makes sense because
in minimizing the GOR more of the light hydrocarbon compounds remain in the liquid phase,
thereby reducing the specific gravity of the stock tank oil.
63
63.5
64
64.5
65
65.5
66
0 50 100 150 200 250 300 350 400 450 500
APIGravity
LP Separator Operating Pressure, psia
API Gravity vs. LP Separator Operating Pressure
for Various HP Separator Operating Pressures
835 psia
935 psia
1035 psia
1135 psia
1235 psia
1335 psia
14. 15
Section 5
Sizing of Separator Vessels
Once the operating pressure of each separator was determined, the dimensions and
orientation of each separator could be determined based on the data generated from the code. For
each separator, both a vertical and horizontal separator were sized so that a comparison could be
made and the most economical vessel orientation could be chosen. Generally, the design which
utilized less material (i.e. smaller vessel volume) was the design chosen for our facility. This
section first outlines the process of sizing the 3-phase vertical separator, followed by the process
for sizing the 3-phase horizontal separator. Once this is done, the two separators are compared
and the one with the smallest volume is chosen for our facility.
15. 16
STAGE 1- HIGH PRESSURE SEPARATOR
3-Phase Vertical Separator:
The following table outlines the results of the 3-phase vertical separator sizing.
Table 2. Stage 1 3-Phase vertical separator sizing
Below is a table of the outputs generated from our code which were necessary inputs in
the calculation of the vertical separator. All of these variables were generated at each stage in the
separation train which allowed sizing at the various stages.
cd 1.2832
Vtog 0.35396 ft/s
Vtwo 0.4732 ft/s
Dv,g 4.81112 ft
Dv,g 5 ft 10.5
Dv,o 1.55135 ft
Dv,o 2 ft
tro=trw 300 sec
Hlc 16.9243 ft
Hil 2.5 ft
Hvd 5 ft
Hme 1.5 ft
Ht 25.9243 ft
Ht 30 ft 30
(L/D) 6 1.5<(L/D)<3 2.857143
Volume 589.049 ft
3
2597.704
3-Phase Vertical Separator
16. 17
Table 3. Fluid and thermodynamic properties for each stage of separation train
The first step necessary for sizing the three phase vertical separator is to determine the
terminal velocity of water through oil and oil through gas (vtwo & vtog). This calculation was done
using the terminal velocity equation derived from force balance, rather than using the Souder’s &
Brown Equation because it is more accurate. The Souder’s & Brown equation uses an empirical
separation coefficient (KSB) which is an approximate range depending on the type of separator.
In order to calculate the terminal velocity, it was necessary to carry out multiple iterations to
derive the drag coefficient (CD). Also a particle droplet size of 100 microns was used for the
calculation of vtog while 500 microns was used for vtwo due to industry standards. These standards
are set so that the mist extractor can operate properly and not become flooded. The table below
outlines the iterative procedure recommended by Arnold & Steward, which calculates the drag
coefficient.
Stage 1 Stage 2 Stage 3
Pressure psia 834.7 60 14.7
alphaG 0.69100874 0.362679 0.1401499
alphaL 0.30899126 0.637321 0.8598501
qg lbmol/d 98312.9001 15943.93 3926.6706
qo lbmol/d 43961.5678 28017.64 24090.969
qg ft
3
/s 6.43480853 16.70387 16.965827
qo ft
3
/s 0.8944496 0.720038 0.6663914
Gas Z Factor ft
3
/s 0.84599191 0.973383 0.9835095
Liquid Z Factor 0.26298065 0.023877 0.0062966
MWg lb/lbmol 18.7936044 27.56189 42.7193
Mwo lb/lbmol 72.5379499 98.13236 107.16433
ρg lb/ft
3
3.32331277 0.30449 0.1144352
ρo lb/ft
3
41.2637631 44.19518 44.839564
Information Needed for Design
17. 18
Table 4. Stage 1 terminal velocity and drag coefficient determination
With these variables established, the two terminal velocities were able to be calculated.
The next step was to determine the vessel internal diameter. The gas and water constraints were
both used to calculate two diameters. Since the diameter was largest for the gas constraint, this
diameter was rounded up to the nearest 0.5 ft. and used for the vessel internal diameter. Liquid
retention times for water and oil were determined based off of the calculated API of the fluid.
The API of the fluid was 65.415, which according to API Specifications meant that an oil and
water retention time (tro & trw) of three to five minutes would be sufficient for separation. We
chose to use the maximum, five minutes, as our retention time to add an additional safety factor
to encounter for surges, foaming or other variables that could impede separation. There are two
procedures that can be carried out to determine the height of the separator, one simplified version
and one more detailed. The detailed approach was chosen to ensure the most accurate
measurements were obtained. The length between the liquid level and inlet nozzle, the length of
the vapor disengagement section, the length required to accommodate a mist eliminator and the
height of liquid collection section were all summed to give a total height of 30 ft. The volume
Cd Vtog Re
0.34 0.68763884 91.94006648
0.913913168 0.41941831 56.07790808
1.168589312 0.37091031 49.59219341
1.249952038 0.35863542 47.95099213
1.273744944 0.35527007 47.50103093
1.280533218 0.35432715 47.37495903
1.28245656 0.35406135 47.33942083
1.283000439 0.3539863 47.32938589
1.283154151 0.3539651 47.32655096
1.283197587 0.35395911 47.32574996
Iteration Table - HP
18. 19
was then determined to be 589.049 ft3
. It is recommended that the design of a vertical separator
should have a slenderness ratio between 1.5 and 3. Using the selected dimensions from this
design produces a slenderness ratio of 6 which is not within this range. Because the slenderness
ratio was not within range, the diameter was increased by increments of 0.5 ft. until this ratio was
achieved. After this manipulation it was determined that the diameter would be 10.5 ft. which
produced a slenderness ratio of 2.86 and a volume of 2,597.704 ft3
. The diameter was able to be
increased from 5 ft. to 10.5 ft. because the calculated diameter of 5 ft. was the minimum required
diameter.
19. 20
Figure 3. Flow chart for designing stage 1 3-phase vertical separator
CD
•Intial guess of CD=0.34 and calculate vt: 𝑣𝑡(
𝑓𝑡
𝑠
) =
4
3
𝑔(
𝑓𝑡
𝑠2)𝑑 𝑝(𝑓𝑡)
𝐶 𝐷
𝜌 𝑜(
𝑙𝑏
𝑓𝑡3)−𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)
𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)
•Calculate Reynolds number using the current value of vt: 𝑅 𝑒 =
𝜌 𝑜
𝑙𝑏
𝑓𝑡3
×𝑑𝑝 (𝑓𝑡)×𝑣𝑡
𝑓𝑡
𝑠
𝜇𝑜
𝑙𝑏
𝑓𝑡−𝑠
•Recalculate CD: 𝐶 𝐷 =
24
𝑅 𝑒
+
3
𝑅 𝑒
+ 0.34
•Recalculate vt
•Iterations are stopped once values of vt converge and CD is obtained
vtog
vtwo
•The terminal velocity of water in oil and oil in gas were calculated using the folowing
equations
•𝑣𝑡𝑜𝑔(
𝑓𝑡
𝑠
) =
4
3
𝑔(
𝑓𝑡
𝑠2)𝑑 𝑝(𝑓𝑡)
𝐶 𝐷
𝜌 𝑜(
𝑙𝑏
𝑓𝑡3)−𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)
𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)
•𝑣𝑡𝑤𝑜(
𝑓𝑡
𝑠
) =
1
18
×
𝑔
𝑓𝑡
𝑠2 𝑑 𝑝𝑤𝑜
2 𝑓𝑡2
𝜇 𝑜
𝑙𝑏
𝑓𝑡−𝑠
× 𝜌 𝑜(
𝑙𝑏
𝑓𝑡3) − 𝜌 𝑔(
𝑙𝑏
𝑓𝑡3
⬚
Dv,g
Dv,o
•The diamater of the vessel was calculated for the gas constraint and water constraint. The
larger diamter was chosen and rounded to 0.5 ft.
•𝐷𝑣𝑔 ≥
4
𝜋
𝑞 𝑔
𝑓𝑡3
𝑠
𝑣 𝑡𝑜𝑔
𝑓𝑡
𝑠
•𝐷𝑣𝑜 ≥
4
𝜋
𝑞 𝑜
𝑓𝑡3
𝑠
𝑣 𝑡𝑤𝑜
𝑓𝑡
𝑠
Hlc
•Liquid Capactity Constraint: Height of the liquid collection section is determined from liquid
retention time, diamater and oil and water flow rates
•𝐻𝑙𝑐 =
4
𝜋
𝑞 𝑜 𝑡 𝑟𝑜 𝑓𝑡3 +𝑞 𝑤 𝑡 𝑟𝑤 𝑓𝑡3
𝐷 𝑣
2 𝑓𝑡2
Ht
•Using the detailed procedure the heights from the various components were added and then
rounded to 0.25 ft. to get the total height
•Ht = Hlc + Hil + Hvd +Hme
20. 21
3-Phase Horizontal Separator:
Table 5. Stage 1 3-phase horizontal separator screening table
The same outputs, generated by the code, which were used in the previous section, were
instrumental in the design of the 3-phase horizontal separator. New inputs that were not
necessary for the vertical design were the fraction of height and fraction of the vessels cross
sectional area occupied by each of the three phases (oil, water, gas). We chose to operate the
vessel at 50% full, due to industry standards and added safety factors to account for surges. It
was also given that the fractional amount of produced water at the surface was a volumetric
ration of 0.32 with respect to the amount of condensate produced at stock tank conditions. This
knowledge, in addition to the oil flow rate at stock tank conditions allowed us to calculate the
flow rate of water. The same equations that were used for terminal velocity in the vertical
separator were also used, including the same droplet diameter target. However, new equations
were required to calculate the diameter which satisfied the liquid and gas capacity constraints.
These diameters were calculated using a range of (L/D)eff values from 1.5 to 5.5 based on
industry practice. The liquid retention times from the previous section were used as they satisfied
21. 22
the conditions outline by the API guide. Once the diameters for the liquid and gas constraints
were calculated, the larger diameter for each (L/D)eff value was chosen and rounded to the
nearest 0.5 ft. The rest of the steps were carried out using the horizontal separator design
screening table which outlines the process to determine the diameter and height of the vessel.
Once the screening table was filled out, values of (Lt/Dmax)actual were chosen that were greater
than 3 but less than 5. We had three values that fell within this requirement. In order to choose
the best of the three options, the volumes of all three were compared and the design was chosen
which had the smallest volume. The smallest volume most often corresponds to the cheapest
cost. The design chosen had a diameter of 7 feet, length of 23.5 feet, and a volume of 904.386
ft3
.
22. 23
Figure 4. Flow chart for sizing stage 1 3-phase horizontal separator
vtog
vtow
•The same terminal velocities which were calculated in the previous section were used
in the following calculations
Dh,g
Dh,liq
•The minimum diamater that satisfies the gas capacity and liquid capacity considerations were
calculated
•𝐷ℎ𝑔 ≥
4
𝜋
𝑓 𝐻𝑔
𝑓 𝐴𝑔
𝑞 𝑔
𝑓𝑡3
𝑠
𝑣 𝑡𝑜𝑔
𝑓𝑡
𝑠
×
𝐿
𝐷 𝑒𝑓𝑓
•𝐷ℎ𝑙𝑖𝑞 ≥
4
𝜋
×
𝑞 𝑜 𝑡 𝑟𝑜 𝑓𝑡3 +𝑞 𝑤 𝑡 𝑟𝑤 𝑓𝑡3
𝑓 𝐴𝑙×
𝐿
𝐷 𝑒𝑓𝑓
1
3
Dh,max
•The largest diameter between the two constraints was chosen and rounded to 0.5 ft.
Leff
•𝐿𝑒𝑓𝑓 = 𝐷ℎ,𝑚𝑎𝑥 ×
𝐿
𝐷 𝑒𝑓𝑓
Lt
•Since the liquid hold up controlled the design for each instance of (L/D)eff the following was
used to calculate Lt
•𝐿 𝑡 =
4
3
× 𝐿 𝑒𝑓𝑓
•This Lt value is then rounded to the nearest 0.25 ft increment
Final Step
•The volume and (L/D)actual are then calculated and the design that falls in the slenderness ratio
of 3<(L/D)<5 and has the smalles volume is chosen
23. 24
Conclusion:
The 3-phase separator design our group chose to implement for the first separation stage
was the horizontal separator. Comparing the two separators, the horizontal separator had a
volume that was 1,693.32 ft3
less than the vertical design. The horizontal separator will be the
best option as it satisfies all of the field requirements and will be cheaper because there is less
material needed for vessel construction. Horizontal separators can handle much higher GOR
well-streams because their design allows for higher gas velocities, this is another reason why
horizontal is more advantageous than vertical for our application. Horizontal separators are also
generally cheaper to produce than vertical separators and cheaper to ship and assemble. It is for
these various reasons that our group decided to go with the horizontal separator design.
24. 25
STAGE 2- LOW PRESSURE SEPARATOR
Vertical
In order to size a vertical 2-phase separator, the terminal velocity for an oil droplet
through the gas must be determined. Because the drag coefficient, CD, is a function of terminal
velocity, Vt, the calculations must be iterated until the values converge. The following flow chart
outlines the process for designing a 2-phase vertical separator.
Figure 5. Flow chart for 2-phase vertical separator design
Vt
•Calculate terminal velocity and drag coefficient by iterating the following three equations
• 𝑣𝑡(
𝑓𝑡
𝑠
) =
4
3
𝑔(
𝑓𝑡
𝑠2)𝑑 𝑝(𝑓𝑡)
𝐶 𝐷
𝜌 𝑜(
𝑙𝑏
𝑓𝑡3)−𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)
𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)
, 𝑅𝑒 =
𝜌 𝑔(
𝑙𝑏
𝑓𝑡3)𝑑 𝑝(𝑓𝑡)𝑣 𝑡(
𝑓𝑡
𝑠
)
𝜇 𝑔(
𝑙𝑏
𝑓𝑡−𝑠
)
, 𝐶 𝐷 =
24
𝑅𝑒
+
3
𝑅𝑒
+ 0.34
•Similar to the 3-phase iteration process for Vt, CD, and Re
DV
•Calculate the vessel internal diameter based on the gas capacity
• 𝐷 𝑉 𝑓𝑡 =
4
𝜋
𝑞 𝑔(
𝑓𝑡3
𝑠
)
𝑣 𝑔(
𝑓𝑡
𝑠
)
•Vessel diameter is rounded to next 6 inch increment
Hlc
•The length of the liquid collection section is given by the following equation:
• 𝐻𝑙𝑐 =
4
𝜋
𝑞 𝑜(
𝑓𝑡3
𝑚𝑖𝑛
)𝑡 𝑅(min)
𝐷 𝑉
2
Ht
•The total length of the vertical separator is found by summing four composite heights
•Total length: 𝐻𝑡 = 𝐻𝑙𝑐 + 𝐻𝑖𝑙 + 𝐻 𝑣𝑑 + 𝐻 𝑚𝑒
•Length between liquid level and inlet nozzle: 𝐻𝑖𝑙 = max{
1
2
𝐷 𝑉(𝑓𝑡), 2𝑓𝑡}
•Length of vapor disengagement section (gravity settling): 𝐻 𝑣𝑑 = max{𝐷 𝑉(𝑓𝑡), 3𝑓𝑡}
•Length required to accommodate a mist extractor 𝐻 𝑚𝑒 = 0 no mist extractor 𝑜𝑟 𝐻 𝑚𝑒 = 1.5 𝑓𝑡 (𝑤𝑖𝑡ℎ 𝑚𝑖𝑠𝑡 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑜𝑟)
25. 26
The following table shows the iteration process results, where the value of CD is updated
in each row before recalculating Vt and Re.
Table 6. Stage 2 terminal velocity and drag coefficient determination
According to the final row of the iteration table, the drag coefficient will be taken as CD =
3.058886739 and the terminal velocity will be taken as Vt = 0.81461405 ft/s. These values are
used to continue with the sizing of the separator. The vessel internal diameter and vessel length
can now be calculated. Our stage 2 separator will include a mist extractor. The following table
summarizes the results of the 2-phase vertical separator sizing process.
Cd Vt Re
0.34 2.44339757 38.3034932
1.451307121 1.18264373 18.5395069
2.331275095 0.93311858 14.6278696
2.765091311 0.85679882 13.4314563
2.945427488 0.83015546 13.0137864
3.015807545 0.82041159 12.8610382
3.042634598 0.81678677 12.8042145
3.052770321 0.81542971 12.7829407
3.056587074 0.81492044 12.7749572
3.058022534 0.81472915 12.7719586
3.05856215 0.81465728 12.7708318
3.058764966 0.81463027 12.7704084
3.05884119 0.81462012 12.7702493
3.058869836 0.8146163 12.7701895
3.058880601 0.81461487 12.7701671
3.058884647 0.81461433 12.7701586
3.058886168 0.81461413 12.7701554
3.058886739 0.81461405 12.7701542
Iteration Table - LP
26. 27
Table 7. Stage 2 2-phase vertical separator sizing
The final dimensions for a 2-phase vertical separator are as follows: DV = 5.5 ft, Ht =
11.75 ft, and Volume = 279.16 ft3
.
Horizontal
For a 2-phase horizontal separator, the terminal velocity for an oil droplet moving
through the separator is assumed to be the same as that moving through a vertical separator.
Therefore, the Vt of 0.81461405 ft/s that was found above will apply to this design as well. For
the case of designing a horizontal vessel, both the gas capacity constraint and liquid capacity
constraint must be satisfied. Therefore, the vessel diameter is calculated using both capacities
and the largest is selected. The dimensions will be calculated for a range of (L/D)eff between 1.5
Cd 3.05888674
Vtog (ft/s) 0.81461405
Re 12.7701542
qg (ft
3
/s) 16.7038651
Dv (ft) 5.10960816
Dv, actual (ft) 5.5
qo (ft
3
/min) 43.2022566
tR (min) 1
Hlc(ft) 1.81840732
Hil (ft) 2.75
Hvd (ft) 5.5
Hme (ft) 1.5
Ht (ft) 11.5684073
Ht, actual (ft) 11.75
L/D 2.13636364
Volume (ft3
) 279.15996
2-Phase Vertical Separator
27. 28
and 5.5. The following flow chart outlines the process for designing a 2-phase horizontal
separator.
Figure 6. Flow chart for designing stage 2 2-phase horizontal separator
The following screening table outlines the process of optimizing the size of the horizontal
2-phase separator. (L/D)eff was set over a range between 1.5 and 5.5. Dhg and Dhl were calculated
for each value of (L/D)eff to find which fluid constrains the design. The design was narrowed
down to the separator dimensions with an actual L/D between 3 and 4. From these two sets of
dimensions, the separator with the smallest volume was selected as the optimal horizontal
Dh,g
•Dh,g is the vessel diameter based on the gas capacity constraint
• 𝐷ℎ,𝑔 =
4
𝜋
𝑓 𝐻𝑔
𝑓 𝐴𝑔
𝑞 𝑔
𝑣 𝑡
𝐿
𝐷 𝑒𝑓𝑓
•Vt is the same value used in vertical separator design
Dh,l
•Dh,l is the vessel diameter based on the liquid capacity constraint
• 𝐷ℎ,𝑙 =
4
𝜋
𝑡 𝑅𝑙 𝑞𝑙
𝑓 𝐴𝑙
𝐿
𝐷 𝑒𝑓𝑓
3
•tRl for our design is 1 minute because the API is larger than 35°
Dh,max
•The maximum of Dh,g and Dh,l is selected to determine if the vessel is gas constrained or liquid constrained
•Dh,max is rounded to the next 6 inch increment to comply with manufacturing specifications
Lt
•First, the effective vessel length is calculated by: Leff = Dh,max x (L/D)eff
•Since all of the cases are liquid controlled, actual vessel length is calculated by: Lt = (4/3) x Leff
•Lt is rounded to nearest 3 inch (0.25 ft) increment to comply with manufacturing specifications
Vol.
•The dimensions are narrowed down to those with 3 < (L/D)actual < 4
•Separator volume is calculated by the following equation: 𝑉𝑜𝑙𝑢𝑚𝑒 𝑓𝑡3
=
𝜋𝐷ℎ,𝑚𝑎𝑥
2
𝐿 𝑡
4
•The separator with the smallest volume and 3 < (L/D)actual < 4 is selected
28. 29
separator design. The final horizontal separator is highlighted and has dimensions of Dh = 3.5 ft
and Lt = 14 ft.
Table 8. Stage 2 2-phase horizontal separator screening table
Conclusion
Now that the sizing process has been completed for both a vertical and horizontal design,
the final separator design should be selected based on economics. In order to minimize the cost
of implementing the 2-phase separator in the surface production facility, the separator with the
smallest volume will be selected. The vertical separator has a volume of 279.16 ft3
and the
horizontal separator has a volume of 134.70 ft3
. Therefore, the selected design for the second
stage of the separation train will be a 2-phase horizontal separator with a diameter of 3.5 ft and
length of 14 ft.
(L/D)eff Dhg (ft) Dhl (ft)
Dh
max (ft)
Leff (ft) Lt (ft)
Lt
Actual (ft)
Volume
(ft
3
)
L/D
Actual
1.5 4.172 4.186 4.5 6.75 9.000 9 143.139 2
2 3.613 3.803 4 8 10.667 10.75 135.088 2.6875
2.5 3.232 3.530 4 10 13.333 13.5 169.646 3.375
3 2.950 3.322 3.5 10.5 14.000 14 134.696 4
3.5 2.731 3.156 3.5 12.25 16.333 16.5 158.749 4.714286
4 2.555 3.019 3.5 14 18.667 18.75 180.396 5.357143
4.5 2.409 2.902 3 13.5 18.000 18 127.235 6
5 2.285 2.802 3 15 20.000 20 141.372 6.666667
5.5 2.179 2.715 3 16.5 22.000 22 155.509 7.333333
29. 30
Section 6
Sizing of Dehydrator System
Glycol Tower Design
Given Information:
P=834.7 psi qgsc= 44.834 MMSCFD Rc=3 galTEG/lbH2O
Wout=4.0 lbH2O/MMSCF T=600
F
Step 1: Calculate Water Removal Target and Required Glycol Rate
From Fig 20-4:
Win=21 lbH2O/MMSCF Dew Point = 600
F
Wout=4.0 lbH2O/MMSCF Dew Point = 150
F
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = (W𝑖𝑛 − W𝑜𝑢𝑡) ∗ 𝑞 𝑔
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = (21 𝑙𝑏 𝐻2 𝑂/ 𝑀𝑀𝑆𝐶𝐹 − 4.0 𝑙𝑏 𝐻2 𝑂/ 𝑀𝑀𝑆𝐶𝐹) ∗ 44.834 𝑀𝑀𝑆𝐶𝐹𝐷
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = 762.178 𝑙𝑏 𝐻2 𝑂/𝐷𝑎𝑦
𝑞 𝑇𝐸𝐺 = 𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 ∗ R 𝑐 = 762.178
𝑙𝑏𝐻2 𝑂
𝐷𝑎𝑦
∗ 3.0
𝑔𝑎𝑙𝑇𝐸𝐺
𝑙𝑏𝐻2 𝑂
= 2286.53
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
Step 2: Calculate all Concentrations Entering and Leaving Contactor
From Fig 20-59
𝑋𝑖𝑛 = 97.5 𝑤𝑡% (Including 150
F safety factor)
From Fig 20-4:
Win=21 lbH2O/MMSCF Dew Point = 600
F
30. 31
Wout=4.0 lbH2O/MMSCF Dew Point = 150
F
From Fig 20-34
ρ 𝑇𝐸𝐺 = 9.39
𝑙𝑏𝑇𝐸𝐺
𝑔𝑎𝑙
𝑚 𝑇𝐸𝐺 = 𝑞 𝑇𝐸𝐺 ∗ ρ 𝑇𝐸𝐺 = 2286.53
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
∗ 9.39
𝑙𝑏𝑇𝐸𝐺
𝑔𝑎𝑙
= 21470.5167
𝑙𝑏𝑇𝐸𝐺
𝐷𝑎𝑦
X 𝑜𝑢𝑡 = X 𝑖𝑛 −
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡
𝑚 𝑇𝐸𝐺
= 0.975 ∗
2286.53
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
21470.5167
𝑙𝑏𝑇𝐸𝐺
𝐷𝑎𝑦
= 93.95 𝑤𝑡%
Step 3: Estimate Number of Stages
From McCabe Thiele plot: Since the operational line crosses the equilibrium line, we can
never reach the required water content leaving the contactor; therefore, N=infinity, and we must
reevaluate our parameters.
31. 32
Figure 7. McCable-Thiele plot for glycol dehydration stage determination: first attempt
Second Attempt
We can increase the wt% lean glycol to improve our results
Given Information:
P=834.7 psi qgsc= 44.834 MMSCFD Rc=3 galTEG/lbH2O
Wout=4.0 lbH2O/MMSCF T=600
F
𝑋𝑖𝑛 = 99.0 𝑤𝑡%
Step 1: Calculate Water Removal Target and Required Glycol Rate
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = (W𝑖𝑛 − W𝑜𝑢𝑡) ∗ 𝑞 𝑔
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = (21 𝑙𝑏 𝐻2 𝑂/ 𝑀𝑀𝑆𝐶𝐹 − 4.0 𝑙𝑏 𝐻2 𝑂/ 𝑀𝑀𝑆𝐶𝐹) ∗ 44.834 𝑀𝑀𝑆𝐶𝐹𝐷
32. 33
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = 762.178 𝑙𝑏 𝐻2 𝑂/𝐷𝑎𝑦
𝑞 𝑇𝐸𝐺 = 𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 ∗ R 𝑐 = 762.178
𝑙𝑏𝐻2 𝑂
𝐷𝑎𝑦
∗ 3.0
𝑔𝑎𝑙𝑇𝐸𝐺
𝑙𝑏𝐻2 𝑂
= 2286.53
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
Step 2: Calculate all Concentrations Entering and Leaving Contactor
From Fig 20-4:
Win=21 lbH2O/MMSCF Dew Point = 600
F
Wout=4.0 lbH2O/MMSCF Dew Point = 150
F
From Fig 20-34
ρ 𝑇𝐸𝐺 = 9.39
𝑙𝑏𝑇𝐸𝐺
𝑔𝑎𝑙
𝑚 𝑇𝐸𝐺 = 𝑞 𝑇𝐸𝐺 ∗ ρ 𝑇𝐸𝐺 = 2286.53
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
∗ 9.39
𝑙𝑏𝑇𝐸𝐺
𝑔𝑎𝑙
= 21470.5167
𝑙𝑏𝑇𝐸𝐺
𝐷𝑎𝑦
X 𝑜𝑢𝑡 = X 𝑖𝑛 −
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡
𝑚 𝑇𝐸𝐺
= 0.990 ∗
2286.53
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
21470.5167
𝑙𝑏𝑇𝐸𝐺
𝐷𝑎𝑦
= 95.45 𝑤𝑡%
From McCabe Thiele Plot: N=3
We can now see a more appropriate depiction of the operational line. Using a higher wt% of lean
glycol has improved our results by decreasing the number of required stages, and thereby
decreasing the necessary height
33. 34
Figure 8. McCabe-Thiele plot for glycol dehydration stage determination: second attempt
Third Attempt
We can also improve results by operating the contactor tower at a higher temperature of
1000
F
Given Information:
P=834.7 psi qgsc= 44.834 MMSCFD Rc=3 galTEG/lbH2O
Wout=4.0 lbH2O/MMSCF T=1000
F
Step 1: Calculate Water Removal Target and Required Glycol Rate
34. 35
From Fig 20-4:
Win=65 lbH2O/MMSCF Dew Point = 1000
F
Wout=4.0 lbH2O/MMSCF Dew Point = 150
F
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = (W𝑖𝑛 − W𝑜𝑢𝑡) ∗ 𝑞 𝑔
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = (65 𝑙𝑏 𝐻2 𝑂/ 𝑀𝑀𝑆𝐶𝐹 − 4.0 𝑙𝑏 𝐻2 𝑂/ 𝑀𝑀𝑆𝐶𝐹) ∗ 44.834 𝑀𝑀𝑆𝐶𝐹𝐷
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 = 2734.8741 𝑙𝑏 𝐻2 𝑂/𝐷𝑎𝑦
From Fig 20-59
𝑋𝑖𝑛 = 99.3 𝑤𝑡% (Including 150
F safety factor)
𝑞 𝑇𝐸𝐺 = 𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡 ∗ R 𝑐 = 2734.8741
𝑙𝑏𝐻2 𝑂
𝐷𝑎𝑦
∗ 3.0
𝑔𝑎𝑙𝑇𝐸𝐺
𝑙𝑏𝐻2 𝑂
= 8204.662
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
Step 2: Calculate all Concentrations Entering and Leaving Contactor
From Fig 20-4:
Win=65 lbH2O/MMSCF Dew Point = 1000
F
Wout=4.0 lbH2O/MMSCF Dew Point = 150
F
From Fig 20-59
𝑋𝑖𝑛 = 99.3 𝑤𝑡% (Including 150
F safety factor)
From Fig 20-34
ρ 𝑇𝐸𝐺 = 9.26
𝑙𝑏𝑇𝐸𝐺
𝑔𝑎𝑙
= 69.26 𝑙𝑏/𝑓𝑡3
𝑚 𝑇𝐸𝐺 = 𝑞 𝑇𝐸𝐺 ∗ ρ 𝑇𝐸𝐺 = 8204.662
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
∗ 9.26
𝑙𝑏𝑇𝐸𝐺
𝑔𝑎𝑙
= 75974.80
𝑙𝑏𝑇𝐸𝐺
𝐷𝑎𝑦
35. 36
X 𝑜𝑢𝑡 = X 𝑖𝑛 −
𝑊𝑎𝑡𝑒𝑟 𝑇𝑎𝑟𝑔𝑒𝑡
𝑚 𝑇𝐸𝐺
= 0.993 ∗
2734.8741
𝑔𝑎𝑙𝑇𝐸𝐺
𝐷𝑎𝑦
75974.80
𝑙𝑏𝑇𝐸𝐺
𝐷𝑎𝑦
= 95.7 𝑤𝑡%
From McCabe Thiele Plot: N=2
This is our best result of the three options since it provides us with the smallest contactor
height which will save on cost.
Figure 9. McCabe-Thiele plot for glycol dehydration stage determination: third attempt
Step 4: Size the Tower
We will use structured packing since packing height it typically shorter than that of
bubble cap trays
37. 38
Inhibitor Calculation
*If the glycol contactor tower should go offline, the mass flowrate of MEG and MeOH
necessary for hydrate inhibition is calculated as follows:
Given Information:
P=834.7 psia
𝑆. 𝐺. =
𝑀𝑊𝑔
𝑀𝑊𝑔
=
20.7715
𝑙𝑏𝑚
𝑙𝑏𝑚𝑜𝑙
29
𝑙𝑏𝑚
𝑙𝑏𝑚𝑜𝑙
= 0.71625
From Fig 20-4
@ 1000
F Win= 65 lbH2O/MMSCF
@ 600
F Wout= 21 lbH2O/MMSCF
Step 1: Calculate Hydrate Formation Temperature at Highest System Pressure
From Fig 20-19
Th=63.50
F
Step 2: Determine Lowest Temperature of the System
Since the entire facility is known to operate at 600
F:
Lowest T= 600
F
Step 3: Calculate Required Hydrate Temperature Depression
𝑑 = 𝑇ℎ − 𝑇 = 63.5 − 60 = 3.50
𝐹
Step 4: Calculate Total Mass of Free Water Expected Within the System
𝑚 𝑤 = 𝑞 𝑔𝑠𝑐(W𝑖𝑛 − W𝑜𝑢𝑡) = 44.834 𝑀𝑀𝑆𝐶𝐹𝐷 ∗ (65
𝑙𝑏𝐻2 𝑂
𝑀𝑀𝑆𝐶𝐹
− 21
𝑙𝑏𝐻2 𝑂
𝑀𝑀𝑆𝐶𝐹
)
38. 39
𝑚 𝑤 = 1972.696
𝑙𝑏
𝐷𝑎𝑦
Step 5: Calculate Required Inhibitor Concentration using Hammerschmidt
Equation
Calculations for MEG:
𝑥𝑖 =
𝑑 ∗ 𝑀𝑊
𝑑 ∗ 𝑀𝑊 + 2335
=
3.50
𝐹 ∗ 64
𝑙𝑏𝑚
𝑙𝑏𝑚𝑜𝑙
3.50 𝐹 ∗ 64
𝑙𝑏𝑚
𝑙𝑏𝑚𝑜𝑙
+ 2335
= 8.5𝑤𝑡%
Step 6: Calculate Mass of Inhibitor Required Based on Available Inhibitor Solution
Assume 75 wt% MEG available
𝑚𝐼 =
𝑋 𝑅 ∗ 𝑚 𝑤
𝑋 𝐴𝑉 − 𝑋 𝑅
=
8.5𝑤𝑡% ∗ 1972.696
𝑙𝑏
𝐷𝑎𝑦
75𝑤𝑡% − 8.5𝑤𝑡%
= 272.649
𝑙𝑏
𝐷𝑎𝑦
𝑜𝑓 75% 𝑀𝐸𝐺
Calculations for MeOH:
𝑥𝑖 =
𝑑 ∗ 𝑀𝑊
𝑑 ∗ 𝑀𝑊 + 2335
=
3.50
𝐹 ∗ 32
𝑙𝑏𝑚
𝑙𝑏𝑚𝑜𝑙
3.50 𝐹 ∗ 32
𝑙𝑏𝑚
𝑙𝑏𝑚𝑜𝑙
+ 2335
= 4.58𝑤𝑡%
Step 6: Calculate Mass of Inhibitor Required Based on Available Inhibitor Solution
𝑚𝐼 =
𝑋 𝑅 ∗ 𝑚 𝑤
𝑋 𝐴𝑉 − 𝑋 𝑅
=
0.0458 ∗ 1972.696
𝑙𝑏
𝐷𝑎𝑦
1 − .0458
= 94.686
𝑙𝑏
𝐷𝑎𝑦
𝑜𝑓 𝑝𝑢𝑟𝑒 𝑀𝑒𝑂𝐻
Additional Step 7: Account for Losses
39. 40
From Fig 20-65
@600
F & 834.7 psia 1.95 lbMeOH/wt%/MMSCF
1.95 lbMeOH/wt%/MMSCF ∗ 44.834MMSCF ∗ 4.58wt% = 400.4
lb
𝐷𝑎𝑦
Total MeOH = 400.4
lb
𝐷𝑎𝑦
+ 94.686
𝑙𝑏
𝐷𝑎𝑦
= 495.098
𝑙𝑏
𝐷𝑎𝑦
𝑀𝑒𝑂𝐻
80.87% of MeOH is lost to the gas phase
40. 41
Appendix A
MATLAB Code
<Final_Project.m>
% PNG 480: Design of a Surface Production Facility
% Group Members:
% Chad DiStanislao
% Christopher Efstathion
% David Hughes
% Michael Silver
% Last Updated: 4/21/15
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Step 1: Input Given Data & Import Mixfile Data
format long
% Import thermodynamic data matrix
mixfile = dlmread('mixfile_final.txt');
% Import interaction parameters
Delta = dlmread('Delta1.txt');
% Temperature of reservoir (Rankine)
TRes = 375+460;
% Temperature of facility (Rankine)
TFacility = 60+460;
% Pressure of reservoir (psi)
pres = 7500;
% Pressure 1 (psi)
p1 = 820+14.7;
% Pressure 2 (psi)
p2 = 60;
% Pressure 3 (psi)
p3 = 14.7;
% Gas Constant (ft^3 psi/R lb-mol)
R = 10.73;
% Create composition vector (mol fraction)
c = mixfile(:,1);
% Create molecular weight vector (lb/lb-mol)
MW = mixfile(:,2);
% Create critical temperature vector (degrees F)
TCF = mixfile(:,3);
% Create critical pressure vector (psi)
PC = mixfile(:,4);
% Create critical Z factor vector (dimensionless)
ZC = mixfile(:,5);
% Create acentric factor vector (dimensionless)
41. 42
Acentric = mixfile(:,6);
% Create Omega A factor vector (dimensionless)
OmegaA = mixfile(:,7);
% Create Omega B factor vector (dimensionless)
OmegaB = mixfile(:,8);
% Number of components (dimensionless)
n=length(c);
% Convert critical temperature vector to absolute (Rankine)
TC = TCF + 460;
% Reservoir Flow Rate (RCF/d/well)
qres = 11750;
% Number of Wells
nwell = 18;
% Fractional Amount of Water (qwater/qST)
fw = 0.32;
% Water Specification (lbH2O/MMSCF)
Wout = 4.0;
% Dehy Pressure (psi)
Pdehy = p1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Step 2: Z-Factor Calculation of Reservoir Fluid
% Check reservoir fluid phase
% Get volatility ratios
splitFactor_Res = splitFunction_Final(c, pres, TRes, TC, PC, ZC, Acentric,
OmegaA, OmegaB, Delta);
K = splitFactor_Res(:,5);
% Evaluate Rachford Rice, alphaG = 0
alphaG=0;
gAlphaG = 0;
for i = (1:n)
gAlphaG = gAlphaG + (c(i)*(K(i)-1))/(1+alphaG*(K(i)-1));
end
gAlphaG_0 = gAlphaG
% Evaluate Rachford Rice, alphaG = 1
alphaG=1;
gAlphaG = 0;
for i = (1:n)
gAlphaG = gAlphaG + (c(i)*(K(i)-1))/(1+alphaG*(K(i)-1));
end
gAlphaG_1 = gAlphaG
% ZOutput = [maxZ, minZ, A, B, aam, bm];
ZOutputRes = ZFactor_Final(c, pres, TRes, Delta, TC, PC, ZC, Acentric,
OmegaA, OmegaB);
% Output gas Z factor
ZRes = ZOutputRes(1)
