IV Journeys in Multiphase Flows (JEM 2015)
March 23-27, 2015, Campinas, SP, Brazil
Copyright © 2015 by ABCM
Paper ID: JEM-2015-0041
COMPOSITIONAL MODELING OF RESERVOIR TO STOCK-TANK
CONDITIONS: SIMULATION AND EXPERIMENTAL DATA
VALIDATION
Sthener Rodrigues Vieira Campos
Petrobras, Centro de Pesquisa e Desenvolvimento Leopoldo Américo Miguez de Mello, Rio de Janeiro, Rio de Janeiro, Brazil
Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, 7491
Trondheim, 6 Norway
sthener@petrobras.com.br
sthener.campos@ntnu.no
Abstract. .
A compositional simulation to perform multiple flash calculations from initial reservoir to stock-tank conditions is
presented. The surface process was defined as a single separator stage and the stock-tank. This process represents the
well test route in the Urucu field at Petrobras. The fluid characterization used the SRK EOS tuned with PVT measured
data. The initial gas cap composition was generated from the oil flashed at the reservoir saturation pressure and
temperature. The original oil composition, at initial reservoir condition, was used for the fluid initialization. A
recombination method calculated the wellbore composition at depleted pressure and temperature by an iterative logic.
In this procedure, the gas cap, the reservoir oil and the water mole fractions were blended to match the production
gas/oil ratio and water cut from the well. The oil and gas density at stock-tank condition, the oil flow rate at separator
condition and the separator oil formation volume factor were used as simulation validation parameters.The simulation
was implemented in the software Hysys from Aspentech to provide the fluid properties and the stream composition for
modeling the multiphase flow expansion process through orifice plates and a choke valve in wellhead pressure and
temperature conditions.
Keywords: Compositional simulation, equilibrium calculation, multi-rate well test, experimental data
1. INTRODUCTION
The Urucu field produces average oil gravity of 43oAPI and condensate gravity of 60o API. The gas/oil ratio GOR
ranges from 250 Sm3/Sm3 in early well life stage to maximum of 9000 Sm3/Sm3. Gas expansion is the primary reservoir
recovery mechanism. The oil saturated interval is a thin oil rim below a large gas cap. Most of the wells experience gas
and water coning. Depending on the influence of bottomhole drawdown in gas-oil contact geometry, the production
stream will have more or less contribution from the gas cap. Gas/water coning is a reservoir phenomenon that modifies
the fluid composition in producing stream, affecting short term management decisions. This near wellbore effect was
described in Campos et al. (2010). The fluid type produced in Urucu field varies from volatile oil to wet gas depending
on the gas cap contribution.
According to McCain (1994), heavy components control reservoir fluid behavior. The heavy components mole
percentage decreases from black oils through volatile oils, retrograde gases, wet gases until none in dry gases. It is not
recommended to use black-oil model in surface conditions to calculate volatile oils stream composition because the
condensate from the gas phase will not be considered. Fevang et al. (2000) compared black-oil and compositional
simulated production performance for gas injection in partial pressure maintenance scenario. The authors have found
that black-oil consistently over-predicts oil production due to excess vaporization. In Urucu field, the secondary
recovery method is gas injection for partial pressure maintenance. So, the compositional approach was chosen for the
numerical simulation. The most used cubic EOS models in the upstream O&G industry are Soave-Redlich-Kwong
(SRK) and Peng-Robinson (PR). Pedersen et al. (1988) discussed that it might be difficult to predict mixture properties
with high degree of accuracy because of the complexity of the mixtures and models limitation. So, improvement of
EOS calculations is necessary by tuning the model parameter to measured PVT data. There is not a single recipe to tune
an EOS. Whitson and Brule (2000) discussed how to match an EOS to measure data in chapter 4. Other references cited
in the SPE Phase Behavior monograph are: Pedersen et al. (1989), Coats and Smart (1986), Agarwal et al. (1990) and
Soreide (1989). It is a consensus that molecular weight of heavy end component, MW Cn+ , should be accurately
determined as it influences the mass-to-mole composition conversion, separator oil/gas ratios and oil FVF calculation.
The last property is one of simulation validation parameter in this paper. There is not an obligatory reason to choose
SRK instead of PR. The default (un-tuned) models deliver similar phase equilibria and phase properties results. The
mandatory step to use any of these cubic models is to correct the volumetric predictions by use of Peneloux et al. (1982)
volume translation.
Campos S.R.V.
Compositional Reservoir to Stock-tank Conditions: Simulation and Experimental Data Validation
The SRK EOS tuning was done in a previous step to this investigation. The EOS was implemented in Hysys basis
environment with eight pseudocomponents. It is not objective of this paper to describe EOS tuning procedures. For this
subject the author suggests read Coats (1985). He discussed the simulation of gas condensate reservoir performance
with different component pseudoization procedure for EOS tuning.
The simulation framework developed in this study was designed to investigate multiphase flow expansion process
through restrictions in surface conditions. To this end, fluid recombination and stream composition were calculated
since initial reservoir to the stock-tank conditions. This approach ensured consistent fluid characterization in subsurface and surface conditions. A field scale experiment was executed in three wells to deliver the input conditions for
phase equilibria calculations. The experimental procedure consisted of a multi-rate well test described in the later
section.
The oil density at stock-tank condition (ρoil@std, kg/m3), the gas density at stock-tank condition (ρgas@std, kg/m3), the oil
flow rate at separator condition (Sep_qo, m3/d) and the separator oil formation volume factor (Sep_Oil FVF) were used
as simulation validation parameters. The results confirmed the simulation capability to calculate correct stream
composition as the fluid experiences pressure and temperature drop through the gathering system. The designed
compositional simulation is an enabler step to performed multiphase flow studies through singularities. 1
2. MULTI-RATE FIELD EXPERIMENT
A multi-rate well test experiment was performed in three wells single routed to a test separator. It provided input
data for the simulation validation. The test procedure consisted of a non-periodic sequential step response test followed
by a transient and a steady state period “a priori” to the next step. Two types of well performance from the Urucu field
were analyzed: production with stream composition variation caused by near wellbore reservoir gas/water coning (Well
1) and production with constant stream composition (Well 2 and Well 3). The ranges of fluid properties and flow
conditions achieved during the experiment were: wellhead pressure: 9073 kPa to 13603 kPa, gas-oil ratio
(GOR):1144 Sm3/ Sm3 to 2179 Sm3/ Sm3, water-cut (Wcut): 4.64% to 58.35%, standard oil specific gravity: 0.7818 to
0.8058, standard gas specific gravity: 0.7340 to 0.7591, standard oil flow rate: 46.86 Sm3/d to 227.47 Sm3/d. The multirate well tests generated a database with total of 1768 production conditions. Typical wellhead instrumentation and the
devices corresponding distances are presented in Fig. 1.
Figure 1. Wellhead instrumentation from 3D wireframe sketch. Pwh= P1 (Unit = mm).
1
“ Experimental and Numerical investigation of Multiphase Flow Expansion Process Through Cage Trim Valves
(unpublished)
“Multiphase flow rate and Composition Estimation Through Modeling of Orifice Meters and Cage Trim Valve”
(unpublished)
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IV Journeys in Multiphase Flows (JEM 2015)
The field experiment rigorous commissioning phase ensured no systematic or random instrumentation errors. The
experimental procedure had duration of 20.29 days in Well 1, 9.5 days in Well 2, and 8.5 days in Well 3. Figure 2 and
Figure 3 show the choke opening and the wellhead variables behavior for Well 1 and Well 3. Figure 4 and Figure 5
present corresponding gas/oil ratio (GOR) for Well 1 and Well 3. While in Well 1 the GOR changed with reservoir
drawdown, the GOR remained constant after the step disturbance in Well 3. The Well 2 and Well 3 had similar behavior
with respect to GOR variation and production parameters, therefore figures were not presented.
Figure 2. Well 1 multi-rate test pressure and temperature responses.
Figure 3. Well 3 multi-rate test pressure and temperature responses.
Campos S.R.V.
Compositional Reservoir to Stock-tank Conditions: Simulation and Experimental Data Validation
Figure 4. The dark trend shows the GOR variation for each choke opening. The Steady State Index (Iss) trend is
plotted in light gray. The dotted line corresponds to the Iss threshold. A transient period is considered when the
calculated steady state index goes below the threshold line.
Figure 5. No correlation was observed between choke opening and GOR in Well 3 (and in Well 2).
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IV Journeys in Multiphase Flows (JEM 2015)
After each choke manipulation, the transient period was quantified through a steady state identification method
based on “Wilcoxon Signed Rank Sum” test proposed by Bebar (2005) In Meija et al. (2010), the Bebar method and
other five steady state identification procedures were discussed. The “Wilcoxon Signed Rank Sum” procedure uses the
data relative position value in the window size instead of the raw observed data. For steady state identification index
(ISS) interval, it was assumed a steady state threshold (index = 0.5) and a window size of 100 points with 30 minutes
time steps. The light grey line in Fig. 4 represents the calculated Steady State Index (ISS) and the dotted line is the
threshold. If calculated ISS is below the threshold, the data is assumed in transient condition. Table 1 lists the Well 1
transient duration data for the gas/oil ratio, the slower variable response. The steady state identification determination
was a post-processing analysis. During the experiment, the stabilization period was extended to guarantee enough data
points in the steady state region before every step. The steady state identification method was not calculated for Well 2
and Well 3 because all variables (including the gas/oil ratio) did not show long transients before each step execution.
Table 1. Well 1 GOR transient period. Threshold limit = 0.5. (See Fig. 4)
Step
Variable
Result
Choke
Opening,
%
Transient
Period
h
Step
Duration
h
1
2
3
4
5
gas/oil ratio
gas/oil ratio
gas/oil ratio
gas/oil ratio
gas/oil ratio
inconclusive
conclusive
conclusive
conclusive
conclusive
64.8 to 50.7
50.7 to 69.4
69.4 to 78.2
78.2 to 60.3
60.3 to 64.9
133
114.5
37
13
2
182.5
204.5
87
15.5
71
Table 2 gives one set of Well 1 input variables to run the reservoir to stock-tank compositional simulation model.
Table 3 shows the reservoir and the stock-tank variables. For each execution thirteen input parameters from the
database provide information to set the equilibrium calculation conditions. Other seven parameters are fix input
variables that does not change per execution but in the reservoir time scale.
Table 2. Input variable to set production conditions for tuning model execution.
Production Condition Variables
Gas Oil Ratio
Water Cut
Well Head Pressure
Well Head Temperature
Pressure Downstream the Choke
Temperature Downstream the Choke
Separator Pressure
Separator Temperature
Oil Flow rate at Standard Condition
Delta Pressure Upstream orifice Plate
Delta Pressure downstream orifice Plate
Orifice Meter Internal Diameter
Orifice Meter Internal Diameter
Symbol
GOR
Wcut
P1
T1
P4
T4
Psep
Tsep
qo@std
∆P1
∆P2
d1
d2
Unit
Sm3/Sm3
%
kPa
o
C
kPa
o
C
kPa
o
C
m3/d
kPa
kPa
m
m
Table 3. Reservoir and stock-tank temperature and pressure variables.
Process Input Variables
Initial Reservoir Composition
Reservoir Pressure
Reservoir Temperature
Depleted Reservoir Pressure
Depleted Reservoir Temperature
Stock-tank Pressure
Stock-tank Temperature
Symbol
Pres
Tres
PRdep
TRdep
Pstd
Tstd
Unit
mole frac
kPa
o
C
kPa
o
C
kPa
o
C
3. COMPOSITIONAL MODELING OF RESERVOIR TO STOCK-TANK CONDITIONS
Campos S.R.V.
Compositional Reservoir to Stock-tank Conditions: Simulation and Experimental Data Validation
A compositional simulation for multiple equilibrium calculation from initial reservoir to stock-tank condition was
developed to investigate a multiple restriction installation according to Fig. 1. To this end, a model was implemented in
the process simulator Hysys from Aspentech. For fluid characterization, it was used the SRK EOS previously tuned
with field PVT data. The standard condition to calculate the GOR and the water cut was simulated as a single stage
separation process and the stock-tank to reproduce the test separator route. The storage tank condition refers to 1 atm /
20oC basis (Petrobras condition). Figure 6 presents the simulation workflow diagram divided in five sections:
I) Initial Condition – The fluid initialization was done in this section. For the initial reservoir pressure, it was assumed
that saturation pressure equals the reservoir pressure, Psat = PR(i). The initial reservoir oil composition at PR(i) was
extracted from a PVT analysis performed in the year 1989 (early development stage). The initial gas cap composition
(Yi) was generated from the oil flashed at the reservoir saturation pressure and temperature. (For PVT analysis is
referred as the incipient gas composition).
II) Depletion – This section was used to calculate the fluid composition at current reservoir condition. The initial gas
and the initial oil streams from previous section were flashed at the current reservoir P, T conditions. These two flash
calculations generated four new streams:
• (Yi)g – The gas composition from depleted gas cap;
• (Xi)g – The oil composition from depleted gas cap;
• (Yi)o – The gas composition from depleted reservoir oil;
• (Xi)o – The oil composition from depleted reservoir oil;
The depleted gas cap oil mobility was considered negligible, therefore the reservoir gas cap oil flow rate was
null. The mole fraction contribution of (Yi)o and (Xi)o for the depleted reservoir oil stream were represented as fog and foo
respectively.
III) Coning – The gas cap contribution was represented by the gas stream from depleted gas cap (Yi)g with
corresponding phase mole fraction (fg). The reservoir oil was represented by the oil stream from depleted reservoir oil
(Zi)o with corresponding phase mole fraction fo . For coning hydrocarbon recombination the relation fg + fo =1
IV) Wellbore (Zwi) – The water content in the wellbore stream was added as immiscible phase to the mixture. The
wellbore composition (Zwi) was formed by blending the gas from depleted gas cap (Yi)g, the oil from depleted reservoir
oil (Zi)o and the water streams. For wellbore hydrocarbon recombination the relation fg + fo =1 is still valid as water was
added as immiscible stream. Therefore, fo = (1- fg)
V) Metering & Process - This section simulates the multi-restriction assembling. Pipe length that encompasses
wellhead instrument assembling is fewer than 10 meters. Local pressure drop generated by the orifice plates in the
system was neglected because orifice efficient pressure recovery. This assumption was tested in 1907 as reported by
Westcott, H. (1922) in the book “Measurement of gas and liquid by orifice”. The results from studies are not published
in this paper.
Figure 7 presents the reservoir fluid recombination method implemented in the process simulator Hysys. The
wellbore composition at depleted pressure and temperature is calculated by an iterative procedure. The gas cap,
reservoir oil and water mole fractions are blended to match the produced GOR and water cut. The original oil
composition at initial reservoir condition is known. The gas cap composition is the incipient gas from reservoir oil at
bubble point. Hysys logical element Recycle was used out of its regular characteristics. Here, the Recycle element is
used to forward the composition for the next section allowing the flash, within the recombination method, to be
calculated for 1 mole basis. So, between the initial reservoir condition, the depletion condition and the coning condition
there is a mass balance discontinuity. The sections represent the gas and oil reservoir equilibrium calculation in
different time scale periods (from initial reservoir to current condition). Then, wellbore composition is forward to the
wellhead. Modeling assumptions are listed in Table 4.
Table 4. Modeling assumptions.
Variable
Initial reservoir pressure
Depletion pressure
fo
Gas cap liquid mobility
BR stock-tank condition
Assumption
Psat = PR(i)
PR(t) < Psat = PR(i)
0.75
λo (Xi)g = 0
101.32 kPa, 20oC
Model Section
Initial Condition
Depletion
Depletion
Depletion
Metering & Process
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IV Journeys in Multiphase Flows (JEM 2015)
Figure 6. Workflow diagram from initial reservoir to stock-tank condition.
Figure 7. Composition calculation from initial reservoir to wellbore condition.
The overall reservoir oil zone composition (Zi)o is calculated by the oil stream from depleted reservoir oil and gas
stream from depleted reservoir oil recombination. The oil zone depleted gas phase mole fraction from the reservoir oil
zone and the oil zone depleted oil phase mole fraction are represented by fog and foo (See Fig. 6). A sensitivity analysis
to evaluate foo influence in the wellbore composition was performed for 0.5<foo<0.95. In the study:
Campos S.R.V.
Compositional Reservoir to Stock-tank Conditions: Simulation and Experimental Data Validation
1) The well stream GOR was kept constant to 1890 Sm3/Sm3 by changing the depleted gas phase mole fraction fg
for each value of foo.
2) No water content was considered in the produced stream composition which results in the relationship foo + fog
= 1.
Table 5 lists the pseudo-components contribution to the overall wellbore composition (Zwi) at depletion condition.
Each column of Tab. 5 refers to a foo sensitivity analysis case. It has been concluded that recombination ratio studied
between foo and fog did not affect the wellbore composition. So, the depleted oil phase mole fraction contribution to
create the reservoir oil zone composition was fixed to foo = 0.75.
Table 5. Sensitivity analysis of depleted reservoir oil mole fraction foo
on wellbore stream composition for 0.5<foo<0.95.
1
2
3
4
5
6
7
8
9
10
Case
GOR
Sm3/Sm3
1890
1890 1890 1890
1890 1890 1890
1890 1890 1890
fg
0.832
0.848 0.860 0.860
0.860 0.889 0.896
0.902 0.902 0.902
fo or 1-fg
0.168
0.152 0.140 0.140
0.140 0.111 0.104
0.098 0.098 0.098
foo
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
fog
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
Pseudo1
0.081 0.081
0.081 0.081 0.081
0.081 0.081 0.081
0.081 0.081
0.670 0.670
0.670 0.667 0.665
0.670 0.670 0.670
0.670 0.666
0.110 0.110
0.110 0.110 0.110
0.110 0.110 0.109
0.109 0.110
0.074 0.074
0.074 0.075 0.075
0.074 0.074 0.074
0.074 0.075
0.042 0.042
0.042 0.043 0.044
0.042 0.042 0.042
0.042 0.044
0.010 0.010
0.010 0.011 0.012
0.010 0.010 0.010
0.010 0.011
[mole frac]
0.012 0.012
0.012 0.013 0.014
0.012 0.012 0.012
0.012 0.014
H2O
Total
0.000 0.000
1.000 1.000
0.000 0.000 0.000
1.000 1.000 1.000
0.000 0.000 0.000
1.000 1.000 1.000
0.000 0.000
1.000 1.000
[mole frac]
Pseudo2
[mole frac]
Pseudo3
[mole frac]
Pseudo4
[mole frac]
Pseudo5
[mole frac]
Pseudo6
[mole frac]
Pseudo7
4. SIMULATION VALIDATION
The oil density at stock-tank condition (ρoil@std, kg/m3), the gas density at stock-tank condition, the (ρgas@std, kg/m3),
the oil flow rate at separator condition (Sep_qo, m3/d) and the separator oil formation volume factor (Sep_Oil FVF) were
used as simulation validation parameters. The oil and gas densities were daily sampled and measured in the laboratory
during the multi-rate well test. The oil flow rate at separator condition was available in as a tag from PI (Plant
Information), the field data acquisition system. The oil formation volume factor root mean square error (Bo RMSe % )
was calculated comparing Vazquez and Beggs oil formation volume factor and the compositional simulation results.
Vazquez and Beggs is the field operation chosen Bo correlation. Equation 1 was used to calculate the RMSe % (root
mean square error in percentage) between measured and calculated variables.
1
1
RMSe % = 
N

 X i − X exp i 


X
i =1 
exp i

N
∑ 
2
2
 * 100


(1)
In Eq. 1, N is the number of samples, Xi is the calculated variable for the i condition and Xexpi is the measured
variable for the i condition. Table 6 gives the root mean square error for the simulation validation parameters. The
results confirmed satisfactory agreement between calculated and measured data. Figure 8 shows Well 1 stock-tank oil
density calculated by the SRK EOS and the lab oil measured density. At first, it was assumed no lean gas breakthrough
in the production wells. In Urucu field, lean gas from NGL process plant is re-injected into the gas cap for reservoir
pressure support. The results confirmed this assumption as there is no injection gas contribution in the wellbore mixture
8
IV Journeys in Multiphase Flows (JEM 2015)
composition. If the wellbore composition had directly lean injected gas contribution, the fluid recombination from the
reservoir oil, the gas cap and the injected gas to match the produced GOR would result in a stock-tank oil density lower
than actual measured values. The lower oil density would be expected because less condensate from the gas cap would
be produced. Figure 9 presents calculated and measured separator oil flow rate with resulted in the RMSe = 3.52% for
Well 3. The results from Fig. 8 and Fig. 9 and Tab. 6 demonstrated the satisfactory performance of three fundamental
elements: The tuned SRK EOS, the mixing rule and the process modeling assumptions.
Data post-processing analysis was necessary before RMSe calculation. Between the real process stabilization and
simulated stabilization periods it was found a lag (time mismatch). In the real process, there is a long distance between
the choke valve and the separator site. So, there is a delay between the choke opening action and the separator flow rate
output stabilization. This transient state is negligible in the simulation time step. Figure 10 shows the delay between
calculated and real process response captured by the absolute relative error. So, the data used to calculate RMSe listed in
Tab. 6 was filtered in intervals immediately after each choke opening step change.
Table 6. Fluid properties and oil flow rate to validate the multi-restriction model simulation.
Well 1
Well 2
Well 3
ρoil@std
ρgas@std
Sep_Oil flow rate
Sep_Oil FVF*
RMSe %
RMSe %
RMSe %
RMSe %
0.28
1.03
2.35
1.27
1.05
0.91
6.58
1.95
3.52
5.52
5.05
2.76
* Oil FVF RMSe % calculated with Vazquez and Beggs correlation.
Figure 8. Well 1 calculated versus measured oil density at stock-tank conditions. Refer to Tab. 6 for RMSe% (root mean
square error in percentage).
Campos S.R.V.
Compositional Reservoir to Stock-tank Conditions: Simulation and Experimental Data Validation
Figure 9. Well 1 calculated versus measured oil flow rate for first stage separation conditions. (Refer to Tab. 6)
Figure 10. Decoupling between measured and calculated separator oil flow rate response caused by the distance
between wellhead and separator sites.
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IV Journeys in Multiphase Flows (JEM 2015)
5. CONCLUSIONS
The following steps were addressed to design and validate a compositional simulation from reservoir to stock-tank
implemented in the Hysys process simulator: The correct EOS implementation in the software fluid package, the design
of a recombination approach to establish the reservoir oil and gas compositions since the initial reservoir conditions,
multiple flash implementation for reservoir depletion and surface separation processes condition, iterative logic to
match the measured GOR and water cut in the wellbore condition, a multi-rate experimental procedure with rigorous
commissioning phase to construct representative production database, post-processing quality analysis to verify
systematic and random data errors.
The conclusions from simulation design and execution were:
- The small error in the calculated oil density at stock tank conditions supported the assumption of no injected gas
influence in the wellbore stream composition.
- The oil zone depleted oil phase mole fraction sensitivity analysis showed that recombination ratio studied in the
depletion condition between gas and oil streams foo and fog did not affect the wellbore composition.
- There is a time delay between the real process stabilization and the simulated stabilization periods because of long
distance between the choke valve and the separator site.
The compositional simulation designed in this paper was an enabler step to performed multiphase flow studies
through singularities in wellhead conditions for a scenario of stream composition variation.
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7. RESPONSIBILITY NOTICE
The author is the only responsible for the printed material included in this paper.