7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Study of Fluid Phase Behavior and Pressure Calculation Methods
of Condensate Gas Well
Bangtang Yin Xiangfang Li'*, Mingming Qi3, Qian Li', Zhenzhen Xu Song Cui' and Meipeng Ren'
*Corresponding author, 18 Fuxue Road Changping, Beijing 102249, China
1. China University of Petroleum (Beijing), faculty of Petroleum Engineering
2. China University of Petroleum (Beijing), faculty of Mechanical and Electronic Engineering
3. Research Institute of Petroleum Exploration & Development, Petro China,
Key words: condensate well, phase equilibrium, phase behavior, flowing pressure, difference scheme
Abstract
Up to now, researchers are still using the method used for conventional gas wells to calculate the wellbore flowing pressure of
condensate gas wells, while the calculating accuracy can not meet the demand of performance analysis and production
management without considering the temperature and phase behavior transition in borehole. From the analysis of wellbore
phase behavior transition in the production process, combining with wellbore temperature distribution change, the pressure
calculation model is established based on gasliquid equilibrium calculation and solved with the fourpoint implicit
difference scheme. At the same time, phase behavior transition law and pressure distribution in this process are studied. The
calculating result agrees well with the actual situation and it shows that this calculating method considering the temperature
distribution and the phase behavior transition can solve the problem that pressure gauge could neither be put in the middle
part of layer nor operate normally so as to save up a great deal of manpower and material resources.
Introduction
At present, the methods of wellbore pressure distribution
calculation for condensate gas wells include: (1 the
correction algorithm based on the ordinary pressure
calculation, such as CullenderSmith method (Cullender
1956); (2) the method based on energy conservation
equation while taking into account the temperature
transitions (Brill 1988) or the phase transitions (Vo 1989,
Coskuner 1999) or taking both into account (Fujie 2004,
Xichong 2002), but a few important parameters were
calculated by the conventional methods causing a big error,
such as gasliquid mixture density, compressibility factor.
Combining with the temperature calculation model which
considering the effect of wellbore liquid, the author
establishes a new model considering the wellbore phase
characteristics and solves it with the fourpoint implicit
difference scheme. It modifies the compressibility factor
and gasliquid mixture density based on gasliquid
equilibrium calculation. According to a specific example,
the phase behavior and wellbore temperature are analyzed
and the distribution regularity of wellbore pressure is
obtained.
Nomenclature
A a time function defined by Eq.4 (m)
Cpm specific heat at constant pressure of mixture fluid,
(J *(kg k) ')
C,, specific heat at constant pressure of gas (J *(kg *k )~'
C,1 specific heat at constant pressure of liquid,
(J *(kg k) ')
d inside diameter of tubing (m)
F(L) Fugacity equation of liquid
FL flOw rate of liquid (kg mol hour ')
Fv flow rate of gas (kg mol hour )
fr friction coefficient
f(t) transient heatconduction time function for earth
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Characteristics of wellbore parameters for
condensate well
The characteristic of wellbore flowing temperature
change
The wellbore flowing temperature is routinely considered
to be linear distribution in the traditional calculating
method of wellbore pressure distribution which causes a
big error (Ramey 1962, Hasan 2005, Kabir 2006) in the
predication of flowing temperature and pressure
distribution. In fact, its distribution is nonlinear. There are
several reasons. Firstly, the wellhead temperature changes
with the well production. If the production is higher, the
wellhead temperature is higher. The prime cause is that the
convective heat transfer coefficient is larger because of the
higher production. Secondly, the wellbore heat transfer
medium and its properties are unalike in different well
depth. Thirdly, the difference between the wellbore and
formation temperature distribution changes greatly. Figure
1 presents the measured wellbore flowing temperature
curve of some well in Tarim oilfield. It is obvious
nonlinear, which is divided into three parts: upper, middle
and lower part.
0 20 40 temperature(O 00 10 4
flowing temperature
1000 a static temperature
24000
Figure 1: The measured wellbore temperature curves
The characteristic ofPhase behavior
The wellbore flowing temperature and pressure changing
in the stable production will lead to the complicated
change in the wellbore and then cause a big error in the
calculation of wellbore parameters. Comparing the dew
pOint pressure and wellbore pressure, there will be three
different phase behaviors when the condensate wells are in
the stable production. Firstly, there is only one phasegas
in the wellbore while the wellhead pressure is larger than
the dew point pressure as shown in Figure 2A. Secondly,
g gravitational acceleration, (m s2)
gd geOthermal gradient ("C m')
H middepth of producing formation (m)
Hm total well depth from surface (m)
Hout variable well depth from surface(m)
Ke thermal conductivity of earth (W (m "C)')
Ki the equilibrium constant of the component i
L volume fraction of liquid
Lw energy loss because of friction ()
P wellbore pressure(MPa)
Pr reduced pressure
P(H) the wellbore pressure at well depth H (MPa)
qse flow rate of fluid (m3 d ')
rto inside radius of tubing (m)
Tebh undisturbed formation temperature at the bottomhole
("C)
Te, undisturbed formation temperature at any given
depth ("C)
Tfbh undisturbed wellbore temperature at the bottomhole
("C)
Tf wellbore fluid temperature ("C)
Tr reduced temperature
u flow velocity (ms')
Uto overall heat transfer coefficient (J (m2 s "C)')
V volume fraction of gas
VL VOlume of liquid (m3)
VG VOlume of gas (m3)
W work on the gas (J)
Wt total mass flow rate (kg d ')
x, volume fraction of the component i in liquid
y, volume fraction of the component i in gas
Z, compressibility factor of gas
Z1 compressibility factor of liquid
Greek letters
a void fraction
y relative density
Pp densityof gas (kg *m3)
p1 density of liquid (kg m3)
p m density of mixture (kg m3)
a interfacial tension (N)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
occur two phase gas liquid flow in the two region.
As shown in the Figure 4, the temperature and pressure
corresponding to different position was superposed to the
phase diagram. Among the Figure 4 and Figure 5, "
represent well bottom "@" and "@" represent well head.
In the Figure 4A, " and "@2" is outside of the
twophase region, which indicates that there is no
condensate liquid. No matter how the pressure and
temperature changes, there is only condensate gas in the
wellbore without phase transformation. With the well
production, "O" is outside of the twophase region, and
"@2" is in the twophase region as shown in the Figure 4B.
It indicates that the condensate liquid would appear in the
wellbore. The condensate liquid content increases by
gradation from the bottom to the wellhead whatever the
temperature or pressure changes in this case. As the
TCServoir pressure continued to decrease, Figure 4C
presents the whole wellbore temperature and pressure lie
in twophase region, in other words, the condensate
phenomenon occur in the whole wellbore in which is filled
with gas and liquid.
Based on Figure 4C, there are four kinds of phase
diagrams in wellbore while the wellbore temperature and
pressure change. Figure 5A and 5B show the influence of
pressure on the phase behavior. If the bottom hole pressure
(Pw,) is less than the maximum retrograde condensate
pressure, the condensate liquid content will increase
gradually from the bottom to wellhead when the wellbore
pressure changes from "9" to "@" in Figure 5A and it
increases when the pressure changes from "O" into "@"
in Figure 5A, then decreases gradually. While the part of
the wellbore temperature and pressure are lower than the
retrograde condensate pressure, the condensate liquid
content increases gradually from the bottom to wellhead
seen in Figure 5B.
Figure 5C and 5D show the influence of temperature on
the phase behavior. The changing trend is equal to it in the
Figure 5A and 5B.
as the well producing, the wellbore pressure decreases.
The wellbore phase will change when the part of the
wellbore pressure P(z) is below the dew point pressure in
the corresponding depth, presented in Figure 2B. Thirdly,
the wellhead pressure is lower than the dew point pressure.
There will be gas and liquid in the whole wellbore seen in
Figure 2C.
o I *
:i I m
I ~m melil Ii
(A) (B) (C)
Figure 2: The wellbore phase transition in stable
production
so 10o iso
ternperature("C)
Figure 3: The phase diagram
The Figure3 indicate the distribution and content of two
phase gas liquid under different temperature and pressure.
As the pressure decrease, condensate would drop out and
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
temperature(C)
temperature(G)
temperature(C )
(A) (B) (C)
Figure 4: Wellbore phase behavior
~ 15
'P,
e
e
io
Pa
Pa
5
20
15
g
pp~r
V
0 50 100 150
(A) temperature(C)
0 50 100 150
(B) temperature(C)
0 50 100 150 0 50 100 150
(c) temperature(C) (D) temperature(U)
Figure 5: The influence of temperature and pressure on wellbore phase behavior
The characteristic wellbore flowing pressure change
As the temperature or pressure increases, liquid
precipitation reduces. From the bottom to the wellhead,
content of condensate liquid don't always increase, it may
decrease sometime. The mixture density of wellbore fluid
is directly related to the condensate liquid distribution. If
the condensate compositions are invariant in the beginning,
the condensate liquid distribution is affected by the
wellbore temperature and pressure distribution. Different
temperature and pressure distribution will cause different
condensate liquid content distribution, and lead to the
further difference of wellbore flowing pressure
distribution.
Because of the complicated changes of temperature and
phase behavior in the wellbore, the calculation error is
large if the quasisingle phase flow or two phase flow
model (Beggs 1973, Qrkiszewski 1967, Aziz 1972 and
Trik 2003) is simply adopted, or the influence of phase
behavior and temperature change are not considered
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
used in the new calculation model of wellbore flowing
pressure, considering the wellbore temperature influence.
(1) The twophase compressibility factor Z
Fugacity equation and PR equation of state fitted for the
condensate well system are transformed as follows:
carefully (Fujie 2004, Xichong 2002) while calculating the
wellbore flowing pressure.
The calculation of wellbore flowing pressure
distribution for condensate wells
Wellbore flowing temperature calculation method
The wellbore flowing temperature models (Ramey 1962,
Hasan 2005) used in the pressure calculation method
currently are given little thought to the effect of
condensate liquid. In fact, even a little liquid will affect
the wellbore heat transfer.
Calculation method of borehole temperature distribution
for gas wells with high gasliquid ratio established by
Xiumin Xue (Xiumin 2006), investigated the sensitivity of
wellhead temperature. The influence of gas production,
liquid production and different liquids on the wellhead
temperature were analyzed. This method is fit for the
condensate well, so the author uses it to calculate the
wellbore flowing temperature.
T, = Te+exp[ A(H Ho,)](Tfbh Tebh
gd / A) + gd / A
A = (2
WC, m(ke + f (t)rroUto)
The specific heat at constant pressure is the key affecting
the calculation of temperature. The formula to calculate
the specific heat at constant pressure is as follows:
p~m pg pl' ,pXL~' i
F (L) = Zi 1
i= L+Ki ( L)
Setting L or V as unknown parameter, the initial value is
assigned to calculate V and L alternately, and then the
twophase compressibility factor Z will be calculated with
the Eq9.
Z = ZpV + ZL
(2) The condensate gasliquid mixture density
In the production process, condensate wellbore pressure
drawdown is affected by condensate liquid density. When
the condensate liquid is precipitation and gathered in the
wellbore, the density of liquid component will increase.
The mixture density can be expressed as:
C M .ptZ~ +y~rl
VL +VyG
FL + FG
P, =
'" L +VyG
) The calculation of flowing pressure with phase transition
in the wellbore
Gas flows from the bottom to the wellhead in the axial
direction, supposed to be steady flow. Taking a length of
dH of the pipe as a unit, the basic equations are as follows:
(1) Continuity equation of mixture
+ =0
dt 8H
x =ap,
a, =1 exp[0.25 I 1001 ~sP
(4)
(2) Momentum equation of mixture
ap='= ) atPV' dp dp
+ + ++P
dt dH dH dH
Calculating method of wellbore phase behavior
It is necessary to study on the gasliquid equilibrium
calculation to recognize the discipline of the phase
behavior in the wellbore. The phase equilibrium is one of
the important technologies and well applied to the
chemistry field. So the method mentioned by Walas
(Walas 1985) and PR equation of state (Peng 1976) are
(3) Gas density calculation
7, P
pg = 3484.4
ZT
(11)
(4) Gas compressibility factor Z
The LXFR model for calculating the gas compressibility
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
_ /
/
factor Z is well fitting the StandingKatz Z factor chart,
shown in Appendix in detail. Part of it is as follows:
If 1.254 Tr 43 and 04 Pr 45,
Z =p6 x,(." + x,(~ l. +xr4 43 5 ~2 +6P 7J~ (12)
Where
x, = 0.00 1647325 3T4 0.0146 114 184T 3
+0.0475274656 T,2 0.067075771T, + 0.034618145
x, = 0.0229859555T,4 +0.204085706T/
0.6644150747 T,2 + 0.9382578115 T, 0.4844210799
x3 =0.1111394368T, 0.9865137646T,3
+3.20900952T,2 4.5239800498T, + 2.3295990023
x, = 0.2094485279T,4 +1.8488625222T,3
5.9679016788 Tr + 8.3218347189T, 4.2215704727
x, = 0.1355945748T,4 1.1671265013T,3
+3.6422385658T, 4.8492897172T, + 2.3132729772
x6 = 0.1096347504T,4 + 0.9901808887T,
3.3141595446T, + 4.9245811950 T, 2.802706215
x, = 0.0253159834T,' 0.2116591283T,3
+0.6391671392T,2 0.8206104172 T, +1.3753755471
According to Eq.1Eq.12, the analytic solutions are
difficult to be derived, so the fourpoint implicit difference
scheme(Nickens 1987) will be used. The discrete equation
is derived according to Figure 6 as follows:
J 2 AH AH
(16)
T~ = G' +c: G'2 [(.,: 'K+ ,
(17)
The gasliquid equilibrium calculation method is used to
Obtain the distribution of wellbore condensate gas
component, liquid content, gas density and liquid density
in different well depth. Then, the twophase
compressibility factor can be deduced. At last, the
wellbore flowing pressure distribution is calculated. The
block diagram in Figure7 shows the calculating details.
Dividing the wellbore depth into n equal
parts and giving the time unit nt
Initialization
Time step: i=i+1
Depth step: j=j+1
*I known point
O unknown point
4 ti+l
Figure 6: Difference grid of fourpoint implicit
difference scheme
P' P' = T, +T, +T, +TD
( +1 1 1
Figure 7: The block diagram
(A) Light components transition (B) Heavy components transition
Figure 8: Components transition
Table 1: The components of condensate gas in the wellbore
component CO? N2 C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7+
% 0.64 3.79 71.83 10.37 3.62 0.8 1.11 0.47 0.45 0.71 6.21
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Calculating component of condensate gas with changing
the wellhead temperature by the new method, the results
of distribution of the light and heavy component are
shown in Figure 8. As seen in the figure, the liquid
precipitation and the light components molar percentage in
the gas phase decrease, such as C1, C2, but the heavy
components increase with pressure decreasing, such as
C7+. In the same depth, the light components molar
percentage decrease but the heavy components molar
percentage increase with temperature increasing.
Example
(1) Basic parameters
middepth of producing formation: 3000 m:
production casing: 7 inch:
production tubing: 2 7/8 inch:
geothermal gradient: 2.6 "C m :
thermal conductivity of earth: 2.06 W (m "C)' :
thermal diffusivity: 1.03x106 2 S.
Tablel shows the component of condensate gas in the
wellbore.
(2) Wellbore gasliquid equilibrium calculation
(1The effect of temperature or pressure on component
distribution
94. 5 ~~~wellheadtepaue()
91~ ~ 2 '
0 500 100 150 2 00 200 00 00
~ depth 6
2.5 r wellhead ternperature(C)
0 500 1000 1500 2000 2500 3000 3500
depth /m
(2) Condensate gas or liquid density influenced by
temperature or pressure
Figure 9 presents the result of density calculation with
different wellhead temperature. It can be seen that the
condensate gas density increases but liquid decreases as
pressure increasing. At the same time, the gas density is
related to temperature. It decreases when temperature
increases. The influence of temperature on gas density
weakens gradually with depth increasing.
II II
Figure 9 Density distribution
Table Condensate component of different wells
component liquid component
CO2 N2 Cl C2 C3 iC4 nC4 iC5 nC5 C6 C7+
well (cm3/m3)
YH301 0.63 3.28 78.67 8.77 2.2 0.46 0.68 0.25 0.26 0.4 4.4 558.77
YH2 0.67 6.07 73.82 8.82 2.59 0.59 0.91 0.31 0.3 0.44 5.48 603.06
YH3 1.09 3.76 70.38 9.49 2.68 0.55 0.6 0.36 0.55 0.74 9.84 665.11
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
wellhead ternperature('C)
. 20
* 40
weledternperature(C)
S20
* 40
620
560
550
540
5$0
" 0
0 500 1000 1500 2000
depth /m
2500 3000 3500
0 500 1000 1500 2000 2500 3000 3500
depth /1
(A) Gas density
(B) Liquid density
(2)The result of the new method considering temperature
distribution and borehole phase behavior transition shows
in Figure 10. The calculation error is less than 1%, so this
new method can meet the requirements of the condensate
well dynamic analysis.
et al, the result calculated by this method shows in Figure
11. It can be seen that the distribution of borehole pressure
is quite different when the condensate content is different,
which means there are different components in the
wellbore. Therefore, the influence of the phase behavior
muSt be taken into consideration while establishing the
wellbore pressure calculating model.
pressure (MPa)
2s so as
4o as
pressure(MPa)
30
500
1000
r 2ooo
35 40
*5301
al 2
*"i
E
1500
S2000
2500
3000
3500
4000
B
Figure 10: Result of pressure calculation
(3)The influence of condensate liquid on wellbore
pressure
There are three different condensate components of three
wells in table 2. Suppose the basic parameters of those
wells are same, such as well depth is 4000m, wellhead
pressure is 20MPa, and daily gas production is 150000 m3,
Figure 11: Wellbore pressure distributions
Conclusions
(1)Based on the characteristics of wellbore pressure and
temperature combined with phase diagram, it provides the
distribution of gas and liquid in wellbore under different
pressure and temperature.
(2)From the analysis of wellbore phase behavior transition
in the production process, combining with wellbore
temperature distribution change, the pressure calculation
model is established based on gasliquid equilibrium
calculation and solved with the fourpoint implicit
difference scheme.
(3)The calculation error is less than 1%, and it shows that
the calculating result agrees well with the actual situation.
This method can solve the problem that pressure gauge
could neither be put in the middle part of layer nor operate
normally so as to save up a great deal of manpower and
material resources.
Acknowledgements
This paper was sponsored by The National Natural
Science Foundation Project (50974182) and the Project
(PLNO614) from National Key Laboratory of Oil and Gas
reservoir Geology and Development Engineering in
Southwest Petroleum University. We recognize the
support of China University of Petroleum (Beijing) for the
permission to publish this paper.
Reference
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Flow Equation for Wells and Pipelines With Large
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Brill, J.P. and Beggs, H.D. TwoPhase Flow in Pipes,
selfpublished, Tulsa, OK, 387(1988).
Vo, D.T and Jones, J.R. Performance predictions for
gascondensate reservoirs. SFESE, 576584(1989).
Coskuner, G. Performance prediction in gas condensate
reservoirs. JCPT, 38(8), 1999.
Gorodensky, E. and Panfilov, M. NearCritical Model of
Thermodynamic Behavior for GasCondensate Mixture,
SPE60177(2000).
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Fujie Sun, Xiaoping Zhang, Linsong Cheng, et al. Exact
and simple method for calculating pressure distribution in
deep gas condensate well with high temperature and
pressure. Journal of the University of Petroleum, China,
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Xichong Yu, Yongquan Hu, et al. Computational Analysis
of Borehole Pressure Drop and Temperature Drop for Gas
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25, 3739(2002).
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427434(1962)
Hasan, A.R. and Kabir, C.S. Analytic Wellbore
Temperature Model for Transient Gaswell Testing.
SPEREE 8(3),240247.
Peng, D.Y. and Robinson, D.R. Two and ThreePhase
Calculations for Systems Containing Water. Ind Eng
Chem Fundam, 15, 5964(1976).
Beggs, H.D., and Brill, J.P. A New TwoConstant
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vertical pipes. JPT, 829838(1967).
Aziz, K., Govier, G.W., Fogarasi. M. Pressure drop in
wells producing oil and gas. JPT, 3848(1972).
Trik, M.D., Comparison of Correlations for Predicting
Wellbore Pressure Losses in GasCondensate and
GasWater Wells. PETROLEUM SOCIETY, Vol. 19,
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SI Metric Conversion Factors
= g *cm
= m
m
"standard" m3 d '
103 pm
=MPa
= Pa s
" API
bb1
ft
scf D '
millidarcy
lbf in2 (psi)
cp
141.5 (131.5+"
X 1.589873
X 3.048
X 2.863640
X 9.869233
X 6.894757
X 1.0
API)
E01
E01=
E02 =
E01=
E03
Appendix
LXFR model for calculating the gas compressibility
factor Z
The LXFR model is a new model for calculating the gas
compressibility factor Z and modified basing the LXF
model(Xiangfang 2001). The results of the model fit the
StandingKatz Z factor chart well. The model is written
as:
(1) If 1.254 Tr 43 and 04 Pr 45,
Z = xCp~ + x~ +xpl +xCqr +xPI +xCS, t+x (1)
Where
x, = 0.00 1647325 3T, 0.0146 114 184T,3
+0.0475274656 T,2 0.067075771T, + 0.034618145
x = 0.0229859555T,4 +0.204085706T,
0.6644150747 T,2 + 0.9382578115 T, 0.4844210799
x, = 0.1111394368T,' 0.9865137646T3
+3.20900952T2 4.5239800498T, + 2.3295990023
x, = 0.1355945748T," 1.1671265013T,3
+3.6422385658T2 4.8492897172T + 2.3132729772
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
x, = 0.1096347504T,4 +0.9901808887T,3
3.3141595446T,2 + 4.9245811950 T, 2.802706215
x, = 0.0253159834T,' 0.2116591283T3
+0.6391671392T2 0.8206104172 T, +1.3753755471
(2) If 1.054 Tr 41.25 and 04 Pr 41.4,
Z~x,P 2+x2P + x (2)
Where
x, = 344. 093 979223 79T, 1 536.2745 1048 601T,3
+2557.3 8540613 578 T, 1879.42667748251T,
+513.82138916368
x = 445.88088119790T4 + 2016.41973092931T3
3409.01495384261T 2 + 2553.46463833851 T
715.16521324379
x3 = 27.63594024318T4 124.58057992837T3
+209.88911172567T2 156.58827909801T,
+44.63445263641
(3) If 1.054 Tr 41.25 and 1.44 Pr 45,
Z= xb t4.~ + x,P(. +~, x3(.Z + 4.+ .+x,P, + x
(3)
Where
x, = 2.4022772054T,3 8. 1790277964 T,2
+9.2403 18093 5T, 3.463 65 0673 2
x, = 54.2376736812T,3 +185.0744207839 T,2
209. 5883311823 T, + 78.7612902470
x,=492. 5654 18607 8T,3 1684.45 967 83 944T,
+1912.0090609194T, 720.2672768417
x, = 22953.453 3413 64T,3 + 7867.610413 8199 T,
8952.01671498 18 T, + 33 80.7466699922
x, = 5766.4144424767T,3 19816.3647131134 T,
+226087.117390521T, 8561.9898714384
6, = 7371.517654565 1T3 + 2541 1.3 595 824411 T2
29086.9630663022T, +11052.4342062749
x, = 3721.71920763 16T3 12880.4663 827836T2
+14806.6858848422T, 5651.2636018419
