Simplified graphical correlation for determining flow rate in tight gas wells in the Sulige gas field
Received October
Simplified graphical correlation for determining flow rate in tight gas wells in the Sulige gas field
Xiao Wei 1
Wu Xiaodong 1
Liu Xiaojuan 0
0 Xi'an Shiyou University , Xi'an, Shaanxi 710065 , China
1 Laboratory of Petroleum Engineering, Ministry of Education, China University of Petroleum , Beijing 102249 , China
The Sulige tight gas reservoir is characterized by low-pressure, low-permeability and lowabundance. During production, gas flow rate and reservoir pressure decrease sharply; and in the shutin period, reservoir pressure builds up slowly. Many conventional methods, such as the indicative curve method, systematic analysis method and numerical simulation, are not applicable to determining an appropriate gas flow rate. Static data and dynamic performance show permeability capacity, kh is the most sensitive factor influencing well productivity, so criteria based on kh were proposed to classify vertical wells. All gas wells were classified into 4 groups. A multi-objective fuzzy optimization method, in which dimensionless gas flow rate, period of stable production, and recovery at the end of the stable production period were selected as optimizing objectives, was established to determine the reasonable range of gas flow rate. In this method, membership functions of above-mentioned optimizing factors and their weights were given. Moreover, to simplify calculation and facilitate field use, a simplified graphical illustration (or correlation) was given for the four classes of wells. Case study illustrates the applicability of the proposed method and graphical correlation, and an increase in cumulative gas production up to 37% is achieved and the well can produce at a constant flow rate for a long time.
Low-permeability reservoir; sand thickness; fuzzy optimization method; gas flow rate
1 Introduction
The Sulige gas field, located in the western part of the
Yishaan slope, Ordos Basin, China, is a giant gas fields. The
Sulige reservoir is comprised of Upper Palaeozoic clastic
sandstone (H8S2) in the Shanxi Formation. The development
block has a total area of 20,000 km2. The gas reservoir is
predominantly developed in the H8S2 sandstone formation,
with a thickness of 15-35 m and at a depth of approximately
2,800 m. And it is embedded between shale and coal layers,
with an average permeability of 0.1-4.0 mD.
Up to August 31, 2007, 65 wells have been put into
production, and 2.8×106 L of methanol, glycol, and diethylene
glycol have been injected into the formation, and a total of
3.684×108 m3 of gas have been recovered. The average water/
gas ratio was 0.466 m3/104m3, and oil/gas ratio was 0.056 m /
3
104m3. The maximum individual-well gas flow rate was 3.744
×104 m3/d, while the average gas flow rate was 1.1×104 m3/d.
The Sulige gas reservoir is characterized by low-pressure,
low-permeability and low-abundance. The complicated
geological conditions present a number of challenges in
successful development of this reservoir.
1) The reservoir in H8S2 in the Sulige gas field is a
typical braided river sedimentary system and effective sands
overlap irregularly. Moreover, sand continuity and pay sand
connectivity are poor
(Wang et al, 2002a)
.
2) Production tests show that gas flow rate was low (below
1.4×104 m3/d in average) and the reservoir pressure drops
sharply, even at a decline rate of 0.2 MPa/d. In the shut-in
period, reservoir pressure builds up slowly. This demonstrates
that gas supply is insufficient
(Li et al, 2006b)
.
3) Laboratory experiments show that the sands are
stresssensitive
(Zhang et al, 2007)
.
4) After a period of production, intermittent production
had to be adopted in some wells due to low reservoir pressure.
For such a low-permeability reservoir, a suitable well
scheduling is of great importance to obtain a relatively high
ultimate gas recovery.
2 Determination of appropriate flow rate for
tight gas wells
2.1 Conventional methods
Because fluid flow in the extremely low-permeability
Sulige gas reservoir is complicated, indicative curve method,
systematic analysis method and numerical simulation are
invalid in determining the initial gas flow rate
(Wang et al,
2002b; Wu et al, 2007; Zhu et al, 2007)
.
1) Indicative curve method
Indicative curve was applied to one typical well drilled
in the Sulige reservoir, and the so-called allocated initial
gas flow rate determined by this method was 20×104 m3/d.
However, field practice shows that the appropriate gas flow
rate should be 1.5×104 m3/d. This indicates that this method
was not suitable for determining the initial flow rate of gas
well in the Sulige reservoir.
2) Systematic analysis method
The initial gas flow rate of a well, obtained by using the
systematic analysis method, were 21×104 and 17×104 m3/d at
wellhead pressures of 4 and 10 MPa, respectively (as shown
in Fig. 1). The method was not suitable for this reservoir. In
Fig. 1, green curves are outflow curves of gas at wellhead
pressures of 4 and 12 MPa, respectively.
3) Numerical simulation
IPR curve
pwh=12 MPa
pwh=4 MPa
30
25
a
PM 20
,fw
pe 15
r
ssu 10
e
rP 5
0
0
5
10 15 20
Gas flow rate Qsc,104m3/d
25
30
Fig. 1 Result of systematic analysis method used in a typical well in the
Sulige gas field
(pwf is bottom hole flowing pressure and pwh is well head pressure; IPR is the
abbreviation of inflow performance relationship)
Numerical simulation could not be used to predict
initial gas flow rate because understanding of fluid flow
in extremely-low permeability gas reservoirs is seriously
lacking, and a large number of parameters and history
matching data required are usually not available. Thus it is
difficult to apply numerical simulation to such a new
lowpermeability reservoir.
2.2 Multi-objective fuzzy optimization method
Field data, as shown in Table 1, indicate that even at
the same gas flow rate, pressure decline rates in different
wells varied from 0.008 to 0.16 MPa/d in the first 5 months.
Downhole chokes were set almost in every well drilled in the
Sulige gas field to prevent gas hydrate formation, which can
block tubes. So tubing pressure cannot reflect the real change
of reservoir pressure, and casing pressure was recorded and
used to analyze the variation of reservoir pressure
(Ding et al,
2006; Tang et al, 2006;Wu et al, 2007)
.
Production-rate history indicates that the wells producing
at the same volumetric rate had very distinct casing pressure
decline rates. Also, similar gas wells producing at different
volumetric rates performed diversely. Intermittent pumping
had to be introduced when casing pressure dropped below a
given value. Consequently, it is very important for the wells
to be correctly classified and to produce at an appropriate
flow rate
(Li et al, 2006a; Song and Zheng, 2006)
.
2.2.1 Formation characteristics
Laboratory experiments on rock samples from the Sulige
reservoir show that with the decline in pore pressure and
increase in actual stress, effective permeability dropped
sharply at the early stage; when the effective stress increased
to approximately 15 MPa, effective permeability leveled off,
as shown in Fig. 2.
The Sulige reservoir is stress-sensitive, if the existing
effective stress increases due to production and then reaches
D
m
,
k
y
iilt
b
a
e
m
r
e
P
14
12
10
8
6
4
2
0
ki 1.05
/
iiltyk 1.00
ab 0.95
e
rem 0.90
p
ss 0.85
e
l
ion 0.80
s
ne 0.75
m
i
D 0.70
0
10
20
30
40
Effective stress, MPa
Fig. 3 Relationship between relative permeability and effective stress
0
20
40
60
80
Effective stress, MPa
the critical effective stress, plastic deformation of reservoir
rock will occur upon further increase in effective stress,
as shown in Fig. 3. In actual field practice, the pressure
difference between reservoir pressure and bottom hole
flowing pressure may be 10-20 MPa, which could cause a
20-85% permeability loss
(Palacio and Blasingame, 1993)
.
As a result, a low-permeability zone would form in the
immediate vicinity of bottom hole, thereby seriously affecting
reservoir productivity. In this case, it is important for the
Sulige reservoir to maintain producing pressure drop at a low
level (generally below 15 MPa).
The first forward pressure release
The first reverse pressuring
The second forward pressure release
The second reverse pressuring
2.2.2 Well classification
The influences of most sensitive factors, including
reservoir permeability k, reservoir thickness h, porosity ,
saturation Sg, absolute open flow (AOF), on flow potential
were studied. Of them, k value reflects the flow capacity of
gas in reservoir and h value shows the gas capacity.
Permeability capacity k is the product of effective
thickness multiplied by permeability. The deliverability
e q u a t i o n ( E q . ( 1 ) ) f o r S u l i g e g a s w e l l s s h o w s t h a t
permeability capacity, kh is one of key factors influencing
gas well productivity. Well test interpretation also indicates a
high positive correlation between gas well productivity and
permeability capacity.
(1)
where k is reservoir permeability, mD; h is effective
thickness of the gas-bearing formation, m; pe is reservoir
pressure, MPa; pwf is bottom hole flowing pressure, MPa; T
is reservoir temperature, K; is gas viscosity, mPa·s; is gas
compressibillity factor; re is drainage radius, m; rw is wellbore
radius, m; is apparent skin factor, dimensionless.
Statistical analyses of formation data, testing parameters
and dynamic behavior indicate that an apparent relationship
exists between well performance and kh. Thus the tight gas
wells could be classified into four groups: Class I, II, III and
IV. Classification criteria are as follows.
Class I: kh≥6.336
Class II: 5.49≤kh<6.336
Class III: 3.418≤kh<5.49
Class IV: kh<3.418
kh can be expressed as:
where ki is the permeability of layer i, mD; hi is the thickness
of layer i, m.
2.2.3 Determination of reasonable gas flow rate
Field production analysis shows that semi-empirical
curves and graphical correlation are useful and practical
without going into details of the complex fluid mechanics in
low-permeable porous medium
(Agarwal et al, 1998; Litvak
et al, 1997)
.
A multi-objective fuzzy optimization method was selected
to determine the gas flow rate of tight gas wells drilled in
the Sulige gas field. And dimensionless gas flow rate, period
of stable production in months, and recovery at the end of
the stable period were selected as optimizing objectives
(Gringarten et al, 1974)
. A comprehensive factor was used as
a criterion in determining optimum gas flow rate.
Dimensionless gas flow rate is defined as:
where Qsc is gas flow rate, m3/d; and AOF is absolute open
flow potential, m3/d.
Recovery at the end of the stable production period, , is
defined as:
where Gp is the cumulative gas production at the end of the
stable production period, m3; and Gg is recoverable reserves,
3
m .
The comprehensive factor, fta is calculated with following
equation:
where μ is the membership function; and is the weight.
Membership function of gas production rate, is:
Membership function of the period of stable production,
is:
Membership function of recovery at the end of the stable
production period, is:
(8)
The weights of gas flow rate, period of stable production,
(3)
(4)
(5)
(6)
(7)
and recovery at the end of the stable production period are set
as R =0.3, T =0.3, and V =0.4.
The detailed optimization procedure is described as
follows:
1) Calculate the value of kh, and determine the class of the
well;
2) Set an initial value of casing pressure, pc;
3) Set an initial gas flow rate, Qsc;
4) Calculate the bottom hole flowing pressure and
reservoir pressure at the initial gas flow rate;
5) Calculate dimensionless gas production rate ( V), period of
stable production in months ( t ), and recovery at the end of the
stable production period ( R );
6) Calculate comprehensive factor, fta;
7) If the comprehensive factor is maximum, the initial
set gas flow rate is appropriate; otherwise, go to Step 3) until
obtain the maximum comprehensive factor;
8) Reset an initial value of casing pressure, and repeat step
3) to step 7)
9) A set of data (Qsc, pc) are obtained for a gas well of
permeability capacity of kh.
2.2.4 Simplified graphical correlation
Several sets of data (Qsc, pc) corresponding four classes
of gas wells were plotted on the same graph, where abscissa
is gas flow rate, ordinate is casing pressure, as shown in Fig.
4. When a vertical well has been drilled, the permeability
capacity kh should be first calculated by using reservoir
parameters available, according to the corresponding curve
shown in Fig. 4, the allocated range of gas flow rate is
obtained.
a40
P
M
,e30
r
u
s
s
re20
p
g
n
isa10
C
0
0
0.5
1.0 1.5 2.0
Gas flow rate, 104m3/d
2.5
3.0
3 Application
At present, theoretical method is not suitable to determine
the appropriate gas flow rate for tight wells drilled in the
Sulige gas field. This paper gives a semi-empirical method
based on production data analyses.
However, because the number of production wells is
limited, the accuracy of gas flow rate determined by the
multi-objective fuzzy optimization method is not so high.
With more wells being put into production and more data
becoming available, the reliability of the method proposed in
this paper will become higher.
30
3.00
2.50
2.00
1.50
1.00
0.50
Take Well Su 14-15-36 as an example. It is a production
well located in Block 14, Sulige gas field. The sand is 13 m
thick in this well and reservoir permeability is 0.275 mD. The
gas flow rate was originally allocated as 1.55×104 m3/d. As a
result, casing pressure decline rate was as high as 0.109 MPa/
d. After 130 days of production, casing pressure decreased to
11 MPa. Gas flow rate of the well reduced to 0.8-0.9×104 m3/d
and tended to fall-off further, as shown in Fig. 5. Cumulative
gas production from the well was 196×104 m .
3
The initial casing pressure of Well Su 14-15-36 is 26.5
MPa and the well was classified as Class III according
to the product of sand thickness multiplied by reservoir
permeability. The optimized gas flow rate is 1.35×104 m3/d
from Fig. 4. After 130 days of production, casing pressure
would be 16.5 MPa and casing pressure decline rate would
be only 0.077 MPa/d. In this case, the well could produce
at a constant flow rate of 1.06×104 m3/d. Cumulative gas
production of the well could be 270×104 m3, 37.8% more
than the actual cumulative production recorded, as shown in
Fig. 5.
Casing pressure
Gas flow rate
Optimized casing pressure
Optimzed gas flow rate
Time, d
4 Conclusions
1) Conventional methods are not suitable for determining
reasonable gas flow rate of wells drilled in the Sulige tight
gas field.
2) Tight gas wells were classified into four classes
according to the product of sand thickness multiplied by
reservoir permeability, and gas flow rate could be determined
based on the multi-objective fuzzy optimization method.
3) A simplified graphical correlation based on the
multiobjectives fuzzy optimization method was developed and was
successfully applied to determining optimum flow rate of gas
wells in the Sulige gas field.
Acknowledgements
This work was financially supported by National Natural
Science Foundation of China (NO. Z02047) and CNPC
Program (NO. Z03014). The authors would like to thank them
for their approval to publish this paper.
Agarwal R G , Gardner D C , Kleinsteiber S W, et al. Analyzing well production data using combined-type-curve and decline-curve analysis concepts . SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana , 27 - 30 September 1998 (SPE paper 49222)
Ding H , Li X H and Wang Z . The downhole throttle technology test study of Sulige Oilfield . Petrochemical Application . 2006 . (3): 13 - 17 (in Chinese)
Gringarten A C , Ramey H J and Raghavan R . Unsteady-state pressure distributions created by a well with a single infinite-conductivity vertical fracture . Society of Petroleum Engineers Journal . 1974 . 14 ( 4 ): 347 - 360
Li M T , Yao S L and Shan W W. Laboratory research into stress sensitivity of low-permeability gas reservoirs . Petroleum Geology & Oilfield Development in Daqing. 2006a . 25 ( 6 ): 69 - 72 (in Chinese)
Li R Y , Li Z F , He S L , et al. Sensitivity analysis on parameters affecting gas well productivity . Petroleum Geology & Oilfield Development in Daqing. 2006b . 25 ( 2 ): 34 - 36 (in Chinese)
Litvak M L , Clark A J , Fairchild J W, et al. Integration of Prudhoe Bay surface pipeline network and full field reservoir models . SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, 5 -8 October 1997 (SPE paper 38885)
Palacio J C and Blasingame T A . Decline-curve analysis with type curves: Analysis of gas well production data . SPE Rocky Mountain Regional/Low Permeability Reservoirs Symposium held in Denver, Colorado, 12 - 14 April 1993 (SPE paper 25909)
Song C Z and Zheng R C. Stress sensitivity of low-permeability tight gas reservoir and its effect on single well productivity . Petroleum Geology & Oilfield Development in Daqing . 2006 . 25 ( 6 ): 47 - 49 (in Chinese)
Tang J W , Jia A L , He D B , et al. Development technologies for the Sulige gas field with low permeability and strong heterogeneity . Petroleum Exploration and Development . 2006 . 33 ( 1 ): 107 - 110 (in Chinese)
Wang D X , Wang C L , Han X G , et al. Setting-up permeability model for the layered low-permeability reservoir in Changqing Gas Field. Natural Gas Industry . 2002a . 22 ( 6 ): 78 - 79 (in Chinese)
Wang S J , Liu J Y and Hao Y H. New equations for determination of non-resistance flow in gas wells . Xinjiang Petroleum Geology . 2002b . 23 ( 5 ): 427 - 428 (in Chinese)
Wu X D , Xiao W , Liu X J , et al. Optimizing production system in Sulige Gas Field . Natural Gas Industry . 2007 . 27 ( 12 ): 108 - 111 (in Chinese)
Zhang L , Zhang M L , Mei H Y , et al. Stress sensibility analysis of lowpermeability gas reservoir and its influence on exploitation . Special Oil and Gas Reservoirs . 2007 . 14 ( 3 ): 55 - 58 (in Chinese)
Zhu S P , Li W H and Lao Y C. Influence factors of open flow potential in condensate gas well . Special Oil and Gas Reservoirs . 2007 . 14 ( 1 ): 84 - 86 (in Chinese)