Characterization of Gas Condensate Reservoirs Using Pressure Transient and Production Data —
Santa Barbara Field, Monagas, Venezuela
Trina Mercedes Medina-Tarrazzi
B.S., Universidad Central de Venezuela (1994)
M.S., Texas A&M University (2002)
Chair of Advisory Committee: Dr. Thomas A. Blasingame
Objectives
The overall objectives of this work are:
 To build a framework for establishing a coherent reservoir model using pressure buildup test data in the
gas condensate zone of Santa Barbara Field (Monagas state, Venezuela).
 To perform the analysis, interpretation and integration of the available petrophysical, fluid, production
and well test data from Block A, Santa Barbara Field (Monagas state, Venezuela).
Present Status
Santa Barbara Field is located in the north of Monagas state in the Eastern Venezuela Basin. Santa Barbara is
one of the most important fields in Venezuela, producing an average of 240 MSTB/D. The reservoirs in Santa
Barbara Field present substantial structural and fluid complexity, which present broad challenges for assessment
and optimization of well performance. In addition, the initial reservoir pressure and temperature are relatively
high (11,877 psia, and 300 °F respectively) at a reference depth of 15,800 ft.
The fluid column is around 3,000 ft thick, with a significant temperature and compositional gradient. The
reservoir fluid was initially undersaturated, developing a transition zone of low interfacial tension between the
gas condensate and volatile oil region1. The hydrocarbon column varies from gas condensate at the top, above a
volatile oil in a transition zone, and further below to light oil at the bottom of the Naricual and Cretaceous zone.
Rock Type
Megaporous
Macroporous
Mesoporous
Microporous
Petrophysical
Flow Units
(Layers)
Nanoporou
s
C1
C2
C3
C4
C5
Fig. 1 — Schematic of Santa Barbara Field (Venezuela) — Multilayer reservoir model (after
Porras2).
2
Based on the study of pore and pore throat geometry data from Santa Barbara Field we can conclude that this is a
heterogeneous flow field, often dominated by local features — possibly by bed boundaries. The integration of a
previous sedimentological study with the petrophysical analysis for the Santa Barbara Field provided the definition of the reservoir flow units — showing that the primary reservoir sequences at Santa Barbara Field occur in
several distinct reservoir layers.2 Twelve separate reservoir layers were defined (10 for Tertiary and 2 for Cretaceous formations) based on the integration of sedimentological and petrophysical studies. Fig. 1 shows the
schematic multilayer reservoir system for Santa Barbara Field.
The multilayer model for Santa Barbara Field suggests that sufficient seals exist between reservoir layers such
that the system can be represented as a commingled reservoir system — implying that individual reservoir layers
communicate only through the wellbore (i.e., the "layered/no crossflow" reservoir configuration).
The traditional mathematical model for a multilayer reservoir is formulated in radial coordinates in order to
represent the pressure drop distribution for vertical well in a commingled multilayer reservoir (without
crossflow). This solution was presented by Lefkovits et al (1961),3 and is given by:


 r 

n
q 
2t
1
 2 h   ln  e   3 
Δp wf (t ) 


j
j
   r  4 
n
2π  n
2
j 1 
  w

  jh j
  h j  j re ct
j 1
 j 1


  Y (t ) ...................................... (1)



and
q j (t )  q
 jh j
n
  jh j
j 1
 Z j (t ) ......................................................................................................................... (2)
where
exp  x 2 t 

 k 
Y (t )   q 
............................................................. (3)
4 k 1 n
1  J 2 ( j x k )
1

2
j 1  2

r

J
(

x
)
ln

x

Y
(

x
)

1 j k
2 j k  1 j k 





and
J1 ( j x k )
2


J1 ( j x k ) ln   j x k   Y1 ( j x k )
n
π
2

Z j (t )   B j
n
1  J12 ( j x k )
k 1


exp  x k2 t 


j  1  2 J ( x ) ln    x   Y (  x )
 1 j k
2 j k  1 j
k 


π

....................................................... (4)
2
Well test analysis in Santa Barbara Field is used to provide estimates of the large-scale flow properties (e.g.
permeability, skin factor, non-darcy flow coefficient) as well as to assess the radial extent of condensate banking
around the wellbore. The reservoir pressure in Santa Barbara Field has declined below the dew point (pdew =
9025 psig); which means that results obtained from well test analysis has substantial value in reservoir monitoring.
For the analysis of well test data, we used the single-phase gas pseudopressure approach as this method does not
require knowledge of relative permeability data and it is more practical in an application sense. The use of the
single-phase pseudopressure approach is justified by the hypothesis that most of the reservoir remains at pressures above the dew point pressure (which is a reasonable assumption).
3
The combined approach of using the single-phase pseudopressure coupled with a homogeneous reservoir model
for the analysis of well performance in gas condensate reservoirs has been well-documented.4-6 This particular
approach should give an accurate estimate of the permeability-thickness product (kh) — however, the estimated
skin factor is much higher than the actual skin factor (near-wellbore skin).7
Single-phase pseudopressure-pseudotime analyses typically yield pressure derivative functions that resemble the
radial composite reservoir model.8 This usually suggests the existence of two mobility-zones, one (inner zone) in
the vicinity of the wellbore with reduced gas effective permeability due to condensate liquid accumulation —
and the other (outer zone) away from the well, with only single-phase gas flow, where the reservoir pressure
remains above the dew point (Fig. 2).
Outer Zone
Wellbore
Inner Zone
a
1,  1, ct1, k1
2,  2, ct2, k2
Fig. 2 — Schematic for a radial composite reservoir.
The application of the two-zone radial composite model for the analysis of well test data from a gas condensate
reservoir was presented by Raghavan et al.4 In our work, the application of the two-zone radial composite
reservoir model is subject to the observation of the inner zone (i.e., the condensate bank) in the well test data.
Solutions for the pressure distributions in the inner and outer zones for a radial composite reservoir were presented by Ramey (1970).9 The dimensionless pressure distribution in the inner zone is given by:
p D1 (rD , t D )  


a2 
a 2  
1
 E i ( )  E i   D   C1 E i   D 1  
2
rD2 
rD2  2  



(Dimensionless Form) ....................... (5)
and the dimensionless pressure distribution in the outer zone is:
  
1
p D 2 (rD , t D )   C1 E i   1 
2
 2 
(Dimensionless Form) ....................... (6)
where the following groups of variables are used in these models:
1 
 k1
................................................................................................................................................ (7)
( c t  )1
2 
 k2
............................................................................................................................................... (8)
( c t  ) 2

rD2
(Boltzman t ransformat ion ) ........................................................................................................... (9)
4t D


a 2 1  1 
C1  1 exp   D
 ...................................................................................................................... (10)
2

rD2  2 
4
Selection of the Pilot Area
Five compartments (reservoirs) have been identified in Santa Barbara Field. 1 The compartments identified as
"Zone 1" and "Zone 2" contain 85 percent of the hydrocarbon reserves, 80 percent of the field production and
101 wells — 89 producers, 9 injectors and 3 abandoned wells. Most of the well tests performed in the gas
condensate zone at Santa Barbara Field are performed in Zone 1. Our selection of the pilot area was based on the
quantity and quality of available well test data in the gas condensate zone, as well as the quantity and quality of
production performance data for each well.
These criteria are satisfied by a small area located in the southeast portion of Zone 1. For the purposes of this
study, we will refer to this area as Block A. The location of Block A is presented in Fig. 3.
Santa Barbara Field
KA
BLOC
Fig. 3 — Location of Block A, Santa Barbara Field (Venezuela).
Block A has 19 wells — 19 producers, 14 dual wells and 5 single wells. The data available for this area are
summarized as follows:
 Production: 19 wells (including dual completions for a total of 33 strings).
 Petrophysical Description: 16 wells
 PVT: 1 well — producing from the condensate zone
 Well Test: 5 Buildups, 1 DST — in the condensate zone (Fig. 4)
1068000
Santa Barbara Field
Block A
1066000
TM-32
1064000
TM-1E
TM-70
TM-86
TM-75
TM-93
WELLTEST DATA AVAILABLE
1062000
414000
416000
418000
420000
422000
424000
426000
428000
430000
432000
meters
Fig. 4 — Well Test data distribution, Block A, Santa Barbara Field (Venezuela).
5
Definition of the Reservoir Model for Well Test Analysis
As we mentioned in previous sections, sedimentological and petrophysical studies describe the reservoirs at
Santa Barbara Field as distinctly layered reservoirs. Based on this description, we will use the model for a
layered reservoir without crossflow as the mechanism to analyze the well test data. The number of layers used
for the well test interpretation are directly related to the distribution of the producing intervals in each well, if the
producing intervals are located in one flow unit, only one layer is input into the reservoir model.
Use of the model for a layered reservoir (no crossflow) should account for anisotropy due to vertical layering —
that is, distributions of rock properties (e.g., , k, h). The pressure behavior due to condensate banking near the
well is modeled using a two-zone radial composite reservoir model
Fig. 5 presents the schematic model of the reservoir used for well test interpretation and analysis in Block A,
Santa Barbara Field.
Fig. 5 — Schematic of the reservoir model used in well test analysis, Block A, Santa Barbara
Field (Venezuela).
6
For the analysis of well test performance in gas condensate reservoir the combined approach of using the model
for a layered reservoir (no crossflow) coupled with the model for a two-zone radial composite reservoir should
provide us with the estimates of the following:
 Effective permeability to gas in both the condensate bank (inner zone) and in the dry gas reservoir
(outer zone) for each layer,
 Mechanical skin factor (inner zone) and total skin behavior (outer zone), and
 Radial extent of condensate banking for each layer.
Analysis and Interpretation of Well Test Data from Block A, Santa Barbara Field.
We present our analysis and interpretation of the 6 well test cases taken from Block A, Santa Barbara Field,
Venezuela. Our intention is to identify certain types of characteristic behavior in the well test data — in
particular:
 Condensate banking — two-zone radial composite model),
 Anisotropy in the reservoir rock properties — layered reservoir without crossflow,
 Effect of non-Darcy flow, and
 Boundary effects.
The following well test cases were analyzed:
 Well TM-1EC [Test Date: 11-04-1998],
 Well TM-1EC [Test Date: 07-26-2001],
 Well TM-32L [Test Date: 01-07-1995],
 Well TM-75 [Test Date: 03-01-1999],
 Well TM-86 [Test Date: 11-22-1998], and
 Well TM-93 [Test Date: 09-01-2001].
Analysis and interpretation of each well test case is structured as follows:
 General well information,
 Porosity and permeability distribution plots,
 Production history plot,
 Well performance plot,
 Test summary plot,
 Semilog plot,
 Cartesian DST analysis plot (only for DST tests), and
 Summary of results.
Test Summary Plot:7 We use a log-log plot of the pseudopressure drop m(p) and pseudopressure derivative m(p)'
versus the effective shut-in pseudotime function (tae). The substance of this plot is the visualization of the
pressure derivative function (curve shape) and the identification of flow regimes encountered during the test.
Semilog Plot: we use the semilog analysis in order to provide the conventional analysis for a particular data set
as well as for the identification of well condensate banking, inner and outer zone permeabilities.
We present the analysis and interpretation Well TM-1EC [Test Date: 07-26-2001] as an illustration of the kind of
work performed during the development of this research. Data and some analysis for the other cases will be
presented in the Appendix.
7
Well Analysis: Well TM-1EC [Test Date: 07-26-2001]
Figs. 6 to 14 correspond to the analyses for this well. Well TM-1EC is the discovery well for Santa Barbara
Field, it was completed in February 1989 and had an initial reservoir pressure of 11,877 psia at the time of
completion. The general data for this case are summarized in Table 1.
Table 1 — Summary of general data for Well TM-1EC [Test Date: 07-26-2001].
Reservoir Properties
 , fraction
Production Parameters
0.1224
q g , MSCF/D
9555
Gas Properties
p , psia
9222
5347
z
h t , ft
163
p wf (at t =0), psia
h p , ft
127
t p , hrs
Temperature , F
300
r w , ft
S wi , fraction
0.11
-6
c t , x10 psi
-1
69840
0.25
1.5279
 g , cp
0.07273
B g , RB/MSCF
0.6311
g
0.692
4.494
Depth , ft
15339
The petrophysical data (i.e., the porosity and permeability) were reviewed to establish major flow units (i.e., the
number of layers). The porosity and permeability data were also analyzed in a statistical sense to establish
median and average values. The petrophysical analysis is presented in Figs. 6 to 10.
Porosity
Permeability
15700
15700
C4
15750
15800
C4
15750
15850
15800
C5
Depth, ft
C6
15900
15950
15850
15900
C6
15900
15950
15950
C7
16000
C7
16000
16050
16050
16100
0.00
16100
1E-02
16000
LAYER 2
Depth, ft
15850
C5
LAYER 1
15800
16050
0.05
0.10
0.15
 , fraction
0.20
0.25
0.30
1E-01
1E+00
1E+01
1E+02
1E+03
1E+04
0 2 PERFORAT
468 1 1 1
0 0 0 0 0 IONS
2 4
0 00 00 0 0
Perm eabilit y, k, md
Fig. 6 — Proposed distribution of reservoir layers, Well TM-1EC (Santa Barbara Field).
For Well TM-1EC two distinct layers were identified using the petrophysical analysis — which includes the
porosity and permeability distribution plots for each layer, as well as the statistical parameters for these
properties.
8
15800
15800
Legend: Well TM-1EC / Permeability Distribution
Legend: Well TM-1EC / Porosity Distribution
LAYER 1
LAYER 1
15850
15900
15900
Depth, ft
Depth, ft
15850
15950
15950
16000
16000
16050
-3
10
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
16050
0.00
0.05
0.10
Permeability, k, md
0.15
0.20
0.25
0.30
Porosity, fraction
Fig. 7 — Permeability and porosity distribution for Layer 1, Well TM-1EC. (Layer 1 data only
shown on figures).
25
25
Legend: Well TM-1EC / Permeability Histogram
LAYER 1
Legend: Well TM-1EC / Porosity Histogram
LAYER 1
20
Frequency, dimensionless
Frequency, dimensionless
20
kavg= 298.86 md
15
10
5
15
avg= 0.1053
10
5
0
-5 -4 -3 -2 -1 0
1
2
3
ln(k)
4
5
6
7
8
9 10
0
0.00
0.05
0.10
0.15
0.20
0.25
Porosity, fraction
Fig. 8 — Permeability and porosity histograms for Layer 1, Well TM-1EC.
0.30
0.35
9
15990
15990
16000
16010
16010
16020
16020
16030
16030
16040
16040
16050
16050
16060
16060
16070
16070
16080
16080
16090
-3
10
10
-2
10
-1
10
0
10
1
10
2
10
LAYER 2
16000
Depth, ft
Depth, ft
Legend: Well TM-1EC / Porosity Distribution
Legend: Well TM-1EC / Permeability Distribution
LAYER 2
3
10
4
16090
0.00
0.05
0.10
Permeability, k, md
0.15
0.20
0.25
Porosity, fraction
Fig. 9 — Permeability and porosity distribution for Layer 2, Well TM-1EC. (Layer 2 data only
shown on figure).
10
10
Legend: Well TM-1EC / Porosity Histogram
Legend: Well TM-1EC / Permeability Histogram
LAYER 2
LAYER 2
8
Frequency, dimensionless
Frequency, dimensionless
8
6
kavg= 330.3 md
4
2
avg= 0.1602
6
4
2
0
-4
-2
0
2
ln(k)
4
6
8
10
0
0.05
0.10
0.15
0.20
0.25
Porosity, fraction
Fig. 10 — Permeability and porosity histograms for Layer 2, Well TM-1EC.
The production performance for Well TM-1EC is presented in Figs. 11 and 12, where we can note the decline of
the wellhead pressure and a relatively stable gas rate production over about a six year period.
10
6000
14000
5000
12000
10000
4000
8000
3000
6000
2000
4000
Oil Rate
1000
Gas Rate, MSCF/D
Oil Rate, STB/D
Well TM-1EC
Production History
2000
Gas Rate
0
0
0
500
1000
1500
2000
2500
3000
3500
Production Time, days
Fig. 11 — Dry gas and condensate rate history, Well TM-1EC, Santa Barbara Field.
Well TM-1EC
Well Performance
25000
8000
7000
6000
5000
15000
4000
10000
3000
Pressure, psia
Gas Rate, MSCF/D
20000
2000
5000
Gas Rate
1000
Flowing Wellhead Pressure
0
0
0
500
1000
1500
2000
2500
3000
3500
Production Time, days
Fig. 12 — Total gas rate and flowing wellhead pressure performance, Well TM-1EC, Santa
Barbara Field.
Test Summary Plot: Fig. 13 shows clearly the two permeability regions (condensate banking) as the
pseudopressure derivative exhibits 2 distinct flat stabilizations. An apparent fault signature is evident in the
derivative shape however; the estimated distance to the fault does not agree with the current structural model of
the reservoir — we presume that this "fault" feature is an artifact.
11
10
Well TM-1EC [Test Date: 07-26-2001]
10
Results:
Results:
Wellbore Storage
C = 0.00593 STB/psi
Non-Darcy Flow
LAYER 1
-5
-1
ds/dq = 5.0x10 (MSCF/D)
LAYER 2
-6
-1
ds/dq = 5.05x10 (MSCF/D)
Model: 2-Layers without crossflow
Radial Composite
LAYER 1
LAYER 2
Pseudopressure Functions , psi /cp
ri = 32 ft
2
10
ri = 70 ft
M = 0.515
D = 1.1
kinner = 2.29 md
M = 0.84
D = 3.0
kinner = 0.588 md
kouter = 0.70 md
9
kouter = 4.45 md
s = 3.1
s' = 11.7
s = 2.4
s' = 2.88
10
8
Possible No-Flow Boundary
at 176 ft
Data:
Bg = 0.6311 RB/MSCF
gi = 0.1175 cp
cti = 4.5x10-6 psi
10
-1
rw = 0.25 ft
7
ht = 164 ft
hLAYER 1 = 138 ft
hLAYER 2 = 26 ft
LAYER 1 = 0.1053
LAYER 2 = 0.1602
qg = 9555 MSCF/D
10
6
10
-3
10
-2
10
-1
10
0
10
1
10
2
Effective Shut-in Pseudotime, hrs
Fig. 13 — Log-log plot of shut-in pseudopressure functions versus effective shut-in pseudotime, Well TM-1EC.
Well TM-1EC [Test Date: 07-26-2001]
7
1.7
9
7
m(p) = 1.841x10 - 3.892x10 log((ta+ta)/ta)
1.6
Data:
Bg = 0.6311 RB/MSCF
gi = 0.1175 cp
9
cti = 4.5x10-6 psi
rw = 0.25 ft
1.5
7
m(p) = 2.023x10 - 7.681x10 log((ta+ta)/ta)
-1
9
LAYER 1
m(p) = 1.758x10 - 1.950x10 log((ta+ta)/ta)
9
2
Shut-in Pseudopressure, m(p) x10 , psi /cp
9
LAYER 2
1.8
7
m(p) = 2.110x10 - 9.613x10 log((ta+ta)/ta)
ht = 164 ft
hLAYER 1 = 138 ft
hLAYER 2 = 26 ft
LAYER 1 = 0.1053
LAYER 2 = 0.1602
1.4
qg = 9555 MSCF/D
ppwf(t=0) = 5347 psia
tp= 69840 hrs
Semilog Results:
LAYER 1
LAYER 2
ri = 25.5 ft
M = 0.80
kinner = 0.897 md
1.3
kouter = 1.12 md
kouter = 4.42 md
s = 6.58
s = 0.17
1.2
3
10
10
4
10
ri = 55.2 ft
M = 0.501
kinner = 2.22 md
5
10
6
10
7
10
8
Horner Pseudotime, (ta+tpa)/ta , hrs
Fig. 14 — Horner (semilog) plot of shut-in time pseudopressure function versus pseudotime,
Well TM-1EC.
12
Semilog Analysis: Fig. 14 shows the two-layer radial composite behavior, verifying the presence of condensate
banking with a semilog straight line for the condensate bank as well as for the dry gas portion of the reservoir for
each layer.
Table 2 — Summary of analysis for Well TM-1EC [Test Date: 07-26-2001].
Semilog
Parameter
Log-log
Layer 1
Layer 2
Layer 1
Layer 2
Inner zone permeability, k inner , md
0.89
2.22
0.59
2.29
Outer zone permeability, k outer , md
1.22
4.42
0.70
4.45
Mobiity radius, M
0.80
0.50
0.84
0.52
Near well skin factor, s
0.17
6.58
2.40
3.10
---
---
2.88
11.7
---
---
5.00E-05
5.05E-06
25.5
55.2
32
70
Total skin factor. s'
Non-darcy flow coefficient, (MSCF/D)
Inner zone radius, r i , ft
-1
Special Cartesian Analysis for Drillstem Test (DST) Interpretation:
A DST is normally run in a zone of undetermined potential in a new well. Analysis of a transient pressure data
taken from a DST can provide estimates of formation properties and wellbore damage. DST pressure buildup
data are analyzed much like any other pressure buildup data. In a DST, the flow period is about the same
duration as the shut-in period, so pressure buildup data from DST's should be analyzed using a Horner plot.
In liquid-producing wells, the flowrate during a drillstem test decreases with time since the backpressure exerted
on the formation face increase as the produced fluid moves up the drillstring. Correa and Ramey (1987)10
presented a method to analyze pressure buildup data taken from drillstem tests for oil wells. This approach
solves the problems due to the variable production rate and decreasing flowing pressure observed in a DST.
Interpretation of DST pressure buildup data has been based on the Horner method. The basic assumption of the
Horner method is that the well is produced at a constant rate prior to shut-in. When the flowrate changes with
time, an awkward application of the superposition principle is required to analyze the pressure buildup data 10.
The solution of the diffusivity equation for a constant production rate yields a declining flowing pressure with
time, but must DST’s show an increasing flowing pressure during production periods. Therefore, the application
of Horner method may lead to inconsistent results in the interpretation of DST pressure buildup data such as
possible existence of linear barriers near the wellbore (common showed in a normal Horner plot for DST buildup
data).10
The DST problem can be viewed as a "slug test" with a changing wellbore storage coefficient for times less than
tp, wellbore storage mechanism is governed by a changing liquid level and after shut-in wellbore storage
becomes compressibility dominated. A practical method of analysis for DST pressure buildup data was
developed based on the long-time approximation for the "slug test" solution10.

p i  p w (t )  C F ( p ff  p fi )  C s ( p i  p ff )
 4πkh 1t
(Darcy Units) ....................................................... (11)
where
CF 
πr 2
w
.................................................................................................................................................. (12)
and
C s  C wVw ................................................................................................................................................. (13)
The average flowrate during the flow period is given by:
q
C F ( p ff  p fi )
.................................................................................................................................... (14)
tp
13
Pressure drop can be written as:
p ws (t )  p i  m
tp
t p  t
, first shut  in period .......................................................................................... (15)
where slope m is defined as
m
q  Cs ( pi  p ff ) 
1 
 ...................................................................................................................... (16)
4π kh 
qt p

pws(t) equation suggests that a Cartesian plot of pws versus tp/(tp+t) for a pressure buildup data gives a straight
line with slope inversely proportional to the reciprocal permeability.
For a second shut-in period the above equations are given by:
pws  pi  m2 Rc(t2 ) ................................................................................................................................. (17)
where
t p2
t p1
q
 1
................................................................................................. (18)
t p2  t 2 q 2 t c1  t p2  t 2
Rc (t 2 ) 
To apply this method to a gas well the problem has to be transformed in terms of pseudopressure and pseudotime
variables. For this purpose we used the Agarwal11 definition of pseudotime.
t
ta 
 c
1
dt .............................................................................................................................................. (19)
t
0
Also the production time has to be transformed to allow the analysis of buildup test data using drawdown type
curves. Lee and Holditch presented a transformation for the pseudoproducing time 11 that should be adequate.
t pa 
tp
 i cti
................................................................................................................................................. (20)
The use of average properties instead of initial fluid properties may lead to erroneous conclusions for the Horner
analysis, showing a sealing or partial sealing boundary in the vicinity of the wellbore due to the doubling slope at
the end of the curve.
For the real gas pseudopressure we used the transformation presented by Ramey et al (1966). This transformation is a correction for the assumption of the slightly compressible fluid taken when deriving the
differential equation governing the pressure transient responses.
p
m( p )  2
  z dp ........................................................................................................................................ (21)
p
p0
Finally, for a gas well, the equations to analyze the pressure transient behavior for a drillstem test are given by:
p ws t1   p i  m1
t pa1
t pa1  t a1
, first shut  in ......................................................................................... (22)
and
p ws (t 2 )  pi  m2 Rc(t 2 ), second shut  in ........................................................................................ (23)
where
Rct 2  
t pa2
t pa1
q
 1
.......................................................................................... (24)
t pa2  t a2 q 2 t ac1  t ap2  t a2
14
The analysis of the DST Well TM-32L under the scheme described above is presented to provide an application
of the special Cartesian approach to analyze DST buildup data (method of Correa and Ramey).
Well Analysis: Well TM-32L [Test Date: 01-17-1995]
Figs. 15 to 18 correspond to the analyses of this case. Well TM-32L was completed in February 1995 and had an
initial reservoir pressure of 11,322 psia at the time of completion. The general data for this case are summarized
in Table 3.
Table 3 — Summary of general data for Well TM-32L [Test Date: 01-17-1995].
Reservoir Properties
0.0771
h t , ft
268
 , fraction
h p , ft
118
Temperature , F
S wi , fraction
-6
c t , x10 psi
Depth , ft
-1
300.4
Production Parameters
Shut-in #1
q g , MSCF/D
p wf (at t =0), psia
t p , hrs
17357
z
1.5338
10540
 g , cp
0.1175
B g , RB/MSCF
0.6104
8.98
g
0.15
Shut-in #2
4.50
q g , MSCF/D
11798
p wf (at t =0), psia
10490
15604
Gas Properties
p , psia
9256
t p , hrs
9.53
Shut-in #3
q g , MSCF/D
5348
p wf (at t =0), psia
10780
t p , hrs
14.09
r w , ft
0.25
0.692
Fig. 15 — Permeability and porosity distribution, Well TM-32L (Santa Barbara Field).
The petrophysical data (i.e., the porosity and permeability) were reviewed to establish major flow units (i.e., the
number of layers). The petrophysical analysis shows that the perforated intervals for Well TM-32L are
producing from only one flow unit — as such, this well was analyzed using only a single layer (Fig 15).
The production performance of Well TM-32L is presented in Figs. 16 and 17, where we can note a relatively
stable gas production over about a five year period followed by a production rate increase.
15
3000
30000
2500
25000
2000
20000
1500
15000
1000
10000
Oil Rate
500
Gas Rate, MSCF/D
Oil Rate, STB/D
WELL TM-32L
Production History
5000
Gas Rate
FRACTURED
0
0
0
500
1000
1500
2000
2500
3000
Production Time, days
Fig. 16 — Dry gas and condensate rate history, Well TM-32L, Santa Barbara Field.
35000
8000
30000
7000
6000
25000
5000
20000
4000
15000
3000
10000
Pressure, psia
Gas Rate, MSCF/D
WELL TM-32L
Well Performance
2000
Gas Rate
5000
1000
Flowing Wellhead Pressure
0
0
0
500
1000
1500
2000
2500
Production Time, days
Fig. 17 —Total gas rate and flowing wellhead pressure performance, Well TM-32L, Santa
Barbara Field.
Cartesian Plot: Fig. 18 shows the 3 shut-in periods plotted using the method proposed by Correa and Ramey 10
and adjusted for the gas case. The permeability results show good agreement for the 3 periods analyzed — and,
in addition the Fig. 18 shows a distinct straight line trend for the radial flow stabilization — thereby avoiding the
erroneous interpretation for a linear no-flow boundary suggested by the Horner semilog (Fig. 19)
16
Well TM-32L [Test Date: 01-17-1995]
1.86
9
7
m(p) = 1.8301x10 -1.441x10 Rc(ta)
1.84
9
Shut-in #1
Shut-in #2
Shut-in #3
7
1.82
2
Pseudopressure, m (p) x10 , psi /cp
m(p) = 1.8380x10 -3.027x10 Rc(ta)
1.80
9
Data:
Bg = 0.6104 RB/MSCF
1.78
gi = 0.1175 cp
cti = 4.5x10-6 psi
-1
rw = 0.25 ft
1.76
ht = 268 ft
 = 0.0771
qg1 = 17357 MSCF/D
qg2 = 11798 MSCF/D
qg3 = 5348 MSCF/D
pwf1(t=0) = 10540 psia
pwf2(t=0) = 10490 psia
pwf3(t=0) = 10780 psia
tp1 = 8.98 hrs
tp2 = 9.53 hrs
tp3 = 14.09 hrs
1.74
1.72
1.70
9
Cartesian Results:
Shut-in #1
pi = 11273 psia, k = 1.73 md, s = -4.1
Shut-in #2
pi = 11305 psia, k = 1.78 md, s = -5.8
Shut-in #3
pi = 11254 psia, k = 1.72 md, s = -5.0
1.68
1.66
0.0
0.2
7
m(p) = 1.8330x10 -4.806x10 Rc(ta)
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Rc(ta), dimensionless
Fig. 18 — Cartesian plot for a DST data analysis, Well TM-32L.
Well TM-32L [Test Date:01-17-1995]
1.82
Fault signature
9
2
Shut-in Pseudopressure, m(p) x10 , psi /cp
1.83
1.81
1.80
Data:
Bg = 0.6104 RB/MSCF
1.79
gi = 0.1175 cp
cti = 4.5x10-6 psi
-1
rw = 0.25 ft
1.78
ht = 268 ft
 = 0.0771
qg3 = 5348 MSCF/D
pwf3(t=0) = 10780 psia
tp3 = 14.09 hrs
1.77
1.76
-1
10
10
0
Semilog Results:
Shut-in #3
k = 4.88 md, s = 1.54
Distance to the fault = 42 ft
10
1
10
2
10
3
10
4
Horner Pseudotime,(ta+tpa)/ta, hrs
Fig. 19 — Horner (semilog) plot of shut-in time pseudopressure function versus pseudotime,
Well TM-32L.
17
10
Well TM-32L [Test Date: 01-17-1995]
9
Data:
Bg = 0.6104 RB/MSCF
Results:
Shut-in #3
C = 0.0138 STB/psi
k = 4.88 md, s = 1.54
Distance to the fault = 42 ft
2
Pseudopressure Functions, psi /cp
gi = 0.1175 cp
10
10
10
cti = 4.5x10-6 psi
8
-1
rw = 0.25 ft
ht = 268 ft
 = 0.0771
qg3 = 5348 MSCF/D
pwf3(t=0) = 10780 psia
tp3 = 14.09 hrs
Possible fault
at 42 ft
7
6
5
10
0.0001
0.001
0.01
0.1
1
10
100
Effective Shut-in Pseudotime, hrs
Fig. 20 — Log-log plot of shut-in pseudopressure functions versus effective shut-in pseudotime, Well TM-32L.
Table 4 — Summary of analysis for Well TM-32L [Test Date: 01-17-1995].
DST Cartesian
Parameter
Shut-in 1
Shut-in 2
Log-log
Shut-in 3
Shut-in 1
Shut-in 2
Shut-in 3
Inner zone permeability, k inner , md
---
---
---
---
---
---
Outer zone permeability, k outer , md
1.73
1.78
1.72
5.22
5.22
5.22
Mobiity radius, M
---
---
---
---
---
---
Near well skin factor, s
---
---
---
---
---
---
-4.10
-5.80
-5.00
0.20
1.54
---
---
---
-2.62
---
---
---
---
---
---
45.0
45.2
44.0
Total skin factor, s'
Non-darcy flow coefficient, (MSCF/D)
Inner zone radius, r i , ft
-1
Expected Conclusions
1. It is possible to develop an integrated reservoir description for the Santa Barbara Field (Monagas, Venezuela) using pressure transient test data, production data, and petrophysical data. Our work provides an
overall description of reservoir properties — based on measured performance and petrophysical data.
2. This work confirms the use of the two-zone radial composite reservoir for the analysis and interpretation
of pressure transient test data.
3. Estimates of flow properties (permeability and skin factor) as well as volumetric properties (fluids-inplace and reservoir drainage area).
4. The correlation of the petrophysical data confirms the "multilayer" structure of the reservoir units in Santa
Barbara Field.
Recommendations and Future Work
1.
This work should be extended to include a "moving radial composite boundary" that would represent
the evolution of the condensate zone.
18
2.
Another possible avenue of investigation could be the incorporation of a functional model for kg (r) —
the effective permeability to gas in the reservoir. This concept shows promise in that kg (r) is generally
well-behaved.
Organization of the Research
The outline of the proposed research is as follows:
 Chapter I
 Introduction
 Research objectives
 Highlights of results
 Outline of the thesis
 Chapter II  Literature Review
 Pressure transient testing in gas wells – use of pseudopressure and pseudotime variables
 Radial composite reservoir model approach
 Layered reservoir model approach
 DST – (Correa and Ramey Cartesian approach)
 Chapter III  Data Analysis
 Petrophysical data analysis
 Well test data analysis
 Production data analysis
 Chapter IV  Analysis Integration
 Properties maps – kh, k, and 
 Crossplots
 Chapter V  Summary and Conclusions
 Summary
 Conclusions
 Recommendations for future research
 Appendices
 Appendix A- Petrophysical Data
 Appendix B- Well Test Data
 Appendix C- Production Data
 Appendix D- Fluid Data
References
1. Embid, S., Avila, M. and Salazar, P.: "From PVT Laboratory to Field: Development of a Methodology
for the Areal and Vertical Characterization of Fluids," paper SPE 69396 presented at the 2001 SPE Latin
American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 25-28 March.
2. Porras, J.C. and Campos, O.: "Rock Typing: A Key Approach for Petrophysical Characterization and
Definition of Fluid Units, Santa Barbara Field, Eastern Venezuela Basin," paper SPE 69458 presented at
the 2001 SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires,
Argentina, 25-28 March.
3. Lefkovits H.C. et al.: "A Study of the Behavior of Bounded Reservoirs Composed of Stratified Layers,"
SPEJ (March 1961) 43-58.
4. Raghavan, R., Chu, W.C. and Jones, J.R.: "Practical Considerations in the Analysis of Gas-Condensate
Well Tests," paper SPE 30576 presented at the 1995 SPE Annual Technical Conference and Exhibition,
Dallas, U.S.A., 22-25 October.
5. Fussell, D.D.: "Single-Well Performance Predictions for Gas Condensate Reservoirs," JPT (July 1973)
860-870.
6. Jones, J.R. and Raghavan, R.: "Interpretation of Pressure Buildup Responses in Gas Condensate Wells,"
paper SPE 15535 presented at the 1986 SPE Annual Technical Conference and Exhibition, New Orleans,
U.S.A., 5-8 October.
19
7. Marhaendrajana, T., Kaczoroeski, N.J. and Blasingame, T.A.: "Analysis and Interpretation of Well Test
Performance at Arun Field, Indonesia," SPE 56487 presented at the 1999 SPE Annual Technical
Conference and Exhibition, Houston, U.S.A., 3-6 October.
8. Gringarten, A.C. et al.: "Well Test Analysis in Gas Condensate Reservoirs," SPE 62920 presented at the
2000 SPE Annual Technical Conference and Exhibition, Dallas, U.S.A., 1-4 October.
9. Ramey, H.J. Jr.: "Approximate Solutions for Unsteady Liquid Flow in Composite Reservoirs," The
Journal of Canadian Petroleum Technology (January-March 1970) 32-37.
10. Correa, F. and Ramey, H.J. Jr.: "A Method for Pressure Buildup Analysis of Drillstem Tests," SPE 16802
presented at the 1987 SPE Annual Technical Conference and Exhibition, Dallas, U.S.A., 27-30
September
11. Spivey, J.P.: "An Investigation of the Use of Pseudotime in Transient Test Analysis of Gas Wells," PhD
dissertation, Texas A&M U., College Station, TX (1984).
Nomenclature
Field Variables
a
Bo
Bg
ct
C
ds/dq
h
hp
k
k
M
m
m(p)
pi
pff
pfi
pwf(t)
q
qg
re
rw
Sw
s
s’
T
t
tc
tp
z





=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=

=
=
=
inner zone radius for a two-zone radial composite reservoir model, ft
oil formation volume factor, RB/STB
gas formation volume factor, RB/MSCF
total compressibility, 1/psi
wellbore storage coefficient, RB/psia or cc/atm
non-darcy flow coefficient, D/MSCF
net thickness, ft
perforated thickness, ft
permeability, md
average permeability, md
mobility ratio, dimensionless
slope of the semilog straight line, psi/cycle
real gas pseudopressure, psi2/cp
initial pressure, psi
final flowing pressure in a DST, psi
initial flowing pressure in a DST, psi
wellbore pressure, psi
production rate from multilayer reservoirs, STB/D or cc/sec
gas rate , MSCF/D
drainage radius, ft
wellbore radius, ft
water saturation
near wellbore skin factor
total skin factor
temperature, °F
time, hrs
cycle time, hrs
production time, hrs
real gas deviation factor, dimensionless
difference
specific gravity, dimensionless
mobility, md/cp
viscosity, cp
porosity, fraction
=
3.1416...
Constants

20

=
Euler's constant, 0.577216...
Functions
Y(t)
=
Zj(t) =
Rc(t) =
transient solution in well-pressure equation for a multilayer reservoir model
transient solution in rate equation for j-th layer for a multilayer reservoir model
function of the shut-in time in a DST
Special Functions
E1(x)
=
first exponential integral
=
=
=
=
=
=
=
=
=
=
=
pseudoproperties for gas wells
average
dimensionless variables
flow in a DST
gas
initial conditions
inner zone for two-zone radial composite reservoir model
j-th layer in a multilayer reservoir model
outer zone for a two-zone radial composite reservoir model
shut-in
layer numbers
Subscripts
a
avg
D
F
g
i
inner
j
outer
s
1,2
21
Appendix
Well Analysis: Well TM-75 [Test Date: 03-01-1999]
Well TM-75 was completed in May 1998 and had an initial reservoir pressure of 10,173 psia at the time of
completion.
Table A-1 — Summary of general data for Well TM-75 [Test date: 03-01-1999].
Reservoir Properties
 , fraction
Production Parameters
0.1129
h t , ft
198
h p , ft
22
Temperature , F
S wi , fraction
-6
c t , x10 psi
Depth , ft
-1
299.17
0.11
Gas Properties
q g , MSCF/D
3718
p , psia
p wf (at t =0), psia
9063
z
0.1531
t p , hrs
8016
 g , cp
0.0729
r w , ft
0.25
B g , RB/MSCF
0.0631
g
0.6315
9238
4.49
15436
Fig. A-1 — Permeability and porosity distribution, Well TM-75 (Santa Barbara Field).
22
Well TM-75
Production History
3000
8000
Oil Rate
2500
Oil Rate, STB/D
6000
2000
1500
4000
1000
2000
Gas Rate, MSCF/D
Gas Rate
500
0
0
0
100
200
300
400
500
600
700
Production Time, days
Fig. A-2 — Dry gas and condensate rate history, Well TM-75 (Santa Barbara Field).
Well TM-75
Well Performance
10000
8000
6000
6000
4000
4000
2000
Gas Rate
2000
Pressure, psia
Gas Rate, MSCF/D
8000
Flowing Wellhead Pressure
0
0
0
100
200
300
400
500
600
700
Production Time, days
Fig. A-3 — Total gas rate and flowing wellhead pressure performance, Well TM-75 (Santa
Barbara Field).
23
Well Analysis: Well TM-86 [Test Date: 11-22-1998]
Well TM-86 was completed in September 1998 and had an initial reservoir pressure of 9,737 psia at the time of
completion.
Table A-2 — Summary of general data for Well TM-86 [Test date: 11-22-1998].
Reservoir Properties
 , fraction
h t , ft
h p , ft
S wi , fraction
c t , x10 psi
Depth , ft
-1
Gas Properties
q g , MSCF/D
8588
p , psia
120
p wf (at t =0), psia
9127
z
1.5089
111
t p , hrs
1992
 g , cp
0.0712
r w , ft
0.25
B g , RB/MSCF
0.626
g
0.692
0.1705
Temperature , F
-6
Production Parameters
292.67
0.11
9112
4.49
14515
Fig. A-4 — Permeability and porosity distribution, Well TM-86 (Santa Barbara Field).
24
Well TM-86
Production History
6000
25000
Oil Rate
Gas Rate
20000
4000
15000
3000
10000
2000
Gas Rate, MSCF/D
Oil Rate,STB/D
5000
5000
1000
0
0
0
100
200
300
400
500
600
Production Time, days
Fig. A-5 — Dry gas and condensate rate history, Well TM-86 (Santa Barbara Field).
Well TM-86
Well Performance
20000
7000
6000
5000
12000
4000
3000
8000
2000
4000
Gas Rate
Pressure, psia
Gas Rate, MSCF/D
16000
1000
Flowing Wellhead Pressure
0
0
0
100
200
300
400
500
600
Production Time, days
Fig. A-6
— Total gas rate and flowing wellhead pressure performance, Well TM-86 (Santa
Barbara Field).
25
Well Analysis: Well TM-93 [Test Date: 09-01-2001]
Well TM-93 was completed in January 1999 and had an initial reservoir pressure of 9,258 psia at the time of
completion.
Table A-3 — Summary of general data for Well TM-93 [Test date: 09-01-2001].
Reservoir Properties
 , fraction
0.1491
h t , ft
273
h p , ft
98
Temperature , F
S wi , fraction
-6
c t , x10 psi
Depth , ft
-1
300.08
0.11
4.49
15564
Production Parameters
q g , MSCF/D
p wf (at t =0), psia
t p , hrs
r w , ft
19579
7603
21936
0.25
Gas Properties
p , psia
9259
z
1.5343
 g , cp
0.0733
B g , RB/MSCF
0.6322
0.692
g
Fig. A-7 — Permeability and porosity distribution, Well TM-93 (Santa Barbara Field).
26
Well TM-93
Production History
7000
50000
Oil Rate
40000
Oil Rate, STB/D
Gas Rate
5000
30000
4000
3000
20000
2000
Gas Rate, MSCF/D
6000
10000
1000
0
0
0
200
400
600
800
1000
Production Time, days
Fig. A-8 — Dry gas and condensate rate history, Well TM-93 (Santa Barbara Field).
Well TM-93
Well Performance
50000
8000
Gas Rate
Flowing Wellhead Pressure
6000
30000
4000
20000
Pressure, psia
Gas Rate, MSCF/D
40000
2000
10000
0
0
0
200
400
600
800
1000
Production Time , days
Fig. A-9 — Total gas rate and flowing wellhead pressure performance, Well TM-93 (Santa
Barbara Field).