INTRODUCTION TO PRESSURE
TRANSIENT ANALYSIS
2/26/2010
WTST 320B
1
What is Pressure-Transient
Analysis
• The analysis of pressure changes over time,
especially those associated with small
variations in the volume of fluid. It involves
allowing a limited amount of fluid to flow from
the formation while monitoring the pressure
over time.
• The well is then shut-in and the pressure
monitored while the fluid in the reservoir
stabilizes.
• Analysis of these pressure changes provides
information on the size and shape of the
formation as well as its producibility.
Origin of Log-Log Type Curves
• The log-log analysis is a global approach as
opposed to straight-line methods that use only
one fraction of the data, corresponding to a
specific flow regime.
• Stallman (1952) published log-log type curves for
both the no-flow and the constant pressure linear
boundaries. His curves are applicable for the
analysis of single well tests and also for
interference tests. These curves may be used to
find the distance of the linear boundary and its
orientation.
• Davis and Larkin (19631, Standing (1964), Witherspoon, et
al. (1967) and Kruseman and De Ridder (1970) extended
the log-log method for a single linear boundary. They
introduced the semilog method for determining the distance
to a linear boundary.
• Loucks and Guerrero (1961) and Bixel and van Poolen
(1967) presented type curves for a well centered in a two
region radial flow system. Ramey (1970) presented
approximate solutions for unsteady liquid flow for a well
centered in a radially concentric composite system.
• The present work concentrates on internal circular
boundaries, yet, the same mathematical methods apply
also to linear boundary configurations.
LOG-LOG SCALE
• For a given period of the test, the change in pressure
is plotted on log-log scales versus the elapsed time. A
test period is defined as a period of constant flowing
conditions (constant flow rate for a drawdown and
shut-in period for a build-up test).
• By comparing the log-log data plot to a set of
theoretical curves, the model that best describes the
pressure response is defined. Theoretical curves are
expressed in dimensionless terms because the
pressure responses become independent of the
physical parameters magnitude (such as flow rate,
fluid or rock properties).
• On log-log scales, the shape of the
response curve is characteristic.
• The shape of the global log-log data plot is
used for the diagnosis of the interpretation
model(s).
• The dimensionless pressure pD and time tD
are linear functions of Ap and At, the
coefficients A and B being dependent upon
different parameters such as the
permeability k.
– log pD =log A + log Ap
– log tD =log B + log At
Equations
• Dimensionless Pressure
• Dimensionless Time
• Dimensionless wellbore storage
coefficient
• Gringarten et al. (1979) dimensionless
time group
Equations
• Pure Wellbore
• Infinite-Acting Radial Flow
Reference Curves
Wellbore Storage
Liquid Re-injection
Types of Flow
Channelling
Infinite Acting Radial Flow
Flow Regimes
For many engineering purposes, the actual flow geometry may be
represented by one of the following flow geometries:
• Radial flow
• Bilinear flow
• Linear flow
• Spherical and hemispherical flow
2/26/2010
WTST 320B
15
• Radial flow
P vs log t gives a straight line i.e. semilog
straight line
2/26/2010
WTST 320B
16
• Linear flow
Linear flow occurs in some
reservoirs with long, highly
conductive vertical
fractures.
Straight line given with
p vs √t with slope of 1/2
log–log graph of Δp vs t
yields a straight line with ½
slope
2/26/2010
WTST 320B
17
• Bilinear flow
It is a new type of flow
behavior called bilinear
flow because two linear
flows occur
simultaneously.
Straight line of p vs t1/4
Can be identified from a
log–log plot of Δp versus t
which will exhibit a straight
line with a ¼ slope
2/26/2010
WTST 320B
18
• Spherical flow
Straight line of p vs 1/√t
2/26/2010
WTST 320B
19
Inflow Performance Relationship
Productivity Index, PI
This is a measure of the ability of a well to produce. It is defined by the
symbol J, and is the ratio of the total liquid flow rate to the pressure
drawdown.
PI changes in time, cumulative production, increased drawdown
2/26/2010
WTST 320B
20
• Inflow Performance Relationship (IPR)
Inflow performance represents ability of well to give up fluids
Plot production rate vs. flowing bottom hole pressure called Inflow
Performance Relationship (IPR)
•
IPR and PI not equivalent
IPR is relationship between flowing pressure and rate
PI represents the special case when Pwf is greater than the bubble
point
• Absolute Open Flow
Maximum rate of flow qmax, corresponding if the bottom hole
pressure opposite the producing face were reduced to zero psia
2/26/2010
WTST 320B
21
• Rate pressure relationships
For under-saturated oil wells
Straight-line IPR
When Pwf = PR, q=0 and no
flow enters the wellbore
qmax , AOF corresponds to
Pwf =0
Slope = 1/J (PI)
2/26/2010
WTST 320B
22
• Saturated Oil wells & Gas wells
• PI curve not normally linear for a solution gas drive field
because: Increased free gas saturation, lowering Kro
IPR curvature, indicating gas and/
or two-phase flow
J decreases with increasing
drawdown
n; 0.5-1.0
Log-log plot of q vs Δp2 is a
straight line with slope 1/n
Vogel (1968) – Saturated Oil wells
2/26/2010
WTST 320B
23
Reservoir pressure above the bubble point but wellbore flowing
pressure below the bubble point
For flowing pressures below
the bubble point :
IPR of an under-saturated oil well
producing at flowing pressure
2/26/2010
WTST 320B
below the bubble point
24
Evolution of PTA
methodologies
1950’s
Specialized plots
(MDH Semi-log
& Horner plots)
1970’s
Log-log type curves
PC-based PTA software
1985 & onwards
1983
Bourdet Derivative
Specialized plots
•
•
•
•
•
•
•
These plots were focused on using a specific flow
regime (IARF), to determine well productivity and
the main reservoir properties:
Effective permeability (keff)
Skin factor (S)
Conductivity (kh)
Pressure drop due to skin (Δps)
Drainage area/OOIP
Time for well bore storage effects to cease, or
IARF to start.
Wellbore storage coefficient.
Specialized plots
MDH Pressure Drawdown
4400
4300
4200
4100
4000
Pwf (psia)
3900
3800
3700
3600
3500
3400
3300
3200
3100
3000
0.01
0.1
1
10
Flowing Time (hrs)
100
1000
Specialized plots
MDH Pressure Buildup
(pi-pwf) (psia)
1000
1100
½
cycles
10
0.01
0.1
1
10
Flowing Time (hrs)
100
1000
Specialized plots
Oil Well Horner Plot
4550
4500
Pws (psia)
4450
4400
4350
4300
4250
4200
1.0
10.0
100.0
(tp + delt)/delt
1000.0
10000.0
Log-log type curves
• Developed to compliment straight line techniques.
• A log-log plot of the pressure response vs. time on
tracing paper is placed over a set of predefined
curves.
 Results obtained from the specialized plots is used
to help position data on the type curves.
• The choice and relative position of the data on the
type curve, called the match point, were used to
calculate physical results.
• This method was of poor resolution until Bourdet
derivative was introduced.
Type Curve matching
technique
Drawdown Type Curves
Manual Drawdown Type Curve
Matching
Bourdet Derivative

Was introduced to address the many
shortcomings of the type curve matching
technique, and was at the origin of what is
called modern PTA methodology.

It is defined as the slope of the
superposition semi-log plot displayed on
the log-log plot.

Considered the single most important
breakthrough in the history of PTA.
Bourdet Derivative
Bourdet derivative: semi-log and log-log
PC-based PTA software
Category I
•
•
•
•
•
Relies heavily on graphics.
User inputs well test data into the
computer after which the
computer graphically displays the
data, derivative of the data, and
derivative type curve on the
screen.
The user can then move the WT
data on the screen until a match
is achieved bet. the data and the
type curve.
The user then enters the match;
as well as required reservoir and
production characteristics.
The program will then calculate
and output k, S & C.
Category II
•
•
•
•
•
•
Relies on numerical techniques to
achieve a fit.
The type curve is num. rep. in the
program.
The user enters the WT data, and
reservoir and production
parameters.
The WT data is then smoothed
using num methods and the
derivative curve calculated.
The program compares the type
curve to the WT data and its
derivative.
When a match is achieved, the
program outputs the reservoir
parameters.
Bourdet Derivative and well/wellbore
effects
• Pure wellbore storage effects are only observed at early
time when the well pressure behaviour is dominated by
well fluid decompression.
• For pure wellbore storage: p  Ct
• The derivative is:
•
dCt
p'  t
 Ct  p
dt
This implies that at early time, when wellbore storage
is present, pressure and the Bourdet derivative curves
will merge on a unit slope line on the log-log plot.
Bourdet Derivative and IARF
• When IARF occurs: ∆p=m’sup(∆t),
where m’ is the slope of the semilog str. line.
• Derivative is:
dp
p' 
 m'
d sup( t )
• This implies that the derivative will have zero slope.
Bourdet Derivative & PSS
• After long stabilized production, PSS is reached, and the
pressure response is: ∆p=A∆t+B.
• The superposition time can again be approximated by
sup(∆t)≈ln(∆t).

• The derivative is:
d ( At  B)
p'  t
 At
dt
• At very large time, Δp = AΔt + B ≈ AΔt.
• So, when PSS is reached, the pressure response on the
log-log plot will tend to a unit slope, while the derivative
will reach the unit slope much earlier.
• In a BU the pressure stabilizes and the derivative plunges
towards zero.
References
• http://www.glossary.oilfield.slb.com/Displ
ay.cfm?Term=pressuretransient%20analysis
• http://earthsci.stanford.edu/ERE/research
/geoth/publications/techreports/SGP-TR065.pdf
• Bourdet D. - Handbook of Petroleum
Exploration and Production 3, Well Test
Analysis, The Use Of Advanced
Interpretation Models
2/26/2010
WTST 320B
38