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WELL TESTING: INTRODUCTIONIn order to characterize the behaviour
of oil and gas reservoirs, and to predict their future performance,
it is essential to track the evolution of fluid pressures and
production rates over time. Obtaining the latter is relatively
straight forward, and fluid production tends to be metered with
reasonable accuracy.
Reservoir pressures are determined by well testing.
During a well test, a transient pressure response is created by
a temporary change in production rate. The well response is usually
monitored during a relatively short period of time compared to the
life of the reservoir, depending on the test objectives.
For well evaluation, tests are commonly conducted in less than 2
days.
In the case of reservoir limit testing, several months of
pressure data may be needed!
Note: Pressures tend to be measured downhole, while production
rates tend to be measured at surface.
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WELL TESTING: INTRODUCTION (2)
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Information obtained from well testingWell testing, often called
pressure transient analysis (PTA), is a powerful tool for reservoir
characterization. The following information can be extracted from
well tests: Permeability The value obtained from a well test is
much more useful than that from core analysis, because it
represents the in-situ, effective permeability averaged over a
large distance (tens or hundreds of metres). Skin (damage or
stimulation) Most wells are either damaged or stimulated, and this
has a direct effect on the deliverability of the well. The skin is
a measure of the completion effectiveness of a well. A positive
skin (typically +1 to +20) represents damage, while a negative skin
(typically -1 to -6) represents improvement. Average reservoir
pressure This parameter, which is either measured directly or
extrapolated from well test data, is used in material balance
calculations for determining hydrocarbons in-place. Deliverability
potential The IPR (inflow performance relationship) or the AOF
(absolute open flow) is used in forecasting a wells production.
(Well productivity index (PI), flow rate per day per unit drawdown
pressure) Reservoir description Reservoir shape, continuity, and
heterogeneity can be determined from pressure transient tests Fluid
samples The reservoir fluid composition and its PVT
(pressure-volume-temperature) properties can have a significant
effect on the economics and production operations.Well testing is
also an integral part of good reservoir management and fulfills
government regulations. (From: Mattar and Dean, 2008)
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TYPES OF WELL TESTSDrawdown tests:The flowing bottomhole
pressure (FBHP) is used for analysis. Ideally, the well should be
producing at a constant rate... sometimes difficult to achieve.
Build-up test:The increase of BHP after shut-in is used for
analysis. Before the build-up test, the well must have been flowing
long enough to reach a stabilized rate. Flow rate is accurately
controlled (i.e., 0)
Injection/Falloff test:Fluid is injected into reservoir.
Pressure rise during injection, and falloff after shut-in, are
analyzed. Properties of injected fluid are different from reservoir
fluids... more difficult to interpret with confidence.
Interference test:BHP monitored in a shut-in observation well
that is distant from the production well.
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Deruyck et al., 1992
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TYPES OF WELL TESTS (cont.)Gas well test:Analogous to oil wells,
but some differences. E.G., Absolute Openhole Potential (AOFP)
tests well is opened to patm (and/or a succession of relatively low
back-pressures). Also, non-Darcy flow may occur, not to mention the
fact that gas is highly compressible.WHEN THE TESTS ARE
RUN:Production test:The well has been completed as a production
well, commonly as a cased hole with a permanent completion (e.g.,
perforations). The well is monitored at surface, from the
wellhead.
Drill stem test (DST):The well is completed temporarily with a
downhole shut-in valve, and isolation is achieved using packers.
The well may cased and perforated OR openhole. Usually conducted
immediately after drilling using the drill stem, but more common to
run the test on production tubing now.Test duration is usually
relatively short compared to a production test.
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Information obtained during the process of productionVella et
al., 1992Testing a cased well: A test valve and pressure gauges
downhole are combined with surface separation and flow measurement
equipment to gather formation drawdown and buildup pressure and
flow rate data. Samples of formation fluid are taken at surface for
analysis.Reverse circulation valveDownhole test valvePackerPressure
dataPressure recorderFm. being tested
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Deruyck et al., 1992
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In the following slides, we will study the pressure response
during a conventional well test (constant production rate)
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TRANSIENT FLOW (EARLY)prpiOuter flow boundaryFBHP response
dominated by skin and reservoir permeability.No information about
reservoir boundaries.FBHP or pwfre
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TRUE STEADY STATE FLOW (E.G., Very Active Aquifer Support,
Waterflooding)prpiOpen flow boundaryNot commonly achieved under
natural conditions.final pwfre
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SEMI (or PSEUDO) STEADY-STATE FLOW (LATE)prpiOuter flow
boundaryFBHP response dominated by reservoir
boundaries.pwf1t1t2pwf2re
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DIFFUSION EQUATION FOR RADIAL FLOWThis equation is derived based
on mass conservation and Darcys law.Top viewSide
viewAssumptions:
HomogeneousIsotropicFully penetrating wellSingle-phase
flowConstant viscositySmall & constant compressibility
e.g., undersaturated oil
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TRANSIENT FLOW:APPROX. SOLUTION FOR INFINITE-ACTING
RESERVOIRprpiFBHP response dominated by skin and reservoir
permeability.Note the logarithmic dependence on time.FBHP or
pwfre
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MECHANICAL SKIN FACTOR: SConsider a well flowing at a given rate
Q. With no near-well permeability impairment, the pressure profile
would be as shown by the dashed line. However, in the case of a
damaged well, the actual pressure required to achieve flow rate Q
is shown by the solid line. The incremental pressure drop close to
the well has been defined by ven Everdingen as:pQ
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MECHANICAL SKIN FACTOR: SIF you know the radius and permeability
of the damaged zone, you can solve for S as follows:Re-arranging
gives:rwkekararepepwf
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CONDITIONS RESULTING IN SKINPositive skin (impaired
production)
Formation damagePartial well penetrationPerforationsNegative
skin (stimulated production)
Hydraulic fracturesAcid fracturesAcid wash/squeezePRODUCTIVITY
INDEX (PI)PI is a popular method of quantifying well performance.
It includes the effect of skin. It is expresses in units of
production rate per day per unit pressure drawdown... in metric
field units: scm / day / kPa
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SEMI (PSEUDO) STEADY-STATE FLOW SOLUTIONFBHP response dominated
by reservoir boundaries (area A; shape factor CA).Note the linear
dependence on time.prpipwft1repe
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SHAPE FACTORS & SEMI STEADY-STATE FLOW (1)The semi
steady-state inflow equation appears to be restrictive in that it
only applies for a well producing from the centre of a
circular-shaped drainage area.
Obviously, reservoirs will not be circular in general, nor will
the producing well(s) be centered within them.
Further, when multiple wells are producing from a common
reservoir, each well will assume its own ~fixed drainage area.
The so-called Dietz Shape Factors (CA) have been derived to
enable the use of the semi steady-state inflow equation for a
number of different geometries.
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SHAPE FACTORS & SEMI STEADY-STATE FLOW (2)
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Variables used in the preceding slides on well testing [SI
units]:
r= radial distance [m]rw= wellbore radius [m]re= outer radius of
the reservoir[m]p= fluid pressure [Pa]pwf= flowing bottomhole
pressure [Pa]pi= initial reservoir pressure [Pa]pe= current
reservoir pressure at the outer boundary [Pa]= porosity= Eulers
number = 1.781= fluid viscosity [Pas]c= fluid compressibility,
isothermal [Pa-1]k= (effective) permeability [m2]t= time [s]S= skin
factorQ= fluid production rate [stcm/s]B= fluid formation volume
factor [rcm/stcm]h= reservoir thickness [m]A= reservoir area (in
plan view) [m2]CA= reservoir shape factor
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EXAMPLE PRESSURE DRAWDOWN TEST (1)A well has been tested by
producing at a constant rate of 240 scm/d for a period of 100
hours. It is suspected, from seismic and geological evidence, that
the well is draining in isolated reservoir block which has
approximately a 4:1 rectangular shape. The extended drawdown test
has been run to confirm this, and to measure other properties of
the reservoir. Following are the known reservoir properties, and
the flowing bottomhole pressures that were measured during the
test.
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EXAMPLE PRESSURE DRAWDOWN TEST (2)Consider the early time flow
data, for which we expect the transient inflow equation to hold
true:We can re-work this equation like this:[Recall that ln(ab) =
ln(a) + ln(b)]We see that a plot of pwf against ln(t) should have a
slope of:no time-dependent terms... and an intercept of:
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EXAMPLE PRESSURE DRAWDOWN TEST (3)A plot of pwf against ln(t)
should have a slope of:From the regression line, we see that:
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EXAMPLE PRESSURE DRAWDOWN TEST (4)The y-intercept of our
regression tells us that:Which can be solved for S as follows:
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EXAMPLE PRESSURE DRAWDOWN TEST (5)Consider the late time flow
data, for which we expect the semi steady-state inflow equation to
hold true:We can re-work this equation like this:We see that a plot
of pwf against t should have a slope of:no time-dependent terms...
and an intercept of:
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EXAMPLE PRESSURE DRAWDOWN TEST (6)A plot of pwf against t should
have a slope of:From the regression line, we see that:
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EXAMPLE PRESSURE DRAWDOWN TEST (7)The y-intercept of our
regression tells us that:Which can be solved for CA as
follows:Error: These two terms should be multiplied by 2. See next
slide for correct version.
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EXAMPLE PRESSURE DRAWDOWN TEST (7)The y-intercept of our
regression tells us that:Which can be solved for CA as
follows:Corrected versionThese two terms have been corrected
here.The final answer that was originally given was correct.
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EXAMPLE PRESSURE DRAWDOWN TEST (8)Here is the closest matchfrom
the table of Dietzshape factors.
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EXAMPLE PRESSURE DRAWDOWN TEST (9)Reservoir shape:Here is what
we have interpreted for this reservoir:
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DIMENSIONLESS VARIABLESIts actually much more convenient to
convert our well test data to dimensionless form, then perform
type-curve matching to obtain our reservoir parameters.
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PRESSURE DERIVATIVESMore advanced well test analyses often
involve fitting to both the dimensionless pressure type-curves, as
well as its derivative.
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Deruyck et al., 1992
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In the preceding slides, we saw how pressure data from a
drawdown test in an oil well could be used to calculate k, S, A and
CA. What about estimating initial reservoir pressure (pi)?
One way to estimate pi is using the bottomhole shut-in pressures
(pws) recorded during a pressure build-up test.
The so-called Horner plot involves graphing:where t is the
length of time that the well was flowed prior to the build-up test,
and t is the time since shut-in.
If we could shut-in the well to infinite time, pws would reach
pi.
Linear extrapolation of the data to ln[(t+t)/t] = 0 is
equivalent to extrapolating the data to infinite shut-in
time.ESTIMATING RESERVOIR PRESSURE:HORNER PLOT ANALYSIS
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(DST Test)t t
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APPENDIX A
Extra Stuff Regarding Well Testing
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The hypothesis of slightly compressible fluids (i.e., small,
constant compressibility) used for oil-well test analysis of not
valid for gas systems.
Recall that gas compressibility is strongly dependent on
pressure... in fact, so is gas viscosity.GAS WELL TESTING (1)
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= 0.85; temperature = 200F).Gas compressibility
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In 1966, Al-Hussaniy et al. demonstrated that the radial flow
equation can be linearized approximately (i.e., rendered into a
form that we can solve analytically) by replacing all pressure
terms with the so-called gas pseudo-pressure, m(p).
The pseudo-pressure, also called the real gas potential, is
defined as:GAS WELL TESTING (2)where:p=the pressure of interestp0=a
reference pressure (chosen arbitrarily, usually a value less than
the lowest pressure to be experience in the well test)=gas
viscosityz=gas z-factor
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The radial diffusion equation then becomes:GAS WELL TESTING
(3)Remember the transient inflow equation for oil?Heres the
analogous solution for gas inflow:
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GAS WELL TESTING (4)Transient gas inflow equation:Note that the
skin factor has been expanded to account for non-Darcy flow
effects:Where D is called the non-Darcy flow coefficient.
With more time, we could go on to do an example calculation
analogous to the one we did last lecture for an oil well.
Please note that the transformation between p and m(p) is not as
stinky as it might seem.
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Gas pseudo-pressure, as calculated in Table 8.1 (Gas gravity =
0.85; T = 200F)m(p), psi/cPp, psi
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For an oil reservoir below the bubble point, we really shouldnt
pretend that the total fluid compressibility (i.e., oil + gas +
water) is small and constant.
There is also a multiphase pseudo-pressure, which linearizes the
inflow equations and allows us to make use of the well test
analysis techniques presented in the last lecture.
SOLUTION GAS DRIVE RESERVOIRSwhere:p=the pressure of
interesto=oil viscosityBo=oil formation volume factor
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CORRECTION FOR VARIABLE FLOW RATESThe mathematical basis for
well test analysis assumes constant flow rate throughout the test.
If rates have varied over time, once technique that allows you to
use conventional interpretation is by calculating an equivalent
flow time (te).
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WORK-AROUNDS FOR TESTS OF NON-CONSTANT RATESee also
Superposition Methods, in any textbook on well test analysis.
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www.fekete.com
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GEOE 412April 2005*