Well Test Design

1. WE LL TES TiNG
Bottomhole pressure
Bubblepoint
∆pA–B
∆pA–C
Wellbore Potential
Testing Design and Analysis
Bruno Deruyck Christine Ehlig-Economides Jeffrey Joseph
Montrouge, France Clamart, France London, England B
A C
Well testing is performed in so many different guises that it is easy to lose
Crossflow rates
These are to confirm the economic potential
Production rate
In its simplest form, testing provides short- tion logging to measure downhole flow. nEstimating producibility by altering the
term production of reservoir fluids to the They are routinely run in horizontal as well production rate and noting changes in
bottomhole pressure (top). A well’s pro-
surface permitting the operator to confirm as vertical wells. ductivity index, or inflow performance, is
the show—indicated by cuttings, cores and Developing the multifarious and intricate the slope of the straight line, measured in
logs—and estimate reservoir deliverability. hardware to accomplish all these tasks is a barrels of oil per day per psi. The straight-
In its subtlest form, measured pressure tran- design engineer’s dream. And juggling the line response curves downward once
sients caused by abrupt changes in produc- many options for conducting a well test pro- pressure falls below bubblepoint and gas
starts coming out of solution.
tion can characterize completion damage, vides endless challenges in the field (see In a layered reservoir, individual pro-
reservoir permeability and distant reservoir “The Nuts and Bolts of Well Testing,” page duction rates measured using a produc-
heterogeneities. 14). This article concentrates not on hard- tion logging tool—layers A, B and C in this
The logistics of well testing are simple in ware but on the information well tests give example—are plotted versus each layer’s
wellbore potential, the wellbore pressure
concept, but complex in practice. Flowing and how tests are designed and interpreted. normalized to a datum. This so-called
an exploration well requires a temporary Primary concerns in testing exploration selective inflow performance technique
completion. Flowing any well not con- wells are obtaining representative samples reveals individual layer inflow perfor-
nected to downstream facilities requires and estimating reservoir producibility.1 Fluid mances and also pressure imbalances
heavy surface equipment including separa- samples are needed to determine various between layers that can promote crossflow.
tors and flares. Obtaining pressure transients physical parameters required for well test
requires alternately shutting and opening analysis, such as compressibility and viscos-
the well, preferably downhole, and making ity, and for pressure-volume-temperature In this article, COMPUTEST (wellsite computer sys-
accurate downhole measurements of pres- (PVT) analysis that unlocks how the hydro- tem), FPE (Fluid Properties Estimation), IMPULSE
(measurement while perforating), MDT (Modular For-
sure. Increasingly, testing is performed in carbon phases coexist at different pressures mation Dynamics Tester), PLT (Production Logging
combination with perforating and produc- and temperatures.2 For oil, a critical PVT Tool), RFT (Repeat Formation Tester), SPG (Sapphire
parameter is bubblepoint pressure, the pres- Pressure Gauge), STAR (Schlumberger Transient Anal-
ysis and Report) and ZODIAC (Zoned Dynamic Inter-
sure above which oil is undersaturated in pretation Analysis and Computation) are marks of
gas and below which gas within oil starts Schlumberger.
being released. Maintaining reservoir pres- 1. Barnum RS and Vela S: “Testing Exploration Wells by
Objectives,” paper SPE 13184, presented at the 59th
sure above bubblepoint is key to successful SPE Annual Technical Conference and Exhibition,
testing since the principle of transient analy- Houston, Texas, USA, September 16-19, 1984.
sis, described below, holds only if flow in 2. Freyss H, Guieze P, Varotsis N, Khakoo A, Lestelle K
and Simper D: “PVT Analysis for Oil Reservoirs,”
the reservoir remains monophasic. Estimat- The Technical Review 37, no. 1 (January 1989): 4-15.
ing reservoir producibility requires achiev-
28 Oilfield Review

2. ing stable flow rates at several choke sizes ity—and it can determine the producing everywhere, eventually reaching the reser-
and then determining the productivity index zone’s permeability-thickness product, kh. It voir pressure that drives production.
from the slope of the flow versus drawdown can see to the limits of the reservoir indicat- The reservoir engineer follows this chain
pressure data (previous page ). ing the probable shape (but not orientation) of events by measuring the pressure
The type of oil as determined by a sample of the reservoir boundaries and can show buildup, or transient, and through analysis
and the ability of the well to produce are whether the primary recovery mechanism is determines information about the reservoir
the first steps toward commercial exploita- from water or gas-cap support. This infor- from near the wellbore to its limits. An anal-
tion. If well productivity is less than mation becomes crucial in the appraisal and ogous chain of events occurs if instead of
expected, then wellbore damage may be production stages of field development shutting in the well, the well is opened and
the cause. This is the next concern in testing when engineers combine testing interpreta- allowed to flow. Again, it is oil near the
exploration wells. Estimating the near-well- tion results with seismic and geologic data wellbore that first senses the disturbance,
bore condition to perform necessary reme- to refine their understanding of the reservoir. but it is only a matter of time for oil deeper
dial action and ultimately to plan a well How does transient pressure testing work? in the reservoir to respond and begin flow-
completion strategy for the field is accom- Imagine first an oil well in stable production ing too. Drawdown pressure measurements
plished from the transient analysis part of a with a certain pressure drawdown between to track these events practically mirror the
well test. the far limits of the reservoir and the well. buildup response. In fact, transients can be
Transient analysis, however, reaches Now shut in the well. In the formation, a obtained simply by increasing or decreasing
deeper than just the near-wellbore region. sort of concertina effect takes place (below). the flow rate.
Today, it contributes so much to characteriz- Oil near the wellbore is the first to sense the Transient testing depends on accurate
ing the reservoir that engineers increasingly shut-in and gets stopped in its tracks as it pressure measurements taken long enough
refer to well testing as reservoir testing. tries to push more oil ahead of it, getting after the flow rate change to observe what
Analysis can indicate the likely producing compressed in the process. Then, the shock the test was designed to detect. Impulse test-
mechanism of the formation—for example, is felt farther away as news of the shut-in, so ing, for example, measures the transient that
how much production comes from frac- to speak, travels to the outer regions of the occurs as a well is perforated, allowed to
tures, how much from intergranular poros- reservoir. Gradually, the pressure builds up produce for a short time and then shut in.
sight of its two real purposes.
of a discovery well and to maximize the cost efficiency of production in a developing or mature field.
Integrated with other measurements, well tests help provide the basis of reservoir characterization.
Fracture
Sealing fault
nPlan view showing the movement of wave fronts of a pressure transient
progressing away from a well. This shows a hydraulically fractured well
drilled near a sealing fault. Once wellbore storage disappears, the tran-
sient moves into the formation along linear paths perpendicular to the
fracture. Farther from the well, the transient moves radially from the
borehole. On hitting the sealing fault, the transient begins reflecting back
toward the borehole.
April 1992 29

3. The primary target is the near-wellbore Impulse Conventional Interference
region (right ).3 The goal is to assess forma-
tion damage and, if necessary, perform stim-
ulation. Tests last just an hour or two. In a
conventional test conducted to investigate
reservoir boundaries, often called a limit
test, the transient must be long enough for
the pressure disturbance to reach the
boundaries and then create a measurable
response in the well. How long this takes
depends on formation and fluid characteris-
tics. In particular, the lower the formation
permeability, the more time is needed—tests
can continue for days. Longest lasting are
interference tests, in which the effect of a
transient created in one well is observed in
another, yielding information about reser-
voir transmissivity and storativity.
The analysis and interpretation of well
tests have evolved remarkably since the
technique became established in the 1930s.
Today, a unified methodology has devel-
Flow
oped to obtain the maximum information
from any transient.4 The conventional test
on a new well comprises two flow periods
and two shut-ins (next page). The first flow
period, perhaps an hour long, is designed to
Pressure
clean up the near-wellbore region and give
the field crew time to manipulate chokes to
establish a practical, stable flow rate. The
well is then shut in and pressure builds up
to reservoir pressure, an important parame-
Time
ter for the reservoir engineer. Then begins a
long flow period, followed by a shut-in last- nThree types of well testing: Impulse, conventional and interference. Impulse testing
ing at least 1.2 to 1.5 times as long. This last measures the transient caused by a very brief flow, typically just as the well is perfo-
step generates the transient designed to rated. Results yield skin and permeability and may indicate if remedial stimulation is
required. Conventional well testing measures the shut-in transient after a lengthy flow
yield the reservoir’s secrets. Of course, there period and is often used to detect reservoir limits. Interference testing measures the
are many variants on this theme (see “Text- transient in a well caused by one or more flow pulses in a nearby well. Results yield
book Well Test from the Congo,” page 33). details about interwell transmissivity and storativity.
3. Ayestaran L, Ayoub J, Campbell J, Fairhurst D, Herrera
The basic data obtained are change in bated if well pressure toward the top of the
IC, Munsell S and Sneed BJ: “IMPULSE Testing,” The pressure, ∆p, versus elapsed time since the well drops below bubblepoint and part of
Technical Review 36, no. 4 (October 1988): 37-45. transient was initiated, ∆t. In traditional the well is filled with compressible gas.
4. For a review: analysis, ∆p is plotted against the logarithm Wellbore storage is substantially reduced by
Horne RN: Modern Well Test Analysis: A Computer-
Aided Approach. Palo Alto, California, USA:
of (tp + ∆t )/∆t , a dimensionless variable in shutting in the well downhole, minimizing
Petroway, Inc, 1990. which tp is the duration of the flow period. the volume of fluids that contribute.
For the development of well test analysis: This is the Horner plot—( t p + ∆ t )/∆ t is As wellbore storage dissipates, the tran-
Ramey HJ Jr: “Advances in Practical Well Test Analy- called Horner time (next page)—and the sient begins to move into the formation.
sis,” paper SPE 20592, presented at the 65th SPE
Annual Technical Conference and Exhibition, New
transient is analyzed by tracing the Pressure continues building up, but at a
Orleans, Louisiana, USA, September 23-26, 1990. progress of the data from right to left. slower rate as the transient moves far
5. Bourdet D, Whittle TM, Douglas AA and Pirard YM: First comes wellbore storage, which refers enough to achieve radial flow toward the
“A New Set of Type Curves Simplifies Well Test to the obfuscating role of the wellbore fluid wellbore. This is the so-called radial-flow
Analysis,” World Oil 196 (May 1983): 95-106.
Bourdet D, Ayoub JA and Pirard YM: “Use of Pressure
when a transient is initiated. The moment a regime that appears as a straight line trend
Derivative in Well Test Interpretation, paper SPE well is shut in or allowed to flow, fluids in on the Horner plot. The radial-flow regime
12777, presented at the 1984 California Regional the wellbore must first compress or expand is crucial to quantitative interpretation, since
Meeting, Long Beach, California, USA, April 11-13,
1984. before formation fluids can react. If flow is it provides values for kh and skin, S, a mea-
controlled from the surface, the entire well’s
fluids contribute to wellbore storage and the
effect can dominate the pressure transient
for hours afterward. The effect is exacer-
30 Oilfield Review

4. sure of the extra pressure drop caused by most complex series of drawdowns and A pressure transient breaks into several
wellbore damage. Skin takes positive values buildups, providing that the radial-flow regimes on the log-log plot, each seeing
in a damaged well when pressure drop near regime is present in the response. deeper than the last. The first regime typi-
the wellbore is greater than expected and Although the Horner plot is acceptable for cally reflects wellbore storage, during which
negative values when stimulation creates interpreting the radial-flow regime of easy- both the pressure and derivative curves
less pressure drop. Next, the transient to-interpret tests, a straight-line trend is often overlay and increase along a straight line of
encounters the limits of the reservoir and difficult to pick out. Alternatively, there may unit slope. As wellbore fluids stabilize, pres-
pressure departs from its straight-line radial- be several straight-line trends, of which only sure continues building up, but at a slower
flow response. one represents radial flow. Also, the plot rate. The derivative curve swings down,
The definition of Horner time is based on fails to provide ready insight into the nature eventually flattening out as the transient
a step change in flow rate, with one flow of reservoir limits. As pressure measure- moves far enough from the wellbore to
period followed by a buildup. In actual ments improved in accuracy, it was this achieve radial flow. Since the radial-flow
tests, there are always at least two prior flow aspect that increasingly engaged the atten- regime is a straight-line trend on the Horner
periods, often many more, and each affects tion of reservoir engineers. The solution, dis- plot, the derivative curve on the log-log plot
the pressure response after it occurs. Never- covered in in the early 1980s, was a double is constant and traces a horizontal line. The
theless, their cumulative effect can be deter- logarithmic, or log-log, plot of two sets of interpreter’s first task always is to identify
mined using the superposition principle, data versus ∆t (below).5 One set is simply this derivative plateau, but this may require
which states that transients occurring ∆p, the other is the gradient, or derivative, waiting a long time in tests dominated by
sequentially simply add up. This results in of the response on the Horner plot. The wellbore storage (page 34, top).
generalized Horner time that takes into virtue of the log-log plot is that reservoirs Lengthy wellbore storage can totally mask
account the flow rates and flow times for all similar in construction but perhaps differing earlier flow regimes that occur for certain
previous flow periods. Using generalized in thickness, porosity and permeability give borehole-formation configurations and for-
Horner time, the Horner plot retains its rise to similar looking responses and can be mation types, causing distinct perturbations
validity in determining kh and skin for the recognized as belonging to a class. (continued on page 34)
Data
1st Flow 1st 2nd Flow 2nd Buildup
Buildup
Pressure
Horner Plot
Limits Radial
flow
Time
Wellbore
∆p
nElements of a conventional two-stage buildup tran- storage
sient test. Testing engineers use the first flow period to
clean up formation damage and adjust the choke to
gauge the producing capacity of the well. The first
buildup provides a first estimate of reservoir pressure.
Then begins a long flow period, followed by a longer
buildup. Analysis of the transient measured during this
(tp + ∆t )/∆t
second buildup reveals details of the near-wellbore
Log-Log Plot
region, formation characteristics such as permeability,
and distant limits of the reservoir.
Traditional analysis centered on the Horner plot
(middle), in particular the straight-line trend that sig-
∆p and Derivative
nals radial flow. Today, the log-log plot (bottom) of ∆p Wellbore
and the derivative, the slope of the Horner plot, is used storage
to first diagnose the various flow regimes of the tran-
sient. Then, specialized plots such as the Horner plot
are used to estimate specific parameters such as per- Limits
Limits
meability, skin and reservoir pressure. Radial flow
∆t
April 1992 31

5. 5 Five pressures, one obtained in surface
readout and four in memory mode, are
compared after normalization for different
gauge depths. Agreement is within 12 psi,
well within bounds of gauge technology.
6 During the buildup, the 104
measured pressure transient (data
3065 points) is compared at the wellsite to S = 20
Surface readout the design (solid lines), which considered
∆p and Derivative, psi
SPG gauge a range of skin values between –3 and 5
Qtz. gauge 2 20. A value of –3 corresponds to a 103
0
Pressure, psi
stimulated formation, 20 to a damaged
one. Finding skin was crucial because –3
it determined the necessity of an acid
job. Overlaying the data on the design 102
shows skin to be between 0 and
Qtz. gauge 1 5—in fact, it was calculated at 1. This
Strain gauge indicated that an acid job would
3035 probably benefit production.
19 19.5 20 Permeability is less important here, 101
Time, hr because it is well known in the area— 10-4 10-3 10-2 10-1 100 101
100 md was assumed for the design, Elapsed time, hr
85 md was estimated
from the data.
2 Downhole pressure jumps
to the reservoir pressure level
4800 and then drops as the well is
opened to clean up perforation 9 The well is shut in as the
acid job is prepared and
Pressure, psi
debris.
performed.
3 The well is shut in so the
surface readout device can be 11 The well is shut in so the
lowered into the hole. surface readout device can
be lowered again and hooked
into the drillstem test tool.
Flow rate, bopd
1000 10 The well is flowed back to
clean up after the acid job.
1000
0
0 10 20 30 40 50 Time, hr 60
1 The test begins with under- 13 Comparison at wellsite between
balanced perforation to 8 A short flow period BOPD/psi pre- and post-acid buildups using
minimize wellbore damage during which a 0 5 surface pressure readout data.
using tubing-conveyed production logging 2035 Using specialized analysis, the data
perforating guns slung below profile is made,
Perfs. indicates pre-acid skin to be 1, and
the drillstem test tool. the tool passing post-acid skin to be –2, a substantial
through the fullbore 2040 improvement.
Limest.
drillstem tool to the Because the post-acid drawdown
Depth, m
4 With pressure now available newly perforated and buildups are comparitively longer,
at the surface (red curve), a reservoir formations 2045 the data sees further into the
6-hour flow period begins, below. The flow profile reservoir. After the radial-flow
followed by a slightly longer shows good production regime plateau, the post-acid
Sandstone
buildup. from the sandstone 2050 derivative goes up and then down,
but not so good from eventually becoming noisy as gauge
the overlying limestone, resolution is coming into play. This is
7 Once the radial-flow regime confirming that
of the buildup is confirmed, 2055 the time to halt the test.
production would
the surface readout device is definitely benefit
pulled out of the hole. from an acid job.
Pressure data change
color, from surface readout
to downhole memory mode.
32 Oilfield Review

6. Textbook Well Test from the Congo
Gilles Bourdarot This textbook case study comes from an Elf exploration well in the Congo. The 2200-m [7218-ft]
Alain Desplanques deep reservoir comprises a limestone overlying a sandstone, both having 20 to 22% porosity. The
Elf Congo well test uses all the modern techniques—tubing-conveyed perforating, production logging and
Pointe-Noire, Congo sampling through fullbore drillstem equipment, surface readout and wellsite validation—and is
designed to accomplish two goals:
Mike Pearson
One is to estimate near-wellbore damage, reducing it if necessary with a matrix acidization and
Montrouge, France
then checking that the acid cleanup worked—all without removing the drillstring from the hole.
This was intended not only to benefit production in the well, but also to help plan a completion
strategy for field development. The other goal was to investigate reservoir volume and identify
reservoir boundaries.
The record of surface oil flow rate and downhole pressure for the 130-hour test tells most of the
story—follow the annotations in sequence. The surface oil flow rate data points are derived from
measuring outflows from the surface separators. The data are stored in the COMPUTEST wellsite
computer system. The lines represent averaged values for the duration of a flow period.
The green pressure curve represents data stored in downhole memory throughout the test and
then read out after retrieving the drillstring. In fact, four pressure gauges were used in this
downhole memory mode: one strain gauge, two quartz gauges and one SPG Sapphire Pressure
Gauge. The red curve represents pressure data obtained with the surface readout device hooked
into the drillstem tool and read in real time at the surface. Over 75,000 17 The sampler is BOPD/psi
pressure data points make up the curves in the plot. then pulled and a 0 5
second production 2035
Now go to 1 . logging profile is made Perfs.
with the well flowing
16 A fluid sampler is run in on at a higher rate. 2040
Limest.
12 A long, 24-hour flow period wireline, through the fullbore Comparing pre- and
Depth, m
and a buildup lasting almost post-acid flow profiles,
drillstem test tool to position
two days then followed. This was the acid job can be 2045
opposite the producing formations.
to confirm the effectiveness of the seen to have
The well is allowed to flow
acid job and to investigate successfully stimulated
gently to preserve bottomhole
Sandstone
reservoir volume and boundaries. the limestone. 2050
pressure above bubblepoint
while sampling takes place.
2055
14 Toward the end of the
buildup, the surface readout
device is pulled out of the hole.
70 80 90 100 110 120 130
101 15 The second buildup was interpreted
using data measured in downhole
∆p and Derivative, psi/BOPD
103
memory mode and thus covering the
buildup to its very end. The data were
∆p and Derivative, psi
analyzed off-site, after the drillstring
100 Pre-acid buildup was pulled. 102
This match (lines) is based on
a no-flow boundary and a constant-
Normalized
pressure boundary (possibly the
10-1 water table). Another good match 101
Post-acid buildup to the data was obtained by
assuming a composite radial model.
Only the reservoir engineer in
cooperation with geologist and 100
10-2
geophysicist can decide which is
10-3 10-2 10-1 100 101 102 10-3 10-2 10-1 100 101 102
more appropriate.
Elapsed time, hr Elapsed time, hr
In five days, with only one pipe trip into the hole, this properly designed and executed well test has
brought the exploration well to maximum potential, determined formation permeability, provided
representative samples for PVT analysis, investigated far-reservoir boundaries, and set in place a
completion strategy for development wells of the field.
33

7. nReduction of Impermeable Boundary
wellbore storage
with downhole Well
shut-in. The log-log
Downhole shut-in plot compares two
100 well tests, one shut
in at the surface,
the other shut in
∆p and Derivative, psi
downhole. In the
surface shut-in test,
10-1 wellbore storage
Surface shut-in Partially Sealing Fault
masks the radial-
flow plateau for Well
over 100 hours
(4 days) (square
data points). The
10-2
plateau emerges
clearly in the down-
hole shut-in data
after just one hour
(triangular data
10-3 points). Intersecting Impermeable Boundaries
10-2 10-1 100 101 102 (From Joseph et al,
Time, hr reference 6.)
Well
on the derivative response. The signs are the special case in which the test is long
varied (next page ). A partially penetrated enough to reach all the no-flow boundaries,
formation produces a linear trend on the thus forming a closed system. Examples of
derivative curve with a slope of –1/2. In wells no-flow boundaries include sealing
where the formation is strongly layered or faults—perhaps several of them—pinchouts, Parallel Impermeable Boundaries
naturally fractured, the derivative tends to and channels. Because no-flow boundaries
dip before it rises to the radial-flow plateau. reflect the transient back toward the well,
If wellbore storage is not too dominating, the they cause ∆p to rise at higher than its nor-
transient can be analyzed to pinpoint the mal radial-flow rate, so the derivative curve Well
most likely explanation. jumps to a higher level. A sealing fault
The last regime on the log-log plot occurs causes the plateau value to double. With
when the pressure transient has travelled far two intersecting sealing faults, the jump is
from the well and encounters the reservoir correspondingly higher. If a fault is partially
Truncated Channel
or drainage-area limits. Testing theorists sealing, the derivative curve starts to jump
have worked out the transient response to a but then falls back to its radial-flow value.
catalog of boundary geometries ( right ). In Constant-pressure boundaries, like a gas
most cases, the transient responses alone do cap or aquifer, allow the pressure transient Well
not offer enough differentiation to enable to flatten out at the boundary pressure, so
the interpreter to definitively establish the the derivative takes a nosedive, which is
boundary type. The choice of the type as instantly recognizable. In a closed system,
well as the orientation of the boundary pressure is completely contained within the
geometry must be guided by geologic, seis- reservoir. How this affects the ∆ p and Pinchout
mic and log data. derivative curves depends on whether the Well
There are three categories: no-flow transient is a drawdown or buildup. In
boundary, constant pressure boundary and drawdown, both curves track a line of unit
slope, again an easily recognizable effect. In
buildup, the derivative curve starts moving
toward the line of unit slope but takes a
nosedive before reaching it, somewhat simi-
lar to the constant-pressure boundary case. nA representative selection of no-flow
These reservoir models are simpler than boundaries studied by well-test theorists.
nature generally allows—in reality, a mix- Any of these may appear in the late-time
ture of responses should be expected. portion of a transient’s diagnostic log-log
Thanks to the superposition principle, how- plot. The associated parameters defining
the boundary may then be estimated by
ever, responses may be combined to pro- regression analysis.
duce a realistic transient response for even
the most complex situation. Simulating data,
though, is the easier forward task. More dif-
34 Oilfield Review

8. Log-log Horner Specialized Flow Regimes
Wellbore
∆p, Derivative
storage
Radial
∆p
∆p
flow
Other
Time Horner time Function of time
Homogeneous
Reservoir
Wellbore storage
coefficient
∆t
Partially
Penetrating Well
Infinite Conductivity
Vertical Fracture
(Fracture half-length)2
× matrix permeability
∆t
Finite Conductivity
Vertical Fracture
Fracture permeability
× fracture width
4
Sealing Fault ∆t
nResponse of log-log plot (left column) to
several common reservoir systems, show-
Constant Pressure ing different flow regimes (see legend).
Boundary
The log-log plot is used by analysts to
diagnose the flow regimes present in the
transient. Once regimes are identified, the
Horner plot (semi-logarithmic) and other
specialized plots (linear) are used to eval-
uate parameters characterizing the system.
Linear Channel
Matrix permeability
× (channel width)2
∆t
Dual-Porosity
35

9. ficult for the analyst is the inverse procedure Using a workstation, the reservoir engi- established in the second buildup to predict
of finding the best model to match actual neer interacts with a computer program, pressure response throughout all four peri-
test data (below ).6 such as STAR Schlumberger Transient Anal- ods of the test and confirms that the model
For the traditional test comprising two ysis and Report and ZODIAC Zoned satisfactorily accounts for all data. This may
flow periods and two buildups, transient Dynamic Interpretation Analysis and Com- result in more parameter adjustment
analysis focuses on the second buildup. The putation programs,7 to build a comprehen- because every period must now be matched
first step is to identify the various regimes on sive model using all the parameters found simultaneously, even though the second
the log-log ∆p and derivative-curve plots for the various flow regimes, predict what flow period is planned intentionally long to
and then choose the most likely model for the entire transient should look like, and minimize the influence of previous periods.
each. Estimation of model parameters is compare the results with the data. In this In some cases, interference from earlier
then made using specialized plots that allow forward modeling process, the interpreter well manipulations may obscure key
a focused analysis of each flow regime (pre- tweaks parameters, either manually or auto- regimes of the transient being analyzed.
vious page ). For example, wellbore storage matically using a nonlinear regression Interpreters then resort to a process called
in the early data is determined from the scheme, and perhaps alters the choice of desuperposition that attempts to isolate the
slope of the straight-line portion of a linear model for one of the regimes to obtain the transient from earlier ones and in particular
∆p versus ∆t plot. Confirmation and charac- best possible fit. There may be several com- reform the given transient’s data to mimic
terization of a vertical, high-conductivity binations of models that match the data how the reservoir would have reacted if the
fracture, recognized by a half-slope deriva- equally well. In this case, other data must flow rate change had been an isolated, per-
tive trend on the log-log plot, come from a be sought to decide which model is the fect step.8
plot of ∆ p versus ∆ t . The radial-flow most appropriate (next page ). Designing well tests involves many of the
plateau is best analyzed using the general- The final interpretation step, called history same steps the interpreter uses. This is
ized Horner plot. And so on. matching or verification, uses the model because once a test has been proposed,
both the pressure data and the data’s inter-
pretation can be simulated to show that the
Raw data test as designed meets its goals—design sim-
ulation requires estimates of formation and
fluid parameters from nearby wells or the
well in question. By predicting the likely
shape of the log-log ∆ p and derivative
Preprocessing curves, the engineer can demonstrate the
feasibility of detecting and characterizing
the anticipated reservoir features. For exam-
ple, design simulation ensures that wellbore
Openhole logs storage does not smother the feature being
PVT data Model diagnosis sought and guarantees a test that is long
Production logs enough to view suspected reservoir bound-
aries. Another important feature of simula-
tion is determining the accuracy and preci-
sion required of the pressure gauges.
Specialized plots The design phase not only maps out the
mechanics of a test, but also ensures that,
once underway objectives are met. For
example, the progress of the planned tran-
sient can be followed at the wellsite and
Parameter estimation compared with that forecast during the
design. To avoid the costly mistake of rig-
ging down before the transient indicates a
desired feature, wellsite validation of data
during the test remains a must. This is best
History matching accomplished with surface readout of
downhole gauges and enough computing
power at the surface to produce appropriate
plots, notably the log-log diagnostic plot. If
the reservoir response is quite different from
Results that assumed in the design, wellsite diagno-
sis permits an instant correction of the job,
perhaps a lengthening of the transient, to
nThe order of business
in pressure transient
analysis.
36 Oilfield Review

10. Sealing Fault ensure optimum use for the data. In certain
101
cases, real-time readout is not feasible and
downhole recording must be used. Data
validation can still be performed onsite right
∆p and Derivative
after retrieving the gauges.
Integral to well test design is selection of
100 hardware, which involves many options. To
minimize wellbore storage, should the well
be shut in downhole rather than at surface?
In a low producer, will the act of shutting in
actually kill the well? How sensitive must the
pressure gauges be? To some extent, these
10-1
questions are decided by the operator’s stan-
Two Intersecting Perpendicular Faults
101 dard practices, the current status of the hole,
the configuration of the downhole hardware
and, not least, safety considerations.
The options have expanded in recent
∆p and Derivative
years. While drillstem test (DST) equipment
has always guaranteed downhole shut-in in
100
new wells, downhole shut-in devices for
completed wells did not become commer-
cial until the early 1980s. Pressure gauges
have evolved from crude mechanical
devices to quickly reacting, highly accurate
10-1 quartz gauges. Perhaps the most unexpected
Dual-porosity Model innovation is a downhole flow measurement.
101 Traditional well testing theory dispensed
with a flow measurement because it
assumed constant wellbore storage,
∆p and Derivative
enabling flow to be estimated from early
pressure data. But reality is less predictable.
100 Wellbore storage often varies as the fluids in
the wellbore change during the test, and a
downhole flow measurement in fact offers a
valuable complement to conventional pres-
sure data.
Downhole flow measurements are cur-
10-1
rently performed using production logging
Dual-permeability Model
101 6. Joseph J, Ehlig-Economides CA and Kuchuk F: “The
Role of Downhole Flow and Pressure Measurements
in Reservoir Testing,” paper SPE 18379, presented at
the SPE European Petroleum Conference, London,
∆p and Derivative
England, October 16-19, 1988.
Ehlig-Economides CA, Joseph JA, Ambrose RW Jr and
Norwood C: “A Modern Approach to Reservoir Test-
100 ing,” Journal of Petroleum Technology 42 (December
1990): 1554-1563.
7. The newer ZODIAC program includes all the features
of the older STAR program.
8. Ehlig-Economides CA, Ambrose RW and Joseph JA:
“Pressure Desuperposition Technique for Improved
Late-Time Transient Diagnosis,” paper SPE 20550,
10-1 presented at the 65th SPE Annual Technical Confer-
10-1 100 101 102 103 ence and Exhibition, New Orleans, Louisiana, USA,
Time September 23-26, 1990.
nFinding the best model to fit the data. In this case, four scenar-
ios fit quite well, but the dual-permeability model fits best. Dual
permeability means a two-layered formation with a different
permeability in each layer.
April 1992 37

11. tools and therefore not deployable when
downhole shut-in is planned. The most
∆p and Derivative
common uses are to measure transients
caused by either shutting in or altering the
flow rate at the surface—the tool, entered
into the well through a conventional riser
and lubricator, is suspended just above the
producing zone. A drawback of the current
technology is the threshold and resolution
of the spinner in the logging tool that mea-
Time Model sures flow. Well testing experts dream about
a robust flow measurement incorporated
T into the DST tool, enabling continuous flow
P(t) = 0
q(τ) p(t-τ) dτ measurements in newly drilled wells.
If flow measurements are at hand, how
does that change testing analysis? The nec-
essary theoretical ground was broken in the
Pressure 1980s. The underlying principle is, once
again, superposition.9 Suppose the pressure
response to a unit step change in flow is
p(t – t 0 ), where t 0 is when the step change
occurs. Then the pressure response, P(t ), to
a gradual change in downhole flow rate,
Flow rate q (t ), may be computed by approximating
the gradual change with a series of stair
steps, then considering each step as provid-
Time ing a minitransient, and finally through the
superposition principle summing all the
nThe convolution integral that converts pressure response to a unit step change in flow, minitransients (left ). As the steps are made
p(t), and actual measured flow rate, q(t), into measured pressure response, P(t). Convo-
lution revolutionizes transient analysis when downhole flow measurements are avail- smaller, this sum becomes the convolution
able, for example as measured by production logging in a flowing test. The mathemat- integral:
ical manipulation virtually wipes out wellbore storage, leaving later portions of the
T
transient clearly visible.
P ( t ) = q (τ) p (t– τ ) d τ .
nAn example
0
showing wellbore
103 storage virtually During a test, downhole pressure gauges
eliminated using measure P (t ) and a flowmeter measures q(t ).
Convolution derivative Pressure change the convolution But p(t ) is what the interpreter wants. Get-
derivative. The
∆p and Derivative, psi
transient was intro- ting at it requires the reverse process of
102
Pressure derivative duced by chang- deconvolution, which unfortunately is a
ing the well’s pro- rather unstable numerical procedure. More
duction rate and commonly, interpreters favor a procedure
101 downhole flow was
measured using called logarithmic convolution that converts
production logging. the two measurements more easily into
something that fits existing analytical tech-
100 niques (left ).
Logarithmic convolution is a mathemati-
cal trick in which a form for p ( t ) is
assumed—usually the response for infinite-
10-1
acting radial flow—that simplifies the above
10-5 10-4 10-3 10-2 10-1 100 101
convolution integral to a simpler expression
Time, hr involving a rate-normalized pressure
P(t )/q (t ), written J (t ), and a new time-scale
called sandface rate convolution time, tsfrc .
J (t ) and its derivative with respect to tsfrc
offer the same diagnostic power as the con-
ventional well testing analysis described
earlier with the advantage that most of the
wellbore storage is removed.
38 Oilfield Review

12. There are several advantages to testing a A B C
well with downhole pressure and flow mea-
Surface flow rate
surements under drawdown—and one dis-
advantage. The disadvantage is that reservoir
shut-in pressure is not measured. The advan-
tages are:
•in producing wells, little production is lost A
since the well is never shut-in.
•in poor producers, production is not killed
as may occur during a shut in.
•in layered reservoirs, testing under draw-
down reduces the possibility of crossflow Downhole
between producing layers, while this can C
easily occur in a buildup test complicating
the interpretation. Pressure
The technique’s most popular application in
layered reservoirs, though, is in analyzing
individual layer kh and skin values.10
This involves measuring a series of tran- B Flow
sients created by changing the production
rate, one for each layer with the production
logging tool situated at the top of the layer
(right ). The amount of data acquired is huge
and can be analyzed in several ways with A B C
varying degrees of sophistication. The key, Time
however, is to first analyze the transient nSequence of downhole pressure and flow transients measured using a production log-
measured with the tool situated just above ging tool in a layered reservoir test. A separate transient is measured with the tool posi-
the bottom layer, yielding that layer’s reser- tioned at the top of each zone. Analyzing the transients yields individual zone perme-
voir properties. Then, a second transient is ability and skin values.
measured with the tool situated above the
next layer, revealing reservoir properties of innovation provides a solution. Samples of 9. Meunier D, Wittmann MJ and Stewart G: “Interpreta-
the new layer and bottom layer combined. extraordinary reliability may now be tion of Pressure Buildup Test Using In-Situ Measure-
Since reservoir properties for the bottom obtained from any number of zones using ment of Afterflow,” Journal of Petroleum Technology
37 (January 1985): 143-152.
layer are already estimated, the transient the new wireline-conveyed MDT Modular 10. Kucuk F, Karakas M and Ayestaran L: “Well Test
can be analyzed to reveal just the new Formation Dynamics Tester, but this has to Analysis of Commingled Zones Without Crossflow,”
layer’s properties. The process continues up be planned in advance because the sam- paper SPE 13081, presented at the 59th SPE Annual
Technical Conference and Exhibition, Houston
the well. pling takes place in open hole (see “The Texas, USA, September 16-19, 1984.
Layered reservoir testing (LRT) was origi- MDT tool: A Wireline Testing Break- Ayestaran L, Ehlig-Economides C, Shah P, Kuchuk F,
nally conceived to investigate production through,” page 58). Nicolson B and Wittmann M: “Layered Reservoir
Testing,” The Technical Review 35, no. 4 (October
wells. Recently in offshore Congo, AGIP In addition to convolution and layered 1987): 4-11.
used the technique to evaluate a layered reservoir testing, there are other advantages
reservoir encountered by an exploration to supplementing conventional pressure
well. Conventional testing of individual pay data with production logging measure-
zones in an exploration well would nor- ments. A flow profile run during stabilized
mally call for a separate DST-perforation run production or shut-in can pinpoint where
for each zone. But using layered reservoir production is coming from and provide
testing, AGIP obtained reliable kh, skin and invaluable data on crossflow between
productivity index values for individual zones. The information may directly influ-
zones with only one trip in the hole, at a ence testing interpretation. For example, if a
considerable cost savings (see “Exploration zone is producing only from its upper part,
Layered Reservoir Testing in the Congo,“ a portion of the transient will react as if the
next page). well were only partially completed. The
The drawback of using an LRT in the diagnosis must be adjusted accordingly. The
exploration setting is that production from fluid density measurement in production
different zones commingles, ruling out rep- logging also plays a role by indicating
resentative sampling from different pay whether gas is coming out of solution, giv-
zones. Fortunately, a recent technological ing a warning that a test may be occurring
at below bubblepoint conditions.
Perhaps the most valuable contribution of
downhole flow measurements is in testing
(continued on page 45)
April 1992 39

13. Exploration Layered Reservoir Testing in the Congo
Luigi Piero Augustine Alagoa
AGIP Congo Pointe-Noire, Congo
Pointe-Noire, Congo
AGIP’s innovative use of layered reservoir testing RFT Pressure Lower layer
(LRT) in an exploration well occurred offshore Upper layer
Pressure potential, bar
Congo. The goal of the test was to evaluate two Composite
308
producing layers only a few meters apart with
only one trip into the hole, a much less costly
300
undertaking than the usual two trips. The LRT
technique was originally developed for testing
292
production wells, in which several layers produce
commingled—in this case, LRT is a must to eval-
uate each layer’s dynamic properties. Here, AGIP 0 10 20 30 40
extended the method to the exploration environ- Bottomhole flow rate, m3/hr
ment, where openhole data suggest several pay nSelective inflow performance plot for the
two reservoir layers, showing the lower
zones quite close to each other.
nReservoir geometry near the two layers The discovered field is an elongated structure
layer to be easily the more productive
and the reservoir pressure corrected to a
investigated by a layered reservoir test in
depth datum of 2735 m to be the same in
AGIP’s Congo exploration well. bounded by two faults forming a V shape (left).
both layers—315 bars.
The well penetrates several reservoirs. Five tests
were performed in the well, two using the LRT in. tubing-conveyed perforating (TCP) guns to
technique. Each LRT test looked at two distinct enhance cleanup and control perforation damage.
layers. This example presents results from the The test began with a flow period to clean up
shallower pair. the well, then a shut-in during which a production
The bottom layer is a 17-m [56-ft] thick sand- logging profile was recorded. The well was then
stone/limestone mix of 26% porosity, while the opened on a 3/8-in. choke, and transient pressure
top layer is a 7-m [23-ft] thick limestone of 20% and flow measurements were recorded with the
porosity. The layers are separated by about 4 m production logging tool positioned above the top
[13 ft] of silts. The well was completed with 7-in. zone (above). After flow stabilized, a second pro-
casing and perforated underbalanced with 4 1/2- duction logging profile showed that 95% of pro-
duction came from 10 m [33 ft] of the bottom
layer and just 5% from the top layer. The tool was
then moved to the top of the bottom zone and a
new transient measured after the choke was
increased to 1/2 in. The choke was finally
increased to 3/4 in. and a final transient mea-
sured with the tool back above the top zone.
First, the flow profiles were analyzed to obtain
the inflow performance of and reservoir pressure
in each layer. Plots of pressure normalized to a
40 Oilfield Review