The Nuts and Bolts of Falloff Testing
Sponsored by EPA Region 6
March 5, 2003
Ken Johnson
Environmental Engineer
(214) 665-8473
johnson.ken-e@epa.gov
Susie Lopez
Engineer
(214) 665-7198
lopez.susan@epa.gov
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Table of Contents
Page
Topic Number
Purpose of a Falloff Test 1
Background and Definition 1
Sequence of Events During a Falloff Test 2
Effects of Injection and Falloff 3
Pressure Transients 3
Falloff Test Planning 3
General Planning 3
Reservoir Considerations 3
Operational Considerations 4
Offset Well Considerations 4
Recordkeeping 4
Instrumentation 5
Pressure Gauges 5
Types of Pressure Gauges 5
Pressure Gauge Selection 6
Falloff Test Design 7
Test Design Calculations 8
Wellbore Storage Coefficient 8
Time to Reach Radial Flow 8
Test Design Criteria 10
Data Needed to Analyze a Falloff Test 11
Test Design Checklist 11
Pressu re Transient Theory Overview 12
P-T Theory Applied to Falloff Tests 12
PDE Solution at the Injector 18
Semilog Plot 18
MDH Plot 19
Horner Plot 20
Agarwal Time Plot 20
Superposition Time Function 20
Which Time Function Is Correct? 21
i
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Other Uses fo the Semilog Plot 22
Radius of Investigation 22
Wellbore Storage and Skin Factor 23
Effective Wellbore Radius 25
Skin Pressure Drop 25
Corrected Injection Pressure 26
False Extrapolated Pressure versus Average Reservoir Pressure 26
Injection Efficiency 27
Identifying Flow Regimes 27
Log-log Plot 27
Log-log Plot Pressure Functions 28
Log-log Plot Time Functions 28
Log-log Plot Derivative Function 29
Specific Flow Regimes 32
Wellbore Storage 32
Linear Flow 33
Spherical Flow 33
Radial Flow 34
Hydraulically Fractured Well 36
Naturally Fractured Rock 37
Layered Reservoir 38
Typical Derivative Flow Regime Patterns 39
Falloff Test Evaluation Procedure 41
Type Curves 44
Key Falloff Variables 46
Effects on the Length of the Injection Time 46
Effects of the Injection Rate 47
Effects of the Length of the Shut-in time 49
Effects of Wellbore Storage and Skin Factor 50
Boundary Effects 51
Typical Outer Boundary Patterns 55
Gallery of Falloff Log-log Plots 55
Other Types of Pressure Transient Tests 59
Injectivity Test 59
Multi-rate Injection Test 59
ii
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Interference Test 59
Pulse Test 60
Interference Test Design 60
Falloff Test Impact on the Area of Review Evaluation 63
Determination of Fracture Pressure 64
Step Rate Test 64
Other Uses of Injection Rates and Pressures 68
Hall Plot 68
Hearn Plot 72
Nomenclature 73
References 75
iii
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Purpose of a Falloff Test
Satisfy regulatory requirements
Measure injection and static reservoir pressures
Downhole pressure
Surface pressure: requires measurement or estimation of specific gravity
of the injectate to calculate bottomhole pressure
Obtain reservoir properties
Calculate transmissibility, kh/
Provide data for Area of Review (AOR) calculations
Characterize the nature of the injection zone
Observe and identify reservoir anomalies
Faults or boundaries (multiple or single)
Dual porosity (naturally fractured)
Evaluate completion conditions
Skin factor
Identify completion anomalies
Partial penetration
Layering
Presence of a hydraulic fracture
Background and Definition
UIC Class 1 Well Regulatory Requirements
§146.13 Operating, monitoring and reporting requirements
(d)(1) ...At a minimum, the Director shall require monitoring of the
pressure buildup in the injection zone annually, including at a minimum, a
shut down of the well for a time sufficient to conduct a valid observation of
the pressure falloff curve.
Hazardous wells:§146.68 Testing and monitoring requirements
(e)(1) .. .At a minimum, the Director shall require monitoring of the
pressure buildup in the injection zone annually, including at a minimum, a
shut down of the well for a time sufficient to conduct a valid observation of
the pressure falloff curve.
Requirements for Hazardous Wells Injecting Restricted Hazardous Waste
§148.21 Information to be submitted in support of petitions
(b)(1) Thickness, porosity, permeability and extent of the various strata in
the injection zone.
(b)(4) Hydrostatic pressure in the injection zone
1
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Though the regulations may not require a falloff test for Class II wells, the Director can
request additional testing to assure protection of the USDW prior to issuing a permit.
Additional Testing Requirement of Any Class of Injection Well
§146.8 Mechanical integrity8.21
(f) The Director may require additional or alternative tests if the results
presented by the owner or operator under §146.8(e) are not satisfactory to
the Director to demonstrate that there is no movement of fluid into or
between USDWs resulting from the injection activity.
Falloff testing is part of pressure transient theory that involves shutting in an injection
well and measuring the pressure falloff
Equivalent to a pressure buildup test in a producing well
Analyzed using the same pressure transient analysis techniques used for
pressure buildup and drawdown tests
Sequence of Events During a Falloff Test
The falloff is replay of the injection portion of the test. Therefore the injection period
controls what is seen on the falloff. A falloff test tends to be less noisy than an
injectivity test because there is no fluid passing by the gauge.
E
n.
U)
S
£
SHUT IN
INJECTING
Falloff start
Time, t
* CL
o ..
t 2!
| 5
£ $
O i-
m °-
Time, t
Falloff pressure decline
-------
Nuts and Bolts of Falloff Testing
Effects of Injection and Falloff
March 5, 2003
Time, t
Pressure transient
from injection well
continues at the well
Pressure recover/ at
injection well from
initial pressure
transient due to
ceasing injection
Pressure Transients
Any injection rate change in the test well or offset well creates a pressure
transient in the reservoir
Simplify the pressure transients in the reservoir
Do not shut-in two wells simultaneously
Do no change the rate in two wells simultaneously
e.g., shut-in test well and increase rate in offset well during the falloff test
Falloff Test Planning
General Planning
Successful welltests involve considerable pre-planning
Most problems encountered are within the operator's control and are avoidable
Allow adequate time in both injection and falloff periods
Injection at a constant rate during the injection period preceding the falloff
Reservoir Considerations
Reduce the wellbore damage, if necessary, with a stimulation prior to conducting
the test
Type of reservoir:
3
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Sandstone or carbonate (naturally fractured)
Single or multiple injection intervals
Operational Considerations
Injection well construction
wellbore diameters, changing dimensions
Type of completion
Perforated, screen and gravel packed, or open hole
Downhole condition of the well that may impact the gauge depth
e.g., wellbore fill, liner, junk in the hole
Wellhead configuration
Installation of the pressure gauge without shutting in the well
e.g., install a crown valve
Shut-in valve should be located near the wellhead
Minimizes the portion of the test dominated by wellbore hydraulics instead
of the reservoir
Surface Facility Constraints
Adequate injection fluid to maintain a constant injection rate prior to the
falloff
Availability of plant waste
Brine brought in from offsite: Location of storage frac tanks
Combination of both
Adequate waste storage for the duration of the falloff test
Tests are often ended prematurely because of waste storage issues
Offset Well Considerations
Locate any offset wells completed and operating in the same injection interval
Obtain a map with offset well distances relative to the injection well
Shut-in offset well prior to and during the test
Requires additional waste storage capabilities
Maintain a constant injection rate must be maintained both prior to and during
the falloff test if not shut-in (Same rate both before and during the test)
Confirm that diverting waste from the test well does not impact the offset well
rate
Recordkeeping
Maintain an accurate record of injection rates
Adequate rate metering system
Injection well - prior to shut-in
Offset wells - prior to and during the falloff test
Obtain viscosity measurements of the injectate fluid
Confirms the consistency of the waste injected
4
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Rule of Thumb:
ik .*
At a bare minimum, maintain injection rate data
equivalent to twice the length of the felloff
Instru
mentation
Pressure Gauges
Use two, one serving as a backup
The backup gauge does not have to be an identical type gauge
Pressure span of the gauge should not grossly exceed the expected test
pressures
Accuracy and resolution is usually based on a % of the full range of the gauge
Calibration
Ask to see the vendor calibration sheet
Types of Pressure Gauges
Mechanical downhole gauges
Amerada/Kuster: chart recorder with bourdon tube
Wind up clock is not reliable for long test periods
Typical resolution is approximately 0.05% of full range
Mechanical surface gauges
Surface chart recorders (cheap, but not better)
Bourdon tube
Can be difficult to read with any accuracy
Echometer
Pressure gauge
requires someone to take pressure readings
Electronic downhole
Quartz crystal
Torque capacitance
Panex/McAllister/Terratek/HP
Much better resolution, approximately 0.0002% of full range
Temperature compensated
Electronic surface
Spidr gauge
Internal data logging
Good for hostile environments
Plant transducer
Questionable resolution
5
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Pressure Gauge Selection
Surface readout (SRO) versus downhole memory gauges
SRO enables tracking of the downhole pressures in real time
More expensive than a memory gauge
Pressure gauge selection checklist
Surface gauge may be impacted by ambient temperature (sunrise to
sunset)
Wellbore configuration orwastestream may prevent the use of a
downhole gauge
Surface gauges are insufficient if the well goes on a vacuum
Pressure gauge must be able to measure the pressure changes at the
end of the test
Confirm the accuracy and resolution of the gauge is suffucient for
the pressure changes anticipated throughout the welltest
Ideally, the maximum test pressure should be at least 50% of the
gauge pressure limit
Typical electronic downhole pressure gauge limits:
2000/5000/10000 psi
Example: What pressure gauge is necessary to obtain a good falloff test for the
following well?
Operating surface pressure: 500 psia
Injection interval: 5000'
Specific gravity of injectate: 1.05
Past falloff tests have indicated a high permeability reservoir of 500 md
Injection well goes on a vacuum toward the end of the test
Expected rate of pressure change during the radial flow is 0.5 psi/hr
1. Calculate the flowing bottomhole pressure to pick a pressure gauge range:
500 psi + (0.433 psi/ftX1.05)(5000') = 2773 psi neglecting tubing friction
2. Select a pressure gauge type and range:
2000 psi gauge is too low
5000 psi and 10000 psi gauges may both work
Check resolution levels: Mechanical gauge: 0.05% of full range
Electronic gauge: 0.0002% of full range
Mechanical gauges:
5000(0.0005) = 2.5 10000(0.0005) = 5 psi
Electronic gauges:
5000(0.00002) = 0.01 10000(0.00002) = 0.02 psi
6
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
The mechanical gauges do no provide enough resolution for the 0.5 psi/hr
anticipated at the end of the test. Both the 5000 and 10000 psi electronic
gauges provide adequate resolution.
Select the 5000 psi electronic gauge so that more of the full range of the
pressure gauge is utilized during the test.
Falloff Test Design
Questions that must be addressed prior to conducting the test:
How long must the injection period last?
How long must the well remain shut-in?
Is there a need to look for a boundary or "x" distance in the reservoir?
The answer to these questions requires making some preliminary assumptions and
calculations. If appropriate software is available, it is good to simulate the falloff test
using the assumed parameters.
The ultimate objective of the falloff test is to reach radial flow during the injection and
falloff portions of the test. The radial flow portion of the test is the basis for all pressure
transient calculations.
For wells that have been injecting with no previous falloff data:
Review the historical well pressure and rate data from plant monitoring
equipment
Look for "pressure falloff" periods when the well was shut-in
This information may provide some information that can be used to design the
fallfoff test.
Wellbore Storage: The initial portion of the test when the pressure response at the
well is governed by wellbore hydraulics instead of the reservoir.
Radial Flow: Follows the wellbore storage and transition period. The pressure
response is only controlled by reservoir conditions during radial flow.
Transition Period: The time period between identifiable flow regimes.
It is necessary to calculate the time to reach radial flow during both the injectivity and
falloff periods.
7
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Test Design Calculations
Wellbore Storage Coefficient
To calculate the time to reach radial flow, first estimate the wellbore storage coefficient,
C in bbl/psi. There are two different equations to calculate C depending on whether the
well goes on a vacuum or maintains a positive pressure at the surface throughout the
duration of the test.
For a fluid filled well with positive pressure at the surface during the falloff test:
where, Vw is the total wellbore volume, bbls
cwaste is the injectate compressibility, psi"1
For a falling fluid level or well that goes on a vacuum during the falloff test:
C = ——— where, Vu is the wellbore volume per unit length, bbls/ft
p- s
144 -ge
is the injectate density, lb/ft3 or psi/ft
These empirically derived equations can be used with limitations:
If C is small, the well is connected with the reservoir within a short timeframe if
the skin factor is not excessively large
If C is large, a longer transition time is warranted for the well to display a
reservoir governed response
High skin prolongs wellbore storage
Some carbonate reservoirs contain vugs which cause larger C values
C can be minimized by downhole shut-in
Time to Reach Radial Flow
The equations used to calculate the time to reach radial flow, tradialflow, are different for
the injectivity and falloff portions of the test. The t^, flow can be approximated using the
following equations:
To calculate the time to reach radial flow for an injectivity test use:
(200000+12000s)- - ;—; — hours
k ¦ n
M
8
-------
Nuts and Bolts of Falloff Testing
To calculate the time to reach radial flow during the falloff test use:
March 5, 2003
tradialflow }
170000- C-e
0.14-(
k-h
M
hours
Note: Skin factor, s, influences the falloff more than the injection period
Example: What injection and falloff timeframes are necessary to reach radial flow
given the following injection well conditions? Assumption is that the well
maintains a positive wellhead pressure during the test.
Reservoir
h=120'
k=50 md
s=15
=0.5 cp
cw= 3e-6 psi"1
Wellbore
7" tubing (6.456" ID)
9 5/8" casing (8.921" ID)
Packer depth: 4000'
Top of the injection interval: 4300'
1. Calculate the wellbore volume, Vw:
Tubing volume+casing volume below the packer
K =
IT
^ 6.456V \ f8.921^a
K2-12J
(4000)+ it
U'12
(300)
1 bhl
\
5.615ft"
= 185.1 bbls
2. Calculate the wellbore storage coefficient, C
Fluid filled wellbore: C=VW cwaste
C =185.16fcb- 3x11^ =5.5x10-'^
psi psi
Note: Assume the
wellbore storage coefficient is the same for both the injection and falloff periods
C is small since the wellbore is fluid-filled
9
-------
Nuts and Bolts of Falloff Testing March 5, 2003
3. Calculate the minimum time to reach radial flow during the injection period
(200000+ 1200Ck)- C
Lradialfkrw > ; ; rtOtirS
SZ ¦ h
U
(200000+ 12000 -15)- 5.5x10"4
tra&t&flow > ^ ' =0.017 hours
0.5
Note: The test should not only reach radial flow, but also sustain a timeframe sufficient
for analysis of the radial flow period.
4. Calculate the minimum time to reach radial flow during the falloff period
170000- C• e°'14's
tradirilflmt > ; ; FlOtifS
k ¦ k
V
170000-5.5x10"4-e°14(15'
tradiaifUm > = 0.064 HOUFS
0.5
The time to radial flow is still short, but the falloff needed four times the time the
injection period needed to reach radial flow.
Use with caution! This equation tends to blowup in large permeability reservoirs or
wells with high skin factors
Test Design Criteria
Decide on test objectives
Completion evaluation
Need to reach radial flow to calculate the skin factor which
indicates the condition of the well
Determining the distance to a fault or boundary
Seeing "x" distance into the reservoir to confirm geology
Use the radius of investigation, rh to calculate time
Determine the type of test needed to produce analyzable results
Falloff, multi-rate, or interference test
10
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Simulate the test using estimated parameters
Sensitivity cases can evaluate the effects of varying reservoir parameters
Review earlier test data, if available
Data Needed to Analyze a Falloff Test
Time and pressure data
Surface and bottomhole pressure measurements can be used
Rate history prior to the falloff
Include rate history of offset injection or production wells if completed into
the same interval
Basic reservoir and fluid information
Wellbore and completion data
Wellbore radius, rw
Record sufficient pressure data to analyze
Consider recording pressures more frequently earlier in the test
More frequent data with an electronic gauge generally provides a better
quality derivative curve, by providing more points to average when
calculating the slope
Consider plotting data while the test is in progress to monitor the test
Net thickness, h (feet)
Obtain from well log, cross-sections, or flow profile surveys
Permeability, k (md)
Obtain from core data or previous well tests
Porosity, (fraction)
Obtain from well log or core data
Viscosity of reservoir fluid, f (cp)
Direct measurement or correlations
Total system compressibility, ct (psi1)
Correlations, core measurement, or welltest
Viscosity of reservoir fluid, w (cp)
Direct measurement or correlations
Specific gravity, s.g., of injectate
Direct measurement
Rate, q (bpd)
Direct measurement
Test Design Checklist
Wellbore construction: Prepare a wellbore schematic for completion depths,
well dimensions, obstructions, fill depth, injection
interval depths
Injection rate period: Constant rate if possible, minimum duration, injection
11
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
history, waste storage capacity, offset well rates
Falloff period: Time and pressure data, rate history, duration to radial flow,
offset well rates, waste storage capacity
Instrumentation: Resolution of the gauge, surface versus bottomhole gauge,
backup gauge, rate measurments
General reservoir and waste information: h, , ct, f, w
Area geology Boundaries, net thickness trends, type of formation
(sandstone or carbonate)
Pressure Transient Theory Overview
Pressure Transient (P-T) theory attempts to correlate well pressures and rates as a
function of time in terms of reservoir, fluid, and well completion parameters. P-T theory
is the basis for drawdowns, buildup, injectivity testing, interference or pulse tests,
falloffs, step-rate tests, multi-rate tests, drill stem tests, slug tests, inflow performance,
and decline curve analysis. P-T theory is used in petroleum engineering, groundwater
hydrology, solution mining, waste disposal, and geothermal projects.
P-T theory involves working the problem backwards:
From the measured pressure response, determine the reservoir parameters
Start at the wellbore and work out to the reservoir boundaries
Late time data is a pressure response from farther in the reservoir
Start with what you know:
Well and completion history
Geology
Test conditions
Pressure responses show dominant features called flow regimes
P-T Theory Applied to Falloff Tests
Falloff testing is part of P-T theory. Falloff tests are analyzed in terms of flow models
which are derived from basic concepts to obtain pressure-rate behavior as a function of
time. Flow models are analytical solutions to the flow equations or numerical
simulators.
The starting point is a partial differential equation (PDE) based on Darcy's Law and the
material balance equation. The PDE is solved for drawdown for a variety of boundary
conditions to calculate pressure or rate as a function of time and distance.
12
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
For non-steady state flow, the PDE is:
dP _ 1 8P_
dr2 r dr 0.000264 k dt
This equation assumes an infinite, homogeneous, isotropic reservoir with a slightly
compressible fluid and q, k, , , are independent of pressure, P.
These equations and assumptions provide a model for injection well behavior and an
analysis approach for the evaluation of reservoir parameters. The equations are only
applicable during the radial flow period of the falloff test.
To solve the PDE some equation constraints must be assumed both near and away
from the well to obtain a flow model. For a typical falloff analysis the following
constraints are assumed:
Inner (near the well constraints)
Wellbore has a finite well radius
Inject rate is constant prior to the falloff, at time t=0
Outer (out in the reservoir constraints)
Infinite-acting reservoir
Welltest reaches radial flow
Isotropic reservoir properties
Reservoir is at a uniform initial pressure, Pt
The exact solution to the PDE is in terms of cumbersome Bessel functions. Fortunately
an approximate solution based on the exponential integral, Ei function, gives almost
identical results. The solution using the Ei function is:
P = P. + 70.
k ¦ h
Bt
' - 948 -
2 \
c-r
t
k ¦ t
where,
Ei(-x) = - du
i u
Ei Function
Tabulated and easy to use
Valid until boundaries affect the data
Give the pressure in the reservoir as a function of both time and distance
from the well center
The Ei function can be simplified further with a logarighmic approximation which
13
-------
Nuts and Bolts of Falloff Testing
is the basis for all radial flow analyses:
March 5, 2003
El = ln( 1.731 ¦ x)
This approximation for the Ei
function leads us to our flow model for falloff test analysis to predict the pressure
buildup in the well using the PDE solution.
and
„ 141.2 q-Bw iu , s
P«f ~ P< = ^ " •(PD +
J txk
Ei
4 ' t,
In
where,
+0.809
^ D ~
0.0002637 k t
¦rz> =
f M ¦ c, ¦ rw
Note these equations use dimensionless variables, PD, tD, and rD
Example: Estimate the injection pressure of a well located in an infinite acting
reservoir with no skin (s=0). The well has injected 100 gpm for 2 days.
Other reservoir data are:
Pi = 2000 psi h = 50'
k = 200 md Bw = 1 rvb/stb
f = 0.6 cp ct = 6e-6 psi"1
= 30% rw = 0.4'
1. After converting to the appropriate units, calculate rD, tD, and PD:
Q =
flOOgaA
( bbl "
' 1440 trim"
v min
v42 gal j
v day J
= 3428.6bpd
£ = {2 days)
^24 hrs^
day
= 48 hrs
14
-------
Nuts and Bolts of Falloff Testing
Since we're calculating the pressure at the well, r = rw and r/rw = rD=1
0.0002637- k t
March 5, 2003
^ D ~
,2
0.0002637 (200 md)(4% hours)
(0.3)(.6cp)(6e-6 psi~l)(0.42 Jt2)
PD can be
tD = 14.65*10
looked up on the
following graph taken from Figure C.2 from SPE Monograph 5, AttD= 1.465x107
and rD=1,
PD= 8.5
tu/rl
rfc. J Dr3sTr.».T^r.' veil T> r/lclt lyitar. ir> v> iix» Ci^ncrul *» •
PD can also be calculated:
P,
D
¦In
14650000
+ 0.809
Pd=S.65
15
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
2. Now calculate the pressure increase at the well, Pwf:
' kxh [d
~ 2251 psi (a pressure increase of 251 psi)
The assumptions that the reservoir is infinite or the injection rate is constant are not
always valid. The solution to the PDE is linear so that Ei solutions can be added
together to account for boundaries and rate changes in the test well or offset well.
The boundaries are handled by representing them as virtual boundaries with the use of
fictitious "image" wells. Pressure contributions of the real injector and image wells are
summed together to account for the boundary.
Where, Pinjectionwell is
the pressure buildup at the injection well due to injection
Pimage weiiis the pressure buildup at the injection well due to the fault
Ptotal is the measured pressure buildup at the injection well
For a single boundary, each injector has an offset image well. In the case of multiple
boundaries, boundaries are treated similarly, but image well location determination and
number is more complex due to interactions of the boundaries and mirroring of the
image wells.
Injection Well
Image Well
Fault
16
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
If the injection rate in the test well or offset wells varies prior to the falloff, each rate
change can be accounted for using the PDE solution. Each rate causes a new
pressure response to be added to the previous response. Each rate change is
accounted for by using an image well at the same location as the injector with a time
delay and summing image well pressure contributions.
,r + ^Jmage well for each rate change with time lag
In dimensionless terms for any point in time, t, the equations results in the following:
141.2 ¦ M ^ ^ ^ ^ ^). [pn. (Jr _ t )+ s])
^totaI
¦: ¦ h
3-1
Superposition is the method of accounting for the effects of rate changes on a single
point in the reservoir from anywhere and anytime in the reservoir including at the point
itself using the PDE solution.
at
"es
P4
Oh
i—i
Ph
t_ Shut-ii
Pressure recovery
from q2 to SI
A
Pressure recovery
from q1 to q2
Pressure recovery
from q1 to SI
17
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
The "Kitchen Sink" solution to the PDE to account for all wells and potential boundaries
(image wells) in a reservoir, the pressure change at any point could be given by:
. " 70.6q(ji
p(x,y,t) = po + 2 ^Ei
j-i
kh
39.5^[(x-x.f +{y-y,J
kt
+ ^"f la fel - ll I"L/~ 395^C.[(J - Xi f + b'-yj
fiZf kh {
This is essentially what an analytical reservoir simulator does!
PDE Solution at the Injector
The PDE can give the pressure at any distance from the wellbore using dimensionless
variables. This is useful for area of review (AOR) calculations.
At the wellbore, rD=1 so:
Pwf = Pi
162.6 ¦ q ¦ B ¦ /i
k - h
log(f)+log
k
+ 3,23 +0.87s
Note: This equation leads to the use of the semilog plot
Semilog Plot
The semilog plot is only used during the radial flow portion of the test. By grouping the
slope and intercept terms together, the solution to the PDE can be written in the
following form, used to define a straight line, which is the basis for the semilog plot.
semilog plot and defined as:
m ¦ log (t) + Pj
1 hr
where, m is the slope of the
m = -
162.6- q ¦ B- /i
k ¦ h
18
-------
Nuts and Bolts of Falloff Testing
The semilog slope, m, can be determined from the semilog plot:
March 5, 2003
P
if tj/1, = 1 ~ (one log cycle),
then log (t./t,) = 1 and the
slope is P2-P,
lu
to
CD
CL
i°g(t,)
logy
0.01 0.1 1.0 10.0 100.0
Elapsed time, hrs
AP _ P2-t[
J °P Alog(Af) logfe)-logfe)
There are four different semilog plots typically used in pressure transient analysis:
Miller Dyes Hutchinson (MDH) Plot
Pressure vs log t
Horner Plot
Pressure vs log (tp+ t)/ t
Agarwal Time Plot
Pressure vs log equivalent time
Superposition Time Plot
Pressure vs log superposition time function
Pressure/rate vs log superposition time function
MDH Plot
Semilog plot of pressure versus log t, where t is the elapsed shut-in time of
the falloff period.
Applies to wells that have reached psuedo-steady state during injection.
Psuedo-steady state means the response from the well has encountered all the
boundaries around the well.
Only applicable to wells with very long injection periods at a constant rate.
Note: EPA Region 6 does not recommend the use of the MDH Plot.
19
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Horner Plot
Semilog plot of pressure versus log (tp+ t)/ t, where tp is the time of the injection
period preceding the falloff
Used only for a falloff preceded by a constant rate injection period.
Calculate the injection time, tp:
tp = Vp/q hours
where, Vp = injection volume since the last pressure stabilization
Vp is often calculated as the cumulative injection volume since
completion
Caution: Horner time can result in significant analysis errors if the injection rate
varies prior to the falloff
Aqarwal Time Plot
Semilog plot of pressure versus log equivalent time, te
Calculate equivalent time, te:
te = log ((tp t)/(tp+ t) where ^ is defined above for a Horner Plot
Similar to a Horner plot except the time function is scaled to make the falloff look
like the injectivity portion of the test. In the case with a short injection period and
long falloff period, the equivalent time function will compress the falloff time to
that of the injection period.
Superposition Time Function
Semilog plot of pressure or normalized pressure versus a superposition time
function
The superposition time function can be written several ways. Below is for a
drawdown or injectivity test:
Af
sp
Z
j'-i
log Af-Af
j-u
J
Used to account for rate variations. Pressure function can be modified for the
rate preceding the falloff by the following:
AP.
( p. - P )
sp
<2*
20
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Which Time Function is Correct?
The correct time function to use is dependent on the available information and
software.
If no rate history or cumulative injection total, use elapsed time on a MDH plot.
If there is not rate history other than a single rate and cumulative injection, use
Horner time on a Horner plot.
If the injection period is shorter than the falloff test and only a single rate is
available, use Agarwal equivalent time.
If you have a variable rate history use superposition when possible. As
alternative to superposition, use Agarwal equivalent time on the log-log plot to
identify radial flow. The semilog plot can be plotted in either Horner or Agarwal
time if radial flow is observed on the log-log plot.
Horner is a single rate superposition and may substitute for superposition if:
The rate prior to shut-in lasts twice as long as the previous rate and
The rate prior to shut-in lasts as long as the falloff period
Agarwal, Horner, or MDH plots can be generated in a spreadsheet, however, the
superposition time function is usually done with welltest software.
Rule of Thumb:
%
Use MDH time only for very long injection times
(not recommended)
Use Horner time when you lack rate history or
software capability to compute the superposition
function
Superposition is the preferred method if a rate
history is available
21
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Example of the same falloff test plotted using three semilog methods:
The test consisted of a 24 hour injection period followed by a 24 hour falloff.
Notice the invalid permeability and skin values calculated by the MDH plot.
r't aitiK hun«n|i>nn
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Two equivalent equations to calculate r, in feet are taken from SPE Monograph 1 (Eq
11.2) and Well Testing by Lee (Eq 1.47):
r,= 0.00105—= —
' 1 ct 1J 948|i p. ct
where, k = permeability, md
= viscosity, cp
ct = total system compressibility, psi"1
= porosity, fraction
t = time, hours (depends on the falloff and injection periods of
the test)
Wellbore Skin and Skin Factor
The skin factor, s, is included in the PDE. Wellbore skin is the measurement of
damage near the wellbore, i.e., completion condition. The skin factor is calculated from
the radial flow portion of the welltest using the following equation:
£ = 1.1513
Pits- Pwf
m
log
kt„
ctrw
+ 3.23
The slope of the semilog straight line, the injection pressure prior to shut-in, and the
pressure value of the extended semilog straight line at a t = 1 hr are used to calculate
the skin factor.
Note: The term tp/(tp+ t), where t=1 hr, appears in the log term and this term is
assumed to be 1. For short injection periods, e.g., drill stem tests, this term could be
significant.
The assumption that the skin exists as a thin sheath is not always valid for injection
wells. This is not a serious problem in the interpretation of the falloff test, but can
impact the calculation for correcting the reservoir injection pressure for skin effects.
Wellbore skin creates a pressure change immediately around the wellbore. The effect
may be a flow enhancement or impediment.
23
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Damaged
Zone "*
Pressure
wf
APs)lin= Pressure drop across skin
stiic
¦ w
Distance
Wellbore skin is rw quantified
by the skin factor:
+ positive value indicates a damaged completion. The magnitude is dictated by
the transmissibility of the formation
- negative value indicates a stimulated completion. Negative value results in a
larger effective wellbore and therefore a lower injection pressure
-4 to - 6 generally indicates a hydraulic fracture
-1 to -3 typical of an acid stimulation results in a sandstone reservoir.
Wellbore skin increases the time needed to reach radial flow in a falloff. Too high a
skin may require excessively long injection and falloff periods to establish radial flow.
The larger the skin, the mote the pressure drop is due to the skin
24
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
There are several causes or sources of skin damage. Some impediments may include
mud invasion and partial penetration, whereas an enhancement may come from an
acid or a frac job. The total skin calculated from the welltest may be a combination of
several skin components, for example:
Sty^. = S. + £ + S, + + S
t&tal a ]?p 5 jt# J7 €
where, sd is skin due to damage or stimulation
spp is skin due to partial penetration
ss is skin due to a slanted wellbore
spt is skin due to perforation turbulence
sft is skin due to formation turbulence
se is skin due to equipment upstream of pressure gauge
Effective Wellbore Radius
The calculation for the effective wellbore radius, rwa, ties in the skin factor. The rwa is
also referred to as the wellbore apparent radius.
rwa = rw e"s where, rw - wellbore radius, in
s - skin factor, dimensionless
Example: A 5.5" cased well had a skin of +5 prior to stimulation and -2 following the
acid job. What was the effective wellbore radius before and after stiumlation?
Before: rwa = (5.5 in)(e"5) = 0.037 in
After: rwa = (5.5 in)(e"("2)) = 40.6 in
A little bit of skin makes a big difference in the effective wellbore radius!
Skin Pressure Drop
The skin factor is converted to a pressure loss using the skin pressure drop equation.
Pskin = 0-868 m s
where, Pskin = pressure drop due to skin, psi
m = slope of the semilog plot, psi/cycle
s = skin factor, dimensionless
This equation quantifies what portion of the total pressure drop in a falloff test is due to
formation damage.
25
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Corrected Injection Pressure
The following equation is used to calculate the injection pressure with the skin effects
removed:
P = P. - AP
corrected " sfon
where, PCOrrected = adjusted bottomhol pressure, psi
Pinj = measured injection pressure prior to shut-in at t=0, psi
Pskin = pressure drop due to skin, psi
The corrected injection pressure, Pcorrected.is based on the pressure loss through the
formation only. This term is used for comparison to modeled pressures in a no
migration petition.
False Extrapolated Pressure versus Average Reservoir Pressure
False extrapolated pressure, P\ is the pressure obtained from the Horner or
superposition semilog time of 1 as illustrated from Figure 5.5 taken from SPE
Monograph 5.
For a new well in an infinite acting reservoir, P* represents the initial reservoir pressure.
Whereas for existing wells, P* must be adjusted to the average reservoir pressure, p.
This requires an assumption of reservoir size, shape, injection time, and well position
within the shape.
For long injection times, P* will differ significantly from p. P* to p conversions are based
on one well reservoirs with simple geometry or specific waterflood patterns.
26
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Rule of Thurnb:
EPA Region 6 does not recommend using P\ Use the
final measured shut-in pressure if the well reaches
radial flow for the cone of influence calculations.
Injection Efficiency
Injection efficiency calculation is identical to the flow efficiency equation:
This equation requires an estimation
of the average reservoir pressure, P.
Identifying Flow Regimes
To identify the radial flow portion of the test, the falloff data is first plotted on a master
diagnostic plot called the log-log plot. The log-log plot identifies the various stages and
flow regimes that can be present in a falloff test.
Key stages and flow regimes found on the log-log plot include wellbore storage, partial
penetration, radial flow, and boundary effects. Not all stages and flow regimes are
observed on every falloff test.
The critical flow regime is radial flow, from which all analysis calculations are
performed. Therefore identifying the radial flow portion of the test is necessary before
any reservoir parameters or well completion conditions can be determined.
Individual flow regimes have characteristic slopes and a sequencing order on the log-
log plot. These dominant features are a result of the pressure responses observed
during the welltest.
Log-log Plot
The log-log plot contains two curves:
Pressure curve
Plot of measured pressures from start of the test on the Y-axis versus the
appropriate time on the X-axis
27
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Derivative curve
Plot of the slope of the semilog pressure function on the Y-axis versus the
appropriate time function on the X-axis
Example log-log plot:
¦S
^ 100
24 hrs Inject 12 hrs St, Q=300 GPM
0.1
eiapseii Time (hours). Tp~2*.0
Pressure Curve
100DQ-
Derivative Curve
100D
Log-log Plot Pressure Functions
Rate variations in the test well prior to shut-in determine how pressure will be plotted on
the Y-axis.
Constant rate: Plot pressure
Variable rate: Normalize pressure (P/q term) using the rate data
Log-log Plot Time Functions
As with the semilog plot, injection rate variations prior to the falloff period dictate the
log-log plot time function. The time function is plotted on the X-axis
Elapsed Time, t
Use if the injection rate preceding the falloff is constant arid the injection
period preceding the falloff is significantly longer than the falloff period
Calculate as. t - tshut_jn - teach data point
28
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Agarwal Equivalent Time, te
Use if the injection period is short
Calculate as the following for each test point, t:
where, tp = Vp/q, hours
fp /sj Vp = injection volume since last
te = pressure equalization
tp + At Vp = often taken as the cumulative
injection volume since
completion
q = injection rate prior to shut-in
Superposition Time
Use if the injection rate varied prior to the falloff and rate history is
available
Calculate as the following for each test point, t:
2
/-i
in J
log
[At- At
j-1
Most rigorous time
function for the log-
log plot
Log-log Plot Derivative Function
The derivative function is graphed on the log-log plot with the pressure change trend
(slope). Its main use is to magnify small changes in pressure trends to identify flow
regimes, boundary effects, layering, or natural fractures. This methodology has been
popular since 1983 when an article by Bourdet was published in World Oil in May 1983.
The derivative for a specific flow regime is independent of the skin factor, while the
pressure is not.
The derivative essentially combines a semilog plot with a log-log plot. It calculates the
running slope of the MDH, Horner, equivalent time, or superposition time semilog plots.
Derivatives amplify reservoir signatures and noise so the use of a good pressure
recording device is critical.
Derivative curves are usually based on the semilog pressure plot, but it can be
calculated based on other plots such as the following. Some flow regimes are easily
identified when plotted with one of these time functions.
Cartesian plot
square root of time plot
1/square root of time
quarter root of time
29
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Example: Well in a channel - well observes linear flow after reaching the channel
boundaries
Li.11 L
¦ \ :
T i i
_j_ i
o
emi
log d
I77T"*t=t'
eriv
ative plot
H ¦
J ['
¦ : : :
s
m
—
U1'
Radial Flow
144
TT
Is
•-HT
*
-¦r
i/i
time
derivative
plo
t
L
m
inee
i j j | ;
*r Flow
Ml
DOM 00! D.1 I ID 100
DcpsW finw |tHWB|
The logarithmic derivative is defined by:
p, £[g] 4p]
.^[in(Af)] d[h£\
For an infinite acting reservoir with radial flow:
PD =0.5(In [tj + 0.80907 )
When dealing with dimensionless variables, the derivative is always 0.5
d\P„\
"SI"
P,B=tD-^= 0 5
For cases when a reservoir is in radial flow and infinite acting and dimensionless
variables are not used, the derivative will plot as a constant value which is graphically
depicted as a flat spot on the derivative curve.
30
-------
Nuts and Bolts of Falloff Testing March 5, 2003
At any t during the wellbore storage period, the pressure changes, P, and derivative,
P', are given by:
AP = M P-Ar.4^-Ar
24-C 4A7] 24 -C
taking logs of both sides of the pressure change equation:
log[AP] = log + log[Af]
The above equation plots on a
log-log plot as a slope of 1. This is known as the "unit slope" during wellbore storage.
Since the pressure derivative is described by the same equation during wellbore
storage, it overlays the pressure change trend with the same unit slope on the log-log
plot.
For linear flow:
PD - ¦ tL
therefore
log [p'D'] = log [0,5] + 0.5 ¦ log [x ] + 0.5iog [ij]
so a log-log plot will have a slope of 0.5 (half slope)
The derivative, P':
ST
^'=^'0.5'-ir = 0.5^OJ,4J
D
for tD =1.0, PD = 0.5 log[ ] = 0.248
log[pDJ=0.5-log[s-]+ 0.5-log[/D]
again we get a slope of 0.5, but the line is lower because when tg = 1,
log [P'] = -0.1
On the log-log plot, flow regimes are characterized by specific slopes and trends for the
pressure, P, and derivative, P', curves as well as specific separation between P and P'
curves.
Recent type curves make use of the derivative by matching both the pressure and
derivative curves simultaneously to get one match for the parameter evaluation.
31
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Specific Flow Regimes
Flow regimes are characterized by mathematical relationships between pressure, rate,
and time. They provide a visualization of what goes on. Flow regimes have readily
identifiable signatures on diagnostic log-log plots or specialized plots. A test can show
several flow regimes with "late time" responses correlating to distances farther from the
wellbore.
Examine the well completion history and wellbore fill to determine what flow regimes
may be present in and near the wellbore during the early time behavior.
Examine the reservoir geology, logs, etc., to determine late time behavior. Typical late
time flow regimes may include faults, layering, or natural fractures.
Wellbore Storage
Occurs during the early portion of the test. It is caused by the shut-in of the well being
located at the surface rather than the sandface resulting in afterflow as fluid continues
to fall down the well after it is shut-in. The location of the shut-in valve away from the
wellhead will also prolong the wellbore storage period.
The pressure responses governed by wellbore conditions, e.g., wellbore storage, are
not representative of reservoir behavior. Wellbore skin or low permeability reservoirs
results in a slower transfer of fluid from the well to the formation extending the duration
of the wellbore storage period.
A wellbore storage dominated test is unanalyzable.
Identifying characteristics:
Log-log plot: unit slope for both the pressure and derivative curves
Cartesian plot: straight line for the pressure curve
¦
Mv
L.
1i - ur
->j
4w
3ressu
curves
ine du
re and derivative
ov e rl ay o n a u n it s lo p e
ing wellbore storat
e
¦
32
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Linear Flow
Results from injection into a channel sand, a well being located between parallel faults,
or a well with a highly conductive fracture.
Identifying characteristics:
Log-log plot: half slope on both the pressure and derivative curves with the
derivative curve appoximately 1 /3 of a log cycle lower than the pressure curve
Square root time piot: straight iine for the pressure curve
Spherical Flow
Results from wellbore fill covering the injection interval or only a portion of a larger
injection interval is completed.
Identifying characteristics:
Log-log plot: negative half slope on the derivative curve
1/square root time plot: straight line for the pressure curve
Partial Penetration characterized
by a negative 1/2 slope line
Falloff Dominated fay Partial Penetration
Q.0O1
01
Equrralwl Time (hours)
33
-------
Well bore Storage Period
Semilog Pressure
Derivative Function
Radial
Flow
Transition period
Unit slope during
well bore storage
Derivative flattens
Nuts and Bolts of Falloff Testing
March 5, 2003
Radial Flow
The critical flow regime from which all analysis calculations are performed. This flow
regime is used to derive key reservoir parameters and completion conditions.
Identifying characteristics:
Log-log plot: flattening of the derivative curve
10DC0
01 t
Elsp&ed I I hours) - Tp=24J0
Semilog plot: straight line for the pressure curve
F;iill ftcowgraM
»¦)
¦f. rd
Mi xfi930I.J86l rd I
Pav ¦XXQ 3&K t
FE -11®
Ebpnd far* (twurcp
533
253 6IT
9
a
t
s
£
B. I??
34
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
In tests where the derivative did not reach a plateau (i.e. radial flow), a minimum
estimate for transmissibility can be obtained from either log-log plot derivative or
semilog plot slope. The transmissibility obtained at this point in the test is a minimum
because the derivative has not reached its minimum value. The derivative reaches its
minimum value at the radial flow plateau, resulting in a smaller slope value and,
consequently, a larger transmissibility.
The minimum vaiue for transmissibility is estimated as follows:
k h 162.6 q-B
f1
where m is determined from drawing a straight line at the end of the semilog plot or by
taking the antilog of the derivative value at the test end as follows:
m — 1 ft fteste xa
test end -iU
Well Dominated by Spherical Flow =
(—)-
"1
Ar
—te;
v-
>
s
j--
szFt
\
V
¦
v--
V
•
l_i—
—
J :
—
=
—
:
V
S3
—L
_L
,-J L—
¦H'
?
V
~
i i
3Gi
301
Time on a Log1D scale
i ne vaiue tor permeamiuy
is derived from this
maximum slope estimate
of the derivative curve
35
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Hvdraulicallv Fractured Well
Typical flow regimes arid identifying characteristics:
Wellbore storage
log-log plot - unit slope of both derivative and pressure curves
Fracture linear flow
Usually hidden by wellbore storage
Bilinear flow
Result of simultaneous iinear flows in the fracture and from the formation
into the fracture
Log-log plot - quarter slope on the derivative curve
Quarter root plot - straight line for the pressure curve
Formation linear flow
Linear flow from formation into fractures
Log-log plot - half slope on both the pressure and derivative curves
Square root time plot - straight line for pressure curve
Psuedo-radial flow
Log-log plot - horizontal line (flattening) of derivative
Log-log plot type curve - dervative will fall about a dimensionless
derivative value of 0.5
Semilog plot: straight line for pressure curve
Semilog plot valid for determining reservoir parameters and fracture
characteristics
Hydraulic Fracture Type Curve Responses:
36
-------
Nuts and Bolts of Falloff Testing
Example from a fractured injection well
March 5, 2003
Half slope on
both curves -
—r"
In
ie
arflow
*
Derivative
drop due to
constant
pressure
•
Cuidc Ntfrh
nUh
,--r
- ririt raiijrtvi*
Irisifiy arts;
rrn?i»;.;j3 fcy
K. -6
mtf
ft -0
» - iW ft
p. -itt>PTC? pm
I
a.
~S
3
t to
cgul.tferr: Tims (hours) - Tf=M£.0
Naturally Fractured Rock
Fracture system will be observed first on the falloff followed by the total system
comprised of the fracture and tight matrix rock.
Analysis is complex. The derivative trough indicates the level of communication
between the fracture and matrix rock.
37
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Layered Reservoir
Analysis of a layered reservoir is complex because different boundaries may exist for
each layer. The falloff objective for UIC purposes is to get a total transmissibility from
the whole reservoir system.
V\
Cross flow
Homogeneous behavior of
the higher permeability layer
Laye re d S yste m w ith C ro 5 sfI ow
PRESSURE RESPONSE Of- LAYERED SYSTEM
WITH FORMATION CROS5FLOW
|-
2
1 CL
s ¦
1 1
: I . 1
*+s
a—r-«r,
— .
(i.
D
TrrjinrlCTj lime
¦
6, In a layered reservoir, horncgcriMXJS bwhavlor is exhibited
during two pHjri
-------
Nuts and Bolts of Falloff Testing
Typical Derivative Flow Regime Patterns
Flow Regime Derivative Pattern
Wellbore storage Unit slope
Radial flow Flat plateau
Linear flow Half slope
Bilinear flow Quarter slope
Partial penetration Negative half slope
Layering Derivative trough
Dual porosity Derivative trough
Boundaries Upswing followed by plateau
Constant pressure Sharp derivative plunge
Log P
Wellbore
Storage LofJ p
Log t
Radial
Flow
Log P
Log P'
P"= dP/d(logt)
P1
Log t
. _ 162.6 q ¦ B- /i
¦- k ~ :
\
N ^ . slope =
m
Log t
Linear
Flow
Log P
Log P1
Logt
8.128 q-B
h-m'-L
slope = m"
4i
P' = dP/d(logt)
39
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Example: Partial Penetrating Well
Partial interval perforated in a block sand injection interval. Can predicted the
pressure response based on the completion and injection interval thickness.
Elevation
/f
* *
t
Plan
Very early time:
Radial Flow
Usually hidden by
wellbore storage
Early time:
Spherical Flow
Top of Injec
ion Interval
\
— =1 =
—
\
* +
¦>
Bottom of Injection Interval
Elevation
^ A K
/t T K
t
Plan
Late Time: Radial Flow
Top of Injection Interval
1
!
I
I
^ I /
-> ¦*
Bottom of Injection Interval
Elevation
* A K
71 T \
7T A *\
Plan
40
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Falloff Test Evaluation Procedure
Data acquisition
Well information from well schematic
well radius, rw
type of completion
Get reservoir and injectate fluid parameters
porosity,
total system compressibility, ct
viscosity, f and w
Estimate reservoir thickness, h
- use flow p rofile su rveys
well log or cross-section
Obtain rate histories
test well prior to the test
offset wells prior to and during the test
Time sync injection rate data with pressure data
Prepare a Cartesian plot of pressure and temperature versus time
Confirm stabilization of the pressure prior to shut-in
Look for anomalous data
missing data
pressure rise or jump in data
fluctuations in temperature that may impact pressure
Prepare a log-log plot of the pressure and the derivative
Use appropriate time scale
Identify the radial flow period - flattening of derivative curve
If there is no radial flow period, try type curve matching
Make a semilog plot
Use the appropriate time function
Draw a straight line through the points located within the equivalent time
interval where radial flow is indicated on the log-log plot
Determine the slope, m, and P1hrfrom the semilog straight line
Calculate reservoir and completion parameters
transmissibility, kh/
skin factor, s
radius of investigation, rh based on the Agarwal equivalent time, %
Check results using type curves (optional)
41
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Example Gulf Coast Falloff Test
Well parameters:
rw = 0.4 ft
cased hole perforated completion
6020'-6040'
6055'-6150'
6196'-6220'
Depth to fill-6121'
Gauge depth - 6100' (Panex2525 SRO)
Reservoir parameters
h = 200'
= .28
ct = 5.7 e-6 psi"1
f = 0.6 cp
42
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
cu
¦0 G
OS
, &
0/
ry<$P,4?
<^Z
! o.oai
oooqi
MiiiIhI (IpxiiIIk
R»aji»l homogeneous
Hrfidy »cli«j
C& " Q.Q212 bbVps
Cd - 366.6619
K - 780 011 md
fch -156162.1975 mdt
S - 522368
DC01
D 01
Example: Log-Log Plot
J 1_L_1 ! 1_1 1_1
Log-log Plot
* ¦ .
- "
0,1 1
EcMvafenl Time (fours)
Radial flow
ICO 1DG0 SO0DD
Stperposibon Time Function
10CQDD
43
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Example Gulf Coast Well Falloff Test Results:
k = 780 md
s = 52
m = -10.21 psi/cycle
P1hr = 2861.7 psi
P* = 2831 psi
Simulated test results:
Example: Log-Log Plot
T
1
« y
S
Simulated test results
'
V
i
A
%
l i
«
.
N
/
\
/
/
*1
/
Spherical flow
: - Vi slope
b
/
r^-~
. .
1
r
\
*
\
w.
- _ .
J
II
¦ '-l i o
D 001 001 0.1 1 It 100
Equiva'eril Time (rnurs)
Type Curves
Type curves are graphs of dimensionless variables, PD vs tD for various solutions to the
pressure transient PDE that provide a "picture" of what a solution to the PDE looks like
for a certain set of boundary conditions. The curves can be determined from either
analytical or numerical solutions and cover a wide range of parameter combinations.
Type curves may work even when specialized plots do not readily identify flow regimes.
The process of applying the curves to field data is called type curve matching. It
involves overlaying existing or simulated data to obtain a best fit or match. The
reservoir parameters used to generate the matched curve can be applied to the field
data. Type curves are generally based on the drawdown or injectivity tests and may
require plotting the test data with specialized time functions to use correctly.
44
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Homogeneous Reservoir Type Curves
Hydraulic Fracture Type Curves
Notice the hydraulic fracture type curves do not much of a unique shape as the
homogeneous reservoir type curves. Software is now available that can provide a type
curve, i.e., simulate, a given set of parameters and boundary conditions. The software
can also account for rate fluctuations.
45
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Key Falloff Variables
1. Length of injection time
2. Injection rate
3. Length of shut-in time
4. Weilbore storage and skin factor
1. Effects on the Length of the Injection Time
The length of injection period controls the radius of investigation of the falloff test since
the falloff is a "replay" of the preceding injection period. Since the falloff cannot see any
further out into the reservoir than the injection period, the injection period should last
long enough to establish radial flow prior to shutting in the well.
The injection time may need to be increased if the intent of the test is to observe the
presence of faults or boundary effects or lack thereof. In this instance it is suggested to
calculate the time needed to reach a certain distance away from the injection well
during the planning portion of the test.
The following three plots indicate the results of simulated injection and falloff periods
that were conducted using the same reservoir properties. These tests are for the
injectivity portion of the test with varying injection times.
,™ I
A hnuri ir
| [ [ ||
liprtinn
L.o-U
QT "
.1 Huuia
;
ur ll Irullil
;;;
T|
*
m,
TFF
D
o
5S not reach
A
_T|
i :
1 1
f | 1
* \
1
IK
rad
m
al flow
/
-III llllll
Luif l_
H
Id
Mil
n
ur* or
r
1
8 hours
1
injecl
ion
—
: : \
Bar
rari
mi
i ii
ely reaches
al flow
m
^ :
4
l=t
i
"
4
1
.1:
Ill Mllll
24 hours injection
fciCj
•a
if- •
or
t
E
1
f
" "I
ll
. i
1:\-
1
SB
V
VVB
radi
1 UCVCI
al flow
1 i
46
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
The following plots indicate the results of simulated injection and falloff periods that
were conducted using the same reservoir properties. These three log-log plots are for
the 8 hour falloff portion of the test following varying length injection periods.
IK 1 1 1 1
i 3
35
oil-Los r«
injection
•+ nuurs
8 hours
Ul II lj
shut-
fciL
in
uun
i •
-
:
-4J
Tt
1 L_
J.
EEF
III
8 hours
8 hours
of ir
shu
ljei
t-ir
:tio
n
-r-
-------
Nuts and Bolts of Falloff Testing March 5, 2003
The following plots indicate the results of simulated injection and falloff periods that
were conducted using the same reservoir properties. These plots illustrate that
increasing the injection rate does not make a change on the log-log plot, however the
resulting slope of the semilog straight line is greatly impacted by the injection rate. The
greater the slope, the easier the pressure change is to measure and is less dependent
on the resolution of the pressure gauge.
U
ixnr» » u«*oafTM
BOg
pm
L—Li i r:i
Log-log plots
look similar
t-i v v»*«
m=17.2 psi/cycle
Summary of the effects of the injection rate:
Injection rate impacts the amount of pressure buildup during the injection period
A higher injection rate results in:
A higher injection pressure and greater total falloff pressure change
A larger slope of the semilog straight line during radial flow
An increased semilog slope enables a more reliable measurement of radial flow
48
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
3. Effects of the Length of the Shut-in Time
Too short of a shut-in time prevents the falloff from reaching radial flow making it
unanalyzable. A shut-in time exceeding the injection period length is compressed when
plotted with the proper time function on the log-log plot.
Falloff test data should be plotted on the log-log and semilog plots using the appropriate
time functions to account for the effects of the injection period which were discussed
earlier. Increase the falloff time to observe the presence of faults and boundary effects
if the preceding injection period was long enough to encounter them.
The following log-log plots indicate the effects of the length of the falloff period for
identical injection and reservoir conditions:
a..
Well developed
radial flow
n
c
r
e
a
s
n
g
m
e
Summary of the effects of the shut-in time:
Too short of a shut-in time may result in the test not reaching radial flow
Shut-in time may be dictated by the preceding injection time since the falloff is a
replay of the injection period
Wellbore storage, positive skin factor, and the need to observe a boundary
condition may increase the required shut-in time for a test
49
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
4. Effects of Wellborn Storage and Skin Factor
A positive skin factor indicates a damaged completion and increases the time needed
to reach radial flow in a welltest. A negative skin is indicative of a stimulated completion
and reduced the time to reach radial flow.
A large wellbore storage coefficient may be caused by a well going on a vacuum,
formation vugs, the presence of fractures, or a large wellbore volume. A large wellbore
storage coefficient increases the time needed for a test to reach radial flow.
The following log-log plots compare the effects of increasing skin on identical injectivity
and falloff conditions:
—
-1—1 1
Well developed
radial flow
«=n
=
z
:
=
i
>
a
s
i
n
g
—
—
-
n-r
• <=l
'IT
• j
—w
-
-fc
llll 1
ei«
S:
=250
in
li Mir
rac
li r
lia
ri£
If
ll
low
Summary of the effects of wellbore skin:
The larger the skin factor, the longer the wellbore storage period and time it
takes for the falloff test to reach radial flow.
The derivative hump size increases with the skin factor
A wellbore storage dominated test is unanalyzable
50
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Boundary Effects
Falloff tests can provide information concerning the number of boundaries, shape of the
boundaries, and the position of the well relative to the boundary. A composite reservoir
can give a similar test response signature to a conventional boundary. The area
geology should always be checked to see if a sealing boundary is feasible or if a net
thickness change may be present.
The type of injectate may also impact the test. A mobility change may be observed if a
viscous waste is injected, whereas a composite reservoir may exist in the case of an
acid waste stream being injected into a carbonate formation.
To see a boundary, both the injection and falloff periods must last long enough to
encounter it. Most pressure transients are too short to see boundaries. Additional
falloff time is required to observe a fully developed boundary on the test past the time
needed to just reach the boundary.
If radial flow develops before the boundary effects are observed, the distance to the
boundary can be calculated. Additionally, when planning the falloff test, the time to
reach a boundary can be calculated from the radius of investigation equation:
948 ¦ (j> ¦ fi ¦ ct L
f boundary
^ boundary
where, Lboundary = distance to the boundary, feet
^boundary = time, hours
Rule of Thumb:
Allow at least five time the time to reach the boundary
to see it fully developed on a log-log plot
The shape of the derivative response on the log-log plot can indicate shape will double
for each sealing boundary observed. The derivative response is is a result of the
doubling of the slope of the semilog straight line. However, this slope change is easier
to identify on the derivative curve on the log-log plot.
A single sealing fault causes the semilog slope to double while 2 perpendicular faults
cause the slope to quadruple if fully developed.
51
-------
Nuts and Bolts of Falloff Testing
Log-log plot derivative patterns from sealing fault boundaries:
March 5, 2003
Type &jjve PkG
3f adts in
U shape
£ parallel faults
2 perpend cular faults
The log-log plot derivative patterns resulting from boundary effects from a composite
reservoir can be similar to the sealing fault cases.
CKMpmfii Itwnda "yp Can PM
"rtpnia Irritiw Tyn Cm r Plot
/
Mobility increase away
f ro m t he wel I
Mobility decrease
a way f ro nn th e wei I
The geology must be checked to confirm what type of boundary may be reasonable for
a site.
Summary of boundary effects:
Use the log-log plot as a "master test picture" to see the response patterns
Look for changes in pressure and pressure derivative curves to identify boundary
effects
Inner boundary conditions such as wellbore storage, partial penetration, and
hydraulic fractures are typically observed first
Hopefully outer boundary effects show up after radial flow occurs so that the
distance to the boundary can be calculated
52
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Example: A falloff test is conducted in a well located near two perpendicular faults
Fault 1
Fault Distances:
1000'
-------
Nuts and Bolts of Falloff Testing
The type curve analysis of the falloff test:
March 5, 2003
F
alloff Near Fit fllk Crnr type Crv Match
M
¥
4
J—
j
L
=W
W-*—
—.
TTl
Httt
\
k= 507 md
s= 10
2 faults @ 90" angle
Boundary Distances:
1955'& 995'
¦¦
jff
/
/
t
11
rn—
5ff
i —
¦
|L
|
JJ
ffh-
a«i
•li
0 l
i
10
>00
TftW i.tuS I - Tp-"100M 0
The slope changes are also observed on the semilog plot:
m2 indicates more than 1 boundary
54
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Typical Outer Boundary Patterns
Infinite acting
no outer boundary is observed
only radial flow is observed on the log-log plot
Composite reservoir
change in transmissibility, kh/ , or mobility, k/
derivative can swing up or down depending on the mobilitiy change and
replateau
Constant pressure boundary
derivative plunges sharply
Sealing boundary
derivative upswing followed by a plateau
multiple boundaries cause variations in shape and degree of the upswing
Pseudosteady-state
all boundaries around the well are reached - injection well is in a closed
reservoir
derivative swings up to a unit slope
Gallery of Falloff Log-log Plots
Radial flow with single fault boundary effects:
Falloff with Boundary Effects
5'
a
CD
a
n 0.01
%
Transition to
radial flow
/
2r:
a
a
P
ii Dm
0.0001
Radial flow period
Boundary
effects
¦ ¦¦¦ ipi Pre:sue
II 001
o 01
01
elapsed Time lliojis)
55
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Hydraulically fractured well with surface gauge showing constant pressure at test end:
Surface Pressure - Hyd. Fracture
•
--
H
aff
jrv
si ope on both
es —linear flow
!-
T---'
r-
> -
a
1*^1
\
[
t
lem
D OC
¦^i
nsi
ve
<=rri
dp.
p
:.p due
ressure
+
One* Mffch
VfVll*?
• iii-iii- coriljitMlj
Viiir:;l ftaclur
>
icing
i.Cmilirt COiipi-i-lftKc
K =B
nd
f
09 pii
£J • 0
>J =«C
Pi -
I 10
E<3W'3srt Time (twur;S-TF=l44.Ii
Composite reservoir
Surface Pressure Falloff -Composite Zone
£
-1-
D
irf'.
! Cr«J welter* tfcilft
;2 Be$r trn fatiaJto*
rr+r til*l ft**
i O-JW i*W!
C-Jiufc Miltli Rwjlb
Rattf cinjiuo
W"(tfWS
C» - 1 E-I0.-0Q4
bb.'aii
K - 138? 23
rrd
5 = ITCW2
LfJl -Tfll 0W
n
m - o 5379
w - D E£
P. = 55 92*
fr-i
Eijuwfltert Time ihours)
56
-------
Nuts and Bolts of Falloff Testing
Skin damaged completion
March 5, 2003
Falloff wrt h Sfcin Damage Log-Lay Pl&l
k = 4265 md
s =392
Ric&V "nnjtmiwr
ktrlfif »nst
K - C$5 0938 mJ
fch » ?£77t£i 675 rrd I
5 " 35? tW)
aaoi
oai o.i
Ect-r.»!fcri Tima |t>:cr;'i - Tp=1G B3U.
Negative skin
Fafloff with Negative Skin
n
,3
T
I
a&id«i fttiuh
»J tamoj • 31EUJ.
lifinlal-f
K = 99.4532 r
Ml = 994&.3I93
s - I m
k = 99 md
s = -1
Radial F
:
ow
DI I
Efltfvfilert Tirr£ (ftJttfBl - Tp=240Q 0
57
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Spherical flow
—4-
-
—L
—
.
v-
\
i
F
Partial Penetra
haracterized b
leqative 1/2 sl<
tion
>y a
5pe line
Sl
1
c
r
L
-
*' ¦..
i
¦
'•
-
i
sw
!
;
"=
t.
*
Equr.sfenl TimeIncurs)- Ip=12.0l1
Simulated test in pseudosteady-state
58
-------
Nuts and Bolts of Falloff Testing
Other Types of Pressure Transient Tests
March 5, 2003
Iniectivitv test
Following a stabilization period, an injectivity test involves recording the pressure and
time data from the start of an injection period.
Pros:
Well does not have to be shut-in
Usually maintain surface pressure so less wellbore storage
Less impact from skin
Cons:
Data is usually noisy due to fluid velocity by the pressure gauge
Rates may fluctuate during the test so an accurate rate history is important
Multi-rate injection test
Involves recording the pressure and time data through at least two constant injection
periods. The first injection period should reach radial flow prior to changing the rate.
The injection rate may be increased or decreased, but the rate change should be
significant enough to produce a pressure change at the injection well.
Pros:
Rate can be increased or decreased and the injection well does not have to be
shut-in
Minimizes wellbore storage, especially with a rate increase
Provides two sets of time, pressure, and rate data for analysis
Decreasing the rate provides a signal falloff without shutting in the well
Cons:
Noisy data due to fluid velocity by the pressure gauge
First rate period needs to reach radial flow
Interference test
Involves the use of two wells, a signal and observer well. The signal well undergoes a
rate change which causes a pressure change at the observer well. This pressure
change at the observer well is measured over time and then analyzed using an Ei type
curve. If radial flow is reached, a semilog plot can be used
Pros:
Test can yield the transmissibility and a porosity-compressibility product of the
reservoir between the wells tested
May give analyzable results when a falloff doesn't work
59
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Cons:
Generally involves a small pressure change so accurate an surface or
bottomhole gauge is needed
Observable pressure change decreases as the distance between the two wells
increases
The analysis is complex if more than two injectors are active
The test rate should be constant at the signal well.
Pulse test
Similar to an interference test except the rate changes at the observer well are repeated
several times
Pros:
Test results in multiple data sets to analyze
Verifies the communication between wells
Cons:
Difficult to analyze using SPE Monograph 5 methodology without welltest
software
Requires careful control of the signal well rate
Interference Test Design
The best design approach for both an interference test and pulse testis to use a
welltest simulator. Interference tests can be designed using the Ei type curve.
Test design information needed:
Distance between the signal and observer wells
Desired pressure change to measure - may be pressure gauge dependent
Desired injection rate
Estimates of q, , , k, h, rw
Example: Interference test design
Two injection wells are located 500' apart (r=500'). Both wells have been shut-in for a
month so previous injection is not a factor. An interference test is planned with an
injection rate, q, of 87.5 gpm (3000 bpd). How long will the test need to be run to see a
3 psi pressure change at the observer well assuming no skin?
60
-------
Nuts and Bolts of Falloff Testing March 5, 2003
The estimated reservoir parameters are:
k = 50 md h = 100' =20%
f = 1 cp ct=6x10"6 rw = 0.3 ft
Calculate PD arid rD;
A P k h r
F'd = 141.2 q ¦ ji rD=Vv
The resulting values for PD and rD for a 3 psi pressure change:
PD = 0.0354 and rD = 1666.7
Find tD/rD2 from the corresponding PD value on the Ei type curve located in Figure C.2 in
SPE Monograph 5: yrD2 = 0.15
Solve for tD: tD = 416683
Then solve for t=tlnterference by substituting for tD:
0.0002637 k-t
^ D ~ 2
>t> ¦ c, -rw
tinterference = 3-4 hOUrS
Ei Type Curve: from Figure C.2 in SPE Monograph §
61
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Example: Interference test analysis
An interference test was conducted between two injection wells located at a Gulf Coast
area facility. The two wells are 150' apart.
reservoir conditions: h = 55', = 28%, ct = 6x10"6 psi"1
Well data: rw = 0.25 ft, q = -120 gpm
Prepare a log-log plot of the measured pressure data at the observer well:
Interference Test Log-Log Plot
5
3
X
/
/
X
jf
Radial flow
/
/
/
/
/
/
MdilCl I!. .. "i.
R^Jiil hmiL^bUk-OLri
tli'n ly wi I vi l|
Ck ¦> 10 24H bti'pti
Cd - I
0.1
Elapsed Tirr* ihoursl
Type curve match the pressure data using the Ei type curve:
Type Cunre Plot
hfatch Results
k= 4225 md
(pAf= 4.015x1 tH1 psi1
a xil 3 DI
bL^iw-i Tin* i>wii|
The type curve match results in a permeability and porosity-compressibility product.
62
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Falloff Test Impact on an Area of Review Evaluation
The transmissibility obtained from the falloff test arid the solution from the PDE can be
used to project the pressure increase due to injection at the injection well or a distance
away from the well. The PDE solution can also be used to estimate the cone of
influence location. Both the pressure buildup projection and cone of influence location
estimates can be set up in a spreadsheet.
Example Pressure Buildup Projection Spreadsheet:
rpi RraTBtn
FS.ait1:
H ilrlia re iv. prei ins n pla f
lifltj
furott1;:
dllifil):
'JlOOlt,'
Of "tit" USDA'tQB (ttj
~ptl 11" GramvHte r (ttj
fansr'rtrlLJd 93:
FJTi atenl ',wl i^m r f In j
Ui ± cicolntr'fll fit):
CDQiUslcn
Fdtrr
IfcC&l
l4ecCbk
DUttBla feH
Cittd
CtT£l£blk&
DiTpeifbifcsT&fcl Piesifi kcna«
CO I
III. FSfe
H.F&fe
*
Tire
Tine
P nasi re
PfiKire
FHhf
dlfcctti Wfel
Fans
m
«
"Jr#
P'r^i
£*>
0)
1H429
3]
Zl
«S»
5
14143
O.ffl
35*223
3S63LS
loceas?
irus
II
a]
E
32034&«i
14143
O.ffl
4732274
747. tZ
14B&B2
1 rus
3]
a]
13«J»
15
4B125&C6
14143
o.a
sres&29
ysas
17337.49
1H4B
3]
a]
irawi
a:
&41ff&i*
14143
O.ffl
SG5Q44G
E101
20ff7.S4
iru»
a
a]
2SB00
3]
&.ffl51&i»
14143
O.ffl
8«iS9
ZEij.iC
24E 9.62
E«3rrpfe
tan
a
02
CL3
oIDEOS
1 jn
3D
B
1DiO
yJHl
533
3ID
Glial Rhiili* QioJaloni
Cittapmsi e rfc-tfte TlidtcftHfe (w):
cuapKiifirte -mKfflfed toiekcfe p-ty:
CtttapBsi k rte tBfr ^rtrmidcfbitfo:
141«
33234
tche
J 6 66 6. 66
J- £ 66 6. 66
j- 6 66 6. 66
I >66 6.66
I 6 66 6.66
£666.66
6.6 6
C O I vt. In I* t dan Tin
I n | *¦ i. d a n Tin i y rt
¦ i #rl*d i
63
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Determination of Fracture Pressure
Fracture pressure usually varies with depth, lithology, and geographical region.
Specifically, fracture pressure increases with depth because the compaction of the
formation tends to increase with depth and requires higher pressures to initiate a
fracture. The rock type and composition are also important factors in determining how
brittle the rock is and ultimately the pressure necessary to part or fracture the rock.
The fracture gradient is typically estimated from correlations, (e.g. Hubbert and Willis,
Eaton). Another method of determining fracture pressures is from a step-rate test.
Step-Rate Test
A step-rate test consists of a series of pressure transient tests caused by rate increases
at the injection well. Each rate change creates a pressure transient in the reservoir.
Data is analyzed using log-log and linear plots. The linear plot is used to estimate
fracture pressure, also called the formation parting pressure. The log-log plot is used to
verify that fracturing occurs and to estimate kh/u and skin.
Ideally, the sequence of events for a step-rate test consists of a series of constant rate
injection over an equal time duration and the length of each step is of sufficient duration
to reach radial flow. Practically, each rate is not maintained long enough to reach radial
flow. In fact, maintaining a constant injection rate at each step is itself a challenge
since the reservoir pressure and therefore the injection pressure typically increases with
the increase in rate and duration of the test. Pump trucks are often used to conduct the
step-rate test. As a result, injection volumes maybe limited and maintaining a constant
rate as injection pressures increase is difficult. Preplanning is important so that an
adequate injection volume is available and constant rates can be maintained.
Elapsed test tim e, t (hrs)
64
-------
Nuts and Bolts of Falloff Testing March 5, 2003
Each step increase of the injection rate will result in a corresponding change in
pressure behavior.
Both log-log and linear plots are used to analyze the step-rate test. The log-log plot can
verify that fracturing occurs by observing a half slope on both the pressure and
derivative curves. The log-log plot can also identify if radial flow is observed during a
time step, t, by observing a flattening of the derivative curve. The radial flow portion
of the test can then be analyzed to obtain the transmissibility, kh/ product, and skin
factor.
The linear plot is typically the plot associated with step rate tests. This plot is used to
estimate the fracture pressure or formation parting pressure. This pressure is
estimated at the intersection of two lines drawn through the final injection pressure at
each time step. If a slope change is not observed, the step-rate test was either initiated
above the fracture pressure, or the rate increases did not result in the fracturing of the
formation. If the test is initiated above the fracture pressure, the log-log plot should
show indications of a fracture.
For the linear plot, the injection pressure at the end of each injection rate is plotted on
the y-axis at the corresponding injection rate located on the x-axis. For this pressure
versus rate plot to be of use, the data obtained should not be dominated by wellbore
storage, identified by a unit slope on a log-log plot or a concave upward curve on the
pressure versus rate plot.
65
-------
Nuts and Bolts of Falloff Testing
Linear plot example with fracture observed:
March 5, 2003
Injection rate (bpd)
Linear plot example with no fracture observed:
1200 n
~ 1000
a.
vt
8
o
Z
aj
800
600
400
£ 200
Step Rate Test Linear Plot
~ wellhead pressure
0 2000 4000 6000 80 00 1 0 000 12000
Inj e ctio n R ate (bpd)
66
-------
Nuts and Bolts of Falloff Testing March 5,
Here is an example of a combination of step rate tests and falloff tests conducted in
injection well.
StepRate Sepnert 1 -12thalep Log-fag
Noisy derivative, but suggests radial
flow trend - no fracture signature
16-3DE-
Below is the log-log plot for the 12th step of the first series of step rate tests:
DJCXICII
Equfciatert Urns I Iran)
67
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Other Uses of Injection Rates and Pressures
Though step-rate testing is the principal method used for calculating the reservoir
fracture pressure and establishing a maximum injection rate, there are other methods
for evaluating the condition of an injection well. One method was developed by Hall in
1963 and a second method was published by Hearn in 1983. Both the Hall and Hearn
methods require injection rate and wellhead injection pressure data. This information
should be readily available for Class I wells since continuous monitoring is a regulatory
requirement.
The Hall method involves plotting the cumulative change in bottom hole pressure times
the change in time ( P* t) versus the cumulative injection volume in barrels. The
Hearn method involves a semilog plot of the inverse injectivity index, i.e., change in
pressure divided by the injection rate ( P/q), versus the cumulative injection volume
plotted on a logarithmic axis in 1000 barrel units. As with the step-rate test, these plots
identify well conditions and fracturing of the formation by slope changes on the plot.
Both the Hall and Hearn plots assume piston-like displacement of fluid, steady-state,
radial single phase, single-layer flow. The Hearn plot is applicable to a Class II injection
well prior to reservoir fill-up. The Hall plot is used after fill-up and is best suited for
Class I injection well projects or Class III wells in mature water injection projects. The
pressure at the external drainage radius, Pe must be estimated in the calculations for
both plots. The initial reservoir pressure should be a reasonable approximation for Pe if
there are no nearby pressure sinks or sources that would impact the reservoir pressure.
The slope, m, calculated from each plot has unique units and both are different than the
slope, m, calculated from the semilog plot.
Hall Plot
The Hall plot offers the advantage of using operational data to provide continuous
monitoring methods for injection well operations. The method is based on the use of
the steady-state form of the Darcy flow equation. The only data required are injection
rate, injection pressure, and an estimate of Pe, the reservoir pressure.
For a Hall plot, the P function can be calculated several different ways. The function
is described rigorously by the following equation:
-------
Nuts and Bolts of Falloff Testing March 5, 2003
where:
= Bottomhole Injection Pressure, psi
Bw = Formation volume factor, rvb/stb
w = Viscosity of formation fluid, cp
re = External drainage radius, ft
rw = Wellbore radius, ft
s = Skin factor, dimensionless
k = effective permeability to water, md
h = formation thickness, ft
Wi = cumulative injection, bbl
Pe = Pressure at external radius, psi
with = Pf - hPf + (pgD)
where:
Ptf = Surface injection pressure (tubing flowing pressure), psi
Pf = Pressure due to friction loss, psi
gD = Pressure of static fluid column, psi
g = fluid gradient, psi/ft
D = depth to middle of the injection interval, ft
After substituting, the following equation is obtained:
J Pydt ¦¦
141.2£W/Jln(r, / rW(2)+s
kh
m +
Diet
Typically, to simplify the plot, the integral on the right hand side is dropped and a plot of
the summation of the Ptf, wellhead pressure, or P^, bottomhole injection pressure,
times delta time is plotted versus Wh cumulative injection. However, the change in
bottomhole pressure, Pwf, must be plotted to use the plot for quantitative analysis.
The pressure data are plotted along the y-axis of a linear plot. The graph is used to
identify changes in injection behavior that occur over an extended time period. An
upward slope indicates damage while a flattening of the line indicates some type of
stimulation, e.g. fracturing. Slope changes on these types of plots may result from rate
changes and the transmissibility or skin factor may not have changed. Therefore, it is
recommended to take the additional effort to make a Hall plot using the delta
bottomhole pressure for a quantitative analysis.
For quantitative analysis of a Hall plot, i.e., transmissibility and skin factor
determination, a value for Pe should be estimated or assumed, P^ calculated, and the
69
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
integral (cumulative function) of Pwf-Pe plotted versus \Nr Remember, if only the
wellhead or bottomhole pressure is used, the slope changes observed may only be due
to injection rate changes. The use of Pwf-Pe eliminates slope changes due to rate
changes and smooths the data, but requires a calculation of P^, the bottomhole
injection pressure. Note that the slope of the Hall plot incorporates both skin factor and
transmissibility, so that neither variable can be determined independently from the
slope. However, for single phase flow, the transmissibility should not change
significantly with time and therefore any change in slope will likely be due to skin
effects.
Below is an example Hall Plot:
As noted previously, the bottomhole pressure, Pwf, can be estimated from surface
pressures by subtracting the pressure loss due to friction in the tubing and adding the
hydrostatic head at the midpoint of the perforations. For large tubulars, friction loss can
be neglected.
70
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
The transmissibility of the formation can be calculated by the straight line slope on the
Hall plot. Specifically,
The Hall plot was developed for use in waterfloods, so the relative permeability of oil
and water were a consideration. Additionally there was a oil bank radius, r0, and water
bank radius, rwtr, resulting from water injection. In Hall's 1963 paper, the permeability k
is listed as ke, the specific water permeability. Since the formations used for injection
are assumed to be water wet and the injection is assumed to have characteristics to
that of water, the relative permeability to water is 1.0 and therefore the effective
formation permeability to water, k can be substituted in place of ke. The Hall plot also
involves an effective radius value, re. The effective radius can be approximated by
taking the injection volume and calculating the radius influenced by injection. Another
option would be to calculate the radius of the injected volume based on volumetrics.
The accuracy of re/rwa is not critical since this is a log term in the transmissibility
equation.
As with the step rate test, the well conditions are indicated by slope changes on the
plots:
Decrease in slope indicates fracturing, i.e., decrease in skin factor
Increase in slope indicates well plugging, i.e., an increase in skin factor
Straight line indicates radial flow
k ¦ h
%
¦u
Wellbore plugging
Fracture Extension
Fracturing near the well
Cumulative injected water (bbl)
71
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
Hearn Plot
Another plot that uses operational data is the Hearn plot. This method also based on
the steady-state form of Darcys equation. The Hearn plot P/q function is similarly
based upon the flowing bottomhole pressure and an estimate of Pe. The Hearn plot is
developed from the Muskat form of the Darcy equation. To simplify the plot, flowing
bottomhole pressure is often estimated by adding wellhead pressure and the static fluid
column pressure in the injection well while neglecting friction pressure. Friction
pressure should be added if the injection rate is extremely high. The Hearn plot's
advantage over the Hall plot is that it gives a transmissibility from the slope and a skin
factor from the intercept.
Typically, the Hearn plot was developed for use early in the life of an injection well and
the Hall plot used after the well has operated for an extended time. The Hearn plot
develops a constant slope prior to reservoir fill-up and a second horizontal straight line
occurs after fill-up. The Hall plot develops a straight-line slope after fill-up. Prior to
reservoir fill-up, the Pe is increasing, resulting in upward curvature in the Hall plot.
Though both the Hall and Hearn plots require the estimate of a few parameters, the
results may provide an estimation of the reservoir transmissibility and condition of the
wellbore, valuable data when designing or planning a falloff test. Minimal time and
costs are needed for the potential data that may be obtained.
72
-------
Nuts and Bolts of Falloff Testing
Nomenclature
March 5, 2003
B = formation volume factor, rvb/stb
Bw = formation volume factor of water, rvb/stb
C = wellbore storage coefficient, bbls/psi
cr = rock compressibility, psi"1
ct = total compressibility, psi"1 (ct=c+cw)
cw = formation fluid compressibility, psi"1
Cwaste = injectate compressibility, psi"1
D = Depth, feet
Ei = Exponential Interval
FE=injection efficiency (flow efficiency in a producing well)
g & gc: gravitational constants
h = reservoir thickness, feet
k = effective formation permeability to water, md
•-boundary = distance to boundary, feet
m = slope of the semilog plot, psi/cycle
mHall = slope off the Hall plot, psi-day/bbl
P = pressure, psi
Pe = pressure at external radius, psi
•"'corrected = pressure corrected for wellbore skin effects
PD = dimensionless pressure
Pi = initial pressure, psi
Psp = superposition pressure function, psi or psi/bbl
Pgtatic = pressure at end of falloff or stabilization period, psi
Ptf = surface injection pressure, psi (tubing flowing pressure)
P^ = pressure at end of injection period, psi (flowing pressure -producer)
P1hr = pressure intercept along the straight line portion of the Horner Plot or
superposition plot at a shut-in time of 1 hr, psi
P = change in pressure, psi
Pf = pressure loss due to friction, psi
Pskin = pressure change due to wellbore skin, psi
P* = false extrapolated pressure, psi
P = average reservoir pressure, psi
q = injection rate, bpd or gpm
r = distance into the reservoir, feet
rD = dimensionless radius
re = effective wellbore radius, feet
r, = radius of investigation, feet
rw = wellbore radius, feet
rwa = effective wellbore radius, feet (wellbore apparent radius)
s = skin factor, dimensionless
73
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
t = injection time or falloff time, hours
^boundary = time to reach a boundary, hours
tD = dimensionless time
te = Agarwal equivalent time, hours
teiasped = shut-in time or real time, hours
Interference = time until interference between wells is observed, hours
tp = injection time, hours
tradiai flow = time to reach radial flow, hours
tsp = superposition time function, hrs
t = change in time, hrs
Vw = total wellbore volume, bbls
Vu = wellbore volume per unit length, bbls/ft
Vp = injection volume since last stabilization period, bbls
f = viscosity of formation fluid, cp
w = viscosity of injectate, cp
= porosity, fraction
= injectate density, Ibm/ft3
g = pressure gradient psi/ft
74
-------
Nuts and Bolts of Falloff Testing
References
March 5, 2003
1. SPE Textbook Series No. 1, 'Well Testing," W. John Lee, 1982,
2. SPE Monograph 5, "Advances in Well Test Analysis," Robert Earlougher, Jr.,
1977,
3. SPE Monograph 1, "Pressure Buildup and Flow Tests in Wells," C.S. Matthews
and D.G. Russell, 1967,
4. "Well Test Interpretation In Bounded Reservoirs," Spivey, and Lee, Hart's
Petroleum Engineer International, November 1997
5. "Derivative of Pressure: Application to Bounded Reservoir Interpretation," Proano
and Lilley, SPE Paper 15861,1986
6. "Well Test Analysis," Sabet, 1991
7. "Pressure Transient Analysis," Stanislav and Kabir, 1990
8. "Well Testing: Interpretation Methods," Bourdarot, 1996
9. "A New Method To Account For Producing Time Effects When Drawdown Type
Curves Are Used To Analyze Pressure Buildup And Other Test Data," Agarwal,
SPE Paper 9289, 1980
10. "Modern Well Test Analysis - A Computer-Aided Approach," Roland N. Home,
1990
11. Exxon Monograph, 'Well Testing in Heterogeneous Formations," Tatiana
Streltsova, 1987
12. EPA Region 6 Falloff Guidelines, Third Revision, August 8, 2002
13. "Pressure Gauge Specification Considerations In Practical Well Testing,"
Veneruso, Ehlig-Economides, and Petitjean, SPE Paper No. 22752, 1991
14. "Guidelines Simplify Well Test Interpretation," Ehlig-Economides, Hegeman, and
Vik, Oil and Gas Journal, July 18, 1994
15. Oryx Energy Company, Practical Pressure Transient Testing, G. Lichtenberger
and K. Johnson, April 1990 (Internal document)
16. Pressure-Transient Test Design in Tight Gas Formations, W.J. Lee, SPE Paper
17088, October 1987
17. "Radius-of-Drainage and Stabilization-Time Equations," H.K. Van Poollen, Oil
and Gas Journal, Sept 14, 1964
18. "Three Key Elements Necessary for Successful Testing," Ehlig-Economides,
Hegeman, Clark, Oil and Gas Journal, July 25, 1994
19. "Introduction to Applied Well Test Interpretation," Spivey, and Lee, Hart's
Petroleum Engineer International, August 1997
20. "Recent Developments In Well Test Analysis," Stewart, Hart's Petroleum
Engineer International, August 1997
21. "Fundamentals of Type Curve Analysis," Spivey, and Lee, Hart's Petroleum
Engineer International, September 1997
22. "Identifying Flow Regimes In Pressure Transient Tests," Spivey and Lee, Hart's
Petroleum Engineer International, October 1997
75
-------
Nuts and Bolts of Falloff Testing
March 5, 2003
23. "Selecting a Reservoir Model For Well Test Interpretation," Spivey, Ayers,
Pursell, and Lee, Hart's Petroleum Engineer International, December 1997
24. "Effects of Permeability Anisotropy and Layering On Well Test Interpretation,"
Spivey, Aly, and Lee, Hart's Petroleum Engineer International, February 1998
25. "Use of Pressure Derivative in Well-Test Interpretation," Bourdet, Ayoub, and
Pirard, SPE Paper 12777, SPE Formation Evaluation Journal, June 1989
26. "A New Set of Type Curves Simplifies Well Test Analysis," Bourdet, Whittle,
Douglas, and Pirard, May World Oil, 1983
27. "Mechanics of Hydraulic Fracturing,", Hubbert and Willis, SPE-AIME Paper No.
686-G, 1956
28. "Fracture Gradient Prediction and Its Application in Oilfield Operations," Eaton,
SPE-AIME Paper No. 2163, October 1969
29. "An Investigative Study of Recent Technologies Used for Prediction, Detection,
and Evaluation of Abnormal Formation Pressure and Fracture Pressure in North
and South America," Yoshida, Ikeda, and Eaton, SPE Paper No. 36381,
September, 1996
30. "After-Closure Analysis of Fracture Gradient Tests," Nolte, Maniere, and Owens,
SPE Paper No. 38676, October 1997
31. "Systematic Design and Analysis of Step-Rate Tests to Determine Formation
Parting Pressure," Singh, Agarwal, and Krase, SPE Paper No. 16798,
September 1987
32. "Two-Step Rate Test: New Procedure for Determining Formation Parting
Pressure," Singh and Agarwal, SPE Paper No. 18141, January 1990
33. "Case Histories of Step Rate Tests in Injection Wells," Salazar and Kumar, SPE
Paper No. 23958, March 1992
34. "Step Rate Tests Determine Safe Injection Pressures In Floods," Felsenthal, Oil
and Gas Journal, October 28, 1974
35. "Maximizing Injection Rates in Wells Recently Converted to Injection Using
Hearn and Hall Plots," Jarrell and Stein, SPE Paper No. 21724, April 1991
36. "How To Analyze Waterflood Injection Well Performance," N.H. Hall, World Oil,
October 1963
37. "Method Analyzes Injection Well Pressures and Rate Data," Hearn, Oil and Gas
Journal, April 18, 1983
38. "Analyzing Injectivity of Polymer Solutions with the Hall Plot," Buell, Kazemi, and
Poettmann, SPE Paper No. 16963, September 1987
39. "Direct Approach Through Hall Plot Evaluation Improves the Accuracy of
Formation Damage Calculations and Eliminates Pressure Fall-off Testing,"
Hawe, SPE Paper No. 5989, July 1976
40. "Injection/Production Monitoring: An Effective Method for Reservoir
Characterization," Honarpour and Tomutsa, SPE Paper No. 20262, April 1990
76
------- |