U.S. patent application number 14/031877 was filed with the patent office on 2014-03-20 for method to predict overpressure uncertainty from normal compaction trendline uncertainty.
This patent application is currently assigned to BAKER HUGHES INCOROPORATED. The applicant listed for this patent is Anne Bartetzko, Philipp Tesch, Stefan Wessling. Invention is credited to Anne Bartetzko, Philipp Tesch, Stefan Wessling.
Application Number | 20140076632 14/031877 |
Document ID | / |
Family ID | 50273300 |
Filed Date | 2014-03-20 |
United States Patent
Application |
20140076632 |
Kind Code |
A1 |
Wessling; Stefan ; et
al. |
March 20, 2014 |
METHOD TO PREDICT OVERPRESSURE UNCERTAINTY FROM NORMAL COMPACTION
TRENDLINE UNCERTAINTY
Abstract
A method for predicting a pressure window for drilling a
borehole in a formation includes: obtaining a pore pressure related
data value of the formation using a data acquisition tool;
predicting pore pressure uncertainty from the pore pressure related
data value of the formation using a processor; estimating
uncertainty of a pressure window for drilling fluid using the
predicted pore pressure uncertainty using a processor; and applying
the estimated uncertainty to the pressure window to provide a
modified pressure window using a processor.
Inventors: |
Wessling; Stefan; (Hannover,
DE) ; Bartetzko; Anne; (Celle, DE) ; Tesch;
Philipp; (Berlin, DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Wessling; Stefan
Bartetzko; Anne
Tesch; Philipp |
Hannover
Celle
Berlin |
|
DE
DE
DE |
|
|
Assignee: |
BAKER HUGHES INCOROPORATED
Houston
TX
|
Family ID: |
50273300 |
Appl. No.: |
14/031877 |
Filed: |
September 19, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61703567 |
Sep 20, 2012 |
|
|
|
Current U.S.
Class: |
175/48 ; 702/12;
702/7; 702/8 |
Current CPC
Class: |
E21B 47/06 20130101;
E21B 21/08 20130101 |
Class at
Publication: |
175/48 ; 702/12;
702/8; 702/7 |
International
Class: |
E21B 47/06 20060101
E21B047/06 |
Claims
1. A method for predicting a pressure window for drilling a
borehole in a formation, the method comprising: obtaining a pore
pressure related data value of the formation using a data
acquisition tool; predicting pore pressure uncertainty from the
pore pressure related data value of the formation using a
processor; estimating uncertainty of a pressure window for drilling
fluid using the predicted pore pressure uncertainty using a
processor; and applying the estimated uncertainty to the pressure
window to provide a modified pressure window using a processor.
2. The method according to claim 1, further comprising defining an
operating margin and applying the operating margin to the modified
pressure window to provide an operating pressure window using a
processor.
3. The method according to claim 2, further comprising monitoring
at least one equivalent of drilling fluid pressure and determining
if the monitored drilling fluid pressure equivalent is within
equivalents of an upper bound and a lower bound of the operating
pressure window.
4. The method according to claim 2, further comprising: defining a
drilling parameter for drilling a borehole in the formation within
the operating pressure window using a processor; and drilling into
the formation using a drilling tool and the operating pressure
window for the drilling fluid.
5. The method according to claim 4, wherein the drilling parameter
comprises at least one of a drilling fluid density, a drilling
fluid flow rate, an equivalent circulating drilling fluid density,
an equivalent static drilling fluid density, and a standpipe
pressure.
6. The method according to claim 1, further comprising determining
at least one pore pressure related trendline using the pore
pressure related data value and extrapolating the at least one pore
pressure related trendline.
7. The method according to claim 6, wherein the pore pressure
related value is obtained from a pore pressure related log acquired
by the data acquisition tool.
8. The method according to claim 6, wherein the formation comprises
a normal compaction zone and an overpressure zone below the normal
compaction zone and method further comprises determining the at
least one pore pressure related trendline from data from the normal
compaction zone and extrapolating the at least one pore pressure
related trendline into the overpressure zone.
9. The method according to claim 6, wherein the pore pressure
uncertainty accounts for at least one selection from a group
consisting of instrument error, equipment calibration error,
statistical error of measurement apparatus or method, regression
error of trendlines when the trendline comprises a plurality of
trendlines, and variation of trendlines when the trendline
comprises a plurality of trendlines.
10. The method according to claim 9, further comprising identifying
a correlation between pore pressure uncertainty and the uncertainty
of the pore pressure related data value using data from at least
two previously drilled boreholes and wherein calculating the pore
pressure uncertainty further comprises using the uncertainty of the
pore pressure related data value and the correlation.
11. The method according to claim 6, further comprising deriving a
representative pore pressure related trendline from the at least
one pore pressure related trendline.
12. The method according to claim 6, wherein the at least one pore
pressure related trendline comprises a plurality of pore pressure
related trendlines and the method further comprising determining an
upper bound line having an upper bound line slope and a lower bound
line having a lower bound line slope, wherein the upper bound line
slope is less than a slope of the plurality of pore pressure
related trendlines and the slope of the plurality of pore pressure
related trendlines is less than the lower bound line slope, the
upper bound line indicating positive uncertainty with respect to
the pore pressure related trendline and the lower bound line
indicating negative uncertainty with respect to the pore pressure
related trendline.
13. The method according to claim 12, wherein the upper bound line
is a function of an uncertainty of the plurality of pore pressure
trendlines and the lower bound line is a function of an uncertainty
of the plurality of pore pressure trendlines.
14. The method according to claim 6, wherein the at least one pore
pressure related trendline comprises a plurality of pore pressure
related trendlines and the method further comprising determining an
upper bound line having an upper bound line slope and a lower bound
line having a lower bound line slope, wherein the upper bound line
is a pore pressure related trendline in the plurality of pore
pressure related trendlines having a minimum slope and the lower
bound line is a pore pressure line in the plurality of pore
pressure related trendlines having a maximum slope.
15. The method according to claim 1, wherein calculating pore
pressure uncertainty in the overpressure zone comprises calculating
a Q-factor by solving: Q = z ( .DELTA. R N * ) , ##EQU00007## where
d/dz is the derivative of .DELTA.R*.sub.N with depth z, and
.DELTA.R*.sub.N=log.sub.10 R.sub.N.sup.u-log.sub.10 R.sub.N.sup.l
represents the difference between the upper (R.sub.N.sup.u) and
lower (R.sub.N.sup.l) bounds at depth z that envelope an estimate
of a pore pressure related value.
16. The method according to claim 15, wherein Q=constant value
q.
17. The method according to claim 1, wherein the pressure window is
defined at least in part by a fracture gradient, a pore pressure
gradient, and a collapse gradient and the pore pressure uncertainty
affects at least partly one of the fracture gradient and the
collapse gradient.
18. An apparatus for predicting a pore pressure window for drilling
a borehole in a formation, the apparatus comprising: a data
acquisition tool configured to perform formation measurements
related to pore pressure of the formation at a plurality of depths
in the borehole; and a processor in communication with the downhole
tool and configured to implement a method comprising at least one
of the steps: obtaining a pore pressure related data value of the
formation from the data acquisition tool; predicting pore pressure
uncertainty from the pore pressure related data value of the
formation; estimating uncertainty of a pressure window for drilling
fluid using the predicted pore pressure uncertainty; and applying
the estimated uncertainty to the pressure window to provide a
modified pressure window.
19. The apparatus according to claim 18, wherein the processor is
further configured to: define an operating margin and apply the
operating margin to the modified pressure window to provide an
operating pressure window; and define a drilling parameter for
drilling a borehole in the formation within the operating pressure
window.
20. The apparatus according to claim 19, further comprising a
drilling tool configured to drill the borehole within the operating
pressure window.
21. The apparatus according to claim 19, further comprising a
controller configured to control a drilling fluid pump or a
drilling fluid control valve to maintain drilling fluid pressure
equivalent within the operating pressure window.
22. The apparatus according to claim 19, further comprising a
controller configured to control a drilling fluid flow control
valve to maintain drilling fluid pressure within the operating
pressure window.
23. The apparatus according to claim 19, further comprising a
drilling fluid sensor configured to sense a drilling fluid
parameter and to provide input to a controller configured to
provide an output to maintain drilling fluid pressure within the
operating pressure window.
24. The apparatus according to claim 18, wherein the data
acquisition tool comprises a downhole tool comprising at least one
of a gamma ray tool, a resistivity tool, a dielectric permittivity
tool, a density tool, a neutron porosity tool, a pulsed neutron
tool, a nuclear magnetic resonance tool, and an acoustic tool.
25. The apparatus according to claim 18, wherein the data
acquisition tool is configured to acquire formation data at the
surface of the formation.
Description
BACKGROUND
[0001] Geologic formations are used for many purposes such as
hydrocarbon production, geothermal production and carbon dioxide
sequestration. Boreholes are typically drilled into the earth in
order to access the formations. Prior to a borehole being drilled,
forces or loads in the rock mass of a formation are substantially
in equilibrium with each other. Keeping the drilled formation
stable generally requires a support pressure be applied by drilling
mud in the borehole. The proper support pressure is related to the
pressure of the formation fluid in the pores of the formation
(i.e., pore pressure). If the applied support pressure is
insufficient, the formation surrounding the borehole may become
unstable and collapse into the borehole damaging equipment and
causing costly delays, or formation fluid may enter into the
wellbore causing a kick or even a blowout.
[0002] During drilling, the pressure of the drilling mud is
maintained within a pressure window, for instance by a mud program.
It is important that the pressure window is accurately determined
in order to efficiently drill the borehole and prevent damage.
Hence, it would be well received in the drilling industry if
estimates of pore pressure were provided with an uncertainty that
could be used as input to the mud program in order for the pressure
window to compensate for the uncertainty. In particular, it would
be well received if the pore pressure and associated uncertainty
could be predicted ahead of the drill bit, i.e., before the
formation is drilled.
BRIEF SUMMARY
[0003] Disclosed is a method for predicting a pressure window for
drilling a borehole in a formation The method includes: obtaining a
pore pressure related data value of the formation using a data
acquisition tool; predicting pore pressure uncertainty from the
pore pressure related data value of the formation using a
processor; estimating uncertainty of a pressure window for drilling
fluid using the predicted pore pressure uncertainty using a
processor; and applying the estimated uncertainty to the pressure
window to provide a modified pressure window using a processor.
[0004] Also disclosed is an apparatus for predicting a pore
pressure window for drilling a borehole in a formation. The
apparatus includes a data acquisition tool configured to perform
formation measurements related to pore pressure of the formation at
a plurality of depths in the borehole and a processor in
communication with the downhole tool. The processor is configured
to implement a method comprising at least one of the steps:
obtaining a pore pressure related data value of the formation from
the data acquisition tool; predicting pore pressure uncertainty
from the pore pressure related data value of the formation;
estimating uncertainty of a pressure window for drilling fluid
using the predicted pore pressure uncertainty; and applying the
estimated uncertainty to the pressure window to provide a modified
pressure window.
BRIEF DESCRIPTION OF THE DRAWINGS
[0005] The following descriptions should not be considered limiting
in any way. With reference to the accompanying drawings, like
elements are numbered alike:
[0006] FIG. 1 illustrates an exemplary embodiment of a downhole
porosity tool disposed in a borehole penetrating the earth;
[0007] FIG. 2 illustrates an exemplary pressure window for drilling
operations;
[0008] FIG. 3 presents a flow chart depicting aspects of a method
for estimating formation pore pressure and an associated
uncertainty;
[0009] FIG. 4 depicts aspects of one approach for estimating
formation pore pressure and an associated uncertainty;
[0010] FIG. 5 depicts aspects of another approach for estimating
formation pore pressure and an associated uncertainty;
[0011] FIGS. 6A and 6B, collectively referred to as FIG. 6, depict
aspects of nomenclature of an algorithm to calculate pore pressure
uncertainty form variations of the normal compaction trendline as
demonstrated on an acoustic log;
[0012] FIGS. 7A, 7B, and 7C, collectively referred to as FIG. 7,
depict aspects of first and second methods for establishing
uncertainty trendlines;
[0013] FIG. 8 depicts aspects of q-factor derived from the
increasing difference between the maximum and minimum uncertainty
trendlines developed from the first method for resistivity and
acoustic data from various regions throughout the world;
[0014] FIG. 9 depicts aspects of q-factor derived from the
increasing difference between the maximum and minimum uncertainty
trendlines developed from the second method for resistivity and
acoustic data from various regions throughout the world;
[0015] FIG. 10 depicts aspects of pore pressure uncertainty versus
q-factor for acoustic log data obtained from the Asia-Pacific
region;
[0016] FIG. 11 depicts aspects of pore pressure uncertainty versus
q-factor for resistivity log data obtained from the Asia-Pacific
region;
[0017] FIG. 12 depicts aspects of pore pressure uncertainty versus
q-factor for acoustic log data obtained from the Gulf of Mexico
region;
[0018] FIG. 13 depicts aspects of pore pressure uncertainty versus
q-factor for resistivity log data obtained from the Gulf of Mexico
region;
[0019] FIG. 14 depicts aspects of pore pressure uncertainty versus
q-factor for resistivity log data obtained from the North Sea
region; and
[0020] FIG. 15 is a flow chart for a method for determining a
pressure window for drilling a borehole.
DETAILED DESCRIPTION
[0021] A detailed description of one or more embodiments of the
disclosed apparatus and method presented herein by way of
exemplification and not limitation with reference to the
Figures.
[0022] FIG. 1 illustrates an exemplary embodiment of a bottom hole
assembly (BHA) 9 disposed in a borehole 2 penetrating the earth 3,
which includes an earth formation 4. The BHA 9 is conveyed through
the borehole 2 by a drill string 5 for logging-while-drilling
and/or steering applications. The drill string may represent any
drill tubular for drilling a borehole such as coiled tubing drill
pipes, or other equipment known in the art. A drill bit 6 is
disposed at the distal end of the BHA 9 for drilling the borehole
2. The BHA and the drill bit together may be referred to as a
drilling tool. A drill rig 17 rotates the drill string 5 to drill
the borehole 2 and pumps drilling fluid 18 through the drill string
5 in order to lubricate the drill bit 6 and flush cuttings from the
borehole 2. A drilling fluid pump 7 is configured to pump the
drilling fluid 18 at a selected pressure or flow rate that may be
controlled by a controller. A flow sensor 8 configured to sense the
flow rate of the drilling fluid 18 may provide input to the
controller for feedback control. Pressure in the borehole annulus
may also be controlled by a flow control valve 19, which is
configured to control the flow of the drilling fluid 18 exiting the
borehole 2. The flow control valve 19 may also be controller by the
controller. A downhole tool 10 is disposed at (i.e., in or on) the
BHA 9 and configured to perform measurements of the formation 4 at
various depths to produce a measurement log. In one or more
embodiments, the downhole formation measurements are related to the
pore pressure of the formation 4. That is the pore pressure of the
formation 4 can be deduced absolutely or relatively from those
measurements. Non-limiting embodiments of those formation
measurements include gamma ray measurements, resistivity
measurements, dielectric measurements, acoustic measurements,
nuclear magnetic resonance measurements, pulsed neutron
measurements, and density and/or porosity measurements using a
radiation source. In addition, in one or more embodiments, one or
more downhole tools 10 may be configured to discriminate or
identify the presence of shale in the formation 4 by natural
gamma-ray logging in order to apply the methods disclosed
herein.
[0023] Still referring to FIG. 1, a downhole electronic unit 11 is
disposed in the BHA 9. The downhole electronic unit 11 is
configured to operate the downhole tool 10 and/or process
measurement data. In one or more embodiments, raw or processed
measurement data can be transmitted to a computer processing system
12 disposed at the surface of the earth 3 via a telemetry system
13. The telemetry system 13 can be wired drill pipe 14,
electromagnetic telemetry, acoustic telemetry, mud pulses or mud
waves for real time communications as non-limiting examples. Data
processing functions can be performed by the downhole electronic
unit 11, the computer processing system 12 or some combination of
both. In one or more embodiments, the computer processing system 12
is configured to be the controller that controls the drilling fluid
pump 7 and/or the flow control valve 19.
[0024] The downhole electronic unit 11 and/or the computer
processing system 12 includes a processor for executing algorithms
that partly or completely implement a method for estimating the
pore pressure of the formation 4 as a function of depth or time and
an associated statistical or deterministic parameter such as an
absolute or relative standard deviation, variance, minimum and
maximum values, one or moments of a frequency distribution of a
part of the data set or any other parameter to quantify the
uncertainty of the pore pressure estimation. The pore pressure and
its uncertainty parameter may then be provided to a mud program for
maintaining the drilling fluid pressure within the pressure
window.
[0025] The drilling pressure window is depicted in FIG. 2 and is
the acceptable range of pressures established in the borehole
annulus along the open hole section. Although not required, FIG. 2
shows the pressure gradients instead of the pressures as it is
commonly known in the industry. Factors that are part of
establishing the drilling pressure include drilling fluid weight
(or mud weight) and flow rate of the drilling fluid. In one or more
embodiments, the flow rate may be determined by the speed or output
pressure of the drilling fluid pump and/or by the position of a
valve through which drilling fluid exits the borehole, sometimes
referred to as managed pressure drilling. The pressure window is
defined by its upper and lower bounds. The upper bound of the
pressure window is the fracture gradient. There are two lower
bounds of the pressure window. One lower bound is the pore pressure
gradient while the other lower bound is the collapse gradient. The
pressure window is below the upper bound and above the highest of
the two lower bounds. For some established methods, the pore
pressure gradient is an input-factor for determining the fracture
gradient and the collapse gradient. Hence, pore pressure gradient
uncertainty is an input to determining fracture gradient
uncertainty, and collapse gradient uncertainty and, thus, to
determining the drilling pressure window uncertainty. In one or
more embodiments, the drilling pressure window uncertainty reduces
the drilling pressure window by the amount of the uncertainty.
[0026] Appropriate drilling is realized as long as the downhole
annular pressure prevailing along the open hole section is
maintained within the pressure window. In FIG. 2, equivalent
descriptions for the downhole annular pressure are the mud weight
(or equivalent static density, ESD) for flow-off (non-circulating)
conditions, and the equivalent circulating density (ECD) for
circulating conditions.
[0027] If the downhole annular pressure prevailing along the open
hole section of a borehole exceeds the fracture gradient, fractures
are created at the borehole wall which eventually propagate further
into the formation. Drilling fluid then penetrates into these
drilling-induced fractures causing losses of drilling fluid. If the
downhole annular pressure falls below the pore pressure gradient,
formation fluid unintentionally enters into the borehole which is
referred to as a kick. If the kick becomes uncontrollable, a
blowout may occur. If the downhole annular pressure falls below the
collapse gradient, the re-distributed stresses around the wellbore
may exceed the compressive strength of the formation rock causing a
collapse of the wellbore wall which can result in washouts,
breakouts or even total collapse of the borehole. This disclosure
discusses the pore pressure gradient in detail, but the other two
pressure window bounds are also affected.
[0028] Before the pore pressure uncertainty method is discussed in
detail, certain terms related to sedimentary compaction are
presented. Pore pressure in the underground can be hydrostatic,
overpressured, or underpressured compared to hydrostatic
conditions, and different mechanisms exist that can cause a
deviation of the pore pressure from hydrostatic. One such mechanism
is based on the compaction of sedimentary material which is
transported into sedimentary basins. Compaction is referred to as
the decrease of porosity of fine or coarse sedimentary material due
to burial of the settled material eventually with addition of
further material.
[0029] Under normal conditions, fluid existing in the pore space in
the sedimentary material will be squeezed out of the material, so
that the porosity of the sediment will decrease with increasing
load from above. This mechanism of normal compaction results in a
hydrostatic pore pressure distribution. Assuming that compaction is
the main pore pressure generating mechanism, overpressure (also
referred to as undercompaction) is generated whenever fluid within
the pore space is trapped with continuous burial of the
sediment.
[0030] During the drilling operation, the compaction trend of
sediments can be monitored for instance by inspection of pore
pressure related logs (i.e., logs influenced by pore pressure) or
drilling curves. Logs can be the resistivity, dielectric
permittivity, acoustic slowness of the formation, bulk density,
neutron porosity, gamma ray, nuclear magnetic resonance or others.
A drilling curve example is the drilling exponent (DXC).
[0031] Using the resistivity log as an example, an overpressure
zone is indicated by a decrease in resistivity from what would be
expected in a normal compaction zone (i.e., a trend of an increase
in resistivity with increasing depth as porosity decreases). Within
the spirit of this invention, the term porosity is not limited to
pores within the formation, but to any type of void space including
fractures, etc. In one or more embodiments, the disclosed
techniques for estimating pore pressure and associated uncertainty
are applied only to shale in shale containing formations. Hence, in
these embodiments, the pore pressure related formation measurements
are filtered to exclude measurements performed on non-shale
portions of the formation.
[0032] If undercompaction is the main overpressure generating
mechanism, one step in the pore pressure modeling workflow might be
the determination of the normal compaction trendline which
describes the change in porosity with depth under normal compaction
conditions. A deviation between the normal compaction trendline and
acquired porosity-indicating data can be used to calculate the
deviation from normal pressure regimes.
[0033] The normal compaction trendline is defined by establishing a
line in a plot of pore pressure related logs versus depth. This
step is typically performed manually. An alternative which will be
explained later in more detail is performing a linear regression
(using a processor) over the normally compacted depth interval.
However, the regression conducted over different intervals will
give different trendlines, depending on the variability of the pore
pressure related logs. For example, acoustic slowness logs were
noted to be much smoother in the normal compaction zone compared to
formation resistivity logs. Note that the other variables such as
OBG, PP.sub.n, and the Eaton exponent (x) (which are discussed
below) are also affected by some uncertainty, and that the
uncertainty of the pore pressure related log depends on the
measurement precision.
[0034] Reference may now be had to FIG. 3 which presents a flow
chart depicting aspects of a method 20 for determining pore
pressure and pore pressure uncertainty as a function of depth. Step
21 in method 20 calls for conveying a carrier coupled to the
downhole tool 10 through a borehole. Step 22 calls for performing
formation measurements using the downhole tool 10 to obtain a log
of formation measurements related to pore pressure.
[0035] Step 23 calls for defining a first or upper depth interval
and a second or lower depth interval that is deeper in the borehole
than the upper depth interval. Each depth interval includes at
least one formation measurement made within those intervals. Step
24 calls for establishing a plurality of compaction trendlines
extending from the upper depth interval to the lower depth interval
and beyond. Each trendline is defined by a unique set of
measurement points with one measurement point being in the upper
depth interval and one measurement point being in the lower depth
interval. Each trendline may be parameterized by a slope and an
intercept. While the trendlines may be linear, they may also follow
a curved function such as exponential functions or polynomial
functions. Alternatively, steps 23 and 24 may be performed with all
data values coming from one single interval (e.g., the complete
normal compaction zone).
[0036] Various ways may be employed to establish a plurality of
trendlines. One way is to determine a set of points (i.e., one
point in the upper depth interval and one point in the lower depth
interval) that establishes a first trendline having a minimum slope
and minimum intercept and a set of points that establishes a second
trendline having a maximum slope and maximum intercept from all
sets of points in the upper and lower depth intervals. The upper
and lower depth intervals may be predefined or selected according
to techniques disclosed in U.S. patent application Ser. No.
13/229,212, which is incorporated by reference in its entirety.
Alternatively, the first trendline may be established having a
minimum slope and maximum intercept and the second trendline may be
established having a maximum slope and minimum intercept. In
general, the combination providing the widest spread in values may
be selected to provide the basis for representing the most likely
associated uncertainty. Another way of establishing a plurality of
trendlines involves generating trendlines through every combination
or set of measurement points in the upper and lower depth
intervals. Other techniques to establish the plurality of
trendlines may be obtained from U.S. patent application Ser. No.
13/229,212.
[0037] The dependence of the attributes of the calculated normal
compaction trendline on the log variability has been used to
calculate a series of trendlines over different depth intervals by
an algorithm described above. The normal compaction trendline may
be calculated automatically or semi-automatically using a processor
or may be manually entered into a processor. The series of
trendlines can then be used to calculate an average normal
compaction trendline and the uncertainty associated with the
average trendline. Different definitions are proposed for the
uncertainty. One definition (Method 1) is the standard deviation
for the average slope and intercept of all the determined
trendlines. Another definition (Method 2) is the maximum and
minimum slope determined out of all determined trendlines.
[0038] Because there may be many trendlines, such as in the
hundreds or even thousands, it may not be possible to illustrate
all of them on one plot. In cases like this, one or more trendlines
with associated uncertainty may be plotted as a representation of
all the trendlines. Track 1 in FIG. 4 shows an example of a pore
pressure related log, which is in this case a porosity-indicating
resistivity log, overlain by an average normal compaction
trendline. The trendline fits the porosity-indicating log in the
normal compaction interval and starts deviating from the
porosity-indicating log in the overpressure zone. The average
trendline is bounded by trendlines signifying +/- one standard
deviation (+/-1 s). FIG. 4 Track 1 was developed using Method 1.
FIG. 5 Track 3 is an example of representing all the trendlines by
plotting the maximum and minimum slope determined out of all the
trendlines using Method 2. In FIGS. 4 and 5, the resistivity axis
is logarithmically scaled, however, other scaling including linear
scaling can be used as well.
[0039] These two methods to define a representative trendline and a
representative value for the variation of the trendlines will be
explained in more detail. For both methods, two intervals need to
be defined from which the series of trendlines are generated: a
start interval containing i=1 . . . n data points and an end
interval containing j=1 . . . m data points (see FIG. 6A for
nomenclature). In one or more embodiments, both intervals reside in
the normal compaction zone, although this is not required. As a
first step, a regression analysis is performed over the interval
beginning at the first data point from the start interval (i=1) and
ending at the first data point from the end interval (j=1),
yielding the trendline TL.sub.1,1. This trendline may be in the
normal compaction zone although it does not have to be. Step n of
the analysis defines the interval for linear regression from data
point i=n to j=1, giving TL.sub.n,1. The final linear regression
analysis is performed for i=n, j=m to obtain trendline TL.sub.n,m
(see Step n*m in 6B). This approach gives a series of n*m
trendlines.
[0040] Histograms 1 and 2 in FIG. 4 illustrate the spread in slope
values and intercept values (assuming linear regression which is
not a requirement) of a series of trendlines as calculated
according to the procedure explained above, respectively. By
assuming more parameters in the trendline and defining more
intervals, the same method may be applied resulting in trendlines
with more curvature. The distribution of the parameters derived
from the series of normal compaction trendlines may be further used
as input for other pore pressure uncertainty calculating
approaches. These approaches may include for example error
propagation laws, simulations, and neural networks. For example,
Monte Carlo Simulations use a parameter distribution as input
assigned to the modeling parameters. In Monte-Carlo simulation
applied to pore pressure modeling, the modeling approach is first
defined such as using one of Equations (1)-(6). Using Equation (1)
as an example, input data/parameters used to calculate the pore
pressure are the overburden gradient (OBG), the resistivity log
R.sub.0, the hydrostatic pore pressure PPN and the "normal
resistivity value" R.sub.N, which is the resistivity corresponding
to the normal compaction trendline. The resistivity log R.sub.0 is
determined from actual resistivity measurements. Deviations of
R.sub.0 from R.sub.N may result from an overpressure condition. For
a Monte-Carlo Simulation, each of these input parameters is not an
exact value but represented by a probability distribution. For
example, OBG may range from 12-14 ppg with its most likely value at
13 ppg. Likewise, the normal compaction trendline is not a straight
line (defined by its slope and intercept) anymore, but a series of
trendlines defined by a probability distribution of slopes and
intercepts. Then, in Monte Carlo Simulation the necessary input
data are randomly selected (with values within the distribution or
parameter range) and a pore pressure model is calculated. This
procedure is repeated a large number of times (for example 10000
times or more) so that a series of pore pressure models is created
with a certain probability distribution. Hence, the distribution of
slopes and intercepts described above may be used as input for a
Monte-Carlo simulation.
[0041] Step 25 in method 20 calls for calculating a pore pressure
line (i.e., a representative, c.f. most likely estimate of pore
pressure as a function of depth) and associated uncertainty using
the plurality of trendlines. Various methods are known in the art
for converting porosity to pore pressure. One method is referred to
as Eaton's method. Eaton's method can be used with resistivity
logs, conductivity logs, acoustic velocity logs, acoustic slowness
logs, or drilling exponent data. Equations (1)-(5) list various
forms of equations in Eaton's method for calculating pore pressure
(PP) depending on the type of log used to measure porosity. Eaton's
method uses the overburden gradient as an input to the method. The
overburden gradient is determined using established techniques
(e.g., integration of density logs) and is shown in Track 2 in FIG.
4 and Track 4 in FIG. 5.
PP = OBG - ( OBG - PP N ) ( R 0 R N ) x ( 1 ) PP = OBG - ( OBG - PP
N ) ( V 0 V N ) x ( 2 ) PP = OBG - ( OBG - PP N ) ( DT N DT 0 ) x (
3 ) PP = OBG - ( OBG - PP N ) ( C N C O ) x ( 4 ) PP = OBG - ( OBG
- PP N ) ( DXC 0 DXC N ) x ( 5 ) ##EQU00001##
In the above equations: Default value of Eaton exponent x in
equation (1) is 1.2; Default value of Eaton exponent x in equations
(2) and (3) is 3; OBG=overburden gradient (ppg, kPa/m, or
g/cm.sup.3); PP.sub.N=normal (i.e., hydrostatic conditions) pore
pressure gradient (ppg, kPa/m, or g/cm.sup.3); R.sub.0=observed
resistivity (.OMEGA.m); R.sub.N="normal" (expected) resistivity
(.OMEGA.m); V.sub.0=observed interval seismic or acoustic velocity
(m/s or ft/s); V.sub.N="normal" (expected) interval seismic or
acoustic velocity (m/s or ft/s); DT.sub.0=observed transit time
(.mu.s/ft); DT.sub.N="normal" (expected) transit time (.mu.s/ft);
C.sub.0=observed conductivity (S/m); C.sub.N="normal" (expected)
conductivity (S/m); DXC.sub.0=observed DXC; and DXC.sub.N="normal"
(expected) DXC where "normal" means the value taken from the normal
compaction trendline.
[0042] As with establishing the plurality of trendlines, there are
a number of ways to determine the pore pressure line, which
represents pore pressure as a function of depth, and an associated
uncertainty. In one way illustrated in Track 3 in FIG. 5, a
representative trendline is calculated from the first trendline
having the minimum slope and the second trendline having a maximum
slope. The representative trendline can be an average of the two
trendlines in one embodiment. It can be appreciated that other
mathematical techniques can be used to determine the representative
trendline such as calculating a mean trendline. The uncertainty
associated with the average trendline is the spread between the
first trendline and the second trendline.
[0043] Once the representative trendline is calculated, Eaton's
method can be applied to determine the pore pressure gradient log
(i.e., the representative pore pressure gradient log). Similarly,
Eaton's method can be applied to the first trendline and the second
trendline to determine the spread of values or uncertainty about
the pore pressure gradient log. Other methods may also be used to
determine the representative pore pressure gradient log such as
Gaussian error propagation and using only the upper and lower
limits calculated by Eaton's method while representative trendline
is the average of the upper and lower limits. Further, methods
disclosed in U.S. application Ser. No. 13/229,212 may be used to
determine the spread of uncertainty about the pore pressure
gradient log.
[0044] An alternative method for calculating the pore pressure is
the equivalent depth method which also uses the normal compaction
trendline as an input parameter. The method assumes that every
depth point in an overpressured shale interval has a corresponding
(equivalent) point in the normally compacted interval above on the
normal compaction trend line. Both points have the same porosity
(as indicated by an identical resistivity, acoustic, or drilling
exponent value) and thus yield the same effective stress. Knowing
the overburden and hydrostatic gradient, pore pressure can be
determined as given by:
PP = PP N D 1 + ( OBG 2 D 2 - OBG 1 D 1 ) D 2 ( 6 )
##EQU00002##
With D.sub.1 and D.sub.2 being the upper and lower depth,
respectively, and OBG.sub.1 and OBG.sub.2 the overburden gradient
at the respective depth points.
[0045] When the plurality of trendlines involves generating
trendlines through every combination of measurement points in the
upper and lower depth intervals, two approaches may be used to
determine the pore pressure line and associated uncertainty. In the
first approach, Eaton's method using constant parameters is applied
to each trendline in the plurality of trendlines to generate a
plurality of corresponding pore pressure lines. The representative
pore pressure line, such as an average pore pressure line for
example, is then calculated from the plurality of pore pressure
lines. A statistical method is then applied to the plurality of
pore pressure lines to calculate the standard deviation of the
plurality of pore pressure lines. The standard deviation is one
example of the uncertainty associated with the representative or
calculated pore pressure line.
[0046] In the second approach, Eaton's method using a random
varying parameter such as Eaton's exponent is applied to each
trendline in the plurality of trendlines to generate a plurality of
corresponding pore pressure lines. As in the first approach, the
pore pressure line can be calculated as an average of the plurality
of corresponding pore pressure lines. Similarly, a statistical
method is then applied to the plurality of pore pressure lines to
calculate the standard deviation of the plurality of pore pressure
lines where the standard deviation represents the uncertainty. This
approach is illustrated in Tracks 1 and 2 in FIG. 4 with Histogram
3 illustrating the distribution of the Eaton exponents.
[0047] It can be appreciated that certain mathematical techniques
other than calculating an average may be used to determine the
calculated pore pressure line. In one or more embodiments, a mean
value may be calculated. It can also be appreciated that certain
statistical techniques other than calculating the standard
deviation may be used to calculate the uncertainty associated with
the calculated the pore pressure line.
[0048] It can be appreciated that as the borehole 2 is drilled
deeper into the earth 3 in a real time LWD application the second
depth interval can be continuously shifted deeper into the earth 3
or widened so that the lower part of the interval extends deeper
into the borehole 2. In addition, the first depth interval may also
be shifted or widened deeper into the borehole 2. As the depth
intervals are shifted or widened, these new intervals are
continuously populated with formation measurements performed within
these intervals. In one or more embodiments, the second depth
interval maintains a constant length and is continuously shifted to
be at the deepest point of the drilling run up to where the normal
compaction trend ends. In one or more embodiments, the depth
intervals are changed with drilling such as to maintain a
predefined ratio of the lengths of the depth intervals to the total
drilling depth (e.g., the lengths of the depth intervals are
maintained at 0.1 times the total drilling depth). In one or more
embodiments, the upper depth interval and the upper point of the
lower depth interval remain fixed while the lower point of the
lower depth interval is continuously moved deeper in the borehole.
It can be appreciated that there are many approaches to shift or
widen the depth intervals either continuously as the borehole is
being drilled or at certain time or drilling distance intervals and
that these additional approaches are inherently included in this
disclosure.
[0049] It can be appreciated that as the depth intervals are
shifted or widened, the steps of the method 20 are iterated to
provide a latest estimate of the pore pressure line and the
associated uncertainty.
[0050] It can be appreciated that the method 20 can be performed
using more than one pore pressure related log and that a combined
statistical analysis can be performed on all pluralities of
trendlines established from each log. In addition, the pore
pressure line (e.g., the average pore pressure line) and its
associated uncertainty can be calculated from these pluralities of
trendlines.
[0051] It can be appreciated that trendlines can be established by
linear regression of all measurement points in the upper and lower
depth intervals in lieu of a selection of only one measurement
point in each interval to establish a trendline. As the depth
intervals are shifted or widened and more formation measurement
points are obtained, a plurality of trendlines are established and
used to determine the pore pressure line and the associated
uncertainty.
[0052] It can be appreciated that the pore pressure related logs
for the use in the method 20 can be obtained from boreholes
different from the borehole being drilled (e.g., offset boreholes
or wells). In real time LWD applications, the analysis of
trendlines can be performed on pore pressure related logs from
offset wells, for instance on porosity-indicating logs from the
target borehole being drilled. If the pore pressure related logs
originate from different locations, a weighting function may be
applied to the derived trendlines in order to represent the
transferability of characteristics between the locations of the
boreholes wherein the logs were acquired.
[0053] In one or more embodiments, the method 20 can include a step
for identifying the presence of shale such as with a gamma-ray log
for example and for filtering out those pore pressure related
measurements performed on non-shale portions of the formation.
[0054] Disclosed next is a method for estimating pore pressure
uncertainty in the overpressure region of an earth formation from
the uncertainty observed in the normal compaction interval above
the overpressure region. Already while drilling in a still normally
pressured subsurface formation, the method is able to estimate the
order of magnitude of the uncertainty associated with the pore
pressure model in the overpressure region using data obtained while
drilling in a still normally pressured subsurface formation.
Drilling operational procedures, such as determining a pressure
window for drilling, can be developed according to this
estimation.
[0055] The disclosed method uses a series of normal compaction
trendlines, calculated as described above, and calculates a
"trendline envelope" as the upper and lower bounds within which the
series of trendlines vary. Different methods can be used to define
different trendline envelopes. Irrespective of the applied method
for envelope definition, the trendline envelope shows a continuous
increase in trendline uncertainty with depth in the overpressure
zone. This increase is quantified by calculating the depth-based
derivative of the difference between the two trendline bounds as a
measure of the change in trendline envelope with depth. Whereas
this quantity has exclusively been derived from data in the normal
compaction zone, an empirical correlation between this quantity and
the magnitude of the pore pressure uncertainty in the overpressure
(undercompacted) region was observed from different data sets from
Gulf of Mexico, Asia Pacific and North Sea basins.
[0056] Two different methods are introduced here to derive the
uncertainty of the pore pressure model as a result of variations in
the normal compaction trendline: a statistical and a geometrical
approach. The statistical approach calculates one pore pressure
model using any of Equations (1) through (6), for example, for each
trendline of the series that has been calculated by the linear
regression, which likewise results in a series of n*m pore pressure
models. This series is then statistically analyzed to derive an
average pore pressure model and its standard deviation (.+-.one
sigma, see FIG. 4). Of course, a statistically sound result
requires a sufficient amount of trendlines and pore pressure models
in the series. This is achieved by setting the start and end
intervals for linear regression in a way that a sufficient amount
of data points reside in either of the two intervals, yielding a
sufficient amount of trendlines and models. For example, at least
50 data points may need to reside in either of the two intervals,
yielding more than 2500 trendlines and models.
[0057] The second proposed method extracts the two normal
compaction trendlines exhibiting the largest and smallest slopes,
respectively, out of the series of trendlines. These two trendlines
are then used to calculate the pore pressure models by using, for
example, any of Equations (1) through (6).
[0058] An example for the trendline envelopes is shown in FIG. 7.
The track in FIG. 7A shows a logarithmically scaled resistivity
log, an average normal compaction trendline (NCTL) and the
NCTL's.+-.1 standard deviation. In this example, the normal
compaction interval ends at around 900 meter. Note that the NCTL's
do not cross each other at .about.800 meter, hence only the average
normal compaction trendline is a straight line on a
semi-logarithmic scale. The difference between the two enveloping
trendlines (NCTL.+-.1 sigma) becomes larger with increasing depth,
in particular in the overpressure region below 900 meter. The track
in FIG. 7B shows the two extreme normal compaction trendlines with
the maximum and minimum slopes, respectively. These two NCTL's
cross each other at .about.800 meter and behave linearly on the log
10 resistivity scale. Also the difference between these two
enveloping trendlines becomes larger with increasing depth.
[0059] A quantification parameter or "Q factor" is defined
describing the increasing difference between the enveloping normal
compaction trendlines:
Q := z ( .DELTA. R N * ) , ( 7 ) ##EQU00003##
where d/dz is the derivative of .DELTA.R*.sub.N with depth z,
and
.DELTA.R*.sub.N=log.sub.10 R.sub.N.sup.u-log.sub.10 R.sub.N.sup.l
(8)
describes the difference of the upper (R.sub.N.sup.u) and lower
(R.sub.N.sup.l) bounds of the normal compaction trendlines. Of
course, Q can be defined also for calculating the uncertainty
propagation derived from acoustic slowness data or other pore
pressure related logs. The Q factor is thus a measure of how the
normal compaction trendline envelopes will change with depth, and
how this change will affect the uncertainty associated with pore
pressure. The Q factor can be used to compare the uncertainty
resulting from different pore pressure related logs (such as
acoustic logs and resistivity logs) within one well, and the Q
factor can also be used to compare the uncertainty resulting from
the same pore pressure related logs between different wells.
[0060] For the example data set presented in FIGS. 7A and 7B, the Q
factor is shown in FIG. 7C for methods 1 and 2. For method 1, the Q
factor begins with a negative sign, continually increases and
finally approaches a constant value of 0.0003/m at greater depth.
This asymptotic behavior allows the specification of one value that
is characteristic for the opening behavior of the trendline
envelopes, and the asymptotic behavior has been observed on all
test data sets that were available for the present investigation.
Therefore, a q factor is disclosed:
q:=Q where Q(z)=constant value. (9)
[0061] For method 2, the Q factor is constant for all depth,
because the trendline envelope is bound by two straight lines;
hence the change in the difference between these two is
constant.
[0062] The q factor is expected to be different for resistivity and
acoustic logs because acoustic logs generally show less
variability/curvature. A study of the q factor behavior was
performed on data sets from different world wide regions such as
Asia Pacific, Gulf of Mexico, North Sea, Offshore Canada and
Offshore South America as shown in FIGS. 8 and 9. In general, the q
factor from resistivity data proved to be larger compared to the q
factor from acoustic data, and the resistivity q factor is also
more scattered. As also expected, the q factor from method 2 is
larger (FIG. 9) compared to method 1 (FIG. 8).
[0063] For locations where multiple wells were available, a
comparison of the q factor shows that data from the Gulf of Mexico
exhibit the lowest q factor magnitudes, Asia Pacific data sets
exhibit intermediate, and North Sea data exhibit the highest q
factors. This observation implies that the analysis of normal
compaction trendline and pore pressure uncertainties should be
performed on data sets from the same geological basin.
[0064] A series of pore pressure curves PP.sub.i can also be
calculated from the series of normal compaction trendlines
R.sub.N.sup.i, applying Eaton's equation, which is rewritten here
for convenience as Equation (10):
PP i = OBG - ( OBG - PP N ) ( R 0 R N i ) x , ( 10 )
##EQU00004##
where OBG is the overburden gradient (or lithostatic pressure),
PP.sub.N is the hydrostatic pore pressure under normal conditions
(in the normal compaction zone), R.sub.o is the measured
resistivity and x is the Eaton exponent. A similar equation exists
for acoustic logs or other pressure related logs (see Equations
(2)-(6) for example). The series of pore pressure curves can then
be used to determine an average pore pressure and associated
uncertainties such as .+-.1 standard deviation. For the calculated
normal compaction trendline envelopes from FIG. 7, an example for
the calculated pore pressure uncertainty is given in FIGS. 4 and 5
for methods 1 and 2, respectively.
[0065] The pore pressure uncertainty U.sub.PP is a nonlinear
function of the trendline envelopes, as determined from inserting
the upper and lower bound of normal compaction trendlines,
R.sub.N.sup.u and R.sub.N.sup.l, into Eaton's Equation (10):
U PP = PP ( R N u ) - PP ( R N l ) = ( OBG - PP N ) R 0 x ( R N l )
x - ( R N u ) x ( R N u R N l ) x ( 11 ) ##EQU00005##
[0066] Accordingly, similar expressions can be derived from
equations (2)-(6). The pore pressure uncertainty can thus be
calculated while drilling in the overpressure region and once
porosity-indicating or other pore pressure related logs (R.sub.0 in
this case) are available.
[0067] A prediction of U.sub.PP from the q factor was found to be
possible by correlating U.sub.PP with the q factor for acoustic
data or for resistivity data. U.sub.PP was calculated using Eq.
(10) for the overpressure zone, and then depth-averaging PP and
U.sub.PP to obtain one representative value for the pore pressure
and its uncertainty within the overpressure zone. Division of
U.sub.PP by PP gives the relative depth-averaged pore pressure
uncertainty U.sub.rel/(PP).
[0068] The pore pressure uncertainty may be calculated as the
depth-averaged uncertainty of pore pressure uncertainties within
the overpressure zone as in Equation (12).
U.sub.abs(PP)= PP(R.sub.N.sup.u)-PP(R.sub.N.sup.l)
PP(R.sub.N.sup.u)-PP(R.sub.N.sup.l) (12)
Equation (12) may then be used to calculate the relative
depth-based pore pressure uncertainty as in Equation (13) with PP
being the depth-averaged pore pressure.
U rel ( PP ) = U abs ( PP ) PP _ ( 13 ) ##EQU00006##
[0069] The correlation between q and U.sub.rel(PP) was conducted on
the three multi-well data sets from the Asia Pacific region, the
Gulf of Mexico, and the North Sea, both on acoustic and resistivity
logs, respectively. For the data from the Asia Pacific region,
FIGS. 10 and 11 show the correlations for acoustic and resistivity
logs derived for methods 1 and 2. The acoustic data (FIG. 10)
clearly show a correlation between U.sub.PP and q: larger q factors
denote higher pore pressure uncertainty in the overpressure zone.
This correlation is also evident in the resistivity data of FIG.
11.
[0070] A similar observation is made on acoustic data (FIG. 12) and
resistivity data (FIG. 13) from the Gulf of Mexico. Finally, the
acoustic data from the North Sea (FIG. 14) show a very clear
correlation between the uncertainty and the q factor.
[0071] Potential reasons for a poor correlation between the q
factor and the pore pressure uncertainty are inadequately processed
data (no environmental corrections applied to resistivity logs),
short normally compacted intervals for automatic analysis,
geological circumstances (such as shallow water flows, structural
features, salt) which complicate the interpretation of
porosity-indicating or other pore pressure related logs, and
improper application of the automation algorithm. The latter one
requires some experience of the users of the algorithms. For
example, a sufficiently large section of the normal compaction zone
should be covered by the start and end intervals to incorporate
geometric variances in the log (for further calculations). In
addition, the number of data points in the intervals must be
sufficient to ensure a statistically relevant number of
trendlines.
[0072] The disclosed method is thus applicable for data from
similar wells at least within one region (such as the Gulf of
Mexico) and requires a sufficiently large number of drilled wells
so that the correlation between the q factor and U.sub.PP can be
derived. The method can then be applied to newly drilled wells by
calculating the q factor and comparing the q factor against the q
factors from the existing wells.
[0073] A highly beneficial feature of a real-time wellbore
stability model is to predict the uncertainty associated with a
pore pressure model in the overpressure zone by parameters acquired
still in the normally compacted zone, which this disclosure covers
in detail. If a sufficient amount of wells has been drilled in a
specific region so that a correlation between the pore pressure
uncertainty and the q factor can be derived, then a real-time
(while drilling) application as illustrated by the flow chart in
FIG. 15 may be implemented.
[0074] While drilling through the normal compaction zone and
running a real-time pore pressure model (i.e., modeling pore
pressure during the drilling operation on real-time streaming
porosity-indicating or other pore pressure related logs and other
relevant data), the onset of the overpressure zone is monitored.
Once reaching the overpressure zone, the Q or q factor can be
calculated and an expected uncertainty associated with the pore
pressure model in the overpressure zone can be predicted. Also the
uncertainty of the entire pressure window (fracture gradient,
collapse gradient which both use the pore pressure gradient as
input parameter) caused by pore pressure uncertainty can be
estimated and an operating margin be defined around the pressure
window bounds. This estimation of the operating margin is
beneficial because the calculation of pore pressure uncertainty is
based on formation evaluation sensors some meters behind the bit in
addition to the accuracy of the sensors. Further, the operating
margin can take into account the accuracy of equipment (such a
pumps and valves) required to establish a desired drilling fluid or
mud flow rate for dynamic pressure reasons, which can affect the
downhole borehole pressure at the drill bit. Finally, the drilling
conditions such as the mud weight and flow rate can be set to fit
within the operating margins, and drilling into the overpressure
zone can continue.
[0075] FIG. 15 is a flow chart for an exemplary method 150 for
drilling a borehole in an earth formation having a normal
compaction zone and an overpressure zone below the normal
compaction zone. Included in the method 150 is a method for
predicting a pressure window for drilling the borehole. Block 151
calls for drilling the borehole within the normal compaction zone
with hydrostatic pore pressure distribution using a drilling tool.
The drilling tool may include a drill tubular and any cutting tool
such as a drill bit. Block 152 calls for obtaining a pore pressure
related log using a data acquisition tool, which may be a downhole
tool or a surface tool such as a seismic data acquisition tool. The
downhole tool may include at least one of resistivity tool, a
dielectric permittivity tool, a density tool, a neutron porosity
tool, a pulsed neutron tool, a nuclear magnetic resonance tool, and
an acoustic tool in non-limiting embodiments. Block 153 calls for
reaching a transition depth in the borehole from the normal
compaction zone to the overpressure zone using the drilling tool
and identifying the transition depth from the pore pressure related
log using a processor. The transition depth may be identified by
the one or more pore pressure related logs. The processor may be
included in downhole electronics or in a surface processing system
in non-limiting embodiments.
[0076] Block 154 calls for calculating pore pressure uncertainty in
the overpressure zone from the pore pressure related log in the
normal compaction zone using the processor. Alternatively, the pore
pressure uncertainty may be calculated from a pore pressure related
data value, which may be obtained from the pore pressure related
log. The pore pressure related log or data value may also be
obtained from a data acquisition tool, which may be the downhole
tool or the surface data acquisition tool. The pore pressure
uncertainty may be calculated by inputting the pore pressure
related log data and pore pressure indicating values relating to
the normal compaction trendline into a pore pressure model (e.g.,
Eq. (1)-(6)). The deviation of the pore pressure calculated using
the actual pore pressure related log data from the pore pressure
calculated using pore pressure indicating values corresponding to
the normal compaction trendline provides a measure of the
uncertainty. Data from two or more previously drilled boreholes may
be used to generate a curve relating pore pressure uncertainty to
q-factor. At least two previously drilled boreholes will provide a
minimum level of assurance that the data is applicable to the
formation being currently drilled. In a previously drilled
borehole, the q-factor is calculated from data from a
porosity-indicating log using Methods 1 or 2 for example. In one or
more embodiments, a straight line may be drawn through two or more
data points obtained from data from two or more previously drilled
boreholes. In one or more embodiments, a mathematical function,
such as a polynomial, may be used to generate a curve relating
uncertainty to q-factor. Hence, once a q-factor is calculated for a
borehole being presently drilled, an associated pore pressure
uncertainty can be determined using the identified correlation.
[0077] Block 155 calls for estimating uncertainty of a pressure
window for drilling fluid using the calculated pore pressure
uncertainty and applying the estimated uncertainty to the pressure
window to provide a modified (e.g., reduced) pressure window that
accounts for pore pressure uncertainty using the processor.
[0078] Block 156 calls for defining an operating margin and
applying the operating margin to the modified pressure window to
provide an operating pressure window. The operating margin relates
to the distance or margin between the modified drilling pressure
window due to pore pressure uncertainty and the operating drilling
pressure window that a drilling operator desires to maintain in
order to remain within the bounds of the modified drilling pressure
window. In one or more embodiments, instrument uncertainty and
equipment uncertainty (e.g., pump speed, pump output pressure, and
valve position) are used to determine the margins between the
drilling pressure window and the operating pressure window.
Additional margins may be added to account for unknown factors. By
drilling within the operating drilling pressure window (and thus
within the modified drilling pressure window due to pore pressure
uncertainty), the drilling operator has assurance that the drilling
operation will be maintained within the drilling pressure
window.
[0079] Block 157 calls for defining a drilling parameter for
drilling within the operating pressure window. In one or more
embodiments, the drilling parameters include drilling fluid weight
or density, drilling fluid pump speed, drilling fluid pump output
pressure, drilling fluid outlet valve position, a drilling fluid
flow rate, an equivalent circulating drilling fluid density, an
equivalent static drilling fluid density, and/or a standpipe
pressure. And, block 158 calls for drilling into the overpressure
zone using the operating pressure window for the drilling fluid.
The pressure of the drilling fluid in the borehole annulus downhole
is controlled to be within the operating pressure window. In one or
more embodiments, the computer processing system 12 is a controller
that maintains the pressure of the drilling fluid within the
operating pressure window by controlling the drilling fluid pump
and/or the drilling fluid flow control valve.
[0080] The method 150 may also include monitoring pore pressure to
verify the predicted pore pressure uncertainty. If the pore
pressure exceeds the uncertainty bounds, then the drilling pressure
window and subsequently the operating pressure window can be
modified or reduced further to account for the increased
uncertainty. The pore pressure can be monitored by the
porosity-indicating logs and a model relating porosity to pore
pressure or by performing a formation pressure test using a probe
(not shown) that seals to a wall of the borehole to measure the
formation pressure or other pore pressure related measurements.
[0081] The method 150 may include determining at least one pore
pressure related trendline using the pore pressure related data
value and extrapolating the at least one pore pressure related
trendline. Determining here is meant to include calculating,
plotting, and/or estimating. The trendline here may include the
trendline of the pore pressure related log.
[0082] The method 150 may include deriving a representative pore
pressure related trendline from the at least one pore pressure
related trendline. The representative pore pressure related
trendline may be an average, a most frequently measured value,
characteristic value (e.g., average) of data interval the measure
data falls into.
[0083] The method 150 may include monitoring at least one
equivalent of drilling fluid pressure and determining if the
monitored drilling fluid pressure equivalent is within equivalents
of an upper bound and a lower bound of the operating pressure
window. Equivalents of drilling fluid pressure may include
equivalent static density of the drilling fluid, equivalent
circulating density of the drilling fluid, and equivalent drilling
fluid weight.
[0084] In the method 150, the pore pressure uncertainty may account
for at least one of instrument error, equipment calibration error,
statistical error of measurement apparatus or method, regression
error of trendlines when the trendline comprises a plurality of
trendlines, and variation of trendlines when the trendline
comprises a plurality of trendlines.
[0085] In the method 150, the pressure window may be defined at
least in part by a fracture gradient, a pore pressure gradient, and
a collapse gradient and the pore pressure uncertainty affects at
least partly one of the fracture gradient and the collapse
gradient.
[0086] In support of the teachings herein, various analysis
components may be used, including a digital and/or an analog
system. For example, the downhole electronic unit 11, the surface
computer processing 12, or the downhole tool 10 may include the
digital and/or analog system. The system may have components such
as a processor, storage media, memory, input, output,
communications link (wired, wireless, pulsed mud, optical or
other), user interfaces, software programs, signal processors
(digital or analog) and other such components (such as resistors,
capacitors, inductors and others) to provide for operation and
analyses of the apparatus and methods disclosed herein in any of
several manners well-appreciated in the art. It is considered that
these teachings may be, but need not be, implemented in conjunction
with a set of computer executable instructions stored on a
non-transitory computer readable medium, including memory (ROMs,
RAMs), optical (CD-ROMs), or magnetic (disks, hard drives), or any
other type that when executed causes a computer to implement the
method of the present invention. These instructions may provide for
equipment operation, control, data collection and analysis and
other functions deemed relevant by a system designer, owner, user
or other such personnel, in addition to the functions described in
this disclosure.
[0087] Further, various other components may be included and called
upon for providing for aspects of the teachings herein. For
example, a power supply (e.g., at least one of a generator, a
remote supply and a battery), cooling component, heating component,
magnet, electromagnet, sensor, electrode, transmitter, receiver,
transceiver, antenna, controller, optical unit, electrical unit or
electromechanical unit may be included in support of the various
aspects discussed herein or in support of other functions beyond
this disclosure.
[0088] Elements of the embodiments have been introduced with either
the articles "a" or "an." The articles are intended to mean that
there are one or more of the elements. The terms "including" and
"having" are intended to be inclusive such that there may be
additional elements other than the elements listed. The conjunction
"or" when used with a list of at least two terms is intended to
mean any term or combination of terms. The terms "first" and
"second" are used to distinguish elements and are not used to
denote a particular order. The term "couple" relates to coupling a
first component to a second component either directly or indirectly
through an intermediate component.
[0089] It will be recognized that the various components or
technologies may provide certain necessary or beneficial
functionality or features. Accordingly, these functions and
features as may be needed in support of the appended claims and
variations thereof, are recognized as being inherently included as
a part of the teachings herein and a part of the invention
disclosed.
[0090] While the invention has been described with reference to
exemplary embodiments, it will be understood that various changes
may be made and equivalents may be substituted for elements thereof
without departing from the scope of the invention. In addition,
many modifications will be appreciated to adapt a particular
instrument, situation or material to the teachings of the invention
without departing from the essential scope thereof. Therefore, it
is intended that the invention not be limited to the particular
embodiment disclosed as the best mode contemplated for carrying out
this invention, but that the invention will include all embodiments
falling within the scope of the appended claims.
* * * * *