U.S. patent application number 11/022016 was filed with the patent office on 2005-09-29 for contamination estimation using fluid analysis models.
Invention is credited to Akkurt, Ridvan, Proett, Mark A..
Application Number | 20050216196 11/022016 |
Document ID | / |
Family ID | 34748804 |
Filed Date | 2005-09-29 |
United States Patent
Application |
20050216196 |
Kind Code |
A1 |
Akkurt, Ridvan ; et
al. |
September 29, 2005 |
Contamination estimation using fluid analysis models
Abstract
Methods and systems are described for estimating of the level of
contamination of downhole fluid using physical property
measurements, and mathematical modeling of contamination functions
and fluid property mixing laws. The proposed approaches enable
computation of estimates of the pumping time needed to achieve a
certain contamination threshold level.
Inventors: |
Akkurt, Ridvan; (Kingwood,
TX) ; Proett, Mark A.; (Missouri City, TX) |
Correspondence
Address: |
JONES DAY
222 EAST 41ST ST
NEW YORK
NY
10017
US
|
Family ID: |
34748804 |
Appl. No.: |
11/022016 |
Filed: |
December 23, 2004 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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60532502 |
Dec 24, 2003 |
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Current U.S.
Class: |
702/6 |
Current CPC
Class: |
G01N 24/081 20130101;
E21B 49/08 20130101 |
Class at
Publication: |
702/006 |
International
Class: |
G06F 019/00 |
Claims
What is claimed is:
1. A method for estimating levels of contamination in borehole
fluids, comprising the steps of: (a) providing a first mathematical
contamination function model which expresses a time behavior of one
or more fluid properties of a mixture of formation fluids and
contamination fluids drawn from a borehole, where said one or more
fluid properties are sensitive to the fraction of contamination
fluids in the mixture; (b) providing a second mathematical mixing
law function model expressing at least one of said one or more
fluid properties of a fluid mixture in terms of corresponding
properties of formation fluids and contamination fluids in the
mixture; (b) drawing fluids from the borehole into a fluid
analyzer; (c) measuring at least one of said one or more properties
of the drawn fluids by the analyzer; and (d) estimating the level
of contamination in the fluids drawn from the borehole at one or
more points in time based on the at least one measured fluid
property and the provided mathematical models in step (a) and step
(b).
2. The method of claim 1, wherein the provided mathematical models
apply to miscible fluid contamination.
3. The method of claim 1, wherein the provided mathematical models
apply to immiscible fluid contamination.
4. The method of claim 1, wherein the measured property of the
drawn fluids is viscosity.
5. The method of claim 4, wherein viscosity is measured using
nuclear magnetic resonance (NMR) measurement.
6. The method of claim 5, wherein the NMR measurement is one or
both of: the spin-lattice relaxation time T.sub.1 and spin-spin
relaxation time T.sub.2.
7. The method of claim 6 further comprising the step of computing
log-mean values of the T.sub.1 and/or T.sub.2 relaxation times.
8. The method of claim 5, wherein the same mathematical model in
step (a) is applied to two or more bands of a T.sub.1 spectrum.
9. The method of claim 5, wherein two or more different
mathematical models in step (a) are applied to at least one band of
the T.sub.1 spectrum.
10. The method of claim 7, wherein the log-mean values are computed
using the expression: 23 log ( T 1 Lm ) = j a j log ( T 1 j ) j a j
,where aj are the amplitudes of a given T.sub.1 spectrum, and j is
the number of T.sub.1 bins used in the inversion.
11. The method of claim 4, wherein the first contamination function
model provided in step (a) is one or more of: Arctan, Exponential,
Arctan-shifted 1, Arctan-shifted 2, Arctan-shifted 3, and the Error
Function models.
12. The method of claim 1, wherein the measured property of the
drawn fluids is a physical property of the fluid.
13. The method of claim 12, wherein the measured property of the
drawn fluids is one or more of: resistivity, capacitance, density,
viscosity, hydrogen index, compressibility, speed of sound, pumping
pressures, or optical density.
14. The method of claim 4, wherein a viscosity mixing law used in
the second mathematical model is one of: (i) Todd et al.; (ii)
Power-Law, (iii) Arrhenius, or (iv) Modified Arrhenius.
15. A method for downhole formation testing, comprising the steps
of: (a) providing measurement signals corresponding to a mixture of
formation fluids and contamination fluids drawn from a borehole,
the mixture entering a downhole fluid analyzer; (b) based on the
provided measurement signals, determining parameters of a
contamination function, which expresses the time behavior of one or
more fluid properties of the fluid mixture drawn from the borehole;
(c) computing from the determined contamination function of a value
estimate of said one or more fluid properties for at least one low
level of contamination and for at least one high level of
contamination; and (d) computing a contamination index for the
mixture of fluids drawn from the borehole at different time
instants based on the computed value estimates and a fluid mixing
law relating properties of the drawn fluids in terms of the
corresponding properties of the formation fluids and the
contamination fluids.
16. The method of claim 15, wherein the measurement signals are
nuclear magnetic resonance (NMR) signals.
17. The method of claim 16, wherein the NMR measurement signals
correspond to one or both of: the spin-lattice relaxation time T1
and spin-spin relaxation time T2 of the fluids drawn from the
borehole.
18. The method of claim 17 further comprising the step of computing
a log-mean value of at least one of the spin-lattice relaxation
time T1 and spin-spin relaxation time T2 of the fluids drawn from
the borehole, and using the computed log-mean value to determine
parameters of the contamination function.
19. The method of claim 17, wherein a fluid property of the mixture
in step (b) is viscosity.
20. The method of claim 18, wherein in step (c) a value estimate is
obtained for a fluid property at a zero contamination level and at
a 100% contamination level.
21. The method of claim 15, wherein the property of the drawn
fluids in step (b) is one or more of: resistivity, capacitance,
density, viscosity, hydrogen index, compressibility, speed of
sound, pumping pressures or optical density.
22. The method of claim 21, wherein the fluid mixing law is
empirically derived.
23. The method of claim 21, wherein the fluid mixing law is
non-linear.
24. The method of claim 21, wherein the fluid mixing law is
linear.
25. The method of claim 15, wherein the property of the drawn
fluids in step (b) is viscosity, and a viscosity mixing law used in
step (d) is one of: (i) Todd et al.; (ii) Power-Law, (iii)
Arrhenius, or (iv) Modified Arrhenius.
26. The method of claim 15, wherein the fluid property in step (b)
is viscosity and the contamination function is one or more of:
Arctan, Exponential, Arctan-shifted 1, Arctan-shifted 2,
Arctan-shifted 3, and the Error Function.
27. The method of claim 18, wherein the log-mean value is computed
using one or more subbands in the corresponding T1 or T2 spectrum
of the NMR signals.
28. The method of claim 27, wherein two or more subbands of the
corresponding NMR spectrum are combined either linearly or
nonlinearly.
29. An apparatus for estimating levels of contamination of
formation fluids in a borehole, comprising: (a) means for providing
a mathematical model comprising a contamination function which
expresses the time behavior of one or more fluid properties of a
mixture of formation fluids and contamination fluids drawn from the
borehole, where said one or more fluid properties are sensitive to
the fraction of contamination fluids in the mixture, and a mixing
law describing at least one of said one or more fluid properties of
the drawn fluids in terms of the corresponding properties of the
formation fluids and the contamination fluids; (b) means for
drawing fluids from the borehole into a fluid analyzer; (c) means
for measuring at least one of said one or more properties of the
drawn fluids by the analyzer; and (d) means for estimating the
level of contamination in the fluids drawn from the borehole at one
or more time intervals based on the at least one measured fluid
property and the provided mathematical model.
30. A computer-usable medium having computer-readable program code
thereon for use with fluid analyzers, the program code including
code structured to: (a) collect measurement signals corresponding
to a mixture of formation fluids and contamination fluids drawn
from the borehole and entering a downhole fluid analyzer; (b)
determine parameters of a contamination function, which expresses
the time behavior of one or more fluid properties of a the mixture
drawn from the borehole, based on the collected measurement
signals; and (c) based on a fluid mixing law for the one or more
fluid properties determined in (c) provide an estimate of at least
one of (i) the level of contamination, or (ii) the pumping time for
reaching a given level of contamination.
31. The computer-usable medium of claim 30, where at least one
mathematical model comprises a viscosity mixing rule.
32. The computer-usable medium of claim 30, wherein in (c) the
fluid mixing rule is a viscosity mixing rule and is one or more of:
(i) Todd et al.; (ii) Power-Law, (iii) Arrhenius, or (iv) Modified
Arrhenius.
33. The computer-usable medium of claim 30, wherein the measurement
signals are NMR signals.
34. The computer-usable medium of claim 30, wherein the fluid
property is viscosity, and the contamination function is one or
more of: Arctan, Exponential, Arctan-shifted 1, Arctan-shifted 2,
Arctan-shifted 3, and the Error Function models.
Description
[0001] This application claims priority from provisional
application Ser. No. 60/532,502, filed Dec. 24, 2003, the content
of which is incorporated by reference for all purposes.
1. FIELD OF THE INVENTION
[0002] This invention relates to systems and methods for
determining the level of mud filtrate contamination in formation
fluids.
2. BACKGROUND OF THE INVENTION
[0003] Many oil industry applications require the analysis of
downhole fluids. In the prior art this was typically done by
bringing samples to the surface using sealed containers, and
sending the samples for laboratory measurements. A number of
practical limitations are associated with this approach. The main
concern usually is that the samples taken to the surface may not be
representative of the downhole geologic formation. This is due to
the fact that only limited sample material from a limited number of
downhole locations can be extracted and taken to the surface, and
thus laboratory testing provides only an incomplete picture of the
downhole conditions. Furthermore, samples are often contaminated
with mud filtrate, and therefore are not truly representative of
the native formation fluids.
[0004] More recently, fluid analysis became possible using pumpout
formation testers that provide downhole measurements of certain
fluid properties and enable the collection of a large number of
representative samples stored at downhole conditions. Three
families of such tools have been introduced in the past--the
modular dynamic formation tester (MDT) by Schlumberger, the
Reservoir Characterization Instrument (RCI) by Baker Atlas, and
most recently the Reservoir Description Tool (RDT) by Halliburton.
These tools are generally designed to obtain representative
formation fluid samples and provide key petrophysical information
to determine the reservoir volume, producibility of a formation,
type and composition of the movable fluids, and to predict
reservoir behavior during production.
[0005] One of the remaining problems encountered in the operation
of such tools is to avoid contamination of the fluid naturally
present in the formation with other fluids, in particular the
various types of drilling muds used in drilling operations.
Drilling mud, also known as drilling fluid, is typically pumped
down the center of the hollow drill stem to emerge again at the
surface of the borehole. It lubricates the drill shaft, cools the
borehole, carries away the drilling detritus, and serves as a
wetting-phase, which facilitates the flow of hydrocarbons from the
formation and into the borehole. Various types of drilling muds are
generally classified based on the type of filtrate used therein.
The mud filtrate chosen dictates the mud's function and
performance, as well as formation invasion effects.
[0006] There are two major types of mud filtrates: water-based and
oil-based. Water-based mud (WBM) filtrates include, but are not
limited to, freshwater, seawater, saltwater (brine) and others, or
a combination of any of these fluids. In the oil-based mud (OBM),
the filtrate is an oil product, such as diesel or mineral oil. More
generally, oil-based mud is characterized as any type of
non-aqueous fluid. For the purposes of the present disclosure,
oil-based mud also includes the recently developed variety of oil
mud that is also referred to as synthetic-based muds. These
synthetic-based muds include, without limitation, olefinic-,
naphthenic-, and paraffinic-based compounds. Dependent on the type
of mud used in the drilling process, different factors affect the
ability of the tool the accurately estimate the contamination
levels at a given point during pumpout.
[0007] For WBM drilling, mixing with the formation fluid is
considered an immiscible process, and determination of the degree
of contamination of the fluid using is relatively straightforward.
More challenging is the problem of estimating the degree of
contamination in OBM drilling when attempting to obtain high
quality formation fluid samples, because these mud filtrate fluids
are mixed in the formation oil. This mixing can be immiscible or
miscible, but either way complicate the determination of the degree
of contamination (with immiscible invasion the fluids to not
dissolve with each other but mix, with miscible mixing the fluids
dissolve in a diffusion process). For example, the presence of even
small volumes of oil-base filtrate in the sample can significantly
alter the properties of the formation oil. As a result, in-situ
quantification of the oil-base material contamination in the
formation oil is difficult, and poorly quantified samples may not
be representative of the formation fluid of interest.
[0008] Additional difficulties are presented in differentiating
oil-based mud from connate oil when oil-based filtrate invades the
formation. One method for differentiating oil-based mud from
connate oil is disclosed in U.S. Pat. No. 6,107,796, owned by the
assignee of the present invention, which is incorporated herein by
reference. However, no reliable method has been provided for
determining the level of contamination of mud filtrate in formation
fluids.
[0009] The most frequently used prior art approach to estimating
contamination has been based on the optical properties of the
fluids entering a tool. Schlumberger provides for in-situ
contamination estimation using an Optical Fluid Analyzer (OFA).
Baker-Atlas also offers a service similar to the OFA. The OFA
exploits the differences in the absorption spectrum (i.e., color
contrast) between the OBM contaminant and the formation fluid to
deconvolute the spectrum from a fluid measurement (see, e.g., U.S.
Pat. Nos. 6,178,815, 6,274,865, 6,343,507 and 6,350,986, which are
incorporated herein by reference for background). The OFA measures
the optical density (OD) of the flowing fluid and uses empirical
relationships to transform the OD into data on contamination by
determining the composition of the measured absorbed light spectrum
from the sample. Based on this absorption spectrum one can estimate
the types of materials present in the fluid and the proportion of
each material in the fluid. While the industry has learned how to
interpret OFA data over the years, it still is not robust in
certain applications where the color contrast is small, or is
masked, as is frequently the case in light oils and condensates.
One problem with this approach is that it assumes that the measured
property is directly linked to the contamination, which may not
necessarily be the case.
[0010] Another approach to contamination estimation is to use
electrical resistivity methods, which involve the measurement of
the apparent resistivity of fluids entering the tool. While these
measurements are straightforward to implement and, for example, can
easily distinguish between oil and water it cannot reliably
distinguish contaminants in OBM situations. Various other sensors
measuring optical properties, resistivity, capacitance and others
within formation sampling tools have been used to estimate levels
of fluid contamination during the pump-out phase, but no robust
solution has been found yet.
[0011] A more recent approach to contamination estimation is
provided by the use of nuclear magnetic resonance (NMR)
measurements. NMR measurements of geologic formations may be done
using, for example, the MRIL.RTM. tool made by NUMAR, a Halliburton
company, and the CMR family of tools made by Schlumberger. Details
of the structure of the MRIL.RTM. tool and the measurement
techniques it uses are discussed in U.S. Pat. Nos. 4,710,713;
4,717,876; 4,717,877; 4,717,878; 4,939,648; 5,055,787; 5,055,78;
5,212,447; 5,280,243; 5,309,098; 5,412,320; 5,517,115, 5,557,200;
5,696,448; 5,936,405; 6,005,389; 6,023,164; 6,051,973; 6,107,796;
6,111,408; 6,242,913; 6,255,819; 6,268,726; 6,362,619; 6,512,371;
6,525,534; 6,531,868; 6,541,969; 6,577,125 and 6,583,621, all of
which are commonly owned by the assignee of the present
application. The CMR tool is described, for example, in U.S. Pat.
Nos. 5,055,787 and 5,055,788 to Kleinberg et al. and further in
"Novel NMR Apparatus for Investigating an External Sample," by
Kleinberg, Sezginer and Griffin, J. Magn. Reson. 97, 466-485, 1992.
NMR devices, methods and pulse sequences for use in logging tools
are also in U.S. Pat. Nos. 4,350,955 and 5,557,201. The content of
the above patents and publications is hereby expressly incorporated
by reference for background. A brief discussion of the main NMR
measurement parameters follows.
[0012] Basic NMR Properties and Measurement Parameters
[0013] NMR measurements are based on exposing an assembly of
magnetic moments, such as those of hydrogen nuclei, to a static
magnetic field. The assembly tends to align along the direction of
the magnetic field, resulting in a bulk magnetization. A magnetic
field having direction perpendicular to the static magnetic field
is applied to rotate the magnetic moments away from the direction
of the bulk magnetization. The rate at which the rotated moments
return to the equilibrium bulk magnetization after application of
the oscillating magnetic field is characterized by the parameter
T.sub.1, known as the spin-lattice relaxation time. T.sub.1 values
are in the range of milliseconds to several seconds.
[0014] Another related and frequently used NMR parameter is the
spin-spin relaxation time constant T.sub.2 (also known as
transverse relaxation time), which is an expression of the
relaxation due to inhomogeneities in the local magnetic field over
the sensing volume of the fluid in the analyzer, e.g., a logging
tool. In bulk fluids T.sub.2 basically equals T.sub.1, but may
differ in heavy oil components, such as asphaltenes, resins, etc.
Both relaxation times provide information about the properties of
the formation fluid, such as the formation porosity and the
composition and quantity of the formation fluid.
[0015] Another measurement parameter used in NMR is the formation
diffusivity. Generally, diffusion refers to the motion of atoms in
a gaseous or liquid state due to their thermal energy. The
self-diffusion coefficient (D) of a fluid is inversely proportional
to the viscosity (.eta.) of the fluid, a parameter of considerable
importance in borehole surveys. Stokes' equation yields that:
D.varies.kT/.eta., (k=1.38.times.10.sup.-23 J/K) (1)
[0016] Viscosity and diffusivity are both related to the
translational motion of molecules and therefore are interrelated.
At higher temperatures T, a molecule contains more energy and can
move faster against a given "friction" .eta., therefore D is
proportional to the temperature. Diffusivity is a property that can
be precisely determined by NMR techniques without disturbing or
altering the fluid. The relationship D.varies.T/.eta. has been
verified over a wide range of viscosities at different temperatures
and pressures by NMR spin-echo experiments.
[0017] Relationships involving the NMR relaxation times T.sub.1 and
T.sub.2 must be examined with care. The applicability of
expressions of the form:
T.sub.1, T.sub.2.varies.kT/.eta. (2)
[0018] is more limited than that of Eq. (1). The main reason is
that gas/liquid mixtures have more than one relaxation mechanism:
dipole-dipole for the liquid phase and mainly spin-rotation for the
gas phase.
[0019] In a uniform magnetic field, diffusion has little effect on
the decay rate of the measured NMR echoes. In a gradient magnetic
field, however, diffusion causes atoms to move from their original
positions to new ones, which also causes these atoms to acquire
different phase shifts compared to atoms that did not move. This
contributes to a faster rate of relaxation.
[0020] Recently, Halliburton introduced MRILab.RTM., a logging tool
with the ability to analyze key reservoir fluid properties,
including fluid type, viscosity and gas-to-oil ratio (GOR), in
real-time at reservoir temperature and pressure. MRILab.RTM. is
based on NMR measurements and operates as a component of
Halliburton's Reservoir Description Tool.TM. (RDT), making
laboratory-quality measurements on reservoir fluids that are
necessary for reservoir engineering and completion design. FIG. 5
shows a simplified diagram of a downhole NMR fluid analysis
apparatus, such as the MRILab.RTM., that provides NMR measurements
to which the contamination estimation methods of the present
disclosure can be applied in an illustrative embodiment. Fluids
enter the device at the top and pass through two sections, referred
to as polarization and resonance sections, respectively.
Measurements are performed as the fluid flow passes through the
device. U.S. application Ser. No. 10/109,072, which is hereby
incorporated by reference, discloses details of this device, which
are summarized for reference in Appendix A.
[0021] Turning back to the problem of contamination estimation, the
fundamental difficulty in NMR-based approaches to such estimation
is the lack of models that can predict the relaxation spectrum
(i.e., the T.sub.1 or T.sub.2 spectrum) of a mixture of two fluids
that are miscible. Existing NMR methods for estimating
contamination, including when the MRILab.RTM. was first introduced,
were based initially on a parameter called "sharpness." The
sharpness of an NMR distribution is defined as: 1 S = N i a i 2 ( i
= 1 N a i ) 2 ( N - 1 ) ( i a i ) 2 , for 1 i N , ( 3 )
[0022] where a.sub.i are the amplitudes, and N is the number of
components in a T.sub.1 distribution. (See Bouton, J. et al.
"Assessment of Sample Contamination by Downhole NMR Fluid
Analysis", SPE-71714, presented at SPE ATCE, New Orleans, La.
(2001) incorporated herein for background). Although it was thought
that sharpness was sensitive to contamination levels down to 10%,
experience has shown that sharpness in general is not a very robust
indicator of contamination.
[0023] The driving idea behind the use of the sharpness parameter
was that, while OBM has a narrow distribution (implying a lower S
value), distributions associated with native crudes are broader.
However, relaxation spectra of low viscosity crudes are also very
narrow and in the low viscosity/high GOR case, it may not be
possible to distinguish one species from the other. Furthermore,
both bulk water and natural gas have narrow distributions. The
information from sharpness is relative, in that it is an indicator
of the changes taking place, but it may not be sufficient to define
end point states quantitatively. Additionally, the sharpness
parameter is derived from the T.sub.1 distribution, which to a
certain extent can be affected by the level signal-to-noise ratio
(SNR) or distribution shape, which may lead to changes in the
T.sub.1 spectra that are unrelated to changes in contamination.
[0024] Given the difficulties using the prior art approaches, there
exists a need for more accurate and robust methods for determining
the level of contamination of mud filtrate in formation fluids.
3. SUMMARY OF THE INVENTION
[0025] The present invention provides a novel approach for
determining the level of contamination in formation fluids. As used
herein, a contaminant could be any fluid originating from mud
filtrate that invades the reservoir during the drilling of a well;
contamination (c) is the volume fraction of the contaminant in a
fluid sample, where 0.ltoreq.c.ltoreq.1. The following additional
terms and expressions are used in the description of the proposed
approach: a contamination function is a temporal function that
substantially matches the behavior of the contamination fluid
fraction while pumping a sample from an invaded zone. More
generally, a contamination function is applicable to
multiple-component fluid systems including systems comprised of
miscible or immiscible liquids, including liquids containing
dissolved, suspended or dispersed solids. Unless the context
indicates otherwise, the term "fluid mixture" includes in its
meaning a mixture of liquids (either miscible or immiscible) or a
liquid containing soluble, suspended or dispersed solids. In
accordance with the proposed approach, a contamination function is
a mathematical model that may be derived, for example, through
simulations or observation.
[0026] A mixing law (or mixing rule), as used in this disclosure,
is a mathematical function that describes a property of a mixture
in terms of the properties of its constituents. A mixing law would
thus allow for the property of the mixture to be predicted if the
weight or volume functions for the constituents, and the properties
of these constituents, are known. Several examples of mixing laws
are provided in the illustrative embodiment in which the physical
property of the fluid being monitored is its viscosity. Different
mixing laws may apply for other physical properties. In general,
all that is required for the mixing law is to provide a
mathematical expression that relates a property of a fluid mixture
in terms of the constituent components properties (i.e., the values
of such property for 0% and 100% contamination, respectively).
[0027] Using these definitions, the proposed contamination
estimation approach is based on the use of a contamination function
that describes the time behavior of a particular physical property
of the mixture of fluids entering a tool, and a mixing-law or rule
that is used to estimate the volume fractions of the constituent
fluids given information about or measurements of the bulk physical
property. In a specific illustrative embodiment, the physical
property is viscosity, which is monitored indirectly using
relaxation measurements (i.e., T.sub.1 or T.sub.2) obtained from an
NMR fluid analyzer, such as the MRILab.RTM. fluid analyzer. Other
physical properties that can be used in alternate embodiments
include resistivity, capacitance, density, hydrogen index,
compressibility, speed of sound, pumping pressures, optical
density, and others.
[0028] In particular, the determined values of one or more of the
above fluid properties over time are fit to a parameterized
contamination function. By matching a contamination function to the
fluid property measured over a period of time, the variables of
this time function are determined, for example, through regression.
Once the variables of the contamination function are determined,
this function can predict how the fluid property changes over time.
Then, the mixing law function that relates fluid fractions to the
bulk fluid property can be used to estimate the actual
contamination over past or future time periods.
[0029] In one type of embodiments, the contamination function used
to predict the fluid property is either independent or
substantially independent from the fluid fractions in the mixing
law. These embodiments are referred to as uncoupled or loosely
coupled contamination models. In other embodiments, the mixing laws
are taken into account in tracking the bulk fluid property over
time, resulting in a coupled contamination modeling. Different
examples of such models are illustrated in the specific embodiments
described below.
[0030] In specific embodiments monitoring viscosity using NMR
measurements, several empirical contamination functions can be used
in accordance with the proposed approach, including the
exponential, the error and several versions of the arctan
contamination functions, as defined below. In another aspect of
this disclosure, the log-mean value of a NMR spectrum, in
particular the log-mean T.sub.1 value (T.sub.1Lm) is shown to track
the viscosity or other properties of the fluid and is used as an
indirect property measurement. From the contamination function that
best fits the empirical data, and a mixing law that includes
estimates of the property values at two different contamination
levels (typically at 0% and 100% contamination) one can compute the
contamination index of the fluid (considered below) as a function
of time. In the illustrative embodiments using viscosity as the
monitored physical parameter, various mixing laws, such as those
proposed by Todd et al., the power-law, various modifications of
the Arrhenius law could be used, either coupled with or uncoupled
from the select contamination function to estimate the desired
contamination index.
[0031] It will be appreciated that the mathematical modeling
approach based on the use of contamination function and mixing law
can be used to estimate the level of contamination of a sample
taken at a particular time, to compute the time required to reach
certain contamination level during pumping, or to derive other
parameters of interest during oil exploration.
[0032] Various modifications of this general approach can be used
in practice. For example, the contamination function used in a
particular experiment may be determined in advance through prior
knowledge. Further, the accuracy of prediction can be improved if
one has a priori knowledge about the monitored property value at 0%
and 100% contamination. In alternative embodiments, several
contamination functions corresponding to different physical
properties can be used to monitor the time behavior of the fluid
mixture entering the tool. These embodiments are based on the
observation that in certain fluid mixtures one property may be more
sensitive than others to the contaminant. Accordingly, an array of
devices can be used in such embodiments to measure different fluid
properties. Using this approach, for example, different
contamination estimates can be combined into a single average
contamination estimate. Individual contamination estimates may be
weighted, possibly using nonlinear regression techniques. As is the
case with MRILab.RTM. estimates of viscosity, the formation fluid
properties can be more accurately predicted because the end points
are used to determine the in-situ sample properties.
[0033] Accordingly, it is an object of this disclosure to provide
methods for estimation of the level of contamination in the fluids
flowing through an analyzer tool. Another object of the disclosure
is to provide methods for estimating the pumping time needed to
achieve a certain contamination threshold level. Yet another object
of the disclosure is to provide methods for monitoring at least one
physical property of the fluid entering the tool, such as its
viscosity, and based on mixing laws that are known or can be
derived use the monitored property to derive an estimate of the
contamination level. Additional objective is to provide a
computationally efficient algorithm for contamination estimation
that can be implemented substantially in real time.
[0034] Accordingly, in one aspect, the invention is a method for
estimating levels of contamination of formation fluids in a
borehole, and a corresponding system implementing the steps of: (a)
providing a first mathematical contamination function model which
expresses a time behavior of one or more fluid properties of a
mixture of formation fluids and contamination fluids drawn from a
borehole, where said one or more fluid properties are sensitive to
the fraction of contamination fluids in the mixture; (b) providing
a second mathematical mixing law function model expressing at least
one of said one or more fluid properties of a fluid mixture in
terms of corresponding properties of formation fluids and
contamination fluids in the mixture; (b) drawing fluids from the
borehole into a fluid analyzer; (c) measuring at least one of said
one or more properties of the drawn fluids by the analyzer; and (d)
estimating the level of contamination in the fluids drawn from the
borehole at one or more points in time based on the at least one
measured fluid property and the provided mathematical models in
step (a) and step (b).
[0035] In another aspect, the invention is a method for downhole
formation testing, comprising the steps of: (a) providing
measurement signals corresponding to a mixture of formation fluids
and contamination fluids drawn from a borehole, the mixture
entering a downhole fluid analyzer; (b) based on the provided
measurement signals, determining parameters of a contamination
function, which expresses the time behavior of one or more fluid
properties of the fluid mixture drawn from the borehole; (c)
computing from the determined contamination function of a value
estimate of said one or more fluid properties for at least one low
level of contamination and for at least one high level of
contamination; and (d) computing a contamination index for the
mixture of fluids drawn from the borehole at different time
instants based on the computed value estimates and a fluid mixing
law relating properties of the drawn fluids in terms of the
corresponding properties of the formation fluids and the
contamination fluids.
[0036] Other aspects of the disclosure are discussed in the
following detailed description, and are defined in the attached
claims.
4. BRIEF DESCRIPTION OF THE DRAWINGS
[0037] FIGS. 1A and 1B show T.sub.1 data and data analysis from
several experiments performed under downhole conditions;
[0038] FIG. 2 shows the results of sample quality vs. time
(seconds) simulations for an oil-based mud (OBM) systems, where
sample quality is given in percentages;
[0039] FIG. 3 shows the results of sample quality vs. time
(seconds) simulations for a water-based mud (WBM) system at 10
cc/sec pumping rate, where sample quality is given in
percentages;
[0040] FIG. 4 illustrates the use of NMR fluid analyzer
measurements for contamination estimation in one embodiment;
[0041] FIG. 5A is a schematic diagram of a downhole NMR fluid
analyzer; FIG. 5B is a simplified version;
[0042] FIGS. 6A-D illustrate horizontal cross sections of the
analyzer shown in FIGS. 5A and B;
[0043] FIG. 7 illustrates a schematic block diagram of the
electronics of the analyzer in one embodiment;
[0044] FIG. 8 illustrates a saturation recovery pulse sequence
diagram used for T.sub.1 measurements;
[0045] FIG. 9 shows T.sub.1 saturation-recovery data for three
different fluids as seen in an NMR fluid analyzer;
[0046] FIG. 10 shows a re-plot in the T.sub.1 domain of the data
shown in FIG. 9;
[0047] FIG. 11 illustrates a pulse sequence employed for
diffusivity measurements;
[0048] FIG. 12 shows a diffusivity measurement;
[0049] FIG. 13 shows the results of contamination estimation for
the data shown in FIG. 1A using a Coupled Log-mean T.sub.1
model;
[0050] FIG. 14 shows the results of contamination estimation for
the data shown in FIG. 1A using an immiscible fluid model.
5. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0051] The principal objective of contamination estimation is to
secure fluid samples with low levels of contamination for proper
Pressure Volume Temperature (PVT) analysis. Another objective is to
predict when to stop pumping with a high level of confidence as to
not waste rig time on unnecessary clean up pumping. Improved
contamination estimates increase the accuracy of the log analysts'
data interpretation, and help to provide better estimates of
permeability and anisotropy from the pumpout data.
[0052] The proposed contamination estimation approach described in
different embodiments below is based on the use of one or more
contamination functions describing the time behavior of a
particular physical property of a mixture of fluids entering a
tool; and one or more mixing-law models that can be used to
estimate the volume fractions of the constituent fluids given
information about or measurements of the physical property. In a
specific illustrative embodiment considered below, the physical
property is viscosity, which is monitored using indirect
measurements, i.e., T.sub.1 measurements obtained from an NMR fluid
analyzer. Other physical properties that can be used in different
embodiments include resistivity, capacitance, density, hydrogen
index, compressibility, speed of sound, pumping pressures, optical
density, and others. Contamination estimation in accordance with
this approach is done for both miscible fluids (i.e., OBM
applications) and immiscible fluids (i.e., WBM applications).
Accordingly, different contamination models are based on different
set(s) of specific assumptions or requirements, and each model may
have its particular strengths over the others. Mathematically, the
time changes of the contamination index CI over the pumping can be
expressed as:
CI(t)=fc(.alpha..sub.1, .alpha..sub.2, .alpha..sub.m,, t) (4)
[0053] where .alpha..sub.1/2 are the end points in the property
values (0% and 100% contamination), and .alpha..sub.m is the
measured property value. Turning first to the mixing law modeling
problem, in the simplest case a bulk fluid property may be assumed
to depend linearly on the corresponding properties of the
constituent fluid volume fractions (i.e., on a linear combination
of the contamination and virgin reservoir fluids). For example,
light absorption is proportional to the volume fraction of the
constituent fluids. Thus, if the end point properties of the fluid
mixture (0% and 100% contamination) are known or can be estimated,
and there is sufficient contrast in the property of the contaminant
and the reservoir fluid, measurement of the bulk property enables
straightforward contamination determination.
[0054] In the more general case, however, the mixing law is
non-linear and the end point property values are unknown. Consider
for example viscosity. As set forth in Eq. (2), viscosity is
inversely proportional to the T.sub.1 relaxation parameter in a NMR
measurement, which can be obtained substantially in real time using
a fluid analyzer. Accordingly, models based on the time or T.sub.1
domain NMR signatures of the fluids can be used for contamination
estimation in immiscible fluids, as discussed below. But such
models in general are unsuitable for miscible fluids, because there
is no simple mixing rule that relates the end-point NMR properties
to the measured NMR property as a function of the constituent fluid
component saturations.
[0055] In accordance with one important aspect of the disclosure,
the approaches in this application are based on the observation
that the log-mean value of an NMR parameter varies with
contamination over time. Previous research has shown that the echo
amplitudes in NMR measurements of a fluid entering a fluid analyzer
change with time, and as a result have developed time dependent
models where an empirical relationship was used to curve fit the
echo amplitude changes and to relate the combined time decays to
contamination. The embodiment(s) discussed below are based on the
observation that log-mean T.sub.1 (T.sub.1Lm) shifts with
contamination over time, rather than on the tracking of individual
T.sub.1 amplitudes. This observation is also applicable to the
variation in the log-mean value of other NMR parameters with
contamination over time.
[0056] In particular, the log-mean T.sub.1 shift over time can be
attributed to changes in viscosity as the fluid being pumped
changes to different proportions of filtrate oil or water. A study
of field results from an NMR fluid analyzer, as well as multi-phase
forward modeling results, shows that contamination (c) varies with
time (t) in a predictable pattern. Therefore, a possible solution
to the contamination estimation problem for miscible fluids is to
use an indirect property, such as T.sub.1Lm, the log-mean T.sub.1.
T.sub.1Lm is inversely related to viscosity and can be used to
estimate contamination when combined with a mixing law that is
based on viscosities of two miscible fluids. Because the log-mean
T.sub.1 is used in the illustrative embodiments discussed below,
some explanation and definitions are in order.
[0057] Calculation of Log-Mean T.sub.1 Values
[0058] In one embodiment, the contamination estimation models are
applied to a log-mean value derived from one or more NMR
measurements. The derivation of the log-mean value of a T.sub.1
spectrum is presented below in a preferred embodiment. However,
similar relations apply for deriving the log-mean value of other
spectra obtained by NMR measurements, such as a T.sub.2 spectrum or
diffusivity spectra. Modifications and variations of the
approaches, disclosed herein, based on the use of a log-mean value
of an NMR-based measurement will be apparent to one of ordinary
skill in the art without undue experimentation.
[0059] As noted, in a preferred embodiment, the contamination
estimation models are applied to log-mean T.sub.1 values. The
log-mean T.sub.1 of a T.sub.1 spectrum is calculated using the
expression: 2 log ( T 1 Lm ) = j a j log ( T 1 j ) j a j , ( 5
)
[0060] where a.sub.j are the amplitudes of a given T.sub.1
spectrum, and j is the number of T.sub.1 bins used in the
inversion.
[0061] The typical range for the T.sub.1 relaxation parameter is
from about 1 ms to 20,000 ms. In one embodiment, all of the
amplitudes that cover the measured range are used in the
computation of T.sub.1Lm. In alternative preferred embodiments,
T.sub.1Lm may be computed for a subset of T.sub.1 spectrum values,
either to reject noisy components in the spectrum, or to focus
around a certain T.sub.1 range, where the change in energy
contained in that particular band has a large dynamic range as a
function of time. In alternate embodiments, the T.sub.1 spectrum
can be subdivided into several bands, and the corresponding
T.sub.1Lm for each band is then computed. This subdivision can be
based on computational simplicity or observations concerning the
temporal characteristics of different T.sub.1 sub-bands.
[0062] Accordingly, in one embodiment, contamination estimation is
based on the use of one or more of the bands of a subdivided
T.sub.1 spectrum. A band of the T.sub.1 spectrum can be selected on
the basis of one or more desired criteria, such as maximum dynamic
range, longest center T.sub.1 value, and others.
[0063] In another embodiment, contamination estimation is based on
a combination of the bands of the subdivided T.sub.1 spectrum. The
contamination estimates resulting from the application of the one
or more contamination estimation models to different bands of the
subdivided T.sub.1 spectrum can be combined in a number of
different ways, either linearly or non-linearly, to form an
averaged contamination estimate.
[0064] FIGS. 1A, B give an example of the computation of T.sub.1Lm
from the T.sub.1 distributions in OBM logging experiments. Panel 10
shows MRILab.RTM. T.sub.1 measurements (in milliseconds) from
ninety-one successive OBM logging experiments (uncorrected for
flow). Vertical scale 12 shows the experiment number in sequential
order, from earlier times (top) to later times (bottom). Panel 14
shows the apparent hydrogen index for each experiment, which is
derived from the area under the T.sub.1 distribution (discussed
below). The hydrogen index is about 0.7 for a majority of the
experiments. The tool has stopped pumping at the very bottom of the
chart, therefore at the very end the hydrogen index is about 1. The
fit error for each wait time group is shown in panel 16. Panel 10
also shows the corresponding T.sub.1Lm (connected diamond markers),
calculated from the MRILab.RTM. T.sub.1 distributions for each
experiment (solid curves). Variations in the T.sub.1 distributions
and T.sub.1Lm include contributions due to changes in contamination
and flow rate. The center of the T.sub.1 distributions is around
3.5 seconds for a majority of the experiments.
[0065] Viscosity Estimates Using NMR Measurements
[0066] The viscosity of a crude oil can be estimated from the
T.sub.1Lm value by the following empirical relationship: 3 =
0.009558 T k T 1 Lm , ( 6 )
[0067] where T.sub.1Lm is the log-mean T.sub.1 value, T.sub.k is
the absolute temperature in degrees Kelvin, and viscosity is in
units of centipoise. A poise is a centimeter-gram-second unit of
dynamic viscosity, equal to one dyne-second per square centimeter.
The relationship between the viscosity of crude oil and the
log-mean value of other NMR parameters can be empirically estimated
or approximated using Eq. (6) in combination with a measurement of
the log-mean T.sub.1 value, and applied to any of the viscosity
mixing rules and/or contamination models presented below or
otherwise known in the art. The T.sub.1Lm can be used to estimate
contamination when combined with a mixing law that is based on
viscosities of two miscible fluids, as discussed in further detail
below.
[0068] The viscosity relationship of Eq. (6) is an approximation
for use mainly with "dead" oils. For "live" oils, which contain gas
components, a better viscosity estimate is: 4 = 0.009558 T k f (
GOR ) T 1 ( 7 )
[0069] where T.sub.1Lm is approximated by T.sub.1 times a function
of the gas-oil-ratio (GOR).
[0070] Viscosity Mixing Rules
[0071] As noted, a mixing law or rule is a mathematical expression
that describes a property of a mixture in terms of the properties
of its constituents. This allows for the property of the mixture to
be predicted if the weight or volume fractions or functions for the
constituents, and the properties of the constituents are known.
[0072] It has been concluded that no single mathematical expression
could represent the viscosities of all hydrocarbon mixtures. See
Shu, W. R., "A Viscosity Correlation for Mixtures of Heavy Oil,
Bitumen, and Petroleum Fractions", SPEJ, June, 277-282 (1984). This
accounts for the variety of mixing rules that are known or can be
developed, all of which may be used in accordance with different
embodiments.
[0073] Several empirical viscosity mixing rules exist that relate
the measured viscosity of a miscible mixture to the volume
fractions of the end-point viscosities, i.e., to the viscosity of
each individual component. The four most commonly used relations
are listed in the following table:
1 5 m = 1 2 [ s 1 2 1 / n + s 2 1 1 / n ] n , (Todd et al). (8) 6 m
= [ s 1 1 n + s 2 2 n ] 1 / n , (Power -Law), (9) ln(.eta..sub.m) =
s.sub.1ln(.eta..sub.1) + s.sub.2 ln(.eta..sub.2), (Arrhenius), (10)
7 ln ( m ) = s 1 s 1 + s 2 ln ( 1 ) + [ 1 - s 1 s 1 + s 2 ] ln ( 2
) , (Modified Arrhenius). (11)
[0074] In the above equations, .eta..sub.m is the measured
viscosity of the mixture, .eta..sub.1 and .eta..sub.2 are the end
point viscosities (i.e., the viscosity of each component of the
mixture), s.sub.1 and s.sub.2 are their respective volume fractions
(or saturations), while n and .alpha. are empirically determined
non-negative constants. Note that s.sub.1+s.sub.2=1, and if it is
taken that c=s.sub.1, then s.sub.2=1-c, where c is the level of
contamination.
[0075] The value of n is typically 4 in the viscosity mixing rule
in Eq. (8), developed by Todd, M. R., et al. "The Development,
Testing and Application of a Numerical Simulator for Predicting
Miscible Flood Performance," Journal of Petroleum Technology
(1972).
[0076] In Eqs. (9) or (10), s.sub.1 and s.sub.2 may represent a
mass fraction, a mole fraction, or a volumetric fraction. In
exponent n in the Power-Law mixing rule in Eq. (9) is an adjustable
value that depends upon the components and the proportions in the
mixture. The Arrhenius rule in Eq. (10) is also known as the log
mixing rule.
[0077] The fourth mixing rule in Eq. (11), is a modified version of
the classic Arrhenius expression, which was originally proposed by
Lederer, E. L., Proc. World Pet. Cong., vol. 2, pp. 526-28, London
(1933). The constant .alpha. is found empirically and has values
between 0 and 1. The volume fractions s.sub.1 and s.sub.2 are
associated with the contaminant and the oil, respectively. Rhames
et al. examined this equation for mixtures with low viscosity
ratios .eta..sub.1/.eta..sub.2, and found that this function
expression provided an excellent fit to their data. See Rhames, M.
H., et al. "Viscosity Blending Relationships of Heavy Petroleum
Oils", Analytical Chemistry, vol. 20, pp. 912-915 (1948). Other
researchers used the same functional expression for mixtures of
high viscosity ratios typical of bitumen and solvent fractions.
Shu, W. R., "A Viscosity Correlation for Mixtures of Heavy Oil,
Bitumen, and Petroleum Fractions", SPEJ, pp. 277-282 (1984). Shu
correlated the parameter .alpha. with properties characteristic of
the individual mixture components including the viscosity and the
densities of solvent and oil.
[0078] As described below, in different embodiments one or more of
the viscosity mixing rules can be applied to the log-mean value of
an NMR spectrum, or the log-mean value of one or more subdivided
bands of the NMR spectrum, for estimating the viscosity of a
formation fluid contaminant and/or a hydrocarbon phase in a
formation fluid. The contamination estimation methods in accordance
with the approach proposed herein will vary according to the chosen
viscosity mixing rule. Several variations of the contamination
estimation models are described below.
[0079] Modeling the Contamination Function
[0080] In addition to the mixing rules considered above in
illustrative embodiments, the contamination estimation approach in
this application is based on the use of a contamination function,
which is a temporal function that substantially matches the
behavior of the contamination fluid fraction while pumping a sample
from an invaded zone.
[0081] As a result of a large number of simulations with miscible
and immiscible mud systems, as well as studying the behavior of
MRILab.RTM. field results, the following models have been developed
to describe the time dependent behavior of the contamination
function c(t), in accordance with different embodiments:
2 8 c ( t ) = a 3 + a 1 arctan ( t p a 2 ) , (ArcTan), (12) c(t) =
a.sub.3 - a.sub.1 exp(-t.sup.p/a.sub.2), (Exponential,) (13) 9 c (
t ) = a 3 + a 1 arctan ( t - a 4 a 2 ) , (ArcTan - Shifted 1), (14)
c(t) = a.sub.3 + a.sub.1 arctan(t.sup.p + a.sub.2), (ArcTan -
Shifted 2), (15) 10 c ( t ) = a 3 + a 1 arctan ( t p a 4 + a 2 ) ,
(ArcTan - Shifted 3), (16) 11 c ( t ) = 1 2 - 1 2 erf [ a 2 log ( t
a 1 ) ] , (Error Function) (17)
[0082] In the models above, a.sub.1, a.sub.2, a.sub.3, a.sub.4 and
p are constants, and erf is the error function defined as: 12 erf (
x ) = 2 0 x - t 2 t . ( 18 )
[0083] The idea in accordance with the proposed approach is to fit
the determined values of one or more fluid properties, such as
viscosity, over time to a parameterized contamination function as
shown in the table. By matching a contamination function to the
fluid property measured over a period of time, the variables of
this time function are determined, for example, through regression.
Matching could be done over the individual functions listed. For
example, the error function in Eq. (17) is a solution for
well-defined cases of invasion and these curves have a strong
resemblance to the form of a sample quality function given by
.function..sub.sq(t)=1-c(t), where .function..sub.sq is the sample
quality (0 to 1, dimensionless), c(t) is given by Eq. (17), t is
time, a.sub.1 is time at 50% contamination, and a.sub.2 is the time
scaling parameter. A detailed numerical simulation study was
performed to determine the pumpout contamination versus time.
[0084] FIG. 2 shows the results of a large number of sample quality
simulations with OBM systems using a sample quality function
developed from the Landmark VIP reservoir simulator. Invasion was
simulated first and used as the initial condition for the sampling
pumpout sequence. The contamination curves were developed by
tracking the volume fraction of the fluids entering the sampling
tool. FIG. 3 shows how these simulations can be closely mimicked
using the Error Function contamination function in Eq. (17). The
parameter a.sub.1 controls the shape of the curve (inflection point
at 50% contamination) and has units of time. The dimensionless
parameter a.sub.2 scales the independent variable t. Typical ranges
for a.sub.1 and a.sub.2, for OBM systems are
[0085] 0.50.ltoreq.a.sub.1.ltoreq.100, and
[0086] 0.50.ltoreq.a.sub.2.ltoreq.0.75.
[0087] The other contamination functions in the preceding table
(Eqs. 12-16) can be matched to the simulated curves in a similar
manner. Experience with field data, the mixing models and the
sensor data aids in determining the best contamination model for a
particular fluid property. More specifically, in a preferred
embodiment, matching can be done by defining a vector .rho. of
unknown parameters: .rho.=[a.sub.1, a.sub.2, a.sub.3, a.sub.4,
p].sub.T. The objective is to adjust the vector of unknown
parameters such that the time function c(t) matches the measured
fluid property data. Thus, to determine .rho., in a specific
embodiment a nonlinear least squares problem is posed and solved
such that the following function is minimized, as known in the art:
13 min i = 1 N ( ^ m ( i ) - m ( i ) ) 2
[0088] where i denotes an experiment, N denotes the total number of
experiments in the dataset and the measurement is done using
estimated values for the bulk fluid viscosity. Based on two recent
studies of laboratory data, as well as MRILab.RTM. data it appears
that the Eq. (16) has the greatest potential of accurate results.
After the optimizer has determined the unknown parameters, the
viscosity index of the contaminant .eta..sub.1 and of the formation
fluid .eta..sub.2 is determined by extrapolating c(t) to t=0; and
t=.infin. respectively.
[0089] It will be appreciated that the application of the
contamination estimation methods of this disclosure vary according
to the contamination model chosen to be applied, for example, i.e.,
to an NMR spectrum, or to one or more subdivisions of the NMR
spectrum. The methods may also change dependent on whether the
contamination model is applied in conjunction with one or more
mixing rules.
[0090] Variations of the Miscible Fluid Models (MFMs)
[0091] The above modeling is applicable to OBM applications, in
which it is assumed that contamination is the result of mixing
miscible fluids. Accordingly, the proposed models are termed
Miscible Fluid Models (MFM). As noted before, in the case of
miscible fluids, the challenge in contamination estimation is to
find a mixing rule that relates the end-point fluid properties to a
measured bulk fluid property as a function of their saturations;
and the basic approach to MFM in preferred embodiments is to relate
the viscosity of the mixture to the log-mean value of an indirect
property measurements, such as the log-mean T.sub.1
(T.sub.1Lm).
[0092] This section provides four variations of the contamination
estimation methods used in different embodiments, based on four
different contamination estimation models. It will be appreciated
that other contamination estimation models can be formulated from
variations of the approaches discussed herein. While the
contamination estimation models are described relative to T.sub.1
spectra and the log-mean T.sub.1 value (T.sub.1Lm), the variations
of the contamination estimation methods, based on contamination
estimation models that are expressed in terms of other NMR
measurement parameters, including, but not limited to, T.sub.2 and
diffusivity measurements, are also envisioned and will be
appreciated by those of skill in the art.
[0093] Implicit Log-Mean T.sub.1 (ILMT1)
[0094] At present, there is no model that can fully predict the
T.sub.1 spectrum of a miscible mixture, given the T.sub.1 spectra
of the end points and their volume fractions in the mixture. In the
real-life cases, strictly speaking neither the end point spectra,
nor the volume fractions are known. However, given that T.sub.1Lm
is correlated to viscosity and that the viscosity mixing laws
predict two very clearly defined end points, one can reason that
T.sub.1Lm is a bounded function, where the asymptotes at time zero
and infinity correspond to the T.sub.1Lm of the contaminant and the
formation fluid (e.g., the crude), respectively.
[0095] A first embodiment of the invention, called the Implicit
Log-mean T.sub.1 (ILMT1) model, provides that the two limits can be
defined as follows:
lim c(t)=T.sub.1Lm,0
t.fwdarw.0 (19)
lim c(t)=T.sub.1Lm,.infin.
t.fwdarw..infin. (20)
[0096] In the ILMT1 model, the T.sub.1Lm values are fit using a
contamination model in order to compute the two limits given in
Eqs. (19) and (20). Given these two quantities, the contamination
level at time t.sub.k is determined in the ILMT1 model using the
relation: 14 c ( t k ) = T 1 Lm ( t k ) - T 1 Lm , .infin. T 1 Lm ,
0 - T 1 Lm , .infin. ( 21 )
[0097] The parameter c(t) is assumed to conform to the shape of one
of the contamination function models discussed above. The problem
to be solved is an over-determined non-linear least squares
problem, where the parameters in the contamination function are
solved using well-known nonlinear least-squares (NLLS) solvers.
[0098] In one embodiment, the level of contamination of a formation
fluid or an estimation of the pumping time needed for achieving a
given contamination level can be provided based on application of
the ILMT1 contamination estimation model. In a specific embodiment,
using the ArcTan-Shifted 2 contamination model in Eq. (15), the
model is solved (using NLLS techniques) to compute the parameters
a.sub.1, a.sub.2, a.sub.3, and p. The limits of the function are
then calculated using the computed parameters to obtain the
T.sub.1Lm for the endpoints (see Eqs. 19 and 20). Finally, Eq. (21)
is used to compute the contamination at time t.sub.k. The
contamination estimate at time t.sub.k can then be used to estimate
the pumping time necessary for achieving a given contamination
level. This estimation can be based on examining the time-function
of the contamination parameter.
[0099] In a second aspect of the ILMT1 model, the inverse of the
log-mean value (i.e., 1/T.sub.1Lm) can be substituted for the
log-mean value (T.sub.1Lm), and the exact same steps can be carried
out. The main advantage of this approach is that the inverse of the
log-mean value of the NMR parameter could provide information about
other materials properties, e.g., 1/T.sub.1Lm is directly
proportional to viscosity.
[0100] Explicit Log-Mean T.sub.1(ELMT1)
[0101] The Explicit Log-mean T.sub.1 (ELMT1) model, used in another
embodiment, where the relationship between the log-mean T.sub.1 and
viscosity is used explicitly, is an extension of the approach
described above.
[0102] In the ELMT1 model, the T.sub.1Lm values are fit using a
contamination model, as in the ILMT1 model, in order to compute the
two limits given in Eqs. (19) and (20). The two end point
viscosities are obtained from the end point T.sub.1Lm values using
Eq. (6), where: 15 1 = 0.009558 T k T 1 Lm , 0 , ( 22 ) 2 =
0.009558 T k T 1 Lm , .infin. , ( 23 )
[0103] Finally, a viscosity mixing rule, e.g., Eqs. (8) through
(11), is applied to compute c(t.sub.k) for a given mixture. For
example, Eq. (8) can be recast in terms of c using the relation
that s.sub.1=c, and s.sub.2=1-c: 16 m = 1 2 [ c 2 1 / n + ( 1 - c )
1 1 / n ] n , ( 24 )
[0104] after which the equation is solved for c(t.sub.k). It will
be appreciated that contamination estimates at different times can
be used to compute the time necessary to achieve a given
contamination level at a given pump time.
[0105] Coupled Log Mean T.sub.1 (CLMT1)
[0106] In the ELMT1 model, the contamination model and the mixing
rule are applied in two discrete steps. However, in a third
embodiment of the invention, referred to as the Coupled Log-Mean
T.sub.1 (CLMT1) model, the contamination model is coupled with the
viscosity mixing rule. The resulting nonlinear system is then
solved for a greater number of unknowns.
[0107] In a first aspect according to the third embodiment, the
ArcTan contamination model given in Eq. (12) is coupled with the
Arrhenius viscosity mixing rule given in Eq. (10), which results in
the following non-linear couple system: 17 ln ( 0.009558 T k T 1 Lm
) = { ( a3 + a1 arctan ( t p a 2 ) ) ln ( 1 ) } + { ( 1 - a 3 - a 1
arctan ( t p a 2 ) ) ln ( 2 } ( 25 )
[0108] In a second aspect according to the third embodiment, the
viscosity mixing rule of Todd et al. given in Eq. (8) is coupled
with the error function contamination model c(t) given in Eq. (17),
which results in the following non-linear couple system: 18 m = 1 2
[ c ( t ) 2 1 / n + ( 1 - c ( t ) ) 1 1 / n ] n , ( 26 )
[0109] where the value of n is typically 4, .eta..sub.m is the
measured viscosity, c(t) is the contamination level at time t,
.eta..sub.1 is the viscosity of the OBM, and .eta..sub.2 is the
viscosity of the native crude.
[0110] There are many other possible specific forward models for
the CLMT1 model resulting from the coupling of a contamination
function model with a viscosity mixing rule, given the four
viscosity mixing rules and the six contamination function models
described above, and other contamination models or viscosity mixing
rules available to one of ordinary skill in the art. It is intended
that such alternative contamination function and mixing law models
are within the scope of the present invention and the appended
claims.
[0111] Immiscible Fluids Models (IFM)
[0112] An assumption implicit in the MFM models and methods is that
the mixing is miscible. However, in many instances the distinction
between miscible and immiscible may disappear, and models
specifically designed for immiscible mixing (i.e., in WBM
applications) may be necessary for a particular application.
[0113] Another embodiment in accordance with this disclosure
provides the Immiscible Fluid Model (IFM), which is designed for
WBM applications. The IFM can be applied for NMR measurements
either in the time domain or in the T.sub.1 domain. In preferred
embodiments, the NMR data derives from MRILab.RTM. T.sub.1
measurements. An assumption of the IFM model is that the measured
response, whether in the time or in the T.sub.1 domain, is a linear
combination of the signatures of the two end members, where the
weighting is governed by the contamination level. The IFM method
used in a preferred embodiment includes two steps. First, the two
end members are determined from the available data. Given the
end-member signatures, the contamination levels are then determined
in the second step.
[0114] The first step of the IFM model is to determine the
end-point signatures x and y. The major unknowns in this step are
the NMR signatures of the two fluids (either in time, or T.sub.1
domain), in addition to the contamination levels. If the NMR
signature of the two fluids at the two end-point, i.e., the NMR
signal of the uncontaminated fluids, is represented by x and y, and
given a data matrix of:
B={b.sub.1, b.sub.2, b.sub.3, . . . ,b.sub.k) (26)
[0115] where b.sub.k is the kth column representing the NMR
measurement corresponding to the kth experiment, then the
measurements are modeled as follows:
b.sub.k=c.sub.kx+(1-c.sub.k)y (27)
[0116] Equations (26) and (27) are given as discrete functions only
for ease of notation, and the IFM is not so limited. The c.sub.k of
Eq. (27) are not ordered in time, in that the unknown vectors x and
y would be the same if the columns of B are reshuffled. As a
result, an advantage of the IFM model is that the end point vectors
can be estimated independent of the dynamics of fluid flow. The
contamination function is generally a monotonically decreasing
function of time. However, if the flow rate changes during the
measurements, e.g., if pumping is stopped, the mud filtrate can
flow back in around the probe in the analyzer. This may result in a
higher level of contamination when the pump starts again. As a
result, if contamination is modeled as a function of time while
determining the two end points, then some otherwise valid data
points would be interpreted as misfits.
[0117] The parameters can be solved using well-known NLLS solvers.
For example, a separable non-linear least squares approach can be
used where a bi-linear problem is solved to get x, y first,
followed by c.sub.k.
[0118] The second step of the IFM contamination estimation model
includes fitting the c.sub.k obtained from the first step using a
contamination model. For example, the error function is also a
solution for well defined cases of WBM invasion, having a strong
resemblance to the form of the sample quality function previously
discussed for the case of OBM. FIG. 3 shows the results of a large
number of sample quality simulations with WBM systems using the
sample quality function discussed above based on the Error Function
contamination function in Eq. (17). Typical ranges for a.sub.1 and
a.sub.2, for WBM systems are:
[0119] 0.50.ltoreq.a.sub.1.ltoreq.100, and
[0120] 0.25.ltoreq.a.sub.2.ltoreq.0.50.
[0121] Another possible contamination model is a logarithmic arctan
function: 19 c ( t ) = 1 2 - 1 arctan [ a 2 log ( t a 1 ) ] , ( 28
)
[0122] The IFM method described above can be modified without
departing from the teachings of this disclosure as will be
appreciated by those of skill in the art. For example, in alternate
embodiments, the input data can be weighted based on flow rate,
hydrogen index, fit error, noise level, and others. Also,
contamination can be estimated in different embodiments either in
the time-domain, or T.sub.1 domain, where preferably the user can
specify either the time or T.sub.1 range. Additionally, while Eq.
(27) solves for two end-points, the IFM model could be extended in
straightforward manner to the case of three or more fluids by
weighting. Thus, a possible scenario is fluid 1 being clean crude
from a previous logging station, fluid 2 being the OBM filtrate
that enters when flow starts, and fluid 3 being crude at the
current depth, which may have a different viscosity from fluid
1.
[0123] Summary of Contamination Estimation Using NMR
Measurements
[0124] The following algorithm summary is provided for the
convenience of the reader in the illustrative embodiment using
viscosity as the fluid property being monitored, and indirect NMR
measurements to determine these properties. The input curve for the
algorithm is T.sub.1Lm. In particular, from acquired echoes in an
NMR measurement, the T.sub.1 distribution is computed by standard
inversion algorithms, and then converted to T.sub.1Lm using Eq.
(5). Next, it is assumed that the sample being analyzed is a
mixture of two fluids--the contaminant and the formation fluid.
Using the T.sub.1Lm curve one can obtain viscosity indices for
these fluids, i.e., the values of .eta..sub.1--the viscosity of the
contaminant, and .eta..sub.2 as the viscosity of the native fluid.
Subsequently, the volumetric fraction of the contaminant and the
formation fluid at each experiment is computed by applying a fluid
mixing-model. The algorithm can be summarized in the following
steps:
[0125] (1) Read T.sub.1Lm data;
[0126] (2) Compute the viscosity index of the fluid mixture
.eta..sub.m for each experiment by applying the oil viscosity
formula in Eq. (6);
[0127] (3) In a least squares fashion, fit .eta..sub.m to a
parameterized viscosity index function c(t) of a given structure
(Eq. 12-16).
[0128] (4) Compute the viscosity indices of the contaminant:
.eta..sub.1=c(t), t=0; and of the formation fluid .eta..sub.2=c(t),
t=.infin..
[0129] (5) Compute the contamination index for each experiment by
applying a fluid mixing model in Eq. (8-11).
[0130] In the above summary, the time-function and mixing-model are
uncoupled. It will be appreciated that both uncoupled and coupled
estimates can be provided based on principles discussed above. In a
particular embodiment, several tests may be performed to determine
the estimation model that optimally fits the data.
[0131] It will be appreciated that in the embodiments discussed
above the end point properties--either apparent viscosity or
T.sub.1 spectrum--are treated as unknowns. While this is generally
true, there are some instances when there is a-priori information
about the properties of one or more fluids. For example, if the
application involves gas (methane) and OBMF, then the T.sub.1 (or
the T.sub.1Lm, since it is uniexponential) of gas is known, and can
be treated as a known-quantity, simplifying the inversion. In some
cases, a-priori information can exist about the contaminant OBMF,
its viscosity or T.sub.1 spectrum may be treated as known. In
either case, the a-priori information improves the performance of
the inversion, since the number of unknowns is reduced.
[0132] Application of the Contamination Estimation Models
[0133] In another aspect, this disclosure also provides methods for
applying the contamination estimation models to the non-ideal
conditions encountered while drilling. The equation of the
contamination estimation models are developed based on an
assumption of ideal behavior of the formation fluids. One
assumption of the contamination estimation models is that there are
two end point fluids, e.g., the contaminant and the hydrocarbon.
However, the fluid that is measured at the beginning of each
experiment may not contain either of the end-point materials. The
fluid measured in the experiments at earlier times may be the fluid
left in the flow line from a previous station, possibly measured at
a different depth where the reservoir fluid could be completely
different. For the very first measurement using a new analyzer in
the well, the fluid in the flowline may be water left in the tool
during calibration in the shop. Also, contamination is usually
modeled as a monotonic phenomenon, in that contamination is taken
to decrease as a function of time as the pump-out time increases.
For example, T.sub.1Lm (or its reciprocal) may actually decrease
until the fluid left in the flowline is pumped out, then reverse
direction during the relevant portion of the clean-up process.
[0134] An example of such behavior can be seen in the top graph of
FIG. 4, where the diamonds and circles represent actual data
points. The top graph shows a log-log plot of contamination
estimation models in the specific embodiments to a viscosity vs.
time measurement, where the diamonds (.diamond.) and the circles
(.smallcircle.) are data points, while the curve is the fit of a
model to the data points. The middle graph shows spin-echo data
from a number of experiments. These and other complications may
result in the actual contamination trend not being monotonic. If
left uncorrected, the artifacts due to flow rate changes may
produce data points that are outside the expected range, yielding
unreliable contamination estimates.
[0135] Accordingly, in a preferred embodiment, an inflection-point
detection algorithm may be applied to identify the relevant time
window that contains data from the fluids of interest. Once the
relevant time window is identified, data outside this window can be
excluded from the inversion. The application of an inflection-point
detection algorithm to a data set is demonstrated in the top graph
of FIG. 4, where the data points represented by diamonds are within
the desired range, while the data points represented by circles are
determined to be outside this range. Data points in the window that
fall within the desired range are weighted more in application of
the contamination estimation models as compared to the data points
outside the window. In the embodiment illustrated in the top graph
of FIG. 4, an arctan-like function is used in the weighting. The
reliable and automatic identification of the relevant time window
is significant to real-time measurements, since no expertise is
required on the part of the user to define the preferred data range
on which to perform the analysis.
[0136] Earlier contamination estimation models have been developed
based on the assumption that the contamination approaches zero if
pumping continues indefinitely (i.e., c(.infin.).fwdarw.0). See,
e.g., U.S. Pat. No. 6,178,815; 6,274,865; 6,343,507 and 6,350,986,
which are incorporated herein by reference. Unless the well is
drilled under-balanced, this would generally not be the case. The
overbalance pressure that exists in most wells allows a small
amount of mud filtrate to continually leak through the mudcake.
With sampling, the filtrate leakage near the probe would be
diverted and mixed with the formation fluids entering the tool,
causing some residual contamination. Factors that can influence
this residual contamination include overbalance, permeability, and
(to a lesser degree) anisotropy. The permeability influences how
quickly the mudcake forms and the flow rate at which the formation
tester can pump a sample. As a result, the residual contamination
increases with reduced permeability. The residual contamination can
be estimated, and in most cases is less than 1%.
[0137] The present disclosure also provides methods of adjusting
the contamination models to take into account the residual
contamination. Using additional simulations, it is possible to
develop a correlation function, where the residual contamination
(related to the overbalance and permeability) is estimated before
pumping starts. The limits of the contamination estimation
functions (e.g., Eqs. 12-18) used to estimate the contamination
while pumping, i.e., the two end points, are then rescaled, so that
the projected sample contamination is asymptotic to the residual
contamination.
[0138] Comments and Algorithm Extensions
[0139] Fluid Properties
[0140] While the contamination estimation models described in the
illustrative embodiment using viscosity and NMR measurements for
illustration, the principles of this disclosure can be applied to
any other physical parameters or measurements of the formation
fluid that are sensitive to contamination. For example,
resistivity, capacitance, density, viscosity, HI (hydrogen index),
compressibility, speed of sound, and even the pumping pressures can
be sensitive to changes in contamination. The specifics of the
mixing rule(s) or contamination function models applicable in each
case are believed within the scope of knowledge of a person of
ordinary skill in the art and will not be considered in further
detail. The interested reader is directed to the discussions in
[LIST OF REFERENCES] for background information.
[0141] The use of different fluid properties in accordance with the
principles of this disclosure is illustrated using the Implicit
LogMean T.sub.1 approach, discussed above. Suppose that in a
particular implementation, the choice of the contamination function
model is the ArcTan model in Eq. (8). An error measure could be
defined as:
.epsilon..sub.k=c.sub.k-d.sub.k,
[0142] where
c.sub.k=x.sub.3+x.sub.1
arctan(t.sub.k.sup.x.sup..sub.3/x.sub.2),
d.sub.k=T.sub.1Lm,k
[0143] The elements of the vector of unknowns x=(x.sub.1, x.sub.2,
x.sub.3, x.sub.4).sup.T correspond to the parameters (a.sub.1,
a.sub.2, a.sub.3, p) in the ArcTan Model. The objective function in
a simplest form can be defined as: 20 ( x ) = k = 1 K k 2
[0144] The task is then to find the vector x that minimizes the
above function, like in any other least squares problem. While the
illustrative embodiments using viscosity d.sub.k is the log mean of
T.sub.1, other parameters, such as log-mean T.sub.2, log-mean
D.sub.0, as well as the hydrogen index, pressure values, or others
can be used instead. It will thus be appreciated that the approach
proposed herein is not limited to a particular fluid property, or a
particular modeling function but rather can be extended without due
experimentation to different properties, different mathematical
model functions or function combinations.
[0145] In accordance with another aspect of the disclosure it will
be appreciated that in certain fluid mixtures one of these
properties may be more sensitive than others to the contaminant.
Accordingly, an array of instruments can be used in a preferred
embodiment to measure individual properties and the approaches
disclosed below applied to each measurement. In a specific
embodiment, different contamination estimates can be combined into
a single average contamination estimate. Individual contamination
estimates may be weighted, preferably using nonlinear regression
techniques. As is the case with MRILab.RTM. estimates of viscosity,
the formation fluid properties can be more accurately predicted
because the end points are used to determine the in-situ sample
properties.
[0146] Multi-Fluid Modeling
[0147] In another aspect, it will be appreciated that the mixing
rules described in the above illustrative embodiments are
applicable to two fluids--generally a contaminant and the native
formation fluid. In certain applications, it may be advantageous to
consider three different fluid types, for example, in the
production of a well, where fluids of different viscosities are
produced from different zones. It will be appreciated that in such
cases, for example, a gas zone, and two oil zones may be
encountered, where the oils have different viscosities. The
viscosity mixing rules given for 2 fluids (Eqs. 8 thru 11), have
counterparts for 3 or more fluids. For example, the 2-fluid mixing
rule, referred to as Todd et al, given by 21 m = 1 2 [ s 1 2 1 / n
+ s 2 1 1 / n ] n ,
[0148] where
s.sub.1+s.sub.2=1,
[0149] can be extended for 3-fluids in the following way (Todd et
al): 22 m = 1 2 3 [ s 1 2 1 / n 3 1 / n + s 2 1 1 / n 3 1 / n + s 3
1 1 / n 2 1 / n ] n ,
[0150] where
s.sub.1+s.sub.2+s.sub.3=1.
[0151] It can be seen from the above that extension of the other
mixing rules, for 3 or more fluids, in many cases is
straightforward.
[0152] NMR Measurements of Viscosity
[0153] The relationship between viscosity and T.sub.1Lm, as given
in Eq. (6), strictly speaking applies for dead oils, generally not
having any substantial portion of gas. The relationship is
dependent on the Gas-Oil-Ratio (GOR), as shown in Eq. (7), if the
oil is live. Since f(GOR) is not known at the time of the NMR
measurement, the two end-point viscosities that are outputs of the
contamination algorithm may not be correct in certain instances.
For this reason, diffusion measurements, as discussed in Appendix
A, may be used for viscosity determination, because the
relationship between D.sub.0 and viscosity is fundamental and is
governed by Eq. (1), whereas the relationship between T.sub.1Lm and
viscosity is empirical.
[0154] It should be noted, however, that in not knowing f(GOR) does
not adversely impact on the contamination estimates obtained in
accordance with this disclosure, because whether the oil is "live"
or "dead," the values for T.sub.1Lm of the fluid are inversely
proportional to its viscosity, only the proportionality constant is
different. Therefore, in the case where f(GOR) is unknown, while
the end-point viscosities may be inaccurate, the saturations of the
fluids (or the contamination levels) are still correct. Strictly
speaking, therefore, the above disclosure is applicable to
measurements of an apparent viscosity or a "viscosity index,"
instead of viscosity. It will be appreciated that in many instances
the apparent viscosity from the contamination analysis will be
correct, as in the case of higher viscosities (i.e., low GOR),
where the T.sub.1-viscosity relationship approaches that of the
dead-oil relationship.
[0155] Effects of Flow on T.sub.1 Data
[0156] FIG. 1A illustrates that the flow, dependent on the pumpout
rate affects the T.sub.1 distributions. The magnitude of the flow
effect can be appreciated by comparing the T.sub.1Lm values, which
are in the order of 3 seconds while flowing at 30 cc/min, to
stationary values in the order of almost 10 seconds (near the
bottom of the log). Faster flow rates result in less polarization
in the case of long T.sub.1s.
[0157] If the fluid is viscous, in which case the T.sub.1 values
are relatively short, the flow rate does not affect the T.sub.1
distributions substantially, and the flow effect can be ignored. In
a similar way, if the fluid has low viscosity (long T.sub.1s), but
the flow rate is low, then once again, the T.sub.1 distributions
are not affected for practical purposes. In either case, the
effects of flow are minimal and no corrections are needed.
[0158] In accordance with another aspect, the contamination
algorithms presented herein may function well without flow
corrections to the data even in the worst case of long T.sub.1 s
and high flow rates, as long as the transition from stationary to
non-zero flow is made quickly and the flow rate is not varied for
the remainder of the time. In such measurements, the most
significant effect of flow is to change the apparent viscosity. The
artifacts caused by high flow rates are analogous to that of
viscosity in the case of dead vs. live oil. In similar fashion,
while the apparent viscosity may not be close to the true
viscosity, the volume fractions of the two end points, i.e.,
contamination is still accurate. It will be appreciated, however,
that if the flow effects reduce the dynamic range in T.sub.1Lm, the
sensitivity of the contamination estimates may be reduced. These
issues can be taken into account with proper adjustment of the
pumpout rate of the device in operation.
EXAMPLES
Example 6.1
[0159] The results of the contamination estimation for data shown
in FIG. 1A using a CLMT1 contamination estimation model (Eq. (26))
are shown in FIG. 13.
[0160] In the top report section, several parameters and answers
are listed. The results of the inversion, for the end-point
viscosity indices, as well as the parameters a.sub.1 and a.sub.2
are listed. The contamination level at the first and the last
experiments, in percent are also listed in the report section.
Finally, the time estimate for reaching the contamination threshold
is given at the bottom. In the example used, the 5% threshold was
already achieved.
[0161] The second section contains a plot of the estimated
contamination vs. time. The estimated contamination is about 2
percent towards the end of the measurement.
[0162] The third section is a plot of the input data (solid curve)
vs. the fit (connected diamonds). The flow rate is shown in the
bottom plot, for reference. In the third section, one can see the
T.sub.1 distributions for the two end members.
Example 6.2
[0163] The top graph of FIG. 4 shows viscosity vs. time data points
(diamonds and circles) from an MRILab.RTM. Fluid analyzer, obtained
from a well drilled with OBM. An inflection-point detection
algorithm was applied to identify the relevant time window
(diamonds) that contains data from the two fluids of interest. The
data in the relevant window (diamonds) is weighted by an arc-tan
function as compared to the data outside the window (circles).
[0164] The top graph of FIG. 4 also shows the results of the
application of the ELMT.sub.1 model to the data from the
MRILab.RTM. (shown by the curve fit). The estimated contamination
value of 4.7% is obtained from application of the ELMT.sub.1 model,
using a combination of the Modified Ahrrenius mixing rule in Eq.
(11) and the ArcTan-Shifted 2 contamination model in Eq. (15).
Independent laboratory results were obtained from the analysis of
the actual fluid samples secured with the RDT. The laboratory
measured contamination value is 4.0%.
Example 6.3
[0165] While the IFM is not suitable for OBM, it nevertheless gives
results comparable to the MFM. The contamination estimation results
using the IFM for the data shown in FIG. 1A can be seen in FIG. 14,
where contamination is modeled using the error function (even
though OBM is used during logging).
[0166] The lower plot of FIG. 14 shows the T.sub.1 distribution for
the two end-members. It is interesting to note that the algorithm
used in the analysis chooses the most commonly occurring T.sub.1
spectrum for the crude (see FIG. 1A, experiment range 30 to 80),
and has considered most everything else as a contaminant, including
the very long T.sub.1 values encountered only at the end of the
measurement.
[0167] The upper plot shows the contamination values as a function
of experiment number. The monotonically decaying smooth curve is
the contamination curve. Towards the end of the measurement,
contamination values are on the order of 2 percent. The results
shown here are obtained by constraining the contamination values
between 0 and 1, which explains the abundance of points occurring
at 0 and 1.
[0168] The applicability of an IFM model to an OBM system is
probably due to the nature of the fluids and the type of the data
collected. Basically, when the two end points are very different,
and one has waited long enough for clean up as in this example, any
monotonically decaying function will show that contamination is
low.
APPENDIX A
[0169] The following description summarizes equipment and methods
used in the illustrative embodiment of the application, which
relies on NMR measurements. The interested reader is directed for
additional detail on NMR to the disclosure of the patents and
publications set forth in the background section of the
invention.
[0170] NMR Fluid Analyzer
[0171] FIGS. 5A and 5B show simplified diagrams of a downhole NMR
fluid analysis apparatus, such as the MRILab.RTM., that provides
NMR measurements to which the contamination estimation methods of
the present disclosure can be applied in an illustrative
embodiment. Fluids enter the device at the top and pass through two
sections, referred to as polarization and resonance sections,
respectively. Measurements are performed as the fluid flow passes
through the device. The fluid entering the system is initially
subjected to a strong magnetic field to achieve rapid polarization
of the hydrogen nuclei. NMR measurements take place in the lower
section, where the field strength is lower. In a preferred
embodiment, two separate radio frequency coils are used for pulse
transmission and for reception. This split scheme allows for a
transmitter coil 30 that is longer than the receiver 35. The
practical effect of this split is that relaxation times estimates
are less sensitive to the actual flow rate(s) because signals are
received from only a portion of a larger volume of fluid that is
being pulsed.
[0172] For a saturation-recovery T.sub.1 experiment, a single pulse
can be used to prepare a large volume, while the actual readout may
happen over a smaller volume. This feature is used to render the
measurement of T.sub.1 relaxation times largely independent of flow
velocities, up to a certain practical limit. Transmission and
reception both operate at 4.258 MHZ at room temperature, consistent
with 1,000 Gauss field strength. At higher temperatures, the
operating frequency is reduced to track the reversible reduction in
magnetic field strength.
[0173] The magnetic field in the measurement volume of the device
shown in FIGS. 5A and 5B in general is not entirely uniform. This
volume can be split conceptually into an interior region, where the
field gradient is negligible, and a fringe region, where the field
changes with an approximately uniform gradient. The fringe region
may comprise about one third of the total sensitive volume. During
T.sub.1 measurements and at short pulse-to-pulse spacing (such as
0.25 ms), the effect of the gradient is not noticeable. To perform
a diffusion measurement, the main flow is diverted and a sample is
stagnated within the NMR chamber. Furthermore, the pulse-to-pulse
spacing (Te) is increased to induce diffusion-dependent signal
dephasing. The uniform and the fringe regions are large compared to
the largest possible diffusion length; therefore, these regions are
essentially isolated from each other for the duration of a single
pulse-echo train.
[0174] FIG. 6A is a detailed cross-sectional view of the
polarization section of the apparatus that the flowing fluid
encounters after it enters the measurement chamber. The purpose of
this pre-polarization section is to polarize hydrogen nuclei in the
fluid(s) as rapidly as possible, so that they will exhibit full
polarization under the operating field. The flow tube 60, is made
from ceramic, glass or PEEK material, and is surrounded by a
Faraday shield 45. The magnet consists of segments 25 that are
magnetized as indicated by the arrows and are made of material with
very low temperature coefficient.
[0175] FIG. 6B is a detailed cross-sectional view of the second
section of the apparatus, which is located between the polarization
section and the measurement section(s) (labeled "Resonance Section"
in FIG. 5B). The purpose of this section is to allow the hydrogen
spins to settle to an equilibrium polarization that is close to a
non-flowing magnetization corresponding to an external field of
1,000 Gauss.
[0176] FIG. 6C is a detailed cross-sectional view of the transmit
portion of the measurement section of the apparatus, which follows
the stabilization section. FIG. 6D is a detailed cross-sectional
view of the last section of the apparatus, which is the
transmit/receive section. The NMR time constants T.sub.1 of the
fluid(s) under investigation are determined by varying the delay
time between a broadband saturation pulse and a read-out sequence.
If the flow velocity does not exceed 10 cm/s, the measurement is
generally independent of the flow speed and of the flow
profile.
[0177] The electronics used in the NMR fluid analyzer, which is
illustrated in a block diagram in FIG. 7, is similar to that of an
NMR spectrometer. The comparatively low frequency of 4.2 MHz used
in for some of the measurements allows many traditionally analog
functions to be realized readily as digital signal processing (DSP)
algorithms. A frequency source 34, controlled by a pulse
programmer, sends its signal to a power amplifier 37, which in turn
drives the transmitter antenna 30. All timing functions, like pulse
widths and acquisition windows, are fully programmable. On the
receive side, the signal from the receiver antenna 35 is amplified,
synchronously demodulated and integrated. The system also performs
its own calibration. All pertinent calibration factors are stored
in the tool itself and after calibration echo amplitudes are
reported on a scale of 0-2. The two coils of the device 30, 35 are
connected to resonating capacitors 31. These capacitors are of the
NPO (no temperature coefficient) and PTC type (positive temperature
coefficient), shunted in parallel, as shown. The resultant
temperature characteristic is such that with increasing
temperature, when the static magnetic field weakens (typically 1%
per 100.degree.C.), the capacitance increases at twice the rate
(typically 2% per 100.degree.C.). The resultant LC circuit resonant
frequency drops at half the capacitor rate (1% per 100.degree. C.)
and therefore follows the NMR resonance, making re-tuning of the
circuit unnecessary.
[0178] In a transmit mode, the controller 33 gates the signal
generator 34 of the apparatus and the power amplifier 37 to produce
a radio frequency pulse in both coils. The high voltage applied
causes all crossed diodes 39 to conduct, thereby connecting the two
coils. In receive mode, the crossed diodes stop conducting and
signal is only received from the lower coil 35. The signal is
amplified, digitized and fed into the digital signal processor 33
for demodulation and further processing.
[0179] The MRILab.RTM. described above determines hydrogen density,
self-diffusion rates and NMR relaxation rates of fluids during the
pump-out phase, from which one can compute sample viscosity and
GOR. By design, fluid samples are analyzed under true reservoir
conditions and results are available substantially in real time. In
particular, the MRILab.RTM. measures the hydrogen index and the NMR
polarization time constant (T.sub.1) of flowing fluids, which pass
through the device. In the sensor section, the hydrogen in the
fluid is first polarized by a set of magnets and then pulsed via an
antenna coil to excite the magnetic resonance response. The
excitation and refocusing pulses are fed to a long transmitter coil
that traverses the magnet section. A smaller receiver coil, located
at the bottom of the flow-tube, picks up the NMR echo. The
separated coil arrangement permits NMR measurements while flowing.
The timing sequences for the excitation pulses are
field-programmable for additional flexibility. By default, the
device records the NMR amplitude corresponding to a number of
distinct wait times ranging from 1 millisecond to 16 seconds. The
amplitudes are calibrated in hydrogen index units, where 1 unit
equals the hydrogen density in water under atmospheric
conditions.
[0180] The MRILab.RTM. can also be switched to T.sub.2 mode of
operation. The measurement of the signal decay time T.sub.2 is
flow-sensitive and is generally valid when a sample is stagnant
within the MRILab.RTM., at which time the NMR signal decay induced
by self-diffusion can be observed. Diffusivity is inversely
proportional to viscosity, a relationship that holds true in dead
oils as well as in gas-oil mixtures.
[0181] Relaxation Time Measurements
[0182] The T.sub.1 relaxation times and hydrogen density can be
measured continuously whether or not the fluid is stagnant or
flowing. FIG. 8 illustrates a pulse sequence employed with the
fluid analyzer in a specific embodiment. It will be appreciated
that it is a standard saturation recovery sequence, where an
initial saturation pulse is followed by a variable delay. In a
preferred embodiment, the delay is programmable and is typically
stepped through the values 1, 2, 4, 8, 16, 16384 ms in cyclical
fashion. The recovered magnetization at the end of the delay is
determined by a short read out sequence, consisting of two pulses
and one spin echo. The height of the echo, if plotted as function
of delay time, traces out a recovery curve that is converted into a
T.sub.1 distribution by standard inversion methods. In one
embodiment, the inversion algorithm is a variant of the method
employed to calculate T.sub.2 distributions from wireline data, as
disclosed in U.S. Pat. No. 5,517,115. With the above sequence it
takes about 33 seconds to complete a measurement cycle. The
signal-to-noise ratio of the system is so high that additional
averaging may be unnecessary. The sequence described above is
insensitive to fluid flow and can be used to continuously monitor
the T.sub.1 profile of pumped fluids. Other measurement sequences
may be used in alternative embodiments.
[0183] More specifically, the T.sub.1 measurement sequence is
initiated by a frequency swept saturation pulse. The frequency is
selected such that the entire range of frequencies in the resonance
sections of the apparatus is affected. In a specific embodiment,
this range is typically the NMR center frequency +/1% (4.2 MHz+/40
kHz). Pulse amplitude, frequency sweep rate and pulse length are
adjusted to effect saturation.
[0184] As noted, following the saturation pulse, a variable delay
is inserted. Preferably, consecutive measurements with delay values
of 1 ms, 2 ms, 4 ms, . . . , up to 16384 ms are used. During these
intervals, the nuclear magnetization builds up again to its
equilibrium value. Also during this time, depending on the flow
rate, fluid volume moves into the receiver coil volume, while
unprepared fluid enters the resonance volume. As long as the flow
rate is not high enough to allow unprepared fluid from the
polarization section to enter the receiver coil section, it will be
appreciated that the measurement is independent of the actual flow
rate. After the saturation recovery delay, the instantaneous value
of the nuclear magnetization is determined. This is done with a
short pulse sequence, consisting of a .pi./2 pulse, followed by a
.pi. pulse. The RF phase of these pulses is shifted by 90.degree.
against each other to cancel the effects of B.sub.0 and RF field
imperfections. This is equivalent to the start of a
Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The time between
these pulses is typically 0.125 ms; a spin-echo forms 0.125 ms
after the .pi. pulse. This echo is digitized, quantified and its
amplitude is taken as a measure of the recovered magnetization as
function of the saturation recovery delay. Note that the .pi./2 and
.pi. pulses can be narrow band and need not be frequency swept. The
reason is that they are only relevant for the receiver coil section
which has a very tightly controlled field and resonance frequency
distribution.
[0185] Examples of T.sub.1 distributions for some example fluids
are shown in FIGS. 10 and 11. The data points were acquired
according to the sequence in FIG. 8 and inverted from the time
domain to the T.sub.1 domain. The horizontal axis, "time," in FIG.
9 denotes the time elapsed between the saturation pulse and the
readout sequence, the vertical axis is signal amplitude in
arbitrary units. The results are easier to interpret after
inversion from time domain to T.sub.1 domain, as shown in FIG. 10.
In this example 53 points are specified for the inversion result.
The single, sharp peak at 2-3 seconds is characteristic of water,
the rounded peak in the "oil window" 0.5-1 second indicates oil and
the broad response from the crude oil in the bottom panel is
characteristic for complex hydrocarbons. The figure shows examples
of T.sub.1 saturation recovery data for three different fluids:
brine, Diesel oil and a crude oil.
[0186] The data points illustrated have been acquired by
circulating different fluids through the analyzer. Shown from top
to bottom are: water (mild brine) with a single relaxation peak in
the "water window" at 2 seconds; next a simple hydrocarbon (diesel)
with a single relaxation peak in the "oil window" at 0.5-1 second;
and a complex hydrocarbon (crude), which shows a characteristic
asymmetric distribution that starts in the few tens of milliseconds
and extends to the "oil window." These samples were under
atmospheric conditions at ambient temperature. At elevated
temperatures, Eq. (2) predicts an increase in T.sub.1 proportional
to the absolute temperature in addition to increases due to
reduction in viscosity.
[0187] The determination of long relaxation times no longer depends
on how long an echo train persists. In the implementation discussed
above, small perturbations in the applied field have relatively
limited effect. Additionally, the saturation pulse prepares a much
larger sample volume than what is actually used for the readout
portion. Therefore, as long as the flow rate is low enough, and the
readout is based on a fluid sample that was present anywhere within
the resonance regions during the saturation pulse, the measurement
is valid.
[0188] In contrast to T.sub.1, the T.sub.2 parameter generally
cannot be determined on a flowing sample. Distributions of T.sub.2
times are determined by standard CPMG sequences on samples that
have been stagnated momentarily. Stagnation can be achieved by
closing a valve below the analyzer apparatus and diverting the flow
stream around the sample chamber. The time required for a T.sub.2
measurement is almost entirely determined by the polarization time
("wait time") and is on the order of several seconds.
[0189] Hydrogen Density Measurements
[0190] The hydrogen density or the total number of hydrogen atoms
within the measurement volume is a by-product of any T.sub.1 or
T.sub.2 measurement. It can be represented as the area under any
T.sub.1 distribution and is typically normalized to the hydrogen
density of reference oil at measurement temperatures. At room
temperature, the reference oil and water have the same hydrogen
density. The reported number is the relative hydrogen index (HI) in
the range 0-2, with accuracy around 1%.
[0191] Hydrogen density can be automatically converted to hydrogen
index (HI), which is the hydrogen density of a material relative to
that of water at ambient conditions. The spin density of the fluid
is proportional to the hydrogen index. Under the assumption that
the oil contains only hydrogen and carbon atoms, the mass density
.rho..sub.m, the hydrogen index, and the hydrogen-to-carbon ratio R
are related as follows:
HI.apprxeq..rho..sub.m9R/(12+R) (29)
[0192] See, for example, Zhang et al., (1998), "Some Exceptions to
Default NMR Rock and Fluid Properties, Paper FF: SPWLA." presented
at the 39.sup.th Annual Logging Symposium, Keystone, Colo., May
26-29. Since the hydrogen index is measured, either the mass
density or the hydrogen-to-carbon ratio can be computed from an
estimate of the other variable.
[0193] It has been reported that most saturated hydrocarbon liquids
have relative hydrogen indices of 1 within .+-.5%. The hydrogen
density in gases is significantly lower due to the overall lower
density. Thus, a depressed hydrogen index serves as a first-order
alert to the presence of gas and a change in the relationship
between T.sub.1 and viscosity. Appel et al. reported a reduction of
about 20% on live oil samples at 180.degree. F. (See Appel et al.,
"Reservoir Fluid Study by Nuclear Magnetic Resonance," Paper HH:
SPWLA, presented at the 41.sup.st Annual Logging Symposium, Dallas,
Tex., Jun. 4-7, 2000). Under the assumption that all gas is methane
(CH.sub.4), the observed hydrogen index can be approximated as
follows:
HI=x(9/4.rho.)+(1-x)1, (30)
[0194] where x is the volumetric gas fraction (m.sup.3/m.sup.3) and
.rho., in g/cm.sup.3, is the density of methane. The density of
methane follows from its temperature and pressure, and Eq. (30) can
be used to derive a first-order approximation for the gas fraction
x.
[0195] Diffusion Measurements
[0196] Diffusion measurements can be performed using the NMR fluid
analyzer using steady-gradient spin-echo (SGSE) experiments. The
experiments require that the fluid flow is temporarily stopped. The
concept of using the fringes of a uniform field volume for
diffusometry derives from so called SSF-SGSE methods. The main
advantage of the SGSE method over pulsed-field gradient spin-echo
(PFGSE) diffusometry is instrumental simplicity and superior
stability. The main drawback is a limit on sensitivity, which, for
the downhole implementation, is approximately 10.sup.-6
cm.sup.2/s.
[0197] The sensitive volume of the apparatus can be divided into an
interior, homogeneous region and an exterior gradient region. The
field in the fringe volume, which makes up about 1/3 of the total
volume, can be approximated by a single field gradient value
G.sub.0. At short echo spacing (0.25 ms), the effect of the field
gradient is too small to be relevant. The pulse sequence used both
for diffusion measurements and for diffusivity calibration is shown
in FIG. 11.
[0198] In particular, two CPMG sequences with a short echo spacing
(typically 0.25 ms) and a long spacing (T.sub.e) are alternated.
The long echo spacing is selected as an integer multiple of the
short spacing. In this case, echoes line up in time, i.e., occur at
the same elapsed time, since the excitation pulse and the ratio of
their amplitudes can be formed.
[0199] For a formation fluid with a given relaxation time T.sub.2
and diffusivity D, the two echo trains for the short and the long
echo spacing can be described as follows:
A.sub.1=I.sub.H exp(-t/T.sub.2)
A.sub.2=I.sub.HK.sub.0
exp(-t/T.sub.2)exp(-t/T.sub.D)+I.sub.H(1-K.sub.0)ex-
p(-t/T.sub.2)
[0200] where
1/T.sub.D=1/12(.gamma.G.sub.0T.sub.e).sup.2D. (31)
[0201] The relations also apply for an arbitrary distribution of
times T.sub.2.
[0202] The system parameter K.sub.0 is the gradient volume divided
by the total volume. The hydrogen gyromagnetic ratio .gamma. is
equal to 26,754 rad/s/gauss. Both K.sub.0 and G.sub.0 are
temperature-dependent and are determined during calibration. The
diffusivity D is derived from Eq. (31) by taking the ratio of
corresponding echoes, as follows:
A.sub.2/A.sub.1=K.sub.0 exp(-t/T.sub.D)+(1-K.sub.0) (32)
[0203] This curve is fit to a uni-exponential model plus an
offset.
[0204] In the upper graph of FIG. 12, the two curves are the
A.sub.1 and A.sub.2 signals for water at room temperature. The
lower graph of FIG. 12 is the ratio curve and the best fit
uni-exponential model. Since D for water is known as
2.5.times.10.sup.-5 cm.sup.2/s, these curves determine the
calibration parameters G.sub.0 and K.sub.0.
[0205] The two curves in the upper graph of FIG. 12 are spin echo
amplitudes at different echo spacings. The accelerated decay for
the longer spacing is a manifestation of diffusion in the gradient
region of the magnetic field. The ratio curve (lower graph) is the
sum of an exponential and a constant term, corresponding to the
gradient field region and the uniform field region, respectively.
The best fit model curve is also plotted; however, it is
indistinguishable from the data.
[0206] In a preferred embodiment, viscosity is determined as
follows:
.eta.=5.times.10.sup.-8T/D (33)
[0207] In this expression, the viscosity .eta. is measured in cp,
the temperature T in Kelvin and the diffusivity D in cm.sup.2/s.
The temperature may be obtained from the RDT fluid temperature
sensor. The proportionality factor is determined by fitting Eq. (1)
to data from pure alkanes and methane alkane mixtures.
[0208] Although the present invention has been described in
connection with the preferred embodiments, it is not intended to be
limited to the specific form set forth herein, but on the contrary,
it is intended to cover such modifications, alternatives, and
equivalents as can be reasonably included within the spirit and
scope of the invention as defined by the following claims.
* * * * *