Electricity: measuring and testing – Particle precession resonance – Using well logging device
Reexamination Certificate
2002-05-15
2004-12-21
Fulton, Christopher W. (Department: 2859)
Electricity: measuring and testing
Particle precession resonance
Using well logging device
Reexamination Certificate
active
06833698
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to methods of applying external magnetic fields and Radio Frequency (RF) pulses to fluid saturated porous media and subsequently receiving and analyzing signals therefrom to determine properties of the fluid saturated porous media, and more particularly, to methods which utilize Nuclear Magnetic Resonance (NMR) to analyze properties of subterranean formations and borehole core samples.
BACKGROUND OF THE INVENTION
NMR instruments are known to be used which employ pulsed RF fields to excite porous media containing fluids in pore spaces thereby inducing signals to be emitted from the fluid and porous media. The emitted signals are then analyzed to determine important properties of the fluid and porous media. Emitted signals of particular value include proton nuclear magnetic resonance signals. These signals are analyzed to provide data including porosity, pore size distribution of the porous media, percentage oil and water content, permeability, fluid viscosity, wettability, etc.
NMR measurements can be done using, for example, the centralized MRIL.RTM. tool made by NUMAR, a Halliburton company, and the sidewall CMR tool made by Schlumberger. The MRIL.RTM. tool is described, for example, in U.S. Pat. No. 4,710,713 to Taicher et al. Details of the structure and the use of the MRIL.RTM. tool, as well as the interpretation of various measurement parameters are also discussed in U.S. Pat. Nos. 4,717,876; 4,717,877; 4,717,878; 5,212,447; 5,280,243; 5,309,098; 5,412,320; 5,517,115, 5,557,200 and 5,696,448. A Schlumberger CMR tool is described, for example, in U.S. Pat. Nos. 5,055,787 and 5,055,788 to Kleinberg et al.
The content of the above patents is hereby expressly incorporated by reference.
Proton nuclear magnetic resonance signals measured from a fluid-saturated rock contains information relating to the bulk and surface relaxation and diffusion coefficients of pore fluids, the pore size distribution, and the internal magnetic field gradient distribution within pore spaces. These multiple pieces of information are often coupled together in a complicated fashion making it very difficult to sort out the value of each of the aforementioned individual physical quantities.
Diffusion may be qualitatively described as the process by which molecules move relative to each other because of their random thermal motion. This diffusive action of molecules enhances the relaxation rate of NMR signals in a magnetic field gradient.
For fluids in rock pores, three independent mechanisms are primarily responsible for the relaxation or decay of magnetic resonance signals (Coates, G. R., Xiao, L. and Prammer, M. G., NMR Logging Principles and Applications, p. 46, (1999)):
bulk fluid relaxation processes, which determine the value for T
1
and T
2
for bulk fluids;
surface relaxation which affects both T
1
and T
2
; and
diffusion in the presence of magnetic field gradients, which only affects T
2
relaxation.
All three processes act in parallel, and the apparent T
1
and T
2
of pore fluids are given by:
1
T
1
,
app
=
1
T
1
B
+
1
T
1
S
;
(
1
)
1
T
2
,
app
=
1
T
2
B
+
1
T
2
S
+
1
T
2
D
;
(
2
)
1
T
1
,
2
S
=
ρ
1
,
2
S
V
;
(
3
)
1
T
2
D
=
1
3
γ
2
g
2
D
τ
2
;
(
4
)
where:
T
1,app
is the measured apparent longitudinal relaxation time of the pore fluid;
T
1B
is the longitudinal relaxation time of the pore fluid in bulk phase, i.e., when it is an infinite fluid medium not restricted by pore walls;
T
1S
is the longitudinal relaxation time of the pore fluid due to the surface relaxation mechanism;
T
2,app
is the measured apparent transverse relaxation time of the pore fluid;
T
2B
is the transverse relaxation time of the pore fluid in bulk phase, i.e., when it is an infinite fluid medium not restricted by pore walls;
T
2S
is the transverse relaxation time of the pore fluid due to the surface relaxation mechanism; and
T
2D
is the equivalent relaxation time of the pore fluid of the enhanced relaxation rate due to diffusion of spins in a magnetic field gradient;
where &ggr; is the gyromagnetic ratio, &tgr; is the time between the initial &pgr;/2 pulse and the subsequent &pgr; pulse, or half the echo spacing in a Carr-Purcell-Meiboom-Gill (CPMG) (Carr, H. Y. and Purcell, E. M., Phys. Rev. 94, 630 (1954) and Meiboom, S. and Gill, D., Rev. Sci. Instrum. 29, 668 (1958)) experiment, &rgr;
1,2
is the surface relaxivity for T
1,2
surface relaxation; S is the area of the pore surface; V is the volume of the pore; g is the magnetic field gradient, and D is the diffusion coefficient of the spins in the fluid.
Thus the measured magnetization decay, i.e., the spin echo amplitude as a function of time t
i
(the decay time for the i-th echo) for a single pore size system saturated with a single pore fluid can be expressed as:
M
(
t
i
)
M
0
=
exp
[
-
t
i
T
2
B
-
t
i
T
2
S
-
t
i
T
2
D
]
=
exp
[
-
t
i
T
2
B
-
t
i
T
2
S
-
1
3
γ
2
g
2
τ
2
Dt
i
]
.
(
5
)
Note that Eq.(3) is valid for the fast diffusion limit, i.e., when the diffusion time for a spin to traverse the pore is much shorter than the surface relaxation time. Eq.(4) is strictly valid only for an infinite medium and approximately valid in fluid-saturated porous media when the Gaussian approximation for the phase distribution of spins is satisfied (Dunn, K. J. et al, SPWLA 42
nd
Annual Symposium, Paper AAA, Houston, Tex., June 17-20 (2001); and Dunn, K. J., Magn. Reson. Imaging, 19, 439, (2000)). In the present discussion, it is assumed that such Gaussian approximation is valid. Deviation of the physical quantities from their expected values may be attributed, in part, to the failure of such assumption.
Natural fluid-saturated rocks generally have multiple pore sizes. If the surface relaxation strength is reasonably strong (i.e., &rgr;~10 &mgr;m/s), the spins in the pore fluid can only diffuse a short distance of a few pores, the spins at each pore relax more or less independently of the spins in other pores in a diffusion decoupled situation.
Thus, the spin echo amplitude as a function of time t
i
for a multiple pore size system when there is no magnetic field gradient can be expressed as:
M
(
t
i
)
M
0
=
∑
j
f
j
ⅇ
-
t
i
/
T
2
j
(
6
)
where the first term in the exponent of Eq.(5) is neglected because T
2B
>>T
2S
, and t
i
is the decay time for the i-th echo in a CPMG experiment, f
j
is the volume fraction of the pores characterized by a common T
2
relaxation time T
2j
, and 1/T
2j
=&rgr;
2
S
j
/V
j
(where S
j
is the pore surface area and V
j
is the pore volume of pore size j). T
2j
=&agr;
j
/&rgr;
2
with &agr;
j
=V
j
/S
j
as a measure of the pore size.
The LHS of Eq.(6) can be obtained from a CPMG measurement, whereas the volume fractions f
j
on the RHS of Eq.(6) are to be solved from the data analysis. This problem is usually treated by assuming a set of pre-selected T
2j
values equally spaced on a logarithmic scale and solving for the amplitude f
j
associated with T
2j
. The solution obtained is called the T
2
distribution (i.e., f
j
vs T
2j
). This mathematical procedure of obtaining the T
2
distribution is common in NMR relaxation data analysis and is referred to as an inversion process. Since T
2j
=&agr;
j
/&rgr;
2
in the fast diffusion limit, the T
2
distribution frequently reflects the pore size distribution of the rock.
For a fluid-saturated porous medium in a magnetic field gradient, the problem becomes a bit more complicated. The magnetic field inhomogeneities can come from an externally applied field gradient, which is uniform over the pore scale, and/or from local field gradients which have a spatial variation across individual pores. The latter is caused by the magnetic susceptibility contrast between the solid matrix and pore fluids.
Dunn Keh-Jim
Sun Boqin
ChevronTexaco U.S.A. Inc.
Fulton Christopher W.
Vargas Dixomara
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