Characteristics of the nuclear magnetic resonance logging response in fracture oil and gas reservoirs

Abstract

Fracture oil and gas reservoirs exist in large numbers. The accurate logging evaluation of fracture reservoirs has puzzled petroleum geologists for a long time. Nuclear magnetic resonance (NMR) logging is an effective new technology for borehole measurement and formation evaluation. It has been widely applied in non-fracture reservoirs, and good results have been obtained. But its application in fracture reservoirs has rarely been reported in the literature. This paper studies systematically the impact of fracture parameters (width, number, angle, etc), the instrument parameter (antenna length) and the borehole condition (type of drilling fluid) on NMR logging by establishing the equation of the NMR logging response in fracture reservoirs. First, the relationship between the transverse relaxation time of fluid-saturated fracture and fracture aperture in the condition of different transverse surface relaxation rates was analyzed; then, the impact of the fracture aperture, dip angle, length of two kinds of antennas and mud type was calculated through forward modeling and inversion. The results show that the existence of fractures affects the NMR logging; the characteristics of the NMR logging response become more obvious with increasing fracture aperture and number of fractures. It is also found that T2 distribution from the fracture reservoir will be affected by echo spacing, type of drilling fluids and length of antennas. A long echo spacing is more sensitive to the type of drilling fluid. A short antenna is more effective for identifying fractures. In addition, the impact of fracture dip angle on NMR logging is affected by the antenna length.

Full text

Characteristics of the nuclear magnetic resonance
logging response in fracture oil and gas reservoirs
To cite this article: Lizhi Xiao and Kui Li 2011 New J. Phys. 13 045003
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The open–access journal for physics
New Journal of Physics
Characteristics of the nuclear magnetic resonance
logging response in fracture oil and gas reservoirs
Lizhi Xiao1and Kui Li
State Key Laboratory of Petroleum Resources and Prospecting,
China University of Petroleum, Beijing 102249, China
E-mail: xiaolizhi@cup.edu.cn
New Journal of Physics 13 (2011) 045003 (12pp)
Received 30 July 2010
Published 4 April 2011
Online at http://www.njp.org/
doi:10.1088/1367-2630/13/4/045003
Abstract. Fracture oil and gas reservoirs exist in large numbers. The accurate
logging evaluation of fracture reservoirs has puzzled petroleum geologists for
a long time. Nuclear magnetic resonance (NMR) logging is an effective new
technology for borehole measurement and formation evaluation. It has been
widely applied in non-fracture reservoirs, and good results have been obtained.
But its application in fracture reservoirs has rarely been reported in the literature.
This paper studies systematically the impact of fracture parameters (width,
number, angle, etc), the instrument parameter (antenna length) and the borehole
condition (type of drilling fluid) on NMR logging by establishing the equation of
the NMR logging response in fracture reservoirs. First, the relationship between
the transverse relaxation time of fluid-saturated fracture and fracture aperture
in the condition of different transverse surface relaxation rates was analyzed;
then, the impact of the fracture aperture, dip angle, length of two kinds of
antennas and mud type was calculated through forward modeling and inversion.
The results show that the existence of fractures affects the NMR logging;
the characteristics of the NMR logging response become more obvious with
increasing fracture aperture and number of fractures. It is also found that T2
distribution from the fracture reservoir will be affected by echo spacing, type of
drilling fluids and length of antennas. A long echo spacing is more sensitive to the
type of drilling fluid. A short antenna is more effective for identifying fractures.
In addition, the impact of fracture dip angle on NMR logging is affected by the
antenna length.
1Author to whom any correspondence should be addressed.
New Journal of Physics 13 (2011) 045003
1367-2630/11/045003+12$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

2
Contents
1. Introduction 2
2. Response equation 3
3. Analysis and discussion 5
3.1. Impact of fracture aperture ............................ 6
3.2. Impact of dip angle ................................ 7
3.3. Impact of drilling fluids .............................. 7
3.4. Impact of antenna length ............................. 10
4. Conclusions 10
References 12
1. Introduction
Fractures normally develop well in carbonate and igneous rocks and can also be found in
sandstones. Fracture types in the formation include network fractures, oblique fractures, vertical
fractures, half-filling fractures and induced fractures. Fractures play a very important role in
oil and gas recovery. Fractures could connect isolated vugs, which may generate an effective
reservoir space. They may also be conducive to the secondary transformation of reservoirs
[1,2]. Identifying and evaluating fractures have always been important tasks in well logging.
It is known that nuclear magnetic resonance (NMR) logging provides lithology-
independent porosity and T2distributions. T2distribution is a starting point for further
interpretation and evaluation of NMR logging, and it contains a variety of information about
the fluids in the pore and in the matrix. From T2distribution, one can derive the porosity,
permeability and pore size distribution, which are essential for formation evaluation [3]–[9].
Figure 1shows examples of NMR logging in fracture reservoirs. In figure 1(a), the zone
of interest is between 3590 and 3600 m, and was identified as a gas-bearing formation from
mud logging data. In figure 1(b), the zone of interest is from 3599.6 to 3607.4, and mud log
measurements show an exception. Both of them are well-developed fracture zones, as shown
by formation microimaging (FMI; right side on each). Although their T2distributions of NMR
logging did not show a direct relation to fractures, at some depths, the T2value is small, which
reflects bound fluids, whereas at some other depths, the T2value is large, which normally reflects
movable fluids, from either large pores or fractures. It is necessary to study the characteristics
of the NMR logging response of fracture reservoirs. To date, the study of NMR in fracture
reservoirs is rare; it has been mentioned and analyzed qualitatively in three articles [10]–[12].
Yoshito and Tsuneo [13] proposed a method for estimating fracture apertures using NMR
logging. It was pointed out based on the relation between the T2of fluids in reservoirs and
fracture apertures that if the fracture aperture is greater than 0.2 mm, then one could use NMR
logging (free fluid porosity data) to evaluate fractures quantitatively, and determine the linear
relationship between the free fluid porosity and fracture aperture by calibrating the NMR sensor
in the laboratory. In the same study, fractures in a Holocene andesitic lava were evaluated
quantitatively using NMR logging, electrical micro imaging (EMI, trademark of Haliburton
Energy Services) and neutron logging data comprehensively, which was the first quantitative
evaluation of fractures using NMR logging, but there was no discussion of the effects of NMR
logging on fracture reservoirs. We present here a thorough study of the NMR logging response
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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Figure 1. NMR logging at fracture reservoirs: (a) igneous rock formation and
(b) sandstone formation.
at fracture reservoirs and investigate whether the fracture parameters, borehole conditions and
sensor parameters will affect the NMR logging response.
2. Response equation
The sensitive zone for an NMR logging sensor will depend on the length of its antenna. For
Magnetic Resonance Imaging Logging (MRIL; trademark of Halliburton Energy Services), the
length of antennas is 24 inches. If the tool does not move during the measurement cycle (i.e. a
stationary reading is obtained), the vertical resolution equals the length of the antennas.
Figure 2(a) shows the detection region, marked by a blue line. The sensitive volume is a thin
cylindrical shell with 24 inches height and 1 mm thickness. Fractures cross the cylindrical shell
by a certain width and angle and form an inclined cylindrical shell (the cylindrical shell is
vertical when the dip angle is 0), as shown in figure 2(b); the relaxation time of the fluid-
saturated fracture will vary with fracture parameters (apertures, number and dip) and type of
fluid in the fracture.
There are three relaxation mechanisms for fluids saturated in reservoir rocks: surface
relaxation, bulk relaxation and diffusive relaxation. Without taking into account the impact of
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

4
Figure 2. The detection region of NMR logging (a) and the distribution of
fractures in the detection region (b).
Figure 3. T2values as a function of fracture aperture with different surface
relaxivities.
diffusion, the transverse relaxation time T2of the fluid in fractures can be expressed as
1/T2=ρ2(S/V)+ 1/T2b,(1)
where ρ2is the surface relaxivity of the fracture. Paramagnetic irons in rocks will yield a high
magnetic susceptibility and increased ρ2value. Here, S/Vis the surface-to-volume ratio of the
pore space, and T2b is the T2of bulk fluid.
For a planar fracture with aperture d,S/Vis 2/d. Therefore, equation (1) can be replaced
by equation (2),
1/T2=ρ2(2/d)+ 1/T2b.(2)
Figure 3shows the relationship between T2of the fluid-saturated fracture and fracture aperture
with different transverse surface relaxivities. We assume that T2b of the drilling fluid filtrate
equals 2 s. The study assumes that no solid particles enter the fractures; hence the drilling fluid
filtrate signature is considered.
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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If the matrix porosity, fracture aperture and dip are known, then the volume and porosity of
the fracture in the detection region can be estimated. The volumes of the thin cylindrical shell
and the inclined cylindrical shell are given by equations (3) and (4),
V=Zr2
r1
L·2πrdr,(3)
Vf=Zr2
r1d·2πr
cos θdr,(4)
φf=Vf/V,(5)
φb=φm·(1−φf),(6)
where Lis the length of antennas, ris the radial detection depth, θis the fracture dip, dis the
fracture aperture, φfis the fracture porosity, φmis the matrix porosity without fracture and φbis
the matrix porosity when fractures exist in the detection region.
The response function of NMR logging in the fracture reservoir can be expressed as
ECHO =
N
X
i=1
φ1iHIfluid 1−exp−Tw/T1,pore(i)exp−t/T2,pore(i)
+
M
X
i=1
φ2iHIfluid 1−exp−Tw/T1,fracture(i)exp−t/T2,fracture(i)+ noise,(7)
where Nis the bin number for pore size components, Mis the number of fractures, HIfluid is the
hydrogen index of the fluid, T2,pore is the transverse relaxation time of the fluid in the pore and
T2,fracture is the transverse relaxation time of fluid-saturated fractures.
The first part of the equation is the NMR logging response to pores and the second part is to
fractures’ response. It can be seen that the response of NMR logging in the fracture reservoir is
affected by many factors, such as matrix porosity, fracture porosity, type of fluid, T1,T2, which
are controlled by fracture parameters (aperture, number and dip), type of fluid and the length of
antennas.
Based on the equation, an echo train can be produced by forward modeling plus random
noise, and then T2distribution can be inverted from the echo train.
3. Analysis and discussion
Assuming that the fracture is planar, the dip is 0◦, 45◦and 90◦separately and the fracture
aperture is 0.1, 0.5, 1, 10 and 20 mm; the types of drilling fluids include water-based and oil-
based. Matrix porosity, fracture porosity and T2for fluid-saturated fracture could be calculated
by using equations (2)–(6) with different parameters, drilling fluids and lengths of antennas. The
magnetic gradient is given as 18 ×10−4T cm−1and MRIL is used. It is further assumed that
formations exist in only two kinds of reservoirs: small pores and fractures, rock is hydrophilic,
8m=5%, T2b =1 s, the length of antennas is 24 inches, and the detection region exists in a
single fracture. As shown in table 1,T2values become higher and higher with increasing fracture
aperture when a water-based drilling fluid is used, but do not depend on the fracture aperture
when an oil-based drilling fluid is considered.
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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Table 1. Matrix porosity, fracture porosity and T2of fluid-saturated fractures
with different fracture apertures, dip angles and drilling fluids
Fracture Matrix Fracture
aperture porosity porosity T2(ms) fluid-saturated fracture
Dip θ (◦)d(mm) φb(%) φf(%)Water-based Oil-based
0 0.1 4.99 0.02 47.61 769.20
0.5 4.99 0.08 200 (TE =0.9 ms)
1 4.99 0.16 333.33 623.40
10 4.91 1.64 833.33 (TE =1.2 ms)
20 4.84 3.28 909.09 271.04
45 (TE =2.4 ms)
0.1 4.99 0.02 47.61 139.58
0.5 4.99 0.12 200 (TE =3.6 ms)
1 4.98 0.23 333.33 83.13
10 4.88 2.32 833.33 (TE =4.8 ms)
20 4.77 4.64 909.09 54.69
(TE =6 ms)
90 Fracture is in the slice 2 4.97 0.48 500
Facture is not in the slice 2 5 0 – –
3.1. Impact of fracture aperture
From equation (2), the transverse relaxation time of fluid-saturated fracture will change with
fracture aperture. From table 1, when the fracture aperture increases, the matrix porosity
decreases and the fracture porosity increases.
Figure 4shows the characteristics of the NMR logging response in the detection region
using a water-based drilling fluid, where the transverse relaxation time and hydrogen index of
the drilling fluid filtrate is 1 s and 1, respectively, and Tw=12 s, TE =1.2 ms, L=24 inches.
Different apertures of fractures are given as 0.1, 0.2, 0.5, 0.8, 1, 2, 3, 4, 5, 10 and 20mm. The
S/Vfor each fracture is calculated by 2/d.
As shown in figure 4, when the fracture aperture dis equal to 0.1 or 0.2 mm, the T2
distribution is the same as when there is no fracture. When the fracture aperture is equal to
or greater than 2 mm, bimodal distributions appear on the T2spectrum; with increasing fracture
aperture, the peak of the T2distribution becomes larger gradually.
In a network-fracture or oblique-fracture formation, an NMR sensor will detect more
fracture signals.
Figure 5shows T2distributions when the formations exist in a single or two fractures
(assuming the two fractures are spaced apart by 2 mm). Here, the total width of two fractures
is equal to the width of a single fracture. Their T2distributions are basically the same. From
equation (2) it is seen that the T2values of a single fracture with an aperture of 2 mm and
two fractures with an aperture of 2 mm are different, but when the fracture aperture is small,
the fracture porosity is accordingly small, so its effect could be ignored. Therefore, when the
fracture aperture is very small, the impact of porosity on NMR logging is dominant.
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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Figure 4. NMR signal decay curves (a) and T2distributions with different
fracture apertures (b).
3.2. Impact of dip angle
When the dip angle of the fracture changes, the volume of fracture in the slice will change;
according to equation (4), fracture porosity changes accordingly; when the fracture dip is too
large, the fracture will not fully appear in the detection area owing to the thickness of the NMR
slice, such as vertical fractures (with a dip of 90◦). Therefore, it is necessary to consider two
cases: whether the vertical fracture is in the slice or is not in the slice. After calculating, we
could see that when the fracture dip is 0◦and 45◦, respectively, the reservoir matrix porosity and
fracture porosity vary in the range of 0–0.1% and 0–1.36% at several fracture apertures, which
illustrates that the impact of the change in dip angle on the NMR logging is not obvious when
the aperture of the fracture is small, but becomes increasingly obvious with increasing fracture
aperture. Here we test the shape of the T2spectrum with variation of dip angle when the fracture
aperture is equal to 2 mm.
Figure 6shows six cases: the dip angle of the fracture θequals 0◦,15◦,30◦,45◦,60◦and
90◦,respectively. We can see that the change in T2distribution with dip angle is not obvious
when the fracture aperture equals 2 mm.
3.3. Impact of drilling fluids
The small pores are hydrophilic. When the drill fluid filtrate invades into the formation, the
pores in the flushed zone fractures will fill with filtrate completely. Typical drilling fluids include
water-based drilling fluid, oil-based drilling fluid and gas drilling. Different drilling fluids have
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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Figure 5. NMR T2distributions of the detection region with different fracture
apertures: (a) single fracture; (b) two fractures.
Figure 6. d=2 mm, T2distribution with different dip angles: (a) using water-
based drilling fluid, the sensor coincided with the vertical fractures; (b) using
water-based drilling fluid, the sensor did not coincide with the vertical fractures.
different hydrogen indexes, diffusion coefficients and transverse relaxation times due to their
different densities and viscosities. Any change in parameters in equation (7) may affect the
response of NMR logging. When the diffusion coefficient of the drilling fluid filtrate is large,
the effect of diffusion relaxation could not be ignored, and equation (2) should be written as
1/T2f =ρ2(2/d)+(1/T2b)+Df(rGTE)2
12 ,(8)
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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Figure 7. T2distributions under different drilling fluid filtrates: (a) water-based
drilling fluid, TE =1.2 ms; (b) water-based drilling fluid, TE =6.0 ms; (c) oil-
based drilling fluid, TE =1.2 ms; (d) oil-based drilling fluid, TE =6.0 ms.
where G is the magnetic gradient of the static magnetic field produced by the NMR logging tool
and TE is the echo spacing.
Here, T2f is the transverse relaxation time of the fluid-saturated fracture, Dfis the diffusion
coefficient of the drilling fluid filtrate, and T2b is the bulk relaxation time, which is related to the
temperature and viscosity of the drilling fluid filtrate.
As mentioned in table 1, the T2distribution of the fracture reservoir changes obviously
with fracture aperture when a water-based drilling fluid is used, but does not change when an
oil-based drilling fluid is used.
Figure 7shows T2distributions for different types of drilling fluids, where TE =1.2 and
6 ms, respectively, and the magnetic field gradient is 18 ×10−4T cm−1with MRIL. It can be
seen that when the echo spacing is short, T2distributions are very close for both water-based
and oil-based drilling fluid filtrates. When the echo spacing is long, T2distributions are different.
The diffusion coefficient of the oil-based drilling fluid filtrate is normally greater than that of
the water-based drilling fluid filtrate. The T2values of the fluid filtrate within fractures become
smaller with increasing echo spacing (figure 8), which caused the information about fractures
and small pores to overlap.
Figure 8shows the T2distribution with different echo spacings, where the fracture aperture
is 2 mm (left) and 20 mm (right) with a dip angle of 0 and an oil-based drilling fluid was used.
The T2distribution becomes narrow with increasing echo spacing. The T2distribution has no
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

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Figure 8. T2distributions at oil-based drilling fluid with different echo spacings
and fracture apertures: d=2 mm (a) d=20 mm (b).
information about fracture when the echo spacing is greater than 3.6 ms. Therefore, if one wants
to detect fractures using NMR, echo spacing has to be planned very carefully.
3.4. Impact of antenna length
From equations (3)–(6), we see that the fracture porosity and matrix porosity will increase as the
antenna length decreases. The parameters are: echo spacing TE is equal to 1.2 ms; the fracture
aperture dis equal to 0.05, 0.1, 0.2, 0.5, 0.8, 0.9, 1, 1.2, 1.5, 1.8 and 2 mm, respectively; the
fractures are filled with a water-based drilling fluid filtrate; the antenna length is 24 and 6 inches,
respectively; the magnetic field gradient is 18 ×10−4T cm−1; the simulated and inverted T2
distribution in the fracture reservoir is shown in figure 9; the 6 inch antenna gets a higher vertical
resolution than the 24 inch one; when dreaches 0.8 mm, the T2distribution contains fracture
information.
Figure 10 shows the impact of dip angle on T2distribution. The effect is not so obvious
when Lequals 24 inches but is obvious when Lequals 6 inches.
4. Conclusions
Through theoretical analysis and numerical simulation, it can be concluded that NMR logging
has a clear response at fracture reservoirs and is associated with many factors, such as fracture
aperture, fracture number, fracture dip angle and drilling fluids.
1. If the fracture aperture increases, the T2of a fluid-saturated fracture will also increase
correspondingly. The larger the fracture aperture, the more obvious the response of NMR
logging.
2. With increasing fracture aperture, the peak of T2distribution gradually increases. The
NMR logging response at the fracture becomes more obvious as the number of fractures
increases.
3. The drilling fluid filtrate will affect the response of NMR logging. For different drilling
fluid filtrates with the same fracture parameters, the shape of T2distribution will be related
to echo spacing. When the echo spacing is small, T2distribution at the water-based drilling
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

11
Figure 9. T2distribution with different antenna lengths when oil-based drilling
fluid is used: (a) L=24 inches; (b) L=6 inches.
Figure 10. T2distribution with different antenna lengths when the dip angle
changes, where d=2 mm: (a) L=24 inches; (b) L=6 inches.
fluid filtrate is roughly the same as that at the oil-based drilling fluid filtrate. When the
echo spacing is big, the T2distribution at different drilling fluid filtrates will not be the
same.
4. The antenna length will affect the NMR logging response at the fracture reservoir. For a
short antenna, NMR logging is more sensitive to fractures.
New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)

12
5. NMR logging may be applied to fracture evaluation if the fracture aperture is big enough.
When the fracture aperture is big enough, however, it is still strongly recommended to
integrate any other logging information, such as electronic FMI and ultrasonic scanning,
into NMR logging. Remember that NMR logging with a gradient magnetic field is a sliced
measurement, and it only responds to fracture when the slice measured intersects with the
fracture.
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New Journal of Physics 13 (2011) 045003 (http://www.njp.org/)