Anal. Chem. 2005, 77, 1824-1830
Direct Detection of Hydrocarbon Displacement in a Model Porous Soil with Magnetic Resonance Imaging Yuesheng Cheng,†,‡ Bryce MacMillan,‡ Rod P. MacGregor,‡ and Bruce J. Balcom*,†,‡
Department of Chemistry, MRI Center, Department of Physics, P.O. Box 4400, University of New Brunswick, Fredericton, NB E3B 5A3, Canada
The direct detection of hydrocarbon fluid and the discrimination of water through carbon-13 magnetic resonance imaging (MRI) would be a significant advance in many scientific fields including food, petrogeological, and environmental sciences. Carbon-13 MRI is a noninvasive analytical technique that has great potential for direct detection of hydrocarbons. However, the low natural abundance of carbon-13, low gyromagnetic ratio, and generically short transverse signal lifetimes in realistic porous media all conspire to hinder carbon-13 MRI. A multiple echo pure phase encode MRI technique introduced in this paper helps to overcome these limitations. As a pure phase encode technique, it is immune to artifacts arising from inhomogeneous B0 fields. It is also, by its nature, more quantitative than most MRI methods. Viscous hydrocarbon flow through a sand bed, a simple realistic porous medium, was used as our test system. Flow in this model system was driven by capillary suction. The detection limit, spatially resolved, was determined to be 26 mg. Hydrocarbon contamination of soils is a long-term environmental problem throughout the western and developing worlds. Evaluation, management, and restoration of contaminated sites require a detailed understanding and characterization of hydrocarbon reaction and flow in realistic model systems. In this study, Carbon-13 magnetic resonance imaging (MRI) is used to detect and quantify hydrocarbon content distribution in a realistic porous media. The logical extension of these ideas should permit detailed noninvasive studies, spatially and temporally resolved, of hydrocarbon reaction and flow in a wide variety of media. Magnetic resonance imaging is a noninvasive investigative tool widely used in the health sciences and, more recently, in materials science. Close examination of the scientific literature shows that the vast majority of MRI studies, medical and nonmedical, do not interpret absolute local signal intensity, despite the obvious opportunity, but rather use contrast in the MRI to characterize the geometry and changes in geometry1 of the system under * Corresponding author. E-mail:
[email protected]. † Department of Chemistry. ‡ Department of Physics. (1) Zhang, C.; Werth, C. J. Webb, A. G. Environ. Sci. Technol. 2002, 36, 33103317.
1824 Analytical Chemistry, Vol. 77, No. 6, March 15, 2005
study. In this paper, we outline a method that can determine hydrocarbon concentration and changes in hydrocarbon concentration in a model realistic soil. Several recent papers report MRI investigations of hydrocarbon distribution in porous media. A variety of techniques have been employed including spin-echo,2,3 inversion recovery,4,5 and chemical shift imaging.6,7 Each technique has distinct disadvantages. An underlying problem common to these methods is the assumption that the spectral lines, or relaxation time distributions, of oil and water do not overlap. A truly general method should not be limited to such stringent conditions. In addition, magnetic susceptibility mismatch leads to image artifacts in conventional imaging methods through distortion of the local magnetic field homogeneity.8,9 Perhaps most importantly of all, existing studies employ 1H MRI and are not able to unambiguously distinguish between water and oil phases. Kleinberg and coauthors have extensively investigated relaxation mechanism of oil and water phases in porous media.10-13 The relaxation time distributions of the two phases may be used in bulk measurements to discriminate the oil/water content, but there has been no satisfactory translation of these ideas to MRI. One solution is to use fluorinated oils as a model system and employ 19F for detection of the oil phase. This is, however, a significant departure from natural conditions.14 We seek a more general measurement, choosing natural abundance 13C, which will be found only in the hydrocarbon phase. Normally researchers tend to avoid 13C due to its low natural abundance and reduced sensitivity. The method outlined here (2) Pervizpour, M.; Pamukcu, S.; Moo-Young, H. J. Comput. Civ. Eng. 1999, 13, 96-102. (3) Johns, M. K.; Gladden, L. F. Magn. Reson. Imaging 1998, 16, 665-657. (4) Fisher, A. E.; Balcom, B. J.; Forham, E. J.; Carpent, T. A.; Hall, L. D. J. Phys. D: Appl. Phys. 1995, 28, 384-397. (5) Davies, S.; Hardwick, A.; Roberts, D.; Spowage, K.; Packer, K. J. Magn. Reson. Imaging 1994, 12, 349-353. (6) Chen, Q.; Wang, W.; Cai, X. Magn. Reson. Imaging 1996, 14, 949-950. (7) Horsfield, M. A.; Hall, C.; Hall, L. D. J. Magn. Reson. 1990, 87, 319-330. (8) Posse, S.; Aue, W. P. J. Magn. Reson. 1990, 88, 473-492. (9) Callaghan, P. T.; Forde, L. C.; Rofe, C. J. J. Magn. Reson. B 1994, 104, 34-52. (10) Latour, L. L.; Kleinberg, R. L.; Sezginer, A. J. Colloid Interface Sci. 1992, 150, 535-548. (11) Kleinberg, R. L.; Kenyon, W. E.; Mitra, P. P. J. Magn. Reson. A 1994, 108, 206-214. (12) Kleinberg, R. L.; Farooqui, S. A.; Horsfield, M. A. J. Colloid Interface Sci. 1993, 158, 195-198. (13) Kleinberg, R. L.; Horsfield, M. A. J. Magn. Reson. 1990, 88, 9-19. (14) Doughty, D. A.; Tomutsa, L. Magn. Reson. Imaging 1996, 14, 869-873. 10.1021/ac048540s CCC: $30.25
© 2005 American Chemical Society Published on Web 02/09/2005
improves the experimental sensitivity without special apparatus, thereby making 13C MRI a practical possibility. Since we are focused on the oil content and its longitudinal displacement in a flow experiment, we may reduce the dimensionality of the imaging problem and extract the information desired from one-dimensional profiles. In addition, one-dimensional measurements will yield a more sensitive measurement than two- or there-dimensional measurements. THEORY The basis of MRI is the Larmor equation, ω ) γB0, where ω is the Larmor frequency, γ is the gyromagnetic ratio, and B0 is the static magnetic field. In the presence of a magnetic field gradient, for example in the Y direction, the Larmor equation becomes
ω(y) ) γ(B0 + GyY)
(1)
Spatial position in eq 1 is encoded in the Larmor frequency, ω(y). The signal arising from different positions is a function of the spin density (F0(y)) projected onto the Y direction and weighted by the spin relaxation time. In MRI it is well known that15 the signal-to-noise ratio (SNR) varies with N, the number of signal averages, and FW, the bandwidth of the acquisition, or filter width. SNR is improved by either increasing N or decreasing FW.
SNR ∝ xN/FW
(2)
In conventional frequency encoding techniques such as a spinecho, experimental data are acquired in the presence of a strong magnetic gradient field to overcome image distortions and resolution loss due to magnetic susceptibility variation.9 This leads to a proportional decrease in the SNR because the filter width must be increased to allow for a broader range of frequencies, as indicated in eq 1. In our method, multiple spin-echo single-point imaging, the magnetic field gradient is off during data acquisition. Thus, the minimum filter width should be the natural line width of the sample or the entire spectrum if multiple resonances exist. A simple comparison of the two techniques, gradient on/off during acquisition, shows that the SNR will be increased by the square root of the ratio of filter widths, a factor we denote W. The imaging method proposed is shown in Figure 1. It is an adaptation of the Carr-Purcell-Meiboom-Gill (CPMG) spinecho method. The data acquired are single complex points at the peak of each echo in the echo train. Position is encoded in reciprocal image space, k space, as a function of the stepped phase gradient Gy, where ky ) (1/2π)γGytp. A 13C profile is obtained through Fourier transformation of the experimental k space data. This technique permits one to decrease the filter width and refocus the chemical shift. By collecting multiple echoes, each encoded with position information, we generate more image data without an increase in acquisition time. The XY-4 phase cycle is used to compensate for nonideal rf pulses,16,17 reducing artifacts in multiple echo images and permitting accurate T2 measurements. (15) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, England, 1961; Chapter 4. (16) Gullion, T. J. Magn. Reson. A 1993, 101, 320-323. (17) Maudsley, A. A. J. Magn. Reson. 1986, 69, 488-491.
Figure 1. Multiple spin-echo single point image sequence (1D, Y direction). The horizontal axis is time. Phase encoding is applied between the excitation and refocusing pulses. This method employs an XY-4 refocusing train of 180° pulses. The variable tp is the phase encoding time. TR, the repetition time, is the time between the end of the echo train and the next excitation pulse. Only one data point at the peak of each echo was acquired.
Assuming Sn(ky) is the signal intensity from the nth echo and TR . T1 in Figure 1,
Sn(ky) )
∫
+∞
-∞
F0(y) exp(- nTE/T2(y)) exp(i2πkyy) dy (3)
where F0(y) is the 13C density, n is the echo number, TE is the echo time, T2 is the spin-spin relaxation time, and T1 is the spin-lattice relaxation time. The inverse Fourier transformation of eq 3 yields the 13C density profile weighted by T2, i.e.:
Feff,n(y) ) F0(y) exp(-nTE/T2(y))
(4)
where Feff,n(y)is the effective density profile determined from the nth echo. Equation 4 shows that each echo, with identical phase encoding from the initial gradient, Figure 1, will yield an image profile with progressively greater T2 weighting. It is thus possible to use the image profile generated from n echoes, to produce a spatially resolved map of T2 by fitting the profiles to eq 4. However, when and if n ) 1 and TE is very short compared to T2, the profile will be purely density weighted, i.e., Feff,n(y) ) F0(y). Alternatively, it is possible to increase the overall SNR of the image by summing the image profiles generated from different echoes. The total profile signal intensity is thus M
Feff(y) )
∑F
eff,n(y)
(5)
n)1
where M is the number of echoes added. From eq 4 we know that the profile has T2 weighting when n becomes larger. Therefore, the summed profile will yield better SNR but at the expense of introducing variable T2 weighting in the overall profile. The summed profile signal-to-noise ratio will be M
SNReff )
Feff(y) σxM
∑F
eff,n(y)
)
n)1
σxM
(6)
if the noise on each profile, σ, is equal. Analytical Chemistry, Vol. 77, No. 6, March 15, 2005
1825
Compared to the conventional spin-echo (assuming the same field of view (FOV), and a filter bandwidth W times larger), the ratio of the SNR for multiple spin-echo single-point imaging and the conventional spin-echo is
Let us consider a simplified condition. Assume we acquire only single echoes, M ) 1, with TE < TR, and keep all other parameters constant. The ratio of the SNR per unit time for both methods will be
M
SNReff/SNRSE )
x
∑F
eff,n(y)
W
SNRPM,total,persec /SNRSE,persec )
n)1
x
∑ exp(-nTE/T (y)) 2
W n)1
M
(7)
exp(-TE/T2(y))
where the SNR of the conventional spin-echo is defined as SNRSE ) F0(y) exp(-TE/T2(y)). Equation 7 ignores the signal loss due to diffusion in the conventional spin-echo imaging measurement. However, this is not a significant feature in the discussion that follows and no loss of generality results. As an example, when W ) 20, and assuming a single echo image, M ) 1, the SNR is improved by a factor of 4.5. A factor of 4 improvement for conventional SE requires 16 signal averages, which is a factor of 16 increase in the acquisition time. Therefore, improving the SNR by signal averaging is inefficient. We will elaborate on this point shortly. As a pure phase encoding method, the total time required for our method will be N′(TR+ MTE), where N′ is the number of the steps of the phase encode gradient. The total signal-to-noise per unit time relative to that of a spin-echo method is given by
M
(TR + TE) N′(TR + MTE)
x
∑ exp(-nTE/T (y))
M
(8)
exp(-TE/T2(y))
We denote the new method as PM (phase encode method) in eq 8 and subsequent equations. Compared to a single-frequency encoded spin-echo, the experimental duration of our method, N′(TR + MTE), is much longer. However, this is only really true for the case of high SNR samples, which do not require signal averaging. If signal averaging is required, for example, with insensitive nuclei or for highresolution imaging, the ratio of the SNR per unit time from the two methods becomes important.
SNRPM,total,persec/SNRSE,persec ) M
1
xN
N′(TR + MTE)
x
∑ exp(-nTE/T (y))
W n)1
M
xNW N′xNav
(11)
2
W n)1
N(TR + TE)
From eq 10, we can consider three specific limits. (a) When N ) W and N ) N′, the ratio is 1. This means both methods are equally time efficient. These conditions occur when the acquisition bandwidth for frequency encoding is N(πT2*)-1 whereas the acquisition bandwidth for pure phase encoding is (πT2*)-1. The expression (πT2*)-1 is the intrinsic line-width of the sample.18 Under these conditions, the number of frequency encode signal averages is equal to the number of phase encode steps. (b) (NW)1/2 > N′. This occurs when extensive signal averaging is required for frequency encoding. In this case, the pure phase encode approach is more efficient. As mentioned above, this condition will occur when the intrinsic SNR of the sample is low. This is surprisingly common in MRI microscopy. (c) (NW)1/2 < N′. In this case, extensive signal averaging is not required and ordinary frequency encoding methods are most efficient. We will not concern ourselves further with this limit. One should, for generality, modify eq 10 to allow for the case of signal averaging during a pure phase encode measurement. If Nav is the number of signal averages for each phase encode step then eq 10 becomes
SNRPM,total,persec/SNRSE,persec )
SNRPM,total,persec /SNRSE,persec )
2
exp(-TE/T2(y)) (9)
If the ratio of eq 9 is less than 1, the spin-echo method is more efficient. If the ratio is equal to or more than 1, the multiple spinecho single-point imaging is equally or more time efficient. 1826
(10)
M F0(y) exp(-TE/T2(y)) M
)
xNW N′
Analytical Chemistry, Vol. 77, No. 6, March 15, 2005
This modification of eq 10 does not alter the above discussion of the relative efficiency of the two methods. Frequency encode spin-echo methods may also be limited by a line width restriction on resolution for samples with very short T2*, but sufficiently long T2 to form an echo. This occurs in samples with microscopic heterogeneity in their magnetic susceptibility. Pure phase encode methods, such as those espoused in this paper, do not have the same line width restriction on resolution.19 EXPERIMENTAL SECTION High-resolution 13C spectra were acquired on a 9.4-T Varian Unity 400 spectrometer (Varian, Inc.). All other measurement were carried out on a General Electric (GE NMR Instruments, Fremont, CA) CSI II imaging system with a home-built 21.3-MHZ 13C probe, based on a 4-cm-diameter solenoid, in a horizontal wide-bore (31 cm) 2.0-T Oxford (Oxford Instruments, Oxford, England) magnet. The maximum gradient strength was 12 G/cm. These measurements required only slightly more than half of the maximum gradient strength. Image reconstruction was performed in IDL (Research System, Inc., Boulder, CO). Images generated from (18) Beyea, S. D.; Balcom, B. J.; Bremner, T. W.; Armstrong, R. L.; Cross, A. R. J. Magn. Reson. 2000, 144, 255-265. (19) Gravina, S.; Cory, D. G. J. Magn. Reson. B 1994, 104, 53-61.
Table 1. Fine Silica Sand Properties specific gravitya void ratiob coefficient of uniformity coefficient of curvature grain-size distributionc absorption of waterd a
Figure 2. Schematic of the experimental setup. The sample was oriented vertically in a 31-cm-bore horizontal magnet. A solenoid style rf probe surrounded the sample. An oil collection beaker was placed outside the magnet.
even-number echoes were reversed compared to those produced from odd echoes. This was necessary due to an inversion of the accumulated phase by successive 180° pulses. Images generated from even-number echoes were therefore row reversed as part of the image reconstruction procedure. For data fitting, we utilized Sigma plot 4.14 (SPSS Inc., Chicago, IL). Hydrocarbon migration profiles through sand were acquired at 10-min intervals, with 16 profiles typically acquired. A 5-cm column of sand was packed in 2.8-cm i.d. glass tube with 2 cm of oil on the top. Figure 2 shows a schematic of the experimental setup. A constant fluid head above the sand was maintained by periodic addition of oil. No additional external pressure was applied. The image field of view was 10.5 cm with an encoding time tp of 150 us, TE ) 2 ms, and TR ) 800 ms, with 16 signal averages typically acquired. The 90° degree pulse length was 89 µs. Echo trains of 32 echoes were acquired. The nominal pixel resolution was 0.16 cm. After saturation of the sand bed by oil flow, two conventional spin-echo measurements were undertaken for comparison to multiple spin-echo single-point imaging experiments. These measurements had either the same number of signal averages, 16, or equivalent measurement times, ∼ 16 min. The field of view, TE, and TR were maintained constant. 13C MRI images were acquired with the above parameters to test the sensitivity limits of this method. Five uniform oil-sand mixtures were made in identical glass tubes of 0.70-cm height. The otherwise identical samples had systematically different oil contents (w/w) of 5, 10, 15, 20, and 25% in 5.00 g of sand. The characteristics of the fine silica employed in these measurements (Shaw Brick, Fredericton, NB, Canada) are listed in Table 1.20 A commercial oil SAE 85W-140, viscosity 15000 cP at -12 °C,21 was purchased from a national automobile chain (Canadian Tire, Fredericton, NB, Canada). (20) Aurelle, A. Use of Centrifuge Testing to Characterize LNAPL Entrapment under Hydraulic Flushing. M.Eng. Thesis, UNB Department of Civil Engineering, 2001.
2.64 0.70 1.447 1.196 over 90% are 0.4-0.9 mm 0.44%
ASTM D1556-90. b ASTM C29-97. c ASTM D442-63. d ASTM C642-90.
RESULTS AND DISCUSSION The MR relaxation time behavior of a system is fundamental to the choice of an appropriate imaging or measurement protocol. Therefore T2*, T2, and T1 measurements were undertaken of the oil system, both as pure liquid and as a liquid dispersed in sand. Our chosen oil was a high-viscosity commercial product. We deliberately chose a high-viscosity oil to ensure advantageous T1 values in the early stages of developing the method. The oil T1 and T2 were measured in both environments, by using inversion recovery and CPMG methods, respectively. The oil T2* was determined from the exponential decay of the MR signal resulting from a single-pulse excitation. The sample T1 was 87 ms and T2 was 25 ms, irrespective of the oil environment, neat solution or dispersed in sand. The high-resolution 13C spectrum revealed numerous individual resonances as expected for a nontrivial hydrocarbon sample. The decoupled 13C spectrum revealed at least 26 peaks between 10 and 50 ppm. This is a 190-Hz bandwidth in a 2.0-T magnetic field. Single-pulse free induction decay measurements at 2.0 T yielded single-exponential decays with only one broad peak visible in the 13C spectrum. The static magnetic field in the GE magnet was minimally shimmed. This, in combination with relatively large sample size, ensures that individual resonance lines are not resolved. The single broad peak observed in the frequency domain had a T2* of 1.24 ms. The oil-saturated sand also revealed a single broad 13C line in the frequency domain, characterized by a T2* of 430 µs. The oilsaturated T2* value is reduced from the pure oil value because of the magnetic field distortion effects of the sand particles, which have a magnetic susceptibility that is mismatched to the surrounding space. The effective spin-spin relaxation time, T2*, in an inhomogeneous static magnetic field is usually written as
1 1 ) + γ∆B0 T2* T2
(12)
which assumes a Lorentzian distribution of field offset ∆B0.22 The magnetic field offsets inside an irregularly shaped pore lead to rapid dephasing of transverse magnetization, with subsequent shortening of the T2* relaxation time.23 (21) Society of Automotive Engineers, Inc., Surface Vehicle Standard, 1991; pp 589-591. (22) Haacke, E. M.; Brown, R. W.; Thompson, M. R.; Venkatesan, R. Magnetic Resonance Imaging: Physical Principles and Sequence Design; John Wiley and Sons: New York, 1999; Chapter 20. (23) Beyea, S. D. Magnetic Resonance Imaging(MRI) and Relaxation Time Mapping of Concrete. Ph.D. Thesis, UNB Department of Physics, 2000.
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Figure 3. Sensitivity determination of the 13C imaging method. A plot of the image intensity in a single pixel versus the total oil mass divided by the number of pixels defining the object. The straight line plot has a zero intercept as anticipated for a linear measurement. The detection limit, for 16 signal averages, is 26 mg of oil.
Our T1 and T2 measurement revealed constant values irrespective of the presence of the sand particles. This is not unexpected for a fluid that does not fully wet the pore surface. Surface relaxation will not occur if the hydrocarbon phase does not interact with the surfaces. In water-wet porous media, hydrocarbons will not have access to hydrophilic solid surfaces. A water film of only a few molecular layers covering the solid surface24 is sufficient to hinder surface relaxation. The sand phase employed in our measurements was not dried prior to use, therefore, we did not anticipate surface relaxation. Guided by the bulk measurements, a repetition time TR was chosen that avoided T1 contrast in the imaging experiments. Our goal was to generate the most quantitative 13C images possible. The highest SNR images are generated by summing the individual profiles generated from the first 16 echoes in our multiple spinecho imaging method. The individual images therefore have different T2 weightings. Since T2 is a constant in each sample, the summed profile signal intensity is proportional to the pure density profile signal intensity. A pure density image may be retrieved by fitting the T2 weighted images to eq 4 and extrapolating nTE to time zero. The sensitivity limits of the method were determined by imaging five uniform samples with systematically different oil contents. The image profile in each case displayed a uniform intensity within the test object. Figure 3 shows the results of imaging all five test samples. The signal intensity from one pixel within the test object is plotted versus the sample oil mass, normalized by the number of pixels that define the test object in the image. The result is a linear relationship between signal intensity and the oil content as anticipated from eqs 3 and 4, when T2 is constant. The slope of the straight line relating the image intensity and oil mass was 57.4 ( 2 g, while the y-intercept was 0.14 ( 0.42 (arbitrary units). The uncertainty in the intercept is substantially larger than that of the fit value, confirming that the relationship between image intensity and oil mass is linear with an intercept of essentially zero. (24) Kleinberg, R. L.; Flaum, C. Review: NMR detection and characterization of hydrocarbon in subsurface Earth formations. In Spatially resolved magnetic resonance: Methods, materials, medicine, biology, rheology, geology, ecology, hardware; Blumich, B., Bliumler, P., Botto, R., Fukushima, E., Eds.; WileyVCH: Weinheim, 1998; Chapter 54.
1828 Analytical Chemistry, Vol. 77, No. 6, March 15, 2005
Figure 4. (a) 13C 1D image profiles generated from the first 16 echoes of our measurement after 130 min of oil flow. Each echo, appropriately phase encoded, contributes to one T2 weighted image. The oil reservoir, to the right in the image, is located on the top of the sand bed. The profiles have progressively increasing T2 weighting. (b) T2 decay at a position 3.6 cm along the Y direction, rendered from (a). The spatially resolved T2s were extracted by a fit to eq 4. The discrete symbols (b) are data points measured by 13C MRI. The solid lines represent the best fit to eq 4.
This experiment permits one to determine the detection limit of the measurement. We define the detection limit for one pixel as the mass corresponding to a signal that is three times the standard deviation of the background signal, a simple yet common convention for the detection limit.25 In the measurements of Figure 3, 64 signal averages were acquired. The standard deviation of the background signal was 0.246, using the same units as above. This corresponds to a detection limit of 13 mg of oil for 64 signal averages. For 16 signal averages, the detection limit is therefore 26 mg, due to the N1/2 dependence of SNR on signal averaging. From eq 4, the image from the first echo is a pure 13C mass profile, but as n becomes larger, the image has increased T2 weighting. Figure 4a shows T2 weighted images of the oil distribution in the sand bed after 130 min of flow. Individual profiles generated from the first 16 echoes were displayed. As anticipated, the local image intensity decays exponentially with the echo number n. Therefore, T2 at different positions may be (25) Skoog, D. A. Principles of Instrumental Analysis; Saunders CollegePubl.: Philadelphia, PA, 1984; Chapter 1.
Figure 5. Relative oil concentration, spatially resolved, in the sand bed during an oil imbibition experiment. The profiles displayed are the sum of the individual profiles obtained from the first 16 echoes in each echo train. Profile intensities are normalized by the oil reservoir signal intensity. Each 1D profile corresponds to a different time during the oil penetration experiment. The moving boundary indicates the leading edge of the penetrating oil front.
readily determined (Figure 4b). Fits to eq 4 showed that T2 is independent of the position within the sand bed. The T2 value, 25 ms, agrees with the bulk measurements of pure oil and oilsaturated sand. The optimum number of echoes for best S/N can be found by differentiating eq 6 with M and setting the result equal to 0, eq 13
e-MTE/T2*(1 + 2MTE/T2) - 1 ) 0
(13)
The first term of eq 13 decreases with M; the second term increases with M. We therefore anticipate the maximum value of the expression at some value M. Substituting TE ) 2 ms and T2 ) 25 ms into eq 13, the numerical solution for the optimal number of echoes, M, is 16, corresponding to S/N enhancement when echo images are added. Figure 5 shows a series of profiles of the oil phase migrating through the sand bed. The local image intensity was normalized to the oil reservoir signal intensity. Because the image was the summation from first 16 echo images, the summation image has T2 weighting. However, the T2 was constant in the bulk and oilsaturated sand. The normalized image is representative of a pure 13C relative density image; i.e., the T weighting is common to all 2 parts of the image. In this case, the image intensity within the sand bed is a measure of the volume fraction occupied by oil in the sand bed. The void ratio26 of the sand bed may be readily expressed as
Vvoid Vvoid moil-in-sand ) ) ) Vsolid Vtotal - Vvoid mreservoir - moil-in-sand moil-in-sand mreservoir (14) moil-in-sand 1mreservoir
Figure 6. Position of the oil moving boundary, determined from Figure 5, versus the square root of time. The linearity of this plot indicates that flow is driven by capillary suction.
where (moil-in-sand/mreservoir) is the relative oil concentration. The calculation implicitly assumes that the void volume in the sand is occupied by the oil phase. It also assumes that the pure oil phase in the reservoir is a valid marker for the total sample volume within the sand bed. Local volumes in eq 14 are converted to masses given the constant density of the oil phase. The ratio (moil-in-sand/mreservoir) will be the ratio of the signal intensities in the sand bed and oil reservoir given that the images of Figure 5 are carbon density weighted. The void ratio, directly determined from the images, is 0.82. The theoretical value for a well-packed bed of this sand is 0.70, Table 1. The disagreement between theory and experiment we believe is due to nonideal packing. Movement of a fluid into a porous solid is frequently driven by capillary forces. In this case, we anticipate a moving front behavior, exactly that observed in Figure 5. The position of the moving boundary may be determined by the point of maximum slope in a plot of the derivative of the image intensity versus position. Plotting the position of the maximum slope within the sample versus the square root of time yields a linear plot, Figure 6. The linear relationship suggests that the capillary forces between oil, unwetted sand, and the oil-saturated sand surface are much greater than the gravitational force, and therefore, the driving force for sorption is capillary pressure.27 We use sharp front theory28 to further interpret the slope of Figure 6. The product of the slope and the porosity (readily determined from the void ratio) yields the sorptivity, which in this case is 0.13 cm min-1/2. The capillary potential may be obtained by repeating the basic experiment with a variablepressure head (height of oil phase above sand).27 These experiments will be undertaken in future. To compare the sensitivity of the method presented here with the more traditional spin-echo methods, a static oil-saturated sand sample in a 2.8-cm-i.d. glass tube was measured with both methods. The results are summarized in Table 2. The ring down time of the four-pole Butterworth filter29 in our GE spectrometer forced us to use filter bandwidths larger than the optimum value. (26) Derucher, K. N.; Kopfiantis, G. P.; Ezeldin, A. S. Materials for civil and highway engineers; Prentice Hall: Upper Saddle River, NJ, 1998; Chapter 1. (27) Miyazaki, T. Water Flow in Soils; Marcel Dekker: New York, 1993; Chapter 7. (28) Hall, C.; Hoff, W. Water Transport in Brick, Stone and Concrete; Spon Press: London, 2002; Chapter 4.
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Table 2. Comparisons of Multiple Spin-Echo Single-Point Imaging and Spin-Echo Measurements for an Oil-Saturated Sand Bed (TE ) 2 ms) multiple spin-echo single point imaging techniquea total acquired echos signal averages acquisition time (min) SNR
32 16 ∼16 first echo first 16 echoes 12.3 30.5
spin-echo b
c
1 16
