Permeability Estimation from NMR Time Dependent Methane

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Permeability Estimation from NMR Time Dependent Methane Saturation Monitoring in Shales Andrea Valori,* Sidney Van den Berg, Farhan Ali, and Wael Abdallah Schlumberger Dhahran Carbonate Research, P.O. Box 39011, Dhahran Techno Valley, 31942, Saudi Arabia ABSTRACT: This paper consists of multiple approaches to develop a new model to determine the porosity, permeability, and rate of desorption of 1.5-in. shale samples. Permeability measurements of very tight rocks is difficult and uncertain, and no clear industry standard has yet been agreed upon. Therefore, this technique will investigate a new way to determine the porosity and permeability in shales. The raw NMR signal of the sample is measured before methane injection and is used as a base signal. During the injection of methane, the raw NMR signal increases. The base signal is subtracted from the response during the methane injection. This difference is inverted in multiple exponential distributions to only obtain the T2 distributions and T1−T2 correlations related to the injected methane in the shales. T2 distribution holds information on the pore size distribution. Using cutoff values to separate the signal, different zones can be extracted. During injection and production of fluids, the rate and the total fluid filled porosity are used to calculate the permeability related to the individual pore size distributions. In the majority of shale gas formations, two types of pore systems are present; kerogen-hosted organic pores (OP) and inorganic pores (IP). By fully saturating 1.5-in. shale cores and by continuously measuring the NMR signal, it is possible to determine the individual porosity and permeabilities of the pore system. T1−T2 measurements are made to confirm the individual zones and the mobility of the fluid in the zones. A single exponential decay formula is defined to calculate the permeability. This formula is tested with a reservoir simulation (using Eclipse) to validate the calculated value. Eventually a multiexponential model is used to distinguish the high and low permeability components in shales. This high permeability component is interpreted to represent the inorganic pores and microfractures, while the low permeability component is interpreted to represent the organic pores and the desorption from the pore surface. The Posidonia core samples show better production potential than the Qusaiba samples. Understanding the shale porosities for different storage mechanisms as well as the corresponding permeabilities is essential for developing shale reservoirs and target zone selection.

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INTRODUCTION As conventional hydrocarbon reserves are being depleted and easily accessible reservoirs are probably discovered, gas shale is likely to play a huge role in feeding the human thirst for energy in the near- and middle-term future. Despite the production of gas and oil shale being so successful as to dramatically change the energy market worldwide, the typical approach to this kind of reservoirs is mostly empirical and often still follows a “drill, fracture, and see” approach. In addition, the still limited knowledge of these kinds of reservoirs makes production predictions very difficult. Permeability of very tight rocks is difficult and uncertain, and no clear industry standard has yet been agreed upon. Most of the techniques rely on some variation of the pulse decay technique such as GRI1 or oscillating flow.2 In this technique, a container of known volume is put in communication with the saturated sample and the pressure variation in the container is used to calculate the amount of gas which entered the container and therefore left the plug. NMR is a technique sensitive to the nuclei of some atoms having intrinsic magnetic moment called spin.3,4 Although NMR can be performed on several different nuclei (1-hydrogen (1H), 19-fluorine (19F), 2-hydrogen (2H), 13-carbon (13C), 23-sodium (23S), ...) due to natural abundancy and practical interest, only 1H is widely used for petrophysical applications. Since 1H NMR is sensitive to protons independent of the chemical structure of the molecule where they are hosted, 1H NMR can detect both water and hydrocarbons, either liquid or gaseous. The relatively small © XXXX American Chemical Society

presence of lab based gas measurements in the literature is due to the difficulties in detecting gas at low pressure caused by the low hydrogen index. As pressure increases, the hydrogen index increases as does the sensitivity of the measurement. In addition, in the lab it is impossible to achieve very high pressures which are comparable to those downhole due to the fact that is impossible to use metallic core holders for NMR applications. NMR’s flexibility and its possibility to adjust parameters and experiments to an extremely wide range of situations and sample type makes it a good candidate to study both oil and gas shales. One of the strengths of NMR is that it is a technique which is sensitive to several petrophysical parameters. This high sensitivity and flexibility lead at the same time to high richness and high complexity in the NMR data, with interpretation not always straightforward. In this paper, we will focus only on the interpretation of gas bearing shale, leaving the completely different (in NMR terms) world of oil shale out of the picture. One of the most recent and valuable NMR work done on gas shale can be found in Fleury,5 where the position on the T1−T2 map is used to distinguish and separate gas and water in the different environments. Another interesting piece of work is Kausik et al.6 where the NMR signal is monitored as a function of pressure. Received: February 13, 2017 Revised: March 20, 2017

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DOI: 10.1021/acs.energyfuels.7b00433 Energy Fuels XXXX, XXX, XXX−XXX

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4. Determine the T2 dependent production rate in shale. We refer to apparent permeability rather than absolute permeability because several approximations will be included in this work, but the number extracted will try to be as representative as possible of the transport properties of the samples.

Several other studies based on the gas detection in tight materials have been published in the literature. Kadayam Viswanathan et al.7 investigated the pressure dependence of the NMR T2 distributions of gas in shale using a low field NMR system of 2.2 MHz. Other work on low field NMR detection of gas in artificial nanoporous material is presented in Horch et al,8 where adsorption is studied as a function of pressure. Papaioannou et al.9 performed similar tests on artificial porous media using a high NMR field system. Our approach is different; instead of focusing on the pressure dependence of the signal at applied pressure, we focus on the time dependence of the transient signal during desaturation. The work by Wang et al.10 is closer in concept to the one presented in this paper in the sense that the variable considered is the desaturation time and not the applied pressure. However, there are several aspects for which our work goes one step further. First, the measurements presented by Wang et al. are performed using a high field NMR system (400 MHz) whereas our work is performed using a low field NMR system (2.2 MHz). High frequency measurements of T2 relaxation times on heterogeneous samples are challenging due to internal magnetic field gradients which scale with the field strength.11 As a matter of fact, the work in Wang et al.10 is performed with free induction decays (FIDs) rather than Carr−Purcell−Meiboom−Gill (CPMG) pulse sequence. The use of FID allows to only determine the total amount of signal, whereas the use of CPMGs in our approach allows for T2 dependent information to be acquired; this is the most important difference. A fourth difference is regarding the sample size used. Wang et al.10 used plugs of 2.9 mm diameter; we used samples of conventional size of 1.5 in. (38.1 mm) diameter. The small size caused the transient signal measured in Wang et al.’s study to be naturally much quicker than the one reported in our work. Using their method, the decay times are difficult to extract. In their work, only single exponential decays are reported, whereas we manage to extract also biexponential decays in some cases. Last, the experiments reported by Wang et al. were performed without sample confinement, but only pore pressure. This leads to a more complicated flow geometry because gas production/flow occurs on all the free surfaces of the sample. The confinement in our experimental setup ensures uniaxial gas flow. Applying a confining pressure on the sample also limits drastically the overall net pore pressure. In our case the max net pressure is around 1000 psi. With this limited net pressure, in conjunction with the use of a bigger sample, we hope to avoid core damage, which Wang demonstrates on unconfined small samples for a sudden pressure drop of 3000 psi. The four objectives of the overall work are as follows: 1. Prove that low field NMR (2 MHz) is sensitive enough to measure methane saturating a low porosity shale sample. Experimental limitations are the relatively low gas pressure (∼3000 psi) caused by the maximum pressure attainable in NMR compatible core holders and the fact that commercial methane cylinders come with about 3000 psi. Use of gas boosters has been considered too dangerous. 2. Monitor the variation of the NMR signal as the gas leaves the sample in term of overall saturation and T2 distribution of the gas. 3. Derive a model to extract production rate information and apparent-permeability values from the time dependent NMR T2 data.

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MATERIALS AND METHODS

Samples. We tested four different shale samples that were available. Two shales were from the Poseidonia formation (United Kingdom), and two samples were from the Qusaiba formation (Saudi Arabia). Since all the samples were outcrops, we do not expect the presence of hydrocarbons in them at the “as received condition”. The measurements on the two Qusaiba samples were done first and ended up being learning steps for the following measurements. However, since partially valuable data came up also in these two “learning” samples, they will be presented anyway. Figure 1 shows a photograph of the two type of samples investigated. Note that the Posidonia samples are from a region with a lot of erosion;

Figure 1. Photograph of the two kinds of shale used in this study (left) Posidonia, (right) Qusaiba. therefore, the samples are relatively “fresh”. Qusaiba samples, instead, come from an outcrop emerging from the Saudi desert. The limited erosion made more difficult to obtain a fresh sample. Qusaiba samples were exposed to the extreme atmospheric conditions of the Saudi desert and, therefore, are expected to have less organic content. For one of the Posidonia samples (P48) also a computerized tomography (CT) scan was available. This image is shown in Figure 2. Due to the extremely small pore size and the limited resolution of the CT scan it is not possible to distinguish separate porosity systems. Some of the space, which is now classified as pores, might be organic matter. Pores within the organic matter will not be identified by the CT technique. Core Holder, Confining, and Pressurizing System. We used a core holder manufactured by ErgoTech, no longer in business, to confine the sample and to saturate the sample with methane. The core holder is designed to minimize its NMR signal. The pressure vessel is made by fibre reinforced polyether ether ketone (PEEK), and the sleeve is in fluorinated rubber. A fluorinated oil, FC-43, manufactured by 3M is used as the pressurizing fluid. Despite all the efforts made to minimize the NMR signal of the core holder, there is still a significant background signal that requires removal in postacquisition processing. The confining fluid is maintained thermostatically and constantly circulated during the measurement to stabilize the sample temperature. The confining pressure during the measurement was kept at about 20 MPa (3000 psi). The methane used to saturate the rock came from a cylinder with internal pressure of about 14 MPa (2000 psi). For safety reasons no pressure booster was used, so the saturating pressure was limited to the cylinder pressure. B


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Figure 2. CT image for one of the Posidonia sample (P48). Total porosity is 5 p.u.

Figure 3. (left) Empty circles, CPMG decays (sample 64) measured before injecting methane in blue (t = 0 h; signal of core holder and empty shale) and CPMG decay after injecting methane for 20 h in red circles (t = 20 h). (right) Relative T2 distributions and cumulative T2 distributions. The solid lines in the left figure are the fit determined by the inversion. To minimize risks in case of leaks or core holder failure, the dead volume of gas was kept as small as possible by using 1/16th in. (1.6 mm) tubing. The dead volume of the core holder at working conditions was about 15 cm3. The design of the core holder or the material of the seals were not adequate to achieve 100% tight environment. This made mass balance calculations impossible and required repressurization during the experiments. NMR Experiments. An Oxford Instruments benchtop rock core analyzer with a magnetic field of 0.05 T corresponding to a Larmor frequency of 2.2 MHz for protons was used for the experiments. The permanent magnet was maintained thermostatically above ambient temperature at 35 °C to ensure constant magnetic field during the experimental period. T2. Acquisition. The standard CPMG pulse sequence12 has been used to measure T2 decays:

P90 − [τ − P180 − τ − acq]nech

Each measurement consisted of 192 repetitions with a recovery delay of 0.5 s between the end of a CPMG train and the beginning of the following scan. The mentioned parameters lead to a CPMG measurement every 3.2 min. The T2 distributions were obtained using exponential decomposition.13 The short recovery delay ensures high signal-to-noise per unit of acquisition time as required for our analysis, but may cause the signal from long T1 components to be only minimally polarized. This means that potential gas in big fractures or in the dead volume of the core holder is strongly suppressed. This will not be a worry since our interest is in the gas in the small pores and adsorbed and most of the processing will be performed using T2 cutoffs. An artifact in the total signal decay even for short T2 components may arise if the addition of the gas can increase the mobility of some of the solid-like components in the rock. If solidlike components (heavy oils/waxes) were being mobilized by gas adsorption (dissolving), then the corresponding T1 would drop, leading to an increase in signal not associated with the gas content. To check this hypothesis we performed a T1−T2 correlation measurements with a longer polarization time (or wait time) RD. If the experiments performed with shorter RD were not fully polarized, increasing the RD would lead to an increased signal. Match between the porosity increase determined from the short RD CPMG measurements and the longer RD T1−T2 measurements experiment are used to confirm or disprove that the CPMG were sensitive to the entire gas introduced in the sample.

(1)

where P90 and P180 are the 90° and 180° RF pulses duration, τ = 50 μs is the time between the first P90 excitation pulse and the first P180 refocusing pulse and nech the number of echoes in the CPMG train. This value of τ leads to an inter echo spacing of 2τ = 100 μs. The variable acq in eq 1 represents the acquisition window. Following the initial P90 excitation pulse, the [τ−P180−τ−acq] sequence is repeated nech = 5000 times to acquire 5000 echoes over an overall CPMG duration of 0.5 s. C


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Figure 4. (left blue, noisy) Difference of the traces in Figure 3, therefore the signal from the gas only (sample 64). (right) T2 distributions obtained by the inversion of the differential signal in the left panel. The red smooth line in the left panel is the modeled and fitted decay calculated from the T2 distribution on the right. The high duty cycle of the pulse sequence (short echo spacing and short recovery delay) caused an increase in sample temperature monitored with fiber optic sensors. To ensure thermal stability of the sample throughout the experiments, we introduced a period of acquisition with several dummy scans to bring the system to thermal equilibrium before injecting the gas. The data acquired during such periods was discarded and not processed. Processing. As already mentioned, using parameters targeting short T2 components the core holder showed considerable background signal. The amplitude of this background signal was much higher than the methane signal and masked the changes in methane response in which we were interested. To extract the methane signal, we performed some background measurements on the sample plus core holder before introducing the methane. Figure 3 (blue squares) shows this background measurement. To decrease the uncertainty in this measurement, about 10 of the basic measurements lasting 3.2 min have been averaged effectively achieving a signal-to-noise ratio (SNR) equivalent to 1920 scans. Figure 3 left (red circles) shows the CPMG decay of the shale after 20 h of saturation. We note that the signal amplitude is only slightly increased. The right panel of Figure 3 shows the T2 distributions of the data in the left panel obtained by inversion. The inversion also outputs the multi exponential fit in the left panel of Figure 3 (lines). The intercepts of the fit at t = 0 represent the total NMR signal amplitude. Figure 4 left shows in blue the difference between the two traces in the left panel of Figure 3. Therefore, the signal plotted arises from the methane only. The inversion was performed on the differential signal to obtain the T2 distribution shown in Figure 4 at right and the fit to the time domain data (red, left panel of Figure 4). The background has been subtracted not only from the signal acquired after 20 h of saturation but also from all the other signals acquired at the partial methane saturated state. The subtraction of a high background, typically introduces the risk of instability in the processing when small variations of the background signal are present. This variation, for example, can originate from even minor temperature fluctuations. These fluctuations were seen in the experiments performed by us before the one reported in this paper. The use of accurate temperature control and the introduction of a “dummy” acquisition period before the actual acquisition (already discussed above in terms of sample temperature stabilization) allowed us to obtain a robust background removal procedure. Acquiring CPMG at short intervals allowed us to effectively choose the number of repetitions per experimental point at postprocessing by averaging multiple successive data sets. Averaging more data sets allows us to increase SNR, at the cost of lower temporal resolution. After a look at the speed of the studied phenomenon, we opted for a five steps averaging as a good trade-off between temporal resolution and SNR. T1−T2. The T1−T2 correlation experiment takes much longer than the simple CPMG and therefore was not suitable as time dependent

measurement. For this reason, only two data sets have been acquired: one as background before starting the methane injection and another after completing the saturation with methane. The data sets have been subtracted in the time domain before undergoing two-dimensional inversion similar to what was described for the T2 data. The pulse sequence used is a standard inversion recovery followed by a CPMG:

P180 − wt − P90 − [τ − P180 − τ − acq]nech

(2)

The experiment was repeated for 24 different values of wait time wt logarithmically spaced between 100 μs and 1 s. The parameters for the CPMG part of the experiment have been kept as in the T2 experiment: τ = 100 μs, nech = 5000, CPMG time 0.5 s and recovery delay 0.5 s from the end of the previous scan. The number of repetitions was 160 for a total acquisition time of 72 min. As for the T2 experiments, for the T1−T2 experiments performed in the core holder, the background (considered as the core holder plus the core at the initial state) has been removed to leave the injected methane signal. Methane Injection. The first aim of this experiment is to determine the signal from the methane gas when introduced in the rock after saturating the sample. This should help in determining gas in place and production potential of the rocks. The second aim of the experiment is to monitor the NMR signal of the methane during the depletion of the sample while at ambient pressure following high pressure saturation. Workflow. 1. Measure the NMR signal of the sample outside the core holder (no background signal). 2. Load the sample in the NMR HP core holder. 3. Start dummy CPMG pulse sequences and monitor temperature to confirm stability. 4. Acquire a T1−T2 correlation data set for background removal. 5. Start acquiring CPMG echo trains to be used for background subtraction and baseline. 6. Open methane cylinder and start pressurizing (without stopping acquisition). 7. Repressurize every once in a while to restore the pressure drop caused by gas entering in the sample (and possibly seeping through the core-holder seals). 8. When NMR signal stopped increasing, measure T1−T2 at “max saturation”. 9. Remove pressure and monitor gas leaving the sample with frequent CPMG (as during saturation increase). Hydrogen Index. Hydrogen index (HI) is defined as number of protons per unit of fluid and is the key parameter to convert NMR signal (proportional to number of protons in the sample) into volume of fluid. For a liquid (with good approximation incompressible) substance, this D


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Energy & Fuels parameter can be measured and is well-defined (although can be a function of temperature). In the case of simple brine, the HI can also be easily calculated from density and salt concentration and composition. In the case of a compressible gas as the methane used in this study, the HI is a function of pressure and temperature. Although all the efforts have been taken to keep the temperature of the system as constant as possible, the intrinsic “nonequilibrium” situation in which the experiment is run makes the pressure (and therefore the HI) different in different areas of the sample. Also potential absorption phenomenon may cause the local HI to be different. Figure 5 show the relative

Figure 6. Diagram of the apparatus used. In our case, the smaller volume V2 is distributed in the rock and is the rock pore volume. (Adapted with permission from the work of Sutherland.16 Copyright 1980 Elsevier).

where m is the decay constant. Plotting the decay curve in terms of ln[P(t)] vs t yields a straight line having slope m, and the permeability k can be determined according to Sutherland and Cave16 by

k = mμβ

(4)

where • m is the decay time constant • μ is the gas viscosity (1.28 × 10−05 Pa s) • β is the gas compressibility factor (1.38 × 10−07 1/Pa) • L/A is the length divided by the area of the sample • V1 and V2 are the two volumes in Figure 6 In a first-order approximation, we can consider the gas pressure proportional to the apparent gas-filled porosity and therefore convert eq 3 into eq 5, with the apparent gas-filled porosity decreasing over time Δφ(t)

Figure 5. Hydrogen index of methane relative to water (at 27 °C).

hydrogen index of methane respect to water at 27 °C (our experimental conditions). What can be seen is that the expected methane signal at the maximum pressure of our experimental conditions is about one-quarter that of water. Since, as mentioned before, the pressure is not welldefined in all the pores, we will not extend our discussion on HI further but we will use a fixed HI value (the one at the maximum applied pressure) to convert all the NMR amplitudes into “equivalent water porosity”. This is the preferred solution since it keeps the proportionality between NMR signal and actual gas mass in the sample (independently from pressure) and gives the best estimate of the filled porosity when at equilibrium at maximum pressure. This approach neglects the fact that the behavior of the HI for stored gas in porous media deviates from the bulk behavior. This difference, according to Papaioannou et al.,9 can account for almost an extra 50% of stored gas due to adsorption. Despite the uncertainties on the HI and the overall volume filled by gas, what remains true is that the amplitude of the NMR signal is proportional to the total number of protons (1H) in the sample, and therefore, considering that for this work we focus to methane signal only, the NMR signal amplitude remains proportional to the mass of gas in the sample (or total gas in place).14 Permeability Estimation from Decay Rates. The experiment described in this report allows measuring the gas leaving the sample as a function of time. This is a flow process that can be characterized with some sort of permeability or, to be more general, pseudopermeability. In the analysis which follows, we will not try to differentiate Darcy flow from non-Darcy flow but will focus on the determining decay rates and pseudopermeabilities connected with this phenomenon. Apparent gas permeability can be calculated based on the method originally proposed by Brace et al.15 It uses step changes of differential pressure between two reservoirs connected at the two extreme ends of the sample. Figure 6 is adapted from the original paper16 and shows the diagram of the apparatus used to measure permeability. In our case, one of the two volumes (VS) is considered distributed in the rock and is the total pore volume while the other volume (VL) is the ambient. When a pressure pulse ΔP0 is applied, the differential pressure ΔP(t) decays exponentially as a function of time t15,16

ΔP(t ) = ΔP0e−mt

L V1V2 A V1 + V2

Δφ(t ) = φt = 0e−mt

(5)

16

In, Sutherland et al. V1 and V2 are the volumes of two reservoirs at opposite ends of a sample, with V1 ≫ V2. Since the samples in this study have been saturated (and desaturated) from both ends, the driving (or receiving) volume is represented by the porosity of the sample and is distributed in the material, rather than sitting at one of the two ends of the sample. This geometry makes the calculation much more complicated since the distance between high and low pressure reservoirs and therefore the length of the flow path is not constant. The expression V1V2/(V1 + V2) can be replaced with the initial gasfilled volume as follows V1V2 1 = φt = 0Vbulk V1 + V2 HI

(6)

Such that

L 1 k = mμβ φt = 0Vbulk A HI

(7)

where • Vbulk is the bulk volume of the sample • HI is the hydrogen index of the gas To test if this simple formula was appropriate, we analyzed with eq 7 the output of a simple Eclipse reservoir model (Figure 7). The differences between the exponential model (red) and the Eclipse simulation can be explained through the complexity of Eclipse and simplicity of the exponential model. To run the Eclipse model, many variables need to be defined like the “well bore radius” and “rock properties”. In addition, Eclipse uses a variable Z-factor and viscosity which are related to the pore pressure during the simulation. The exponential model is much more simplistic and only uses variables that are well-known, such as the experimental average Z-factor and the viscosity. The forward model for Eclipse is set to a permeability of 15 nD. The exponential model calculates a permeability of 14.8 nD. This gives us confidence in the realistic (although simplistic) results we will obtain with eq 7.

(3) E


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presented and discussed below, which represent the injected methane only. Figure 9 shows how the T2 distributions change as a function of time while the methane is removed from the rock. Sample Q1 was the first investigated and for this specimen only the monitoring was done during the saturation stage rather than the desaturation. Successively, the monitoring of the desaturation process has been found to be easier to measure and with lower uncertainties and therefore the removal of methane was monitored for the other three samples (details discussed later in the paper). The first characteristic that can be observed, at least in the Posidonia samples, is that the distribution has different peaks indicative of gas in different environments (probably different pore sizes). This clear structure suggest the introduction of cutoff values in the T2 domain to study the peaks independently. The study of shale with NMR is still in its infancy, and the approach is still mostly empirical. This means that there is not much literature on where the T2 cutoff should be and how to address the different peaks. A paper that is worth mentioning is Fleury,5 where shale samples are studied by T1−T2 correlation experiments. In this paper it is suggested that methane in porous media is in the T2 range 1−100 ms and the organic matter in the range 0.05−0.8 ms (but separable on T1−T2 due to higher T1/T2 ratios). We note that the work, however, is performed at 20 MHz rather than 2. This may cause the relaxation values of each component to be different. Another publication on shale saturated with hydrocarbons is Kausik et al.18 In the referenced work, the T2 cutoffs suggested are T2 < 1.5 ms for bitumen and clay bound water, 1 ms < T2 < 10 ms for hydrocarbons in organic pores (OP), T2 > 10 ms for hydrocarbons in inorganic pores (IP). This second reference is for work performed at 2 MHz (as the one presented in this paper), but for water and liquid hydrocarbon (dodecane). We therefore took the cutoffs reported in the literature as “indications” and adapted the values to our sample specifically choosing the T2 values of the valleys in the T2 distribution of sample P45 and P64 (0.6, 5, and 28.5 ms). Following the examples in literature, we will refer to the four different T2 components as originating from bound gas, gas in the organic pores, gas in the inorganic pores, and gas in fractures, going from short to long T2, respectively. The two Posidonia samples (P48 and P64) show a similar T2 distribution, although the relative amplitude of the peaks is quite different. The two Qusaiba samples (Q1 and Q4), instead, show a completely different behavior than the Posidonia samples and even among themselves. This could be related to the poorer condition of preservation of the samples. For consistency of the analysis, all the data will be processed with the same cutoffs, even if not clear cutoff values are visible in the Q samples. For this reason, much more emphasis will be placed on the analysis of samples P, leaving the discussion to samples Q as completion and “additional evidence”. Sample Q4 shows a shape of the T2 distribution with virtually all the signal concentrated below about 0.2 ms. The minor amplitude peaks at longer T2 can most probably be interpreted as fractures of some sort. The fact that they do not change significantly with the saturation time is an indication of good connection with the side of the sample, and therefore they get saturated very fast as the gas pressure is applied. Applying the same cutoffs also to sample Q4 will lead to the natural consequence that almost the entire signal will fall in the first T2 bin. Note also that sample Q1 is the only one for which the experiments are performed while injecting gas in the

Figure 7. Single exponential fit (red) to the decay curve obtained from the Eclipse simulation (details of the model in the text).

One additional source of potential uncertainty is the fact that during the measurements performed for this work, the pressure of the gas inside the rock is variable, and a recent work of Ramakrishnan and Supp17 shows that the measured permeability can depend on the pressure of the fluid used for the measurement.

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RESULTS AND DISCUSSION T2 Distributions and Cutoffs. Figure 8 shows the T2 distribution for the sample “as received”. Note that in this case the NMR signal (converted in p.u.) arises from the organic matter in the matrix of the sample and not only from the fluid in the pore space as is the case on the differential T2 distributions

Figure 8. T2 distributions of the samples in the as received state. Note that the differences in porosities are small while differences in T2 are almost negligible (all T2 log means are equal within 0.1 ms). F


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Figure 9. T2 distributions as a function of time during the gas production (pressurization for sample Q1): (top left) sample P48, (top right) P64, (bottom left) Q1, (bottom right) Q4. The black vertical lines are the T2 cutoffs used in this study (0.6, 5, and 28.5 ms). The bottom panel for each quadrant is cumulative of the distributions. These are derived from the top panels and are useful to better visualize the overall porosity (asymptote at long T2 values). Note the different scales for the different samples.

sample rather than while removing gas from the sample (further discussion in next section). Decay of Different T2 Components. Sample Q1 is the first that has been measured, and the measurements were taken while injecting gas. We quickly discovered that this was not the best approach since it was virtually impossible to keep the pressure of methane constant throughout the saturation process. Deriving permeability information analyzing the increase of apparent porosity (or equivalently gas saturation) is therefore doomed to give inaccurate results due to the uncertain boundary conditions for pressure driving the flow. Therefore, to work with more controlled experimental conditions, for the following samples we analyzed the decay of signal as the methane pressure was

removed and the sample exposed at ambient pressure. For completeness, and since we believe that results of sample Q1 still bear at least some interest, we showed the variation of the T2 distributions in Figure 9, but we will refrain from making further calculations to determine permeabilities. Sample Q4, thanks to the better experimental setup, gave somewhat better results, however, some care has to be taken in the analysis of the signal amplitudes. Already from Figure 9 it can be seen that there are some longer T2 components in the sample compared to P48 and P64. This, considering that for any signal T1 > T2, leads to the observation that there are T1 components in the sample that are almost for sure not fully polarized in the short RD (0.5 s) used in the CPMG. This fact is also confirmed by T1− G


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Figure 10. Decay of each of the T2 components separated using the cutoffs presented in Figure 9. The solid lines are biexponential fits to the data (discussion in the text section of the paper). The forth panel includes an inset highlighting the initial part of the decay.

T2 measured with longer RD (2 s) (Figure 16, top right). In the T1−T2 plot it can be seen that there is signal up to the seconds range. Also, not full polarization is confirmed by the higher porosity measured by T1−T2 compared to T2. Anyway, long T1 components are likely to arise from gas entering the fractures and biggest pores, and therefore, the discussion regarding signal decay for the short T2 components should still be considered valid. The cutoffs defined in Figure 9 allow us to divide the overall signal of each of the T2 distributions acquired into four portions. Each one of these portions can be plotted versus the desaturation time. Figure 10 shows the result of this signal decomposition. Each quadrant refers to a different T2 bin, while the different symbols in each plot refer to the different samples. From Figure 10 we see that both the amplitudes and rates at which each T2 component decreases are different. One interesting feature of each of these data sets is that they are very well fitted with a biexponential decay (solid lines in the plots). Pore Size Dependent Porosity and Permeability Estimation. The biexponential fits in Figure 10 are of the form φ(t ) = φ1,(t = 0)e−m1t + φ2,(t = 0)e−m2t + c

of the different pore types with their relative amplitudes. These results are summarized in Table 1. The two values of Table 1. Results from the Dual Exponential Model for the Bound, OP, and IPa

a

The columns referring to permeability are greyed to improve readability. For the sample for which a single exponential component was fitted, only one value of permeability is reported.

(8)

Equation 8 can be interpreted as two environments of initial amplitude φ1,t=0 and φ2,t=0 that drain at different rates m1 and m2. Due to the uncertainty affecting the hydrogen index, although φ1,t=0 and φ2,t=0 are expressed in units of porosity to give a better feeling of the amount of gas involved, they are actually numbers proportional to NMR signal (and therefore strictly proportional number of CH4 molecules) in each environment. Note that an additional constant c has been required to obtain a good fit. This amplitude may be interpreted as the remaining gas in the sample after the desaturation at ambient pressure. By converting the parameters for the exponential fits (eq 8) using eq 7, we can extract one or two permeability values for each

permeability are referred to as khigh (the higher permeability value) and klow (the lower one). Where only one permeability value is extracted, we consider that to be khigh. From the amplitude of each of the exponential components a porosity value can be calculated. We refer to Φhigh and Φlow as the porosity of the environment with high and low permeability, respectively. Note that, therefore Φhigh can be greater or smaller than Φlow since “high” and “low” refer to the permeability of the component and not to the porosity. The cells with yellow H


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permeability system. We called this two permeability khigh,TOT and klow,TOT to clarify that are extracted from the total signal amplitude. The respective amplitudes (porosities under the HI assumptions discussed above) are called φhigh,TOT and φlow,TOT. This two permeability values are very useful to give information on the short and long-term overall gas production from the shale sample. Even before calculating any permeability values, we can interpret the decays in Figure 13 qualitatively, assuming that the

shading refer to component of very small amplitude and therefore for which the results are affected by high uncertainty. Although these results are based on a newly proposed and not widely tested model, still they are much richer than a simple differential pressure as a function of flow, typical of a standard Darcy permeability measurement. This is because the data set acquired are a function of NMR T2 relaxation times, and therefore allow inferring from which pores the production is occurring. Figure 11 shows the different amount of porosity in the three samples. Note how the ratio between different porosities change

Figure 11. Histogram showing the partitioned porosity for the different pore types (on the basis of the T2 cutoffs). Figure 13. Biexponential fit to the entire methane signal for each of the samples (not separated on the basis of T2 cutoffs).

considerably between the samples. The total porosity plotted in Figure 11 may be slightly different from the sum of porosities in Table 1 since in the histogram the value of the constant c in eq 8 is also considered. A further analysis has been possible by plotting the T2 dependent permeabilities versus the respective T2 values. This is presented in Figure 12. We see that there is no clear relationship between the T2 value of the signal and the respective NMR derived permeability (or permeabilities).

signal decay is faster for samples with higher permeability. Therefore, the highest permeability sample should be sample 4, sample 64 should have intermediate permeability, and sample 48 should be the lowest permeability one. The permeability measurement we have available to compare with our results is the pressure decay method. This technique is based on pressure decay and can be performed on either crushed or full cores. We had availability of both scenarios for sample P48 and P64, while results on crushed rock were available only for Q4. Furthermore, the measurement on sample Q4 does not come from the exact core measured with NMR, but from chips coming from three different twin samples. The presence of two values for permeability for the NMR results and only one for the GRI method make the two not immediately comparable. An attempt has been made to fit the total signal (Figure 13) with a single exponential, but the quality of the fit was so poor that no analysis was performed. To better visualize the relationship between the pressure decay results and our NMR results presented in Table 2, we prepared a cross plot (Figure 14). The first observation possible, before even starting discussing the NMR results, is that the pressure decay permeability results on crushed samples are considerable lower than the results obtained on the full plugs. The shales are likely to part along microfractures and bedding planes, and therefore, any cracks in the structure are destroyed by testing the samples. The geological structures and natural fractures that would contribute to a higher bulk permeability in the formation are neglected. Therefore, this method gives underestimated permeability measurements.19 Note that crushing also removes some porosity and therefore measurements on crushed samples are generally not very realistic. Looking at the NMR results, it can be immediately seen that they correlate much better with the results on full plugs rather

Figure 12. Relationship between the T2 values of the separate components and the calculated permeability (one or two depending if the fit performed was one or two component). Graph compiled with data from Table 1 and the peak of the T2 distributions.

Overall Permeability Estimation: NMR vs Pressure Decay. To be able to derive a permeability value that could be compared with an independent technique (pressure decay), we applied eq 8 also to the decay of the total NMR signal (not separated on the basis of T2 cutoffs). Again, we found that the decay was well described by a biexponential decay and therefore could be interpreted as a dual I


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Table 2. Permeability Results Applying the Model Presented in This Paper (Equation 7) to the Total NMR Signal (Biexponential Fits) and Pressure Decay Measurements (on Full Core and Crushed Samples)a

1 Obtained on cuttings from three different twin samples. aAgain, following the convention of the previous table, the columns referring to permeability are greyed to improve readability.

Figure 15. Relationship between the saturated gas porosity and the native gas porosity.

Figure 14. Cross plot of pressure decay permeability (on crushed or full sample) and the NMR permeability (high and low).

gas filled porosity. In this case, instead, we are interested in converting the gas NMR signal into actual porosities, and therefore we have to assume a specific hydrogen index. For the plot in Figure 15 we chose HI = 0.25, which is the HI of the methane at the conditions applied to the core (ambient temperature and pressure of about 2000 PSI) this value can be seen from Figure 5. From the relationship between the saturated gas porosity and the native gas porosity (Figure 15), we notice that there is an almost perfect linear correlation. This must be interpreted in the broadest term that the amount of gas stored at full saturation is proportional to the number of proton initially in the sample. Two hypotheses can hold for this specific phenomenon: 1. The porosity in the sample (at the native state) was already filled with some gas, and the native NMR signal was therefore proportional to the volume available for saturation and the difference between the native porosity and the saturated porosity arises only from the increased HI. Considering the relationship between HI and pressure (Figure 5), this hypothesis requires taking into account adsorption phenomenon due to the extremely low (likely nondetectable) amount of signal arising from gas at ambient pressure following standard gas law. 2. Another, likely more realistic, hypothesis is that the NMR signal arising from the native sample was proportional to the amount of organic matter in the sample, which, realistically, contains protons, and only this phase in the sample is able to contain methane. This would also justify the linear relationship in Figure 15. T1−T2. Figure 16 (left column) shows the T1−T2 measurement of the shale sample at the “as received” state. Note that for all the samples the signal falls entirely in the range T2 < 20 ms. These data sets are useful to determine the T1−T2 region in which the protons in the organic matter constituting the rock reside. One important consideration is that the three data sets

than with the results on crushed samples. This is expected since the NMR results were performed on full plug samples too. The unavailability of an NMR compatible core holder suitable for powders made impossible to compare pressure decay versus NMR for crushed samples. Comparing the two NMR derived permeabilities for the same sample shows that the ratio between the two is typically around 10. This is only not true for the sample Q4 crushed; however, we note that this is the sample obtained on cutting coming from three twin plugs, and therefore, we expect this result to be affected by high uncertainties. An additional aspect worth mentioning arises when we consider the relative values of permeability for samples 48 and 64 calculated from the two different techniques. From NMR signal decays (Figure 13), we qualitatively concluded that sample 64 should have higher permeability then sample 48, based on the experimental evidence that sample 64 releases gas faster than sample 48. GRI results show a completely different result, with permeability for sample 48 being higher than for sample 64. Considering all the uncertainties affecting both pressure decay and NMR techniques, we consider the correspondence in Figure 14 promising. We checked the correlation between the native porosity measured on the as received samples (Figure 8) and the saturated total porosity coming from the fit in Figure 13. Also in this case, the constant c in eq 8 may cause the values in Table 2 and Figure 15 to differ slightly. Note that the saturated porosity refers to the gas filled porosity only and does not account for the amount of signal in the as received sample that has been removed from all of the measurements used in the permeability calculations. For all the previous plots, we used the porosity in terms of “equivalent water filled porosity”, explaining that this was proportional to the NMR signal and to the gas in place, but clarifying that this required knowledge of the hydrogen index (which is intrinsically unknown) to covert these amplitudes in J


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Figure 16. (left column) Result of T1−T2 measurements at the as received state with projected 1D distributions (red solid). The blue dashed lines refer to the T2 distribution from 1D CPMG. (right column) T1−T2 signal of the injected methane only. Top to bottom are the samples Q4, P48, and P64.

look very similar, with just a slightly lower value for the T1/T2 ratio of the main peak for sample Q4 compared to the two P samples. This means that even adding the T1 dimension, the three shale samples look very similar (as it was for just T2), and with only the as received measurements, it is difficult if not

impossible to extract any useful information to discriminate between the samples. Figure 16 (right column) shows the methane signal injected in the rock (subtraction of the signal at the end of the injection minus the signal before the beginning of the injection). The first K


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Figure 17. Application of the T2 cutoffs to one example of a T1−T2 map and identification of the different pore environments. The dashed lines are guides for the eye to determine T1 and T2 values for the different peaks in the 2D map.

possible observation is regarding the position of the gas signal (right column). Different peaks can be recognized and are typically at longer T2 than the signal for the matrix (left column). However, there are also regions where the gas signal partly overlaps with the organic matter signal already present in the rock. For this portion of the signal, therefore, a T2 cutoff would not be successful in separating matrix and gas. However, T1/T2 ratio cutoffs would be more useful since the signal is more spaced along that direction. T1/T2 Ratio Analysis. The graphs in Figure 16 can be further interpreted with the cutoff values in Figure 9. These different zones will be visibly in the differential T1−T2 correlations. Figure 17 shows this correlation where the zones for the different pore types are identified. Note that, although in the 2D map the OP and IP seem completely merged, the projection along the T2 axis show a hint of bimodality. The dashed lines are guides for the eye to determine T1 and T2 values for the different peaks in the 2D map. A crossplot of the T1/T2 ratio vs T2 provides information on which peaks are in the producible area as done in the study by Rylander et al.20 It can be seen from Figure 18 that the OP and IP peaks are well within the free fluid range according Lewis et al.20 which is known to be producible. The peaks for the shortest T2 times lie at a much higher T1/T2 ratio. This portion of methane is considered to be adsorbed on the pore surface and will be produced through desorption mechanism of the methane.

Figure 18. T1/T2 ratio for the different peaks on the differential T1−T2 maps (right column of Figure 16).

T2 distributions can be acquired fast enough to obtain T2 resolved buildup and fall down curves with time resolution of only few minutes. These curves can be interpreted as pore size resolved production curves. We proposed a way to analyze this data sets to obtain what can be defined “T 2 resolved permeability”. In most of the cases, we found that a dual permeability model is necessary to fit the data satisfactorily. This can have two possible interpretations: 1. Pores of the same size having connection with the outside environment of two characteristic sizes (permeability) or 2. Whatever the pore size, the gas in it is in two different conditions, one producing faster and one producing slower Fitting the total decay signal (without T2 resolution) required a two component exponential too, leading calculation of a dual permeability too. This permeability are in reasonably good

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CONCLUSIONS First, this work proves that is possible to detect methane gas in a shale rock sample using a standard rock core low field NMR instrument and pressures commonly achievable in a core analysis laboratory. L


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(12) Meiboom, S.; Gill, D. Modified Spin-Echo Method for Measuring Nuclear Relaxation Times. Rev. Sci. Instrum. 1958, 29 (8), 688−691. (13) Song, Y.-Q.; Venkataramanan, L.; Hürlimann, M. D.; Flaum, M.; Frulla, P.; Straley, C. T1-T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion. J. Magn. Reson. 2002, 154 (2), 261−268. (14) Kausik, R.; Kleinberg, R.; Rylander, E.; Lewis, R.; Sibbit, A.; Westacott, A. Novel Determination of Total Gas in Place (TGIP) For Gas Shale from Magnetic Resonance Logs. SPWLA 57th Annual Logging Symposium, Reykjavik, Iceland, June 25−29; Society of Petrophysicists and Well-Log Analysts, 2016. (15) Brace, W. F.; Walsh, J. B.; Frangos, W. T. Permeability of granite under high pressure. J. Geophys. Res. 1968, 73 (6), 2225−2236. (16) Sutherland, H. J.; Cave, S. P. Argon gas permeability of new Mexico rock salt under hydrostatic compression. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 1980, 17 (5), 281−288. (17) Ramakrishnan, T. S.; Supp, M. G. Measurement of ultralow permeability. AIChE J. 2016, 62 (4), 1278−1293. (18) Kausik, R.; Fellah, K.; Rylander, E.; Singer, P. M.; Lewis, R. E.; Sinclair, S. M. Nmr Petrophysics for Tight Oil Shale Enabled By Core Resaturation. International Symposium of the Society of Core Analysts, Avignon, France, September 8−11, 2014; pp 4−9. (19) Rosen, R.; Mickelson, W.; Sharf-Aldin, M.; Kurtoglu, B.; Kosanke, T.; Paiangle, M.; Patterson, R.; Mir, F.; Narasimhan, S.; Amini, A. Impact of Experimental Studies on Unconventional Reservoir Mechanisms. SPE Unconventional Resources Conference 2014, DOI: 10.2118/168965-MS. (20) Lewis, R.; Singer, P.; Jiang, T.; Rylander, E.; Sinclair, S.; Mclin, R. H. NMR T2 Distributions in the Eagle Ford Shale: Reflections on Pore Size. SPE Unconventional Resources Conference 2013, DOI: 10.2118/ 164554-MS.

agreement with full plug GRI measurements performed on the same cores. Measurements on the same samples but on crushed material, instead, lead to values between 1 and 3 orders of magnitude lower. We also found that the permeability of each gas reservoir does not look to correlate much with its T2 value. Using T1−T2 correlation experiments we found that the signature of methane saturating the rock is only partially separable from the matrix signal using T2 cutoffs, but discrimination along the T1/T2 ratio direction is higher. The very accurate linear relationship between saturated porosity and native porosity suggests that the gas is stored in the sample in a phase constituted by a material already containing protons, whether this is adsorbed gas or protons in the organic matrix. We found that, despite looking initially very similar, two Poseidonia samples behaved very differently in term of production rates (and therefore extracted permeabilities) but also in terms of different ratios between the different porosity types: one storing relatively more gas in the bound region (short T2) rather than in the long T2 region and the opposite being true for the other.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Andrea Valori: 0000-0002-8138-6691 Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Guidry, K.; Luffel, D.; Curtis, J. GRI-95/0496: Development of laboratory and petrophysical techniques for evaluating shale reservoirs: Final technical report; 1995. (2) Bernabé, Y.; Mok, U.; Evans, B. A note on the oscillating flow method for measuring rock permeability. Int. J. Rock Mech. Min. Sci. 2006, 43 (2), 311−316. (3) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; 1991. (4) Blumich, B. Essential NMR for scientist and engineers; Springer, 2004. (5) Fleury, M. Characterization of Shales With Low Field NMR. International Symposium of the Society of Core Analysts, Avignon, France, September 8−11, 2014; pp 1−12. (6) Kausik, R.; Minh, C. C.; Zielinski, L.; Vissapragada, B.; Akkurt, R.; Song, Y.; Liu, C. B.; Jones, S.; Blair, E. Characterization of Gas Dynamics in Kerogen Nanopores by NMR. In SPE 14718-PP, 2011; pp 1−16. (7) Kadayam Viswanathan, R. K.; Cao Minh, C.; Zielinski, L.; Vissapragada, B.; Akkurt, R.; Song, Y.-Q.; Liu, C.; Jones, S.; Blair, E. Characterization of Gas Dynamics in Kerogen Nanopores by NMR. SPE Annual Technical Conference and Exhibition 2011, DOI: 10.2118/ 147198-MS. (8) Horch, C.; Schlayer, S.; Stallmach, F. High-pressure low-field 1H NMR relaxometry in nanoporous materials. J. Magn. Reson. 2014, 240, 24−33. (9) Papaioannou, A.; Kausik, R. Methane Storage in Nanoporous Media as Observed via High-Field NMR Relaxometry. Phys. Rev. Appl. 2015, 4, 24018. (10) Wang, H.-J.; Mutina, A.; Kausik, R. High-Field Nuclear Magnetic Resonance Observation of Gas Shale Fracturing by Methane Gas. Energy Fuels 2014, 28 (6), 3638−3644. (11) Mitchell, J.; Chandrasekera, T. C.; Johns, M. L.; Gladden, L. F.; Fordham, E. J. Nuclear magnetic resonance relaxation and diffusion in the presence of internal gradients: The effect of magnetic field strength. Phys. Rev. E 2010, 81 (2), 26101. M


Permeability Estimation from NMR Time Dependent Methane

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