Determination of fluid-phase-specific petrophysical properties of geological core for oil, water and gas phases

Abstract

The following invention is used for determining the relative permeability of a fluid in a rock for three different phases: water, oil, and gas, in both conventional and unconventional formations. The permeability of a phase describes how much it can flow in porous media given a pressure gradient and is useful in evaluating reservoir quality and productivity. The following invention is a method to determine the three-phase relative permeabilities in both conventional and unconventional formations using NMR restricted diffusion measurements on core with NMR-active nuclei, combined with centrifugation of the core. In addition, the tortuosity, pore size (surface-to-volume ratio), fluid-filled porosity, and permeability is determined for each of the three phases in a rock.

Claims

1. A method of determining, for each of three different fluid phases (water, oil and gas), a set of one or more fluid-phase-specific petrophysical properties (FPS-PP) of geological core where FPS-PP.sub.WATER is the FPS-PP for the water phase, FPS-PP.sub.OIL is the FPS-PP for the oil phase, FPS-PP.sub.GAS is the FPS-PP for the gas phase, where the FPS-PP is selected from a FPS-PP group which is defined below, the method comprising: a. subjecting the geological core to NMR restricted diffusion measurements for multiple NMR active nuclei with at least two different hydrocarbons for at least the oil and gas phases, and b. centrifuging the geological core over multiple drainage or imbibition cycles so as to produce effluent from the geological core; c. as the geological core is centrifuged, measuring a time dependence of a flow rate of effluent from the geological core; d. computing, from results of the NMR restricted diffusion measurements and from the time dependence of the flow rate of effluent, all of (i) FPS-PP.sub.WATER, (ii) FPS-PP.sub.OIL and (iii) FPS-PP.sub.GAS, wherein the FPS-PP group is defined as the group consisting of: (A) a fluid-phase-specific tortuosity value; (B) a fluid-phase-specific porosity value, the fluid-phase-specific porosity being defined as a fraction of a total pore volume which is occupied by a specific phase (oil, water or gas); (C) a fluid-specific-phase pore diameter, the fluid-specific-phase pore diameter being defined as a pore diameter which is occupied by the specific phase (oil, water, or gas); (D) a fluid-phase-specific body-to-throat ratio, the fluid-phase-specific body-to-throat ratio being defined as a body-to-throat ratio of respective throat and pore volumes which are occupied by the specific phase (oil, water or gas); (E) a fluid-phase-specific permeability, the fluid-phase-specific permeability being defined as the permeability of a specific phase (oil, water, or gas); (F) a fluid-phase-specific relative permeability curve for two specific phases.

2. The method of claim 1 wherein the set of one or more petrophysical properties comprises; (A) 3 phase-specific tortuosity values, one each of the 3 fluid-phases; (B) phase specific pore diameter values, one for each of the 3 fluid-phases where a pore diameter value for a given fluid-phase is defined as the pore diameter occupied by that fluid-phase; (C) fluid-specific-phase body-to-throat ratio, the fluid-specific-phase body-to-throat ratio, one for each of the 3 fluid-phases; (D) fluid-phase-specific porosity values, the fluid-phase-specific porosity being defined as the fraction of total pore volume occupied by the specific phase (oil, water or gas); (E) fluid-phase-specific permeabilities, one for each of the 3 fluid-phases; and (F) fluid-phase-specific relative permeability curves for two specific phases.

3. The method of claim 1 where the NMR restricted diffusion measurements utilize a D-T.sub.2 method.

4. The method of claim 3 wherein a Pad? fit is used with restricted diffusion data of the NMR restricted diffusion measurements for any fluid phase to determine both a fluid-phase-specific surface-to-volume ratio and the fluid-phase-specific tortuosity value for that fluid phase.

5. The method of claim 1 wherein the multiple NMR active nuclei comprise .sup.1H and .sup.19F.

6. The method of claim 1 wherein the water phase comprises D.sub.2O.

7. The method of claim 1 wherein the gas phase is simulated using at least one fluorinated hydrocarbon.

8. The method of claim 7 wherein the gas phase is simulated using Fluorinert FC-770.

9. The method of claim 7 wherein the gas phase is simulated using SF.sub.6.

10. The method of claim 7 wherein at least one of the fluorinated hydrocarbons comprises CF.sub.xH.sub.yCl.sub.z where x and y and z are integers between 0 and 3.

11. The method of claim 1 wherein the multiple NMR-active nuclei comprise .sup.23Na and .sup.2H.

12. The method of claim 1, further comprising determining one or more locations in accordance with all of FPS-PP.sub.WATER, FPS-PP.sub.OIL, and FPS-PP.sub.GAS, and drilling one or more horizontal or vertical wells in accordance with one or more of the determined locations.

13. The method of claim 1, further comprising determining one or more locations in accordance with all of FPS-PP.sub.WATER, FPS-PP.sub.OIL, and FPS-PP.sub.GAS, and performing at least one additional operation in accordance with one or more of the determined locations, wherein the at least one additional operation includes at least one of: (i) caping and perforating; and (ii) deploying a pump.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1: .sup.1H and .sup.19F NMR spectrometer and fluid saturation equipment used in this invention.

(2) FIG. 2: NMR pulse sequence used in this invention.

(3) FIG. 3: Pad? fits to D/D.sub.o vs LE for two chalk cores from a well at depths of 913 m and 920 m.

(4) FIG. 4: Permeabilities computed from this invention and using prior art compared with measured permeabilities for four chalk samples.

(5) FIG. 5: Centrifuge sample cells used in drainage and imbibition experiments.

(6) FIG. 6: Centrifuge relative permeability to oil (k.sub.ro) vs oil saturation (S.sub.o) data for a Berea sandstone (first drainage with decane/nitrogen).

(7) FIG. 7: Fluorine index FI vs pressure for some fluorinated hydrocarbons.

(8) FIG. 8: Bulk diffusion D.sub.o versus pressure for some fluorinated hydrocarbons.

(9) FIG. 9: Maximum diffusion length Lu versus pressure for some fluorinated hydrocarbons.

DETAILED DESCRIPTION OF EMBODIMENTS

(10) Step 1: We begin with a core sample that is cleaned and dried. Soxhlet extraction with chloroform-methanol azeotrope may be used to clean out the hydrocarbons. At this stage, the core sample is fully saturated with air in the pore space. Soxhlet extraction with chloroform-methanol azeotrope is well known to one skilled in the art.

(11) Step 2: A routine core analysis is performed for Klinkenberg-corrected gas permeability (k.sub.meas), total porosity (?.sub.7), grain density (?.sub.q), and bulk density (?.sub.b). Routine core analysis is well known to one skilled in the art.

(12) Step 3: The core sample is then 100% saturated with NaCl brine (S.sub.w1). .sup.1H NMR measurements of D/D.sub.0 versus L.sub.D and T.sub.2 are made at S.sub.w1. FIG. 1 shows a schematic of the NMR spectrometer with laboratory apparatus for fluid saturation used in this invention. The NMR spectrometer may have a probe that can be tuned to different NMR active nuclei, such as .sup.1H and .sup.19F. The NMR spectrometer may have replaceable magnets for applying different magnetic field strengths. Typical NMR spectrometers are available from Oxford Instruments Ltd for 2 MHz, 20 MHz, 40 MHz, and 60 MHz.

(13) FIG. 2 shows a Diffusion-T.sub.2 (a.k.a. D-T.sub.2) unipolar stimulated-echo pulse sequence (Tanner, 1970; Mitchell et al., 2014) used to measure restricted diffusion as a function of diffusion time t.sub.?. Trapezoidal gradient encoding pulses G are shown with duration to (time from half-height to half-height) and ramp-time ?, along with 90? (thin) and 180? (thick) RF pulses of phase ?.sub.1,2,3,4,a, and CPMG echo trains with echo-spacing t.sub.E. Not shown is a set of 6 woodpecker gradient pulses to stabilize the eddy currents before the first RF pulse. More details can be found in the attached references (Chen et al 2017, Chen et al 2019a, Chen et al 2019 b, Wang et al 2020.

(14) FIG. 3 shows diffusion length (L.sub.D) against normalized restricted diffusivity (D/D.sub.0). The dots are the points from the 2D peak of the D-T.sub.2 maps in the region C. Top: C4(D.sub.2O) and C1(D.sub.2O) are shown for 913 m (sample contains less bitumen). Bottom: C10 and C1(D.sub.2O) are shown for 920 m (sample contains more bitumen). The solid black line is the best fit using the Pad? equation. The dashed horizontal line shows the tortuosity limit. To do the parameter estimation, non-linear curve-fitting (Isqcurvefit) in MATLAB is applied. The loss function is the minimum square error on a log scale.

(15) From these measurements, we can determine the total porosity (?.sub.T) from T.sub.2, and the pore-body diameter (d) from the relation for cylindrical pores:

(16) $\frac{S}{V}=\frac{4}{d}$

(17) using the Pad? fit on the D/D.sub.0 versus L.sub.D data, where D is measured diffusion, D.sub.0 is bulk diffusion, and L.sub.D=?{square root over (D.sub.0t.sub.?)} is the bulk diffusion length at a diffusion evolution time of t.sub.?. Note that while the above relation for cylindrical pores is not required in the permeability relations, it is used throughout for convenience. It is on the other hand required when computing the BTR (body-throat ratio) from MICP data (see below) which assumes cylindrical pores.

(18) Step 4: The electrical resistivity (R.sub.o) is measured on the fully brine-saturated core. The electrical resistivity of the brine is also measured (R.sub.w) or calculated from the NaCl concentration. The cementation exponent, m, can be measured using the formation factor from Archie's law:

(19) $\frac{R_o}{R_w}=\frac{1}{{?}_T^m}$

(20) where ?.sub.T is the porosity measured in the previous steps (using either routine core analysis or NMR measurements at S.sub.w1). The cementation exponent indicates how well-connected the pore geometry is. It is about m=2 for many rocks but can be higher for vuggy carbonates. This is well known to one skilled in the art.

(21) The tortuosity (?) of the water phase at S.sub.w1 can also be determined from the electrical resistivity measurements as is well known to one skilled in the art:
?=?.sub.T.sup.1?m

(22) The permeability is now obtained using an equation modified from the Carman-Kozeny equation, which assumes parallel capillary tubes. The modified Carman-Kozeny equation for permeability (k) from d (where S/V=4/d), ?.sub.T, ?, BTR:

(23) $k=A\frac{{?}_T{d}^2}{32?{\mathrm{BTR}}^2}$

(24) where A is a free parameter to be calibrated by comparing to k.sub.meas. FIG. 4 shows a core sample's estimated permeability versus its measured permeability using this invention versus using three older methods. This is explained in more detail in the attached references (Chen et al. 2020, Chen et al. 2019b, Chen et al. 2019a, Chen et al. 2017, Wang et al. 2020).

(25) Another equation besides Carman-Kozeny can also be used. Other equations are listed in the attached references. Note that all the quantities in this equation are measured by .sup.1H NMR or centrifuge, except BTR. Hence BTR may be determined from this data set.

(26) Step 5: Next, the relative permeability of water k.sub.rw (=k.sub.w/k) is determined with decreasing water saturation (S.sub.w) from S.sub.w1 to irreducible water S.sub.wirr using a centrifuge drainage measurement. FIG. 5 shows centrifuge sample holders for drainage experiments and imbibition experiments [Hirasaki 1992}. Examples of a commercial automated centrifuge that can be used in this invention are available from Vinci Technologies (RC4500). The core sample is placed in a centrifuge core holder and centrifuged to air (drainage cycle) at a high speed down to S.sub.wirr. The water in the core sample is replaced with gas (e.g. air, nitrogen) during centrifugation. As the core is centrifuged, the automated centrifuge measures the time dependence of the flow rate of effluent from the core. The fluid production versus time are monitored and then history-matched to determine the curve of k.sub.w versus S.sub.w, as outlined in [Hirasaki 1992] and [Hirasaki 1995]. One advantage of the centrifuge measurement is that it is gravity-stable; that is, no viscous fingering occurs. Another advantage is that extremely small values of k.sub.rw can be measured. This is useful for determining k.sub.rw at endpoint saturations, i.e. at residual oil saturation (S.sub.or) or at S.sub.wirr.

(27) Step 6: At irreducible water saturation, the electrical resistivity of the core sample is measured (R.sub.t). The saturation exponent, n, is measured using the resistivity index from Archie's law:

(28) $\frac{R_t}{R_o}=\frac{1}{S_w^n}$

(29) where S.sub.w is the water saturation (this should be irreducible water saturation S.sub.wirr). The value for n indicates how the fluids affect the resistivity of the rock. In water-wet conventional rocks, it is common for n to be around n?2. In mixed-wet and oil-wet rocks, n is much higher n>2 at lower S.sub.w. In shaly-sands, n may be lower n<2 as S.sub.w decreases.

(30) The tortuosity of the water phase at irreducible saturation can be determined using:
?.sub.w=?.sub.T.sup.1?mS.sub.w.sup.1?n

(31) assuming that Archie's Law is valid.

(32) Step 7: .sup.1H NMR T.sub.2 measurements are made at S.sub.wirr to get pore-body diameter (d.sub.wirr) from S/V=.sup.4/d.sub.wirr using the previously determined ?.sub.2w at S.sub.w1 as such:

(33) 0$\frac{1}{T_2}={?}_{2w}\frac{S}{V}={?}_{2w}\frac{4}{d_{w?rr}}$

(34) This equation assumes the fast-diffusion regime, which is typically the case.

(35) Step 8: The relative permeability of water k.sub.rw is predicted using d.sub.wirr, ?.sub.TS.sub.w, ?.sub.w, k based on Carman-Kozeny relation:

(36) $k_w=A_w\frac{{?}_T{S}_w{d}_{wirr}^2}{32{?}_{w}BT{R}^2}$

(37) where A.sub.w is a free parameter to be calibrated by comparing to centrifuge data in step 5. Another relation besides Carman-Kozeny can also be used.

(38) Step 9: The core sample is cleaned and dried and then saturated with heavy water brine (e.g. D.sub.2O with NaCl matching in situ brine concentration). The reason D.sub.2O is used is that there is no .sup.1H NMR signal from D.sub.2O, therefore the only .sup.1H NMR signal that will later be detected is from the hydrocarbons. The core is centrifuged to air down to S.sub.wirr using the apparatus in FIG. 5. The fluid production and saturation are monitored and then history matched (Hirasaki et al 1992 and 1995) to determine the k.sub.rw. The k.sub.rw using D.sub.2O brine can be checked against k.sub.rw estimated from the centrifugation of the H.sub.2O brine-saturated core in step 5.

(39) Step 10: The core sample is saturated with high-pressure methane (C1), and .sup.1H NMR measurements are made using the sample, where only the hydrocarbon phase is detectable. Restricted diffusivity D/D.sub.0 versus L.sub.D measurements are made to get ?.sub.hc for C1(D.sub.2O) at S.sub.wirr using the Pad? fit. C1 has a large diffusion coefficient D.sub.0, therefore a large L.sub.D. If L.sub.D>>d then ?.sub.hc can be determined from the Pad? fit.

(40) Step 11: The C1 is allowed to evaporate, and the resulting air-filled porosity is then replaced by with decane (C10). .sup.1H NMR D/D.sub.0 versus L.sub.D measurements are made to get pore-body diameter (d.sub.hc) from S/V=4/d.sub.hc for C10(D.sub.2O) saturated cores at S.sub.wirr using the Pad? fit. C10 has a small diffusion coefficient D.sub.0, therefore a small L.sub.D. If L.sub.D<<d then the d.sub.hc can be determined from the Pad? fit. T.sub.2 measurements are also made to get the C10-filled porosity (?.sub.hc) and surface relaxivity (?.sub.2hc) for C10.

(41) Step 12: The core is centrifuged in drainage cycle using air or nitrogen down to S.sub.or at S.sub.wirr. The relative permeability of oil k.sub.ro (=k.sub.o/k) is measured with decreasing oil saturation (S) at S.sub.wirr down to S.sub.or by history matching C10 production. An example is shown in FIG. 6 for a Berea sandstone with n-decane being displaced by nitrogen (first drainage), where k.sub.ro (=k.sub.o/k) is measured versus So down to k.sub.ro=10.sup.?7.

(42) Step 13: The relative permeability to oil k.sub.ro at S.sub.wirr down to S.sub.or is predicted using d.sub.hc, ?.sub.hc, ?.sub.hc, k based on the modified Carman-Kozeny relation:

(43) $k_o=A_o\frac{{?}_{hc}{d}_{hc}^2}{32{?}_{hc}BT{R}^2}$

(44) where A.sub.0 is a free parameter calibrated by comparing to the centrifuge data in step 12. Another relation besides Carman-Kozeny can also be used.

(45) Step 14: The relative permeability ratio (K) between oil and water can be estimated by taking the ratio of the oil relative permeability (k.sub.ro) to the water relative permeability (k.sub.rw):

(46) $K=\frac{k_{ro}}{k_{rw}}$

(47) Step 15: The core is saturated with decane (C10) and then centrifuged with D.sub.2O in an imbibition cycle to measure k.sub.ro vs S.sub.o. This simulates a waterflood.

(48) Step 16: The core is cleaned using Soxhlet extraction with chloroform-methanol azeotrope to remove the residual C10 and D.sub.2O. The core is dried and then fully saturated with D.sub.2O. The core is centrifuged with decane in a drainage cycle to S.sub.wirr. The core is then centrifuged with air or nitrogen in a drainage cycle to S.sub.or and S.sub.wirr. The core sample at this stage should resemble the core sample at the end of step 12.

(49) Step 17: In order to simulate a third phase (gas), the core at S.sub.or is then saturated with high-pressure fluorinated gas that is insoluble in water. This fluorinated gas is the analog of methane (CH.sub.4) used for measuring hydrocarbon-filled tortuosity. The fluorocarbon gas will be selected based on large D.sub.0 and therefore large L.sub.D, as well as large FI (fluorine index) for high SNR (signal-to-noise ratio); see below.

(50) At this stage, the core has three phases in the pore space: D.sub.2O brine at S.sub.wirr (most likely in the smallest pores if the sample is water wet), residual C10 at S.sub.or, and fluorocarbon gas. .sup.19F NMR D/D.sub.0 versus L.sub.D measurements are made to probe the large L.sub.D region of the D/D.sub.0 versus L.sub.D curve in order to measure the tortuosity of the gas phase (?.sub.g), using the Pad? fit.

(51) Step 18: The fluorocarbon gas is evacuated from the core by releasing the gas pressure and the core is then saturated with a fluorocarbon liquid that is insoluble in both oil and water. .sup.19F NMR measurements of D/D.sub.0 versus L.sub.D are made for the short L.sub.D region of the D/D.sub.0 versus L.sub.D curve to measure the pore-body diameter of the gas phase (d.sub.g) from S/V=4/d.sub.g at S.sub.wirr & S.sub.or, using the Pad? fit. T.sub.2 measurements will also be made to get the porosity (q) of the gas phase, as well as the surface relaxivity (?.sub.2g).

(52) Step 19: The core is centrifuged with water in an imbibition cycle down to S.sub.gr at S.sub.or. The relative permeability of gas is measured (k.sub.rg=k.sub.g/k) with decreasing gas saturation (S.sub.g) at S.sub.or down to S.sub.gr by history matching the fluorocarbon production.

(53) Step 20: The relative permeability to gas (k.sub.rg) at S.sub.or is predicted using d.sub.g, ?.sub.g, ?.sub.g, k based on the modified Carman-Kozeny relation:

(54) $k_g=A_g\frac{{?}_g{d}_g^2}{32{?}_{g}BT{R}^2}$

(55) where A.sub.g is a free parameter to be calibrated from the data set. Another relation besides Carman-Kozeny can also be used.

(56) Step 21: The core sample is then evacuated, cleaned by Soxhlet extraction, and dried.

(57) Step 22: A MICP (mercury injection capillary pressure) measurement is made to obtain pore-throat diameter (d.sub.MICP), as well as BTR (body-throat ratio):

(58) $BTR=\frac{d}{d_{MICP}}$

(59) where d is the pore-body diameter from Step 3.

(60) Step 23: Using the data collected from the laboratory analysis above, we then calculate a relationship between the relation for permeability k.sub.rX (=k.sub.X/k) of each of the three phases (X=w, o, g) as a function of the tortuosity (?.sub.X), porosity (?.sub.X), pore-body diameter (d.sub.X) from S/V=4/d.sub.X, and BT R based on the modified Carman-Kozeny:

(61) $k_X=A_X\frac{{?}_X{d}_X^2}{32{?}_X{\mathrm{BTR}}^2}\mathrm{where}X=w,o,g$

(62) It is within the scope of this invention to use another relationship besides the modified Carman-Kozeny equation to determine the permeability.

(63) One skilled in the art can construct a three-phase relative permeability model from the oil/water relative permeability curve and the oil/gas relative permeability curve using linear interpolation.

(64) Alternative to D.sub.2O for .sup.1H Free Aqueous Phase

(65) The above methodology uses D.sub.2O brine to produce a .sup.1H free aqueous phase, thereby leaving only the hydrocarbon phase detectable by .sup.1H NMR. However, D.sub.2O is costly, and it can take a long time to exchange H.sub.2O for D.sub.2O in tight low-porosity rocks.

(66) An alternative is to exchange the H.sub.2O brine with H.sub.2O brine doped with paramagnetic ions, thereby separating the .sup.1H signal in the aqueous phase from the .sup.1H signal in the hydrocarbon phase. Some common paramagnetic ions used in NMR include Mn-EDTA, Gd-EDTA, MnCl.sub.2, or GdCl.sub.3, which are all readily available. In sufficient concentrations, the paramagnetic ions shorten the bulk relaxation times of the aqueous phase to T.sub.1?T.sub.2?1 ms, thereby distinguishing it from the hydrocarbon phase. At even higher paramagnetic ion concentrations, the .sup.1H signal can be made shorter than the echo spacing of t.sub.E?0.1 ms, thereby making the aqueous phase undetectable.

(67) Yet another alternative to diffusing in the D.sub.2O brine or Mn-EDTA brine, a faster route is to do a gravity-stable fluid displacement through the core.

(68) Other NMR active nuclei may also be used in the practice of this invention, including .sup.23Na in the NaCl brine, and .sup.2H (deuterium NMR) in the D.sub.2O and .sup.13C in the hydrocarbons. Also, per-deuterated versions of the hydrocarbons may also be used. However, these other NMR active nuclei have lower signal-to-noise ratio either because of lower gyromagnetic ratios or lower isotopic abundance, or both. .sup.1H and .sup.19F have the highest signal-to-noise ratio and it is easy to retune the NMR probe between .sup.1H and .sup.19F. Higher magnetic fields would improve the signal-to-noise ratio of these lower sensitivity nuclei for the practice of this invention.

(69) .sup.19F may also be used in the brine phase by adding NaF or CaF.sub.2 salt or another fluorinated salt dissolved in the brine.

(70) Another embodiment is to use the fluorocarbon oil instead of the hydrocarbon oil (decane), and in this case, use H.sub.2O instead of D.sub.2O. In this embodiment, .sup.1H NMR provides the information about the water phase, and .sup.19F provides the information on the non-wetting oil phase.

(71) Choice of Fluorocarbon Gas for .sup.19F NMR

(72) The choice of fluorocarbon gas is selected based on large D.sub.0, and therefore large L.sub.D, as well as large FI (fluorine index) for high SNR (signal-to-noise ratio). Another optimization is the pressure and temperature of the experiment. Higher pressure increases FI but decreases D.sub.0, while higher temperature decreases FI but increases D.sub.0. Increasing temperature from 30 C to 100 C reduces the SNR by ?? due to lower FI and the Boltzmann factor, with only a mild increase in L).

(73) The FI are determined by first computing the number density of .sup.19F nuclei (N.sub.19) as such:

(74) $N_{19}=\frac{?n_{19}{N}_A}{M_W}$

(75) where ? is the gas density, Mw is the molecular weight, N.sub.A is Avogadro's number, and n.sub.19 is the number of .sup.19F nuclei per formula-unit. The FI is then divided by the number density of .sup.1H nuclei for water N.sub.1=66.7 .sup.1H/nm.sup.3 as such:

(76) $\mathrm{FI}=\frac{N_{19}}{N_1}\frac{{?}^{Fl}}{{?}^H}$

(77) where ?.sup.Fl/?.sup.H=0.94 is the ratio of gyromagnetic ratios for .sup.19F compared to .sup.1H.

(78) Due to the lack of published measurements, the molecular diffusion for the gases is predicted using kinetic theory of gases:

(79) $D_0?\frac{?}{P}\frac{RT}{M_W}$

(80) where ? is the dynamic viscosity of the gas, P is pressure, R is the ideal gas constant, and T is absolute temperature. The measured value D.sub.0?250 ?m.sup.2/ms for CH.sub.4 at 30? C. and 1200 psia is close to kinetic theory D.sub.0?245 ?m.sup.2/ms, which justifies the above expression in the low-density regime.

(81) FIG. 6 shows the FI for the fluorocarbon gases as a function of P for the accessible laboratory pressure, all at 30? C. Only data in the vapor phase or supercritical phase are shown, i.e. not in the liquid phase, since the vapor phase is of interest for large D.sub.0. The CHF.sub.3 has a maximum FI?0.11 in the vapor phase at 700 psia, while SF.sub.6 has a maximum FI?0.09 in the vapor phase at 400 psia, which are lower than HI?0.14 for CH.sub.4 at 1200 psia in [Chen 2019]. CF.sub.4 has a larger FI?0.15 at 1200 psia, which increases with increasing P in the vapor phase.

(82) FIG. 7 shows D.sub.0 for the fluorocarbon gases as a function of P for the typically accessible laboratory pressure, all at 30? C. At the largest vapor pressure of 700 psia, CHF.sub.3 has a D.sub.0?160 ?m.sup.2/ms. At the largest vapor pressure of 400 psia, SF.sub.6 has a D.sub.0?110 ?m.sup.2/ms. Meanwhile, CF.sub.4 has a D.sub.0?90 ?m.sup.2/ms at 1200 psia, which is lower than for CH.sub.4 where D.sub.0?250 ?m.sup.2/ms at 1200 psia.

(83) Of more interest than D.sub.0 is the maximum diffusion length L.sub.D possible for each gas. FIG. 9 shows the dependence of maximum L.sub.D versus P for the fluorocarbon gases. Also shown for comparison is L.sub.D=?{square root over (D.sub.0t.sub.?)} for CH.sub.4, where the maximum diffusion-evolution time is taken to be t.sub.?=110 ms. The maximum t.sub.? is a consequence of decay due to T.sub.1?150 ms surface relaxation for the wetting hydrocarbon gas [Chen 2019]. As such, the maximum is L.sub.D?160 ?m for CH.sub.4 at 1200 psia.

(84) On the other hand, it is expected the fluorocarbon gas is non-wetting and therefore has no surface relaxation, i.e. it exhibits only bulk relaxation. A bulk relaxation time of T.sub.1?1000 ms is loosely expected for the fluorocarbon gases, which is based on spin-rotation relaxation for bulk CH.sub.4 and the presence of dissolved oxygen. As such, one can expect a maximum t.sub.??550 ms for the fluorocarbon gases, which increases the maximum L.sub.D. At the largest vapor pressure of 700 psia, CHF.sub.3 has a maximum L.sub.D 300 ?m. At the largest vapor pressure of 400 psia, SF.sub.6 has a maximum L.sub.D?250 ?m. Meanwhile, CF.sub.4 has a maximum of L.sub.D 220 ?m at 1200 psia. All three fluorocarbon gases have larger maximum L.sub.D than CH.sub.4 due to larger accessible t.sub.A.

(85) The results are listed as such:

(86) TABLE-US-00002 TABLE 1 Summary of results for the three most promising fluorocarbon gases, and CH.sub.4 for comparison. Fluoro- T P D.sub.0 t.sub.? (ms) L.sub.D (m) carbon (? C.) (psia) FI (?m.sup.2/ms) maximum maximum CHF.sub.3 30 700* 0.11 160 550 300 SF.sub.6 30 400* 0.09 110 550 250 CF.sub.4 30 1200 0.15 90 550 220 CH.sub.4 30 1200 0.14** 250 110 160 *maximum pressure of vapor phase. **HI.

(87) The optimal fluorocarbon gas at operating pressures above P>500 psia is CF.sub.4 since FI is the largest, and D.sub.j(or L.sub.D) are comparable to the other fluorocarbon gases. CF.sub.4 also has the potential to go to higher pressures, which increases FI without significantly decreasing D.sub.0 (or L.sub.D).

(88) The optimal fluorocarbon gas at operating pressures below P<500 psia is SF.sub.6 since FI and D.sub.0 (or L.sub.D) at P?400 psia are comparable to CF.sub.4 at P?1000 psia.

(89) Choice of Fluorocarbon Liquids for .sup.19F NMR

(90) The optimal fluorocarbon liquid is 3M Fluorinert Electronic Liquid FC-770. A list of relevant properties for FC-770 at 25? C. are given in 2.

(91) TABLE-US-00003 TABLE 2 List of selected properties of 3M Fluorinert FC-770 at 25? C. Properties at 25? C. Fluorinert FC-770 Average molecular weight 399 (g/mol) Boiling point (@ 1 atm) 95 (? C.) Liquid density 1.793 (g/cm.sup.3) Vapor pressure 0.953 (psi) Dynamic viscosity 1.359 (cP) Water solubility 14 (ppmw) Solubility in water 1.3 (ppmw) Interfacial tension with air 14.8 (dyne/cm) Interfacial tension with brine 31.6 (dyne/cm) Interfacial tension with n-decane 6.2 (dyne/cm)

(92) The present invention has been described using detailed descriptions of embodiments thereof that are provided by way of example and are not intended to limit the scope of the invention. The described embodiments comprise different features, not all of which are required in all embodiments of the invention. Some embodiments of the present invention utilize only some of the features or possible combinations of the features. Variations of embodiments of the present invention that are described and embodiments of the present invention comprising different combinations of features noted in the described embodiments will occur to persons skilled in the art.

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