WO2015160691A1 - Procédés de mesure de perméabilité et de porosité ultra basses - Google Patents

Procédés de mesure de perméabilité et de porosité ultra basses Download PDF

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WO2015160691A1
WO2015160691A1 PCT/US2015/025542 US2015025542W WO2015160691A1 WO 2015160691 A1 WO2015160691 A1 WO 2015160691A1 US 2015025542 W US2015025542 W US 2015025542W WO 2015160691 A1 WO2015160691 A1 WO 2015160691A1
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Prior art keywords
pressure
sample
upstream
chamber
downstream
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PCT/US2015/025542
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English (en)
Inventor
Terizhandur S. Ramakrishnan
Michael Supp
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Schlumberger Canada Limited
Services Petroliers Schlumberger
Schlumberger Holdings Limited
Schlumberger Technology B.V.
Prad Research And Development Limited
Schlumberger Technology Corporation
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Priority claimed from US14/252,599 external-priority patent/US10288517B2/en
Priority claimed from US14/252,586 external-priority patent/US10274411B2/en
Application filed by Schlumberger Canada Limited, Services Petroliers Schlumberger, Schlumberger Holdings Limited, Schlumberger Technology B.V., Prad Research And Development Limited, Schlumberger Technology Corporation filed Critical Schlumberger Canada Limited
Publication of WO2015160691A1 publication Critical patent/WO2015160691A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/08—Investigating permeability, pore-volume, or surface area of porous materials
    • G01N15/082—Investigating permeability by forcing a fluid through a sample
    • G01N15/0826—Investigating permeability by forcing a fluid through a sample and measuring fluid flow rate, i.e. permeation rate or pressure change

Definitions

  • the subject disclosure relates to apparatus and methods for measuring the permeability and/or the porosity of a solid sample.
  • the subject disclosure more particularly relates to apparatus and methods for measuring the permeability and/or porosity of a rock sample having an "ultra- low" permeability (in the range of hundreds of nanoDarcies to 100 milliDarcies) obtained from a geological formation, although it is not limited thereto.
  • diP P i + dj fa (djUi + diUj ⁇ , (1)
  • Hsieh et al Based on the methods of Grace et al, Hsieh et al, proposed a solution in terms of Laplace and inverse Laplace transforms. See, Hsieh et al., "A transient labaoratory method for determining the hydraulic properties of 'tight' rocks," Int. J. Rock Mech. Min. Sci. and Geomech, 18, 245-252, 253-258 (1981). The analysis of Hsieh et al., however, does not include nonideality of the gas explicitly and its influence of the transient characteristics. Dead-volume connected to the core is also not included.
  • Hsieh et al. interpretation is based on what Hsieh et al. call as an early-time semi-infinite solution or the late-time single exponential result. Hsieh et al. analyze upstream and downstream pressures or their difference with respect to the final pressure. As a result, the solution of Hsieh et al., does not permit for accurate results.
  • a method that accounts for gas non-ideality is formulated and described for perturbed pressure decay between a source and a sink communicating through an ultra-low permeability rock.
  • a perturbed pressure transient method is utilized, whereby the decay of a perturbed difference pressure across two-chambers connected through a porous medium (sample) is measured.
  • the magnitude of the perturbed pressure should be small in comparison to the
  • the perturbation solution that takes into account dead-volumes connected to the core (and by comparison, showing the limitations of the semi-infinite approximation of Hsieh et al.)
  • the method may be used to characterize slip-correction accurately.
  • the perturbation method allows an inference of permeability at a given rock and fluid state, and is therefore capable of characterizing transport property variability. It is also shown that under conditions where the dimensions of the rock are known as a function of pressure and stress, a complete transport characterization of a rock may be obtained. The accuracy of the method may be evaluated through comparison with theoretical decay characteristics and its modal amplitudes. Hence, a quantitative evaluation of the experimental inference is provided.
  • an apparatus for measuring permeability is built based on pressure decay theory.
  • the apparatus has chambers of calibrated volume coupled to a sample chamber.
  • the apparatus has a series of calibrated chambers with valves therebetween both upstream and downstream of the sample chamber, thereby allowing for different upstream (and downstream) volumes to be utilized in experiments.
  • volumes of pipes coupling upstream and downstream chambers to the sample chamber are minimized and known.
  • permeability as a function of (final) fluid pressure is determined by (i) causing a sample chamber pressure and an upstream and downstream pressure to be the same, (ii) increasing the upstream pressure by a small (perturbation) percentage while holding the sample chamber and downstream pressures constant, (iii) monitoring the upstream and downstream pressures as a function of time during equilibration, (iv) finding a decay constant relating to the difference in the measured upstream and downstream pressures over time, and (v) using the decay constant to find the permeability.
  • permeability as a function of fluid pressure is determined by (i) causing a sample chamber pressure and an upstream and downstream pressure to be the same, (ii) causing a perturbation so that the upstream pressure is higher than the downstream pressure and the sample chamber pressure, (iii) monitoring the downstream pressure as a function of time during equilibration, (iv) finding the time of a peak value of the derivative of the downstream pressure signal, and (v) using the peak value time to find the permeability.
  • a measured or assumed value of porosity is utilized in determining permeability.
  • porosity is related to a final (estimated equilibrated pressure)
  • porosity may be determined.
  • Figure 1A is a schematic of one embodiment of an apparatus useful in measuring permeability and/or porosity of a solid sample.
  • Figure IB is a schematic of another embodiment of an apparatus useful in measuring permeability and/or porosity of a solid sample.
  • Figure 2 is a plot of permeability as a function of radial stress comparing results of methods of the disclosure with a steady state experiment.
  • Figure 3 is a plot of permeability as a function of radial stress for steady state experiments.
  • Figure 4 is a plot of permeability as a function of final pressure.
  • Figure 5 is a plot of permeability as a function of fluid pressure.
  • Figure 6 is a plot of left and right pressures and their difference as a function of time.
  • Figure 7 is a plot of right pressure derivative as a function of time.
  • Figure 8 is a plot of average pressure as a function of time.
  • Figure 9 is a plot of permeability as a function of derivative -peak time.
  • Apparatus 10 includes sample chamber 20 (discussed in more detail hereinafter) for a sample 15 (such as a formation core), an upstream or "left" chamber 30, and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), an upstream or "left" chamber 30, and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), an upstream or "left" chamber 30, and a sample 15 (such as a formation core), an upstream or "left" chamber 30, and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a sample 15 (such as a formation core), and a
  • Valves 45L and 45R are optionally remotely controlled solenoid valves and are located respectively between the left chamber 30 and the sample chamber 20, and between the sample chamber 20 and the right chamber 40.
  • the volume between the valve and the sample chamber on the left side is denoted as V h
  • V s the volume between the valve and the sample chamber on the right side
  • the volumes of chambers 30 and 40 are denoted V t and V h respectively.
  • valves 45L and 45R separate V t and V h , and V r and V s , respectively.
  • Two or more pressure sensors are provided for sensing the pressure upstream and downstream of the sample chamber. In Fig.
  • pressure sensors 47L, 47H, 47S, and 47R are shown and sense the pressure at the upstream chamber 30, the upstream side of the sample chamber 20, the downstream side of the sample chamber 20 and the downstream chamber 40 respectively.
  • an apparatus for pressurizing (i.e., pressure charging) the apparatus 10 is coupled to the upstream chamber 30.
  • a sequence of chambers may be connected to the upstream chamber 30 and/or the downstream chamber 40 so that by actuating different valves, the left and right volumes may be chosen before commencing an experiment. Ports to facilitate automated calibration, and multiple solenoids are also described hereinafter.
  • a chamber of volume V t is connected to a line of volume V h via a solenoid 45L that operates almost instantly.
  • Various V t options may be available.
  • a second chamber of volume V r and a line of volume V s separated from each other by solenoid 45R is connected to the downstream side of the sample chamber.
  • V r the total volume downstream of the sample chamber
  • ViPio + V h p V L p L0 , (6) and an equation of state for density at temperature T,
  • PLO OzPzo + , (9) and P L0 may be obtained from the middle expression in equation (8).
  • the hollowed cylinder has a volume V c2 rather than V cl A sufficient difference between V c2 and V cl is allowed in order to provide the necessary resolution for inferring the volumes.
  • xlh2s 7 s (10D)
  • subscript R for P and Z indicate that the initial low pressure side includes V s , V c , V h and V r .
  • subscripts 1 and 2 have not been used to denote pressures and compressibilities.
  • V is the column vector of four unknown volumes
  • M is the column vector of the product of the ten measurements and known bore -volumes from the metal cylinders.
  • the volume vector in the least square sense is explicitly arrived at in terms of the generalized inverse, whereby
  • any minor variations in the core length may be considered to have no material consequence to the final interpretation of permeability since it affects V L and V R negligibly and therefore does little to change a L and a R (the ratios of the pore volume of the core to the upstream and downstream volumes as discussed hereinafter).
  • a L and a R the ratios of the pore volume of the core to the upstream and downstream volumes as discussed hereinafter.
  • the change to V L and V R is easily calculated and accommodated for inferring porosity (as discussed hereinafter).
  • shorter core lengths are preferable. Since the core holder can be designed for a specific core length, the shorter core can be sandwiched between metallic sleeves, thus introducing additional dead volumes to V h and V s . These additional volumes are known from the geometry of the sleeves.
  • any measurement system especially those for differential pressures, affect the measurement itself through membrane deflection.
  • high-accuracy better than 0.1% class and hand-selected absolute transducers are used, with deliberate adjustment of range and accuracy cross-calibration during the experimental procedure.
  • a dead-weight tester is used for routine checks.
  • a NIST National Institute of Standards and Technology
  • traceable secondary calibrator is used for routine checks.
  • Elimination of offset allows the accuracy of interpretation to be improved substantially, and also provides means to infer porosity as described hereinafter.
  • the porosity may be used as a consistency check for the permeability determination, especially when the core porosity is greater than 0.10.
  • a range off-set can also be useful.
  • the same procedure may be carried out at P w and P r0 and then the right side may be bled down to P r0 to get two-offsets at ⁇ ⁇ and P r0 before commencing the transient pressure decay experiment. If the measured cross -calibration pressures are denoted by a parenthetic superscript of / or r that refers to the transducer, and the mean pressure between the two is used as the reference pressure, then the corrected pressure for the left and right sides are
  • v would be scaled with respect to a small parameter (P i0 - P R o) /Pf to keep it on the order of unity (i.e., 0(1)), and the small parameter would be used for a perturbation expansion. However, in one embodiment this is unnecessary for a leading order analysis if it is realized that ⁇ ( ⁇ , ⁇ ) « 1.
  • Zf Z Pf
  • Zf' dZ(Pf)/dP.
  • NIST quoted values of density in the temperature range 290-300 K have been used. More particularly, NIST data on density over the cited temperature range has been used to compute Z(P) and represent it as Pade approximant
  • V L -A PL v x (0, t). (21)
  • V R ⁇ Ap R v x ⁇ l, t).
  • equation (24) The above problem posed by equation (24) and the initial and boundary conditions may be solved by Laplace transforms.
  • a more direct and explicit method of solving equation (24) is through separation of ⁇ and ⁇ .
  • the eigenfunctions will be non-orthogonal since the boundary conditions have time derivatives.
  • Equations (38) and (39) are now multiplied by (0) and (1) respectively, and equation (41) is added, and the extended orthogonality result of equation (36) is utilized to obtain
  • the first eigenvalue ⁇ 1 is the most relevant, since within a short time the remaining eigenmodes become negligible.
  • To ensure sufficiency of retaining just the leading mode in interpreting the pressure equilibration requires appropriate apparatus design for which it is useful to study the amplitudes A n with respect to parameters a L and a R .
  • a proposed design aims for a better than one percent accuracy for the amplitude with the very first eigenmode. This may be accomplished by allowing up to 75 mL for V L and V R .
  • the third case ( ⁇ 3 ⁇ 4 ⁇ 3 ⁇ 4 > n 2 /4, but is less than n 2 ) does not occur in practice. Nevertheless, for completeness, it is noted that the first root is bounded by ⁇ /2 and ⁇ cc L a R . The subsequent roots are such that nn ⁇ ⁇ ⁇ +1 ⁇ (2n + 1) ⁇ /2.
  • ⁇ ( ⁇ ) ⁇ 1 A n e ⁇ ⁇ (cos/? n — 1)— sin/?, n (51)
  • the results of the above sum are compared with the experimental data and the appropriately prescribed best match for permeability is obtained. According to another embodiment, a calculation based on ⁇ is sufficient. Accordingly,
  • valve 45L is closed and the gas pressure in the upstream chamber 30 is increased by a small (perturbation) percentage (e.g., 10% or less).
  • a small (perturbation) percentage e.g. 10% or less.
  • valve 45L is opened to permit equilibration and pressures P L (t) and P R (t) are monitored by the pressure sensors 47L and 47R as a function of time.
  • the difference in the pressures measured by sensors 47L and 47R (PL ( — PR (0) is then characterized. If the decay is observed to be exponential, the characteristic decay time T d is obtained from
  • ⁇ is the porosity
  • ⁇ is the shear or dynamic viscosity of the fluid (gas)
  • L is the length of the sample
  • Gf is obtained from equation (1 )
  • P f is the final pressure
  • T d is obtained from equation (53). Since the betas (/?) depend only on a L and a R , they are known either from equation (32) or the perturbation representation whose accuracy is known a priori.
  • the initial portion of the decay is ignored and Td is obtained from an arbitrary starting time from which an exponential relaxation is observed. In one embodiment, the initial one to two seconds of data is discarded. In one aspect, it is desirable to have negligible offset between the transducers on the left and the right side in the neighborhood of Pf as established by the previously described calibration routine.
  • FIG. IB an embodiment of an apparatus 110 for measuring permeability and/or porosity of a sample 115 is seen.
  • Sample 115 is shown tightly contained in a rubber jacket 117.
  • a metal cylindrical chamber 120 Surrounding the rubber jacket is a metal cylindrical chamber 120.
  • Chamber 120 has an inlet/outlet 121 with a valve/pressure regulator 122 that is coupled to a gas source 123.
  • a desired regulated confining or squeeze pressure(s) may be provided to the rubber jacket 117 and hence to the sample 1 15.
  • a sequence of chambers 130L1 , 130L2, 130L3 with respective volumes V , V i2 and V i3 and to the other side (e.g., "downstream") of the sample chamber 120 are located, in series, a similar sequence of chambers 140R1 , 140R2, 140R3 with respective volumes
  • valves 145L1 , 145L2, 145L3 respectively located between sample chamber 120 and chamber 130L1 , chamber 130L1 and chamber 130L2, and chamber 130L2 and chamber 130L3.
  • Pressure sensor 147L and optional pressure sensor 147H are located respectively between chamber 130L1 and valve 145L1 , and between valve 145L1 and sample chamber 120.
  • valves 145R1 , 145R2, 145R3 respectively located between sample chamber 120 and chamber 140R1 , chamber 140R1 and chamber 140R2, and chamber 140R2 and chamber 140R3.
  • Pressure sensor 147R and optional sensor 147S are located respectively between chamber 140R1 and valve 145R1 , and between valve 145R1 and sample chamber 120.
  • Feedback control regulators 150R and 150L are located between the gas source 123 and chambers 130L3 and 140R3 as well as an optional valve 151.
  • a bleeder valve 153 to the atmosphere may also be provided.
  • the pore volume V c of core 1 15 in sample chamber 120 is between 1 and 10 cc. In another embodiment, the core 1 15 in the sample chamber 120 has a volume V c of between 4 and 8 cc. In one embodiment, the jacket 1 17 in sample chamber is approximately 2.5 cm in diameter and 5.1 cm long, and the core sample is approximately 2.54 cm in diameter and between 1.25 cm and 5.1 cm long.
  • the volume of V h which includes the coupling between valve 145L and sample chamber 120 and the coupling between pressure sensor 147H (if provided) to the coupling between valve 145L and the sample chamber 120 is chosen to be small and is typically similar in volume to the pore volume of the sample.
  • volume V h is between 4 and lOcc.
  • the volume of V s is made as close to the volume of V h as possible.
  • the volume of chambers 130L1 and 140R1 are chosen to be significantly larger than the pore volume.
  • the volume of chambers 130L1 and 140R1 may be chosen to be between 15 and 30cc, or more particularly 25cc. In one
  • the volume of chambers 130L2 and 140R2 are chosen to be greater than the volume of the pore volume.
  • the volume of chambers 130L2 and 140R2 may be chosen to be about 15cc.
  • the volume of chambers 130L3 and 140R3 are chosen to be significantly larger than the volume of the pore volume.
  • the volume of chambers 130L3 and 140R3 may be chosen to be about 30 cc.
  • the volume of each chamber 130L1 - 130L3 and 140R1 - 140R3 is effectively defined as the volume between valves upstream and downstream of that chamber.
  • the volume in the case of chamber 130L1 , the volume includes the volume of the chamber itself as well as the couplings to valve 145L1 and valve 145L2, whereas in the case of chamber 140R2, the volume includes the volume of the chamber itself as well as the coupling to valve 145R2 and 145R3.
  • additional even larger chambers e.g., 100 cc are provided in series between the feedback control regulators 150L and 150R and chambers 130L3 and 140R3 respectively.
  • a medium volume is chosen as an option.
  • the pressure transducers are precalibrated and only small drift and variability in the range of interest is adjusted by local shift calibration.
  • Local shift calibration is done by closing valves 145L1 and 145R1 and opening the other valves.
  • the right side desired pressure P r0 is set from the gas source and pressure readings P r0 and P r0 of the left and right transducers 147L and 147R.
  • the pressure is elevated and Pi 0 and pressure readings and are noted. Given these values, equations (10N) and (10O) are sufficient to compute shift-calibrated Pi and P r .
  • the experiment (with the choice of medium volumes) has all valves open initially.
  • the confining stress is chosen to be P i0 (which is so for the first set of experiments in a newly loaded sample chamber).
  • Valve 145L1 is in a closed state.
  • Pressure is set to P r0 by regulating gas from the source. Subsequently valve 145L1 is opened, dropping the left side pressure slightly below P r0 . Regulator valves 150L and 150R are then shut and equilibration of pressure between the left and right sides is monitored. Once they are within a certain tolerance, the confining pressure may be gradually increased to the desired value. Upon the left and right pressures agreeing within a tight tolerance, valve 145L1 is shut, and pressure on the left side is increased to Pi 0 . At this point valves 145L3 and 145R3 are shut. Since no resistance to flow is present on the left side with valve 145L3 shut, Pi 0 is reached quickly.
  • valve 145L1 is opened. Pressures on the shift-calibrated transducers are continuously monitored, and equations (ION) and (10O) are used to output Pi and P r from the measured P ⁇ and p( r The difference between P t and
  • Equation (54) is then used to get the first pass result for permeability.
  • the tiny option is chosen when the expected permeability is sub-microDarcy; i.e., on the order of tens to hundreds of nanoDarcies.
  • the calibration of the two pressure transducers 147H and 147S in close proximity to the sample chamber is accomplished by leaving valves 145L1 and 145R1 open when setting the calibration pressures of P r0 and Pi 0 .
  • the pressure is elevated to Pi 0 .
  • Valve 145L1 is opened and then shut within a few seconds (e.g., 2 - 5 seconds).
  • the transient T d is interpreted from the difference in pressures between the adjusted transducer pressures of sensors 147H and 147S.
  • V h may be recomputed depending upon the length of the sample in the rubber jacket.
  • the calibrated volumes are known. For a given sample length L, this means that V h to the sample face is known.
  • the sample length is different than the standard metal cylinders (bored and solid) used to determine volumes an adjustment can be made. For small differences, the difference in volume due to the shorter (less volume) or longer (more volume) sample is added or subtracted to V h and V s . Care is taken to properly center the sample.
  • metal cylindrical shells are used as fillers on either side of the sample (in order to hold the rubber jacket open) and the volumes V h and V s are adjusted, taking care to account for the metallic volume of the shell.
  • the apparatus and method previously described for measuring the permeability of a sample is found to be reliable for a wide range of permeabilities, from approximately 1 ⁇ to about 100 mD.
  • results obtained from an apparatus such as shown in Fig. IB, and utilizing a method as previously described were compared to a steady-state measurement permeameter device described in U.S. Patent #5,832,409 having a specified permeability measurement range of 0.1 mD to 20 D.
  • the sample contained in the sample cell was subjected to increasing radial stresses (e.g., 50 psig, 75 psig, 100 psig, 200 psig, 250 psig, 500 psig, 650 psig, 800 psig) and then decreasing radial stresses at the same radial stress levels.
  • increasing radial stresses e.g., 50 psig, 75 psig, 100 psig, 200 psig, 250 psig, 500 psig, 650 psig, 800 psig
  • the experiment involved increasing the upstream pressure slightly above the sample and downstream pressure, monitoring the upstream and downstream pressures over time, characterizing the decay according to equation (52), and finding the permeability according to equation (53).
  • Fig. 2 determinations of permeability as a function of the radial stress is shown in Fig. 2 where the steady-state determinations are shown. It is noted that while the results are in good agreement for radial stresses of 250 psig and above, under approximately 200 psig, the permeability determined according to the present method does not agree particularly well with the steady-state experiments. This is believed due to the variability of the rubber hardness at lower radial stresses of the rubber boots utilized to isolate the sample in its chamber.
  • Fig. 3 plots steady-state gas permeability measurements assuming ideal gas for the sample (as in Equation (3)) and reveals two distinct power law behaviors (dotted lines).
  • a qualitatively different behavior above about a 200 psig radial stress is evident from Fig.3. It is therefore quite possible that in this embodiment, 200 psig or thereabouts is the minimum stress required for the lateral surface seal of the steady-state permeameter apparatus to take effect.
  • Figure 4 plots the determined permeability of an ultra-low permeable sandstone core sample having a length of 1.25 cm that was placed under a radial stress of 500 psi in an apparatus such as shown in Fig. 1A or Fig. IB.
  • data is provided for a sample of about 15 ⁇ as a function of final pressure Pf .
  • the curve shown fit to the data points is a Klinkenberg correction to permeability of the form
  • k Q is the permeability of a liquid or very high pressure gas
  • k is a constant
  • P is the pressure.
  • a second sample with a permeability of about 0.6 mD was used extensively to study the validity of the interpretation and variability with respect to fluid pressure. This sample was sufficiently consolidated and showed only small variations in permeability with respect to stress.
  • the inferred permeability at a radial stress of 500 psi at different fluid pressures (Pf) with a pressure differential ⁇ ⁇ 0 - P r0 of 10 psi (except at the low pressure end, where a smaller difference of 4 psi was used) is shown in Fig. 5 where results of experiments covering a range of approximately 60 psi to 200 psi are shown. A measurable slip correction leading to increased observed permeability is evident from these results.
  • the changes are small but measurable by the devices of Figs. 1A and IB.
  • the decay time constant was 41.83 seconds, whereas at the lowest pressure of about 60 psi, the decay time constant was 120.26 seconds.
  • the final permeability differs by only about 20 percent.
  • the method is seen to be robust, and the correction due to variation of gas compressibility with respect to pressure is the most important.
  • the Klinkenberg curve is also shown in Fig. 5. No additional correction due to effective stress variation was necessary because the sample does not show appreciable variation due to stress at a fixed fluid pressure.
  • the procedure to obtain permeability is as follows. After solenoid operation, a few data points are discarded and then the difference between
  • Fig. 6 the theoretical and experimental curves obtained are shown when the initial left and right side pressures were 190 psi and 170 psi respectively.
  • An excellent match is obtained for the right side pressure, including the delay in the pressure rise.
  • a more noteworthy comparison is between the measured and the theoretical time derivative of pressure of the right side.
  • the excellent match between the two is illustrated in Fig. 7 which shows a pressure transient during an equilibration where the initial pressure differential was about 20 psi. In dimensionless form, the pressure in the right hand side is
  • permeability may be inferred rapidly utilizing dimensionless time ⁇ ⁇ because as shown in Fig. 7, the peak is reached in a matter of seconds (e.g., about 5.5 seconds in Fig. 7).
  • Equation (23) requires knowledge of Pf, that it may take more time to find Pf than to find the peak time t M .
  • Pf may be quickly found as the average of the upstream and downstream pressures.
  • low permeabilities may be inferred.
  • the porosity may be known before the start of the experiment, a useful correlation is obtained by fixing P iQ and P r0 , and computing permeability as a function of the observed time for the peak in dP R /dt (i.e., the time derivative of the downstream pressure signal) such as shown in Fig. 7.
  • This cross-plot which is shown in Fig. 9 for five different porosities, is useful for inferring permeability. For example, using the cross- plot of Fig.
  • the method may be affected by the time scales dictated for initial equilibration. A larger tolerance during equilibration and ⁇ zo — Pro provides permeabilities within acceptable errors.
  • the measurement method for permeability may also be used to infer porosity.
  • porosity should be inferred first. Therefore, in one embodiment, porosity is first computed as discussed below, and then permeability is inferred.
  • VLPLO + V R p R0 + V c p R0 V f pf (59)
  • equation (59) may be used to solve
  • V c i.e., V c + V c + V c
  • Vc Vl ⁇ _ Vr (61) from which the porosity ⁇ can be calculated in that the porosity is the pore volume V c divided by the total volume of the sample. In one embodiment this requires that V R and V L be comparable to V c and requires very accurate pressure measurements.
  • equation (62) does not depend upon knowing the pressure P L0 that is reached instantly after valve 45L is opened.
  • a L and a R should be « 1. Since V c is then small compared to V L and V R , and the pore volume V c in equation (62) is obtained by subtraction of quantities much larger than V c , errors can propagate disproportionately. In one embodiment, temperature changes during the course of the experiment and small errors in the transducer need to be avoided. It is for this reason that very accurate relative pressure calibration can be desirable. As previously discussed, post absolute pressure calibration, each experiment can be preceded by an automated relative transducer adjustment. In one embodiment, forced ventilation is used to counteract heat dissipation from the solenoids and to thereby maintain
  • the sensitivity to porosity may be increased by elevating ⁇ ⁇ - P r0 . Late time transient still provides permeability at Pf .
  • Table 1 A table of porosities for one sample is given along with the left and right side fluid pressures in Table 1. Table 1 was generated using experimental data. While there are fluctuations from one experiment to another, the mean value is in excellent agreement with the pycnometer data. Table 1 - Pressure and porosity values; ⁇ is the experimental minus the theoretical estimate. Porosity from pycnonmetry was 0.1714.
  • samples having permeability as low as 100 nD to about 50 mD have been successfully tested and measured.
  • samples with lower and higher peremabilities may also be successfully tested and measured.
  • a high degree of accuracy in pressure measurements enable porosity measurements for ⁇ 0.10.
  • the fluid pressure and the characteristics of stress should be specified adequately when permeability is assigned.

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Abstract

L'invention concerne des procédés et un appareil permettant de mesurer la perméabilité et/ou la porosité d'échantillons de roche à perméabilité ultra basse. Dans certains modes de réalisation, les procédés utilisent une perturbation de pression de fluide.
PCT/US2015/025542 2014-04-14 2015-04-13 Procédés de mesure de perméabilité et de porosité ultra basses WO2015160691A1 (fr)

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
US14/252,599 2014-04-14
US14/252,599 US10288517B2 (en) 2014-04-14 2014-04-14 Apparatus and calibration method for measurement of ultra-low permeability and porosity
US14/252,586 US10274411B2 (en) 2014-04-14 2014-04-14 Methods for measurement of ultra-low permeability and porosity
US14/252,586 2014-04-14

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