- Email: [email protected]
Novel apparatus to measure the low-permeability and porosity in tight gas reservoir
Journal of Petroleum Science and Engineering 142 (2016) 1–12
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Novel apparatus to measure the low-permeability and porosity in tight gas reservoir Hochang Jang a, Wonsuk Lee b, Junggyun Kim c, Jeonghwan Lee a,n a Department of Energy and Resources Engineering, College of Engineering, Chonnam National University, 77 Yongbong-ro, Buk-gu, Gwangju 500-757, Republic of Korea b Petroleum and Marine Research Division, Korea Institute of Geoscience and Mineral Resources, Daejeon 305-350, Republic of Korea c Research and Development Division, Korea Gas Corporation, 638-1, Il-dong, Sangrok-gu, Ansan, Gyeonggi-do 426-860, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 3 August 2013 Received in revised form 3 August 2015 Accepted 29 January 2016 Available online 30 January 2016
This study proposes a new apparatus which can simultaneously measure the physical properties such as low-permeability and porosity in a tight gas reservoir. The apparatus can also measure bi-directional permeability efficiently. The measurement of bi-directional permeability is designed in consideration of flow direction which can cause different results by heterogeneity. Using the apparatus, the experiments have been carried out to measure the low-permeability and porosity of three tight sand core samples which are from Gyeongsang sedimentary basin in Korea. As the results, the porosity ranges from 5.63% to 11% and the permeability measured in forward and reverse direction is 0.0004 md and 0.0005 md for TS1, 0.0007 md and 0.0011 md for TS-2, and 0.0062 md and 0.007 md for TS-3, respectively. To investigate the effect of geological characteristics inside core sample on rock properties, X-ray scan of the core samples was taken by Microfocus X-ray CT. Obviously, the value of permeability and porosity are subject to geological features such as micro-crack. This means that the micro-crack plays an important factor in terms of permeability variation by its direction and length in a tight gas reservoir. For verification of measurement accuracy, regression analysis was carried out using the dimensionless pseudo-pressure between the measured data and analytical model. As the results, it is shown that both are approximately equal in terms of permeability and porosity. & 2016 Elsevier B.V. All rights reserved.
Keywords: Tight gas Low-permeability Porosity Pulse-decay measurements X-ray scan
1. Introduction For successful development of a conventional and unconventional reservoir, it is necessary to maximize production by analyzing the flow characteristic and reservoir property. In case of tight gas reservoir, however, permeability is lower than 1 md (Rezaee et al., 2012; Gai et al., 2015), experiments spend a lot of time and show inaccurate results. Pulse-decay measurements using a gas or liquid are effective for determining the permeability of rocks in the range from 0.1 md to 0.01 μd (Jones, 1997). The pulse-decay measurements for determining the permeability of homogeneous cores has been the primary application of pressure transient test. The method explains that the core is confined in a cell and upstream and downstream reservoirs are attached to both ends. The upstream reservoir is pressurized and then allowed to make core and the downstream reservoir in same condition. The pressure and time behavior of the reservoirs are measured and used with analytical solutions to calculate n
Corresponding author. E-mail address: [email protected] (J. Lee).
http://dx.doi.org/10.1016/j.petrol.2016.01.037 0920-4105/& 2016 Elsevier B.V. All rights reserved.
permeability. The general solutions for the pressure difference as a function of time were presented by Dicker and Smits (1988) following the original work of Brace et al. (1968) and error function solution and general analytical solution were presented as well by Bourbie and Walls (1982) and Hsieh et al. (1981) respectively. Compressive storage of the rock sample in development of the analytical equations describing a pulse-decay process was neglected by Brace et al. (1968). Determining the permeability using the assumption can create an error. To minimize the error, the study proposed to use enough the reservoirs to exceed the storage in the rock sample. However, the use of large reservoirs causes a restriction in terms of design and leads to a long test time. A significant advantage of Brace et al.'s theory is that permeability can be calculated directly from linear portion of the solution. Several investigators tried to maintain the feature of the theory while including the assumption that core compressive storage is negligible by analyzing different portions of the pressure and time history of the reservoirs with particular combinations of reservoir size, either very large upstream with very small downstream (Bourbie and Walls, 1982; Chen and Stagg, 1984) or very small upstream with very large downstream (Amaefule et al., 1986; Maini and Okazawa, 1986; Kwan et al., 1988). Hsieh et al. (1981)
2
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Nomenclature
A a b cg cgp cpv ct cvd cvu k L P Pd Pu t ta
cross-sectional area of cylindrical core, ft2 volume ratio between upstream reservoir and pore volume ratio between downstream reservoir and pore gas compressibility, psia 1 gas compressibility at initial pore pressure, psi 1 compressibility of sample’s pore volume, psi 1 total compressibility, psi 1 compressibility of downstream reservoir, psi 1 compressibility of upstream reservoir, psi 1 permeability, md length of cylindrical sample, in. pressure, psia pressure in downstream reservoir, psia pressure in upstream reservoir, psia time, s adjusted pseudo-time, s
presented a general analytical solution that accounts for the compressive storage of the rock sample and was valid for all combinations of reservoir size. In the study, however, it takes a long time to set an initial condition of core sample with lowpermeability because the injected gas was flowed in one direction. The main focus of this study is to develop a new apparatus to simultaneously measure low-permeability and porosity, which can reduce total testing time and measure bi-directional permeability efficiently. Using the apparatus, permeability and porosity of tight sand core have been measured and its accuracy has been verified with an analytical model.
2. Experimental setup and procedure 2.1. Experimental apparatus Conceptual schematic of the Low-Permeability Measurement Apparatus (LPMA) is based on pulse-decay measurements as shown in Fig. 1. The study examines the tight gas formation and measurement method for permeability and porosity in the tight sand. The experimental apparatus was designed and set up to conduct a study on tight gas reservoir. The apparatus was composed of core holder, syringe pump, vacuum pump, hand pump, pressure generator, incubator, control box, and acquisition system (Fig. 2). The core holder, which is a main part of the system, was made of 304 SUS material so that it endures high pressure. Inlet and
Vb Vd Vp Vu Z α β γ θn μ ϕ ψ ψd
ψp ψu
bulk volume of core plug, ft3 downstream reservoir volume, ft3 pore volume of core plug, ft3 upstream reservoir volume, ft3 gas compressibility factor dimensionless group defined by Eq. (15) dimensionless group defined by Eq. (16) dimensionless group defined by Eq. (17) the nth roots of Eq. (4), rad gas viscosity, cp porosity of sample, fraction pseudo-pressure, psia2/cp pseudo-pressure evaluated at downstream pressure, psia2/cp pseudo-pressure, evaluated at maximum (pulse) pressure, psia2/cp pseudo-pressure evaluated at upstream pressure, psia2/cp
outlet of the core are hold by end plugs and lateral face of the core is fixed by viton sleeve with confining pressure, which allows the flow direction only in an axial direction. Including the core-in and core-out sections, there are two pairs of sensors, and each pair consists of one pressure transmitter (PT) port and one resistance temperature detector (RTD) sensor. To generate pressure pulse, high pressure generator was installed, which can handle 60 mL/ stroke. The experimental apparatus is covered with an incubator so that the injected gas can be maintained in constant temperature. Nitrogen gas of 99.95% purity was used in this experiment. Gas is injected from the gas cylinder to the core using a syringe pump. Data acquisition system continuously records all the information such as overburden pressure, temperature and pressure difference between upstream and downstream as the experiment is conducted. The cores used in this experiment are tight core samples which have length of 45 mm and diameter of 38.1 mm. 2.2. Key features of the LPMA The LPMA is similar to conventional setup, but contains two changeable cells and two mass flowmeters. The changeable cells, which are comprised of cells of various sizes, can function as manually changing upstream and downstream reservoirs volume to minimize an error in the determining permeability and porosity. These are installed so that upstream and downstream reservoirs size is adjusted according to the pore volume of core. When large cells are used, response of heterogeneous cores may even appear like homogeneous ones. When compressive storage in the cells is
Fig. 1. Schematic diagram of experimental apparatus.
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 2. Photograph of low-permeability measurement apparatus.
Fig. 3. Flow chart of experimental procedure.
3
4
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 4. Geological map of Gyeongsang Basin. Table 1 The experimental results of the tight sand cores in Gyeongsang basin. Samples
TS-1 TS-2 TS-3
Initial equilibrium time (h)
Pulse decay testing time (h)
Conventional injection
Bi-directional injection
84 48 4.5
44 25 3
14 8 1
Permeability (md) Forward
Reverse
0.0004 0.0007 0.0062
0.0005 0.0011 0.0070
Porosity (%)
11.5 6.80 5.63
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
5
Fig. 7. Experimental pressure responses of sample TS-3.
Fig. 5. Experimental pressure responses of sample TS-1.
which result in a significant reduction for experiment time and error. 2.3. Experimental procedure. The measurement procedures of porosity and permeability consists of the following steps (Fig. 3): (1) The sample is mounted into the core holder and desired confining stress is set (1500 psia); (2) Initial equilibrium pressure on sample is set (more than 1000 psia) to make a pseudo-pressure condition through a bi-directional gas injection; (3) Equilibrium pressure can be identified by the mass flowmeters (a flow rate equal to zero between upstream and downstream reservoirs); (4) Pressure pulse (approximately 30 psia) is generated in upstream reservoir; (5) The experimental gas is flowed in forward direction until the final equilibrium pressure is reached; (6) Change the role of upstream and downstream reservoirs using a bypass-line; (7) The experimental gas then flowed in reverse direction until the final equilibrium pressure is established. The pressure and temperature data, which allows us to interactively calculate porosity and permeability by choosing the appropriate data, are collected and monitored by data acquisition system. Fig. 6. Experimental pressure responses of sample TS-2.
of the same order or smaller than the compressive storage in the core sample, deviations from the homogeneous core response can be accentuated. The bypass-line is meant to reduce the total testing time and measure the bi-directional permeability at once. For example, when gas is injected into the core to set the initial condition, the demanding time is decreased through a bi-directional gas injection. The mass flowmeters are located at both ends of core holder. As the use of the mass flowmeters, we can detect the apparatus is set to initial condition. Additionally, if the permeability is measured by reverse direction, all procedure should be repeated again. However, after measuring the permeability of forward direction, the LPMA can change the role of upstream and downstream reservoirs using a bypass-line. The measurement of bi-directional permeability is designed in consideration of flow direction of fluid which can cause different results. These considerations suggest changes in both apparatus and procedure,
3. Determination of rock properties 3.1. Permeability The dimensionless differential pressure ( ΔPD ) between the upstream and downstream reservoirs is defined as:
ΔPD =
Pu (t ) − Pd (t ) Pu (0) − Pd (0)
(1)
If the experiment only involves very small change in pressure (i.e. o5%), the experimental dimensionless differential pressure at larger time becomes a single exponential function of time and can be approximated as (Dicker and Smits, 1988; Jones, 1997):
ln (ΔpD ) = ln (f0 ) + s1t where f0 is a constant and s1 is
(2)
6
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 8. Microfocus X-ray CT images of sample TS-1.
s1 = −
kf1 A (1/Vu + 1/Vd ) μLcg
(3)
where f1 = θ12/(a + b), θ1, the first solution of the transcendental equation, is
tan θ =
(a + b) θ θ 2 − ab
(4)
a and b , the ratio of the compressive storage of the sample's pore volume to that of the upstream and downstream reservoirs, respectively, are
a=
Vp (cg + cpv ) VP (cg + cpv ) and b = Vu (cg + cvu ) Vd (cg + cvd )
(5)
where cpv , cvu and cvd could be neglected because this factors were very smaller than cg . Using the experimental pulse-decay data, the slope ( s1) can be obtained by linear curve fitting. Then, permeability of the sample can be determined by simple rearrangement of Eq. (3):
k=
−s1μLcg f1 A (1/Vu + 1/Vd )
(6)
3.2. Porosity Boyle's Law and Gas Equation of State were used to determine porosity. For fully saturated core, gas was injected to downstream through tight core using a syringe pump. At that time, P1 and P2 are
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
7
Fig. 9. Microfocus X-ray CT images of sample TS-2.
pressure of the syringe pump before and after injection respectively. Also, V1 is volume of the syringe pump container before injection. V2 is the injected gas volume to tight core from a syringe pump.
P2 (V1 + V2 + Vp − Vb ) P1V1 = Z2 n2 RT2 Z1n1RT1
(7)
Then, the porosity of the sample can be determined with simple equation as:
ϕ = Vp/Vb
0.1 md to 0.01 μd. With the low-permeability, leak-tightness of the apparatus is of ultimate importance, and strict temperature control is critical as well (Haskett et al., 1988). Three sets of sample (TS-1, 2, and 3) from the Gyeongsang sedimentary basin in Korea were tested using the LPMA. Gyeongsang basin is the largest Cretaceous non-marine sedimentary basin in Korea and it is located in the southeastern part of the Korea (Fig. 4). The diameter and length of the samples are 38.1 mm and 45 mm respectively. 4.1. 1 Experimental results
(8)
4. Results and discussion The pulse-decay measurements using a gas or liquid are effective for determining the permeability of rock in the range from
The experimental results of three core samples are summarized in Table 1. To set initial pressure, equilibrium time takes about 84 h, 48 h, and 4.5 h for sample TS-1, TS-2, and TS-3 through conventional injection method, respectively. In other hand, the bidirectional injection spends 44 h, 25 h, and 3 h for each sample. Comparing to previous measurements, the apparatus reduces the time by approximately half until setting the initial condition of the
8
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 10. Microfocus X-ray CT images of sample TS-3.
core sample. The maximum of pulse-decay test takes about 14 h in sample TS-1. In case of sample TS-2 and TS-3, the measurements of porosity and bi-directional permeability take about 8 h and 1 h to complete respectively. The porosity ranges from 5.63% to 11% and the permeability measured in forward and reverse direction is 0.0004 md and 0.0005 md for TS-1, 0.0007 md and 0.0011 md for TS-2, and 0.0062 md and 0.007 md for TS-3, respectively. From the results, the differences due to heterogeneity of the core samples revealed as 0.0001 md, 0.0004 md, and 0.0008 md. Figs. 5–7 show the pressure behavior for TS-1, TS-2, and TS-3. The figures show that the pressure responses are different according to the forward and reverse directions. It is evident that each sample follows its own unique path of pore volume with direction although samples from the same set are of the same formation. For analysis of correlation among micro-crack, geological characteristic, and property, X-ray scan of a tight sand core is taken by Microfocus X-ray CT (SMX-225 CT). As the result, in case of TS-1, porosity is bigger than other so that samples the CT images show
that tight sand is alternated with sandstone (Fig. 8). However, micro-crack in the images of cross and plane section were undiscovered. Mostly, when the experimental gas flows in the sample, it moves through the easy route such as fracture. The reason why TS-1 has low-permeability is explained by comparison with other samples. In other samples, micro-crack was discovered in the lower surface of TS-2 and TS-3 as shown in Figs. 9 and 10. In case of TS-3, especially, its permeability is the highest among the three samples as micro-crack was larger than other samples. Therefore, it is shown that the micro-crack improves the permeability. This means that the micro-crack plays an important factor in terms of permeability variation by its direction and length in a tight gas reservoir. 4.2. Validation The measurements and its accuracy from the experimental equipment could be verified by comparison to analytical model.
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
9
Fig. 11. Comparison of experimental data on sample TS-1 to analytical model.
For the verification of measurement accuracy, Haskett et al.'s analytical model was used. The derivation of the final solution is analogous to the derivation presented by Hsieh et al. (1981). The linear flow of liquid in porous media can be described with
The equations were solved for dimensionless pseudo-pressure and adjusted pseudo-time for both the upstream and downstream reservoir volumes
∂ ⎡ P ∂P ⎤ ϕct ⎡ P ∂P ⎤ ⎢ ⎥= ⎢ ⎥ ∂x ⎣ μZ ∂x ⎦ k ⎣ Z ∂t ⎦
Ψu 1 = +2 Ψp 1+β+γ
(9)
For the flow of gas, Eq. (9) is not linear because μ and ct are functions of pressure. For gas flow, Eq. (9) can be linearized through the use of dimensionless pseudo-pressure (DPP) and adjusted pseudo-time
∂ ⎡ ∂Ψ ⎤ μ φct ⎡ ∂Ψ ⎤ ⎢ ⎥ ⎢ ⎥= ∂x ⎣ ∂x ⎦ k ⎣ ∂ta ⎦
(10)
Pseudo-pressure is defined as
Ψ=2
∫p
p 0
P dP μZ
And, adjusted pseudo-time is defined as
ta = μ ct
∫0
t
dt μct
Ψd 1 = +2 Ψp 1+β+γ
(13)
∞
2
e (−αθ n ) (β + γ 2θ n2/β ) ⎡ 2 4 2 ⎤ 2 2 2 2 n = 1 ⎣ γ θ n /β + (γ β + γ + γ + β ) θ n /β + (β + γβ + β ) ⎦ cosθ n
∑
(14)
For the downstream reservoir volume, where θn 's are the roots of the Eq. (4) and
kta 94, 812L2μ ϕct
(15)
and
β= (12)
2
e (−αθ n ) (β + γ 2θ n2/β ) ⎡ γ 2θ 4 /β 2 + (γ 2β + γ 2 + γ + β ) θ 2/β + (β 2 + γβ + β ) ⎤ n n n =1 ⎣ ⎦
For the upstream reservoir volume, and
α=
(11)
∞
∑
ALϕct Vu cgp
and
(16)
10
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 14. Comparison of experimental data on sample TS-2 to analytical model. Fig. 12. Regression analysis of dimensionless pseudo-pressure for sample TS-1 in upstream reservoir.
Fig. 13. Regression analysis of dimensionless pseudo-pressure for sample TS-1 in downstream reservoir.
γ=
Vd Vu
(17)
The terms Ψu/Ψp and Ψd/Ψp are the upstream and downstream dimensionless pseudo-pressures, respectively. The calculated pressure from the analytical model was compared with the experimental results by pressure transient matching. The measured pressure data are converted to dimensionless pseudo-pressure with Eq. (11) and nondimensionalized by dividing the initial pseudo-pressure of the upstream reservoir. Time is converted to adjusted pseudo-time with Eq. (12). In the matching process, there are only two unknowns: porosity and permeability. All other parameters including upstream and downstream reservoir
Fig. 15. Regression analysis of dimensionless pseudo-pressure for sample TS-2 in upstream reservoir.
volumes, core dimensions, and fluid properties are known. As shown in Figs. 11, 14 and 17, the pressure transient is analyzed by matching the measured data to the analytical model. These results illustrate the accuracy and validity of experimental results obtained from the LPMA. A regression analysis of dimensionless pseudo-pressure by two methods for tight samples is shown in Figs. 12, 13, 15, 16, 18 and 19. As the result of a regression analysis, the values of correlation coefficient range from 0.96 to 0.99 in upstream and downstream reservoirs. From the result of a comparative analysis between analytical model and experiment results, it is found that both are approximately equal in terms of permeability and porosity.
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
11
Fig. 16. Regression analysis of dimensionless pseudo-pressure for sample TS-2 in downstream reservoir.
Fig. 18. Regression analysis of dimensionless pseudo-pressure for sample TS-3 in upstream reservoir.
Fig. 17. Comparison of experimental data on sample TS-3 to analytical model.
Fig. 19. Regression analysis of dimensionless pseudo-pressure for sample TS-3 in downstream reservoir.
5. Conclusions The experimental apparatus has been designed and set up so that low-permeability and porosity could be measured in unconventional gas reservoir such as tight gas reservoir. The experiments have been carried out to measure the low-permeability and porosity of tight core sample and to verify the accuracy of the measurement. From the result, the following conclusions have been drawn: (1) The new apparatus which is called LPMA has been developed to simultaneously measure the low-permeability and porosity. The LPMA can reduce the time by approximately half until
setting to initial condition of the core sample and efficiently measure the bi-directional permeability. (2) As the measurements, the porosity ranges from 5.63% to 11% and the permeability measured in forward and reverse direction is 0.0004 md and 0.0005 md for TS-1, 0.0007 md and 0.0011 md for TS-2, and 0.0062 md and 0.007 md for TS-3, respectively. (3) The differences due to heterogeneity of the core samples revealed as 0.0001 md, 0.0004 md, and 0.0008 md. It is evident that each sample follows its own unique path of pore volume with measurement direction although samples from the same set are of the same formation. (4) The X-ray scan of tight sand core samples was taken by Microfocus X-ray CT to investigate the effects of a micro-crack
12
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
and geological characteristics inside core sample on rock properties. As the results, it is shown that the micro-crack plays an important factor in terms of permeability variation by its direction and length in a tight gas reservoir. (5) Comparative analysis between the experimental results and analytical model was performed to verify the accuracy of measurement. From the results, it is found that both are approximately equal in terms of permeability and porosity. Therefore, the LPMA can be efficiently applied to measure the rock properties of unconventional gas reservoir such as tight sand and shale gas.
Acknowledgments This work was supported by the Energy Efficiency and Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy (2011201030001B).
References Amaefule, J.O., Wolfe, K., Walls, J.D., Ajufo, A.O., 1986. Laboratory Determination of Effective Liquid Permeability in Low-Quality Reservoir Rocks by the Pulse Decay
Technique. SPE Paper 15149. SPE California Regional Meeting, Oakland, California, 2–4 April, 1986. Bourbie, T., Walls, J., 1982. Pulse decay permeability: analytical solution and experimental test. Soc. Pet. Eng. J. 22, 719–721. Brace, W.F., Walsh, J.B., Frangos, W.T., 1968. Permeability of granite under high pressure. J. Geophys. Res. 73, 2225. Chen, T., Stagg, P.W., 1984. Semilog analysis of the pulse decay technique of permeability measurement. Soc. Pet. Eng. J. 24, 639–642. Dicker, A.I., Smits, R.M., 1988. A practical approach for determining permeability from laboratory pressure pulse decay measurement. SPE Paper 17578. Presented at the SPE International Meeting in Petroleum Engineering. Tianjin, China, 1–4 November, 1988. Gai, S.H., Liu, H.Q., He, S.L., Lei, G., Mo, S.Y., Huang, X., Yang, Y., Chen, X., 2015. An improved particles model for stress sensitivity in low-permeability sandstones. Geosyst. Eng. 19 (2), 89–95. Haskett, S.E., Narahara, G.M., Holditch, S.A., 1988. A method for simultaneous determination of permeability and porosity in low permeability cores. Soc. Pet. Eng. Form. Eval. 3 (3), 651–658. Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E., 1981. A transient laboratory method for determining the hydraulic properties of tight rocks: I. Theory. Int. J. Rock Mech. Min. Sci. 18, 245–252. Jones, S.C., 1997. A technique for faster pulse-decay permeability measurement in tight rocks. Soc. Pet. Eng. Reserv. Eval. Eng. 12, 19–25. Kwan, M.Y., Okazawa, T., Fortier, R.A., 1988. Application of the Pulse-Decay Technique to the Measurement of Heavy Oil Core Fluid Mobilities and Porosity. J. Can. Pet. Technol. 27 (5), 92–98. Maini, B.B., Okazawa, T., 1986. On the use of pulse technique for minimizing damage during core tests in heavy oil system. Paper CIM 86-37-79 Presented at the 1986 Annual Technical Meeting of the Pet. Soc. Of CIM, Calgary, June 8–11, 1986. Rezaee, R., Saeedi, A., Clennell, B., 2012. Tight gas sands permeability estimation from mercury injection capillary pressure and nuclear magnetic resonance data. J. Pet. Sci. Eng. 88–89, 92–99.
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Novel apparatus to measure the low-permeability and porosity in tight gas reservoir Hochang Jang a, Wonsuk Lee b, Junggyun Kim c, Jeonghwan Lee a,n a Department of Energy and Resources Engineering, College of Engineering, Chonnam National University, 77 Yongbong-ro, Buk-gu, Gwangju 500-757, Republic of Korea b Petroleum and Marine Research Division, Korea Institute of Geoscience and Mineral Resources, Daejeon 305-350, Republic of Korea c Research and Development Division, Korea Gas Corporation, 638-1, Il-dong, Sangrok-gu, Ansan, Gyeonggi-do 426-860, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 3 August 2013 Received in revised form 3 August 2015 Accepted 29 January 2016 Available online 30 January 2016
This study proposes a new apparatus which can simultaneously measure the physical properties such as low-permeability and porosity in a tight gas reservoir. The apparatus can also measure bi-directional permeability efficiently. The measurement of bi-directional permeability is designed in consideration of flow direction which can cause different results by heterogeneity. Using the apparatus, the experiments have been carried out to measure the low-permeability and porosity of three tight sand core samples which are from Gyeongsang sedimentary basin in Korea. As the results, the porosity ranges from 5.63% to 11% and the permeability measured in forward and reverse direction is 0.0004 md and 0.0005 md for TS1, 0.0007 md and 0.0011 md for TS-2, and 0.0062 md and 0.007 md for TS-3, respectively. To investigate the effect of geological characteristics inside core sample on rock properties, X-ray scan of the core samples was taken by Microfocus X-ray CT. Obviously, the value of permeability and porosity are subject to geological features such as micro-crack. This means that the micro-crack plays an important factor in terms of permeability variation by its direction and length in a tight gas reservoir. For verification of measurement accuracy, regression analysis was carried out using the dimensionless pseudo-pressure between the measured data and analytical model. As the results, it is shown that both are approximately equal in terms of permeability and porosity. & 2016 Elsevier B.V. All rights reserved.
Keywords: Tight gas Low-permeability Porosity Pulse-decay measurements X-ray scan
1. Introduction For successful development of a conventional and unconventional reservoir, it is necessary to maximize production by analyzing the flow characteristic and reservoir property. In case of tight gas reservoir, however, permeability is lower than 1 md (Rezaee et al., 2012; Gai et al., 2015), experiments spend a lot of time and show inaccurate results. Pulse-decay measurements using a gas or liquid are effective for determining the permeability of rocks in the range from 0.1 md to 0.01 μd (Jones, 1997). The pulse-decay measurements for determining the permeability of homogeneous cores has been the primary application of pressure transient test. The method explains that the core is confined in a cell and upstream and downstream reservoirs are attached to both ends. The upstream reservoir is pressurized and then allowed to make core and the downstream reservoir in same condition. The pressure and time behavior of the reservoirs are measured and used with analytical solutions to calculate n
Corresponding author. E-mail address: [email protected] (J. Lee).
http://dx.doi.org/10.1016/j.petrol.2016.01.037 0920-4105/& 2016 Elsevier B.V. All rights reserved.
permeability. The general solutions for the pressure difference as a function of time were presented by Dicker and Smits (1988) following the original work of Brace et al. (1968) and error function solution and general analytical solution were presented as well by Bourbie and Walls (1982) and Hsieh et al. (1981) respectively. Compressive storage of the rock sample in development of the analytical equations describing a pulse-decay process was neglected by Brace et al. (1968). Determining the permeability using the assumption can create an error. To minimize the error, the study proposed to use enough the reservoirs to exceed the storage in the rock sample. However, the use of large reservoirs causes a restriction in terms of design and leads to a long test time. A significant advantage of Brace et al.'s theory is that permeability can be calculated directly from linear portion of the solution. Several investigators tried to maintain the feature of the theory while including the assumption that core compressive storage is negligible by analyzing different portions of the pressure and time history of the reservoirs with particular combinations of reservoir size, either very large upstream with very small downstream (Bourbie and Walls, 1982; Chen and Stagg, 1984) or very small upstream with very large downstream (Amaefule et al., 1986; Maini and Okazawa, 1986; Kwan et al., 1988). Hsieh et al. (1981)
2
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Nomenclature
A a b cg cgp cpv ct cvd cvu k L P Pd Pu t ta
cross-sectional area of cylindrical core, ft2 volume ratio between upstream reservoir and pore volume ratio between downstream reservoir and pore gas compressibility, psia 1 gas compressibility at initial pore pressure, psi 1 compressibility of sample’s pore volume, psi 1 total compressibility, psi 1 compressibility of downstream reservoir, psi 1 compressibility of upstream reservoir, psi 1 permeability, md length of cylindrical sample, in. pressure, psia pressure in downstream reservoir, psia pressure in upstream reservoir, psia time, s adjusted pseudo-time, s
presented a general analytical solution that accounts for the compressive storage of the rock sample and was valid for all combinations of reservoir size. In the study, however, it takes a long time to set an initial condition of core sample with lowpermeability because the injected gas was flowed in one direction. The main focus of this study is to develop a new apparatus to simultaneously measure low-permeability and porosity, which can reduce total testing time and measure bi-directional permeability efficiently. Using the apparatus, permeability and porosity of tight sand core have been measured and its accuracy has been verified with an analytical model.
2. Experimental setup and procedure 2.1. Experimental apparatus Conceptual schematic of the Low-Permeability Measurement Apparatus (LPMA) is based on pulse-decay measurements as shown in Fig. 1. The study examines the tight gas formation and measurement method for permeability and porosity in the tight sand. The experimental apparatus was designed and set up to conduct a study on tight gas reservoir. The apparatus was composed of core holder, syringe pump, vacuum pump, hand pump, pressure generator, incubator, control box, and acquisition system (Fig. 2). The core holder, which is a main part of the system, was made of 304 SUS material so that it endures high pressure. Inlet and
Vb Vd Vp Vu Z α β γ θn μ ϕ ψ ψd
ψp ψu
bulk volume of core plug, ft3 downstream reservoir volume, ft3 pore volume of core plug, ft3 upstream reservoir volume, ft3 gas compressibility factor dimensionless group defined by Eq. (15) dimensionless group defined by Eq. (16) dimensionless group defined by Eq. (17) the nth roots of Eq. (4), rad gas viscosity, cp porosity of sample, fraction pseudo-pressure, psia2/cp pseudo-pressure evaluated at downstream pressure, psia2/cp pseudo-pressure, evaluated at maximum (pulse) pressure, psia2/cp pseudo-pressure evaluated at upstream pressure, psia2/cp
outlet of the core are hold by end plugs and lateral face of the core is fixed by viton sleeve with confining pressure, which allows the flow direction only in an axial direction. Including the core-in and core-out sections, there are two pairs of sensors, and each pair consists of one pressure transmitter (PT) port and one resistance temperature detector (RTD) sensor. To generate pressure pulse, high pressure generator was installed, which can handle 60 mL/ stroke. The experimental apparatus is covered with an incubator so that the injected gas can be maintained in constant temperature. Nitrogen gas of 99.95% purity was used in this experiment. Gas is injected from the gas cylinder to the core using a syringe pump. Data acquisition system continuously records all the information such as overburden pressure, temperature and pressure difference between upstream and downstream as the experiment is conducted. The cores used in this experiment are tight core samples which have length of 45 mm and diameter of 38.1 mm. 2.2. Key features of the LPMA The LPMA is similar to conventional setup, but contains two changeable cells and two mass flowmeters. The changeable cells, which are comprised of cells of various sizes, can function as manually changing upstream and downstream reservoirs volume to minimize an error in the determining permeability and porosity. These are installed so that upstream and downstream reservoirs size is adjusted according to the pore volume of core. When large cells are used, response of heterogeneous cores may even appear like homogeneous ones. When compressive storage in the cells is
Fig. 1. Schematic diagram of experimental apparatus.
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 2. Photograph of low-permeability measurement apparatus.
Fig. 3. Flow chart of experimental procedure.
3
4
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 4. Geological map of Gyeongsang Basin. Table 1 The experimental results of the tight sand cores in Gyeongsang basin. Samples
TS-1 TS-2 TS-3
Initial equilibrium time (h)
Pulse decay testing time (h)
Conventional injection
Bi-directional injection
84 48 4.5
44 25 3
14 8 1
Permeability (md) Forward
Reverse
0.0004 0.0007 0.0062
0.0005 0.0011 0.0070
Porosity (%)
11.5 6.80 5.63
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
5
Fig. 7. Experimental pressure responses of sample TS-3.
Fig. 5. Experimental pressure responses of sample TS-1.
which result in a significant reduction for experiment time and error. 2.3. Experimental procedure. The measurement procedures of porosity and permeability consists of the following steps (Fig. 3): (1) The sample is mounted into the core holder and desired confining stress is set (1500 psia); (2) Initial equilibrium pressure on sample is set (more than 1000 psia) to make a pseudo-pressure condition through a bi-directional gas injection; (3) Equilibrium pressure can be identified by the mass flowmeters (a flow rate equal to zero between upstream and downstream reservoirs); (4) Pressure pulse (approximately 30 psia) is generated in upstream reservoir; (5) The experimental gas is flowed in forward direction until the final equilibrium pressure is reached; (6) Change the role of upstream and downstream reservoirs using a bypass-line; (7) The experimental gas then flowed in reverse direction until the final equilibrium pressure is established. The pressure and temperature data, which allows us to interactively calculate porosity and permeability by choosing the appropriate data, are collected and monitored by data acquisition system. Fig. 6. Experimental pressure responses of sample TS-2.
of the same order or smaller than the compressive storage in the core sample, deviations from the homogeneous core response can be accentuated. The bypass-line is meant to reduce the total testing time and measure the bi-directional permeability at once. For example, when gas is injected into the core to set the initial condition, the demanding time is decreased through a bi-directional gas injection. The mass flowmeters are located at both ends of core holder. As the use of the mass flowmeters, we can detect the apparatus is set to initial condition. Additionally, if the permeability is measured by reverse direction, all procedure should be repeated again. However, after measuring the permeability of forward direction, the LPMA can change the role of upstream and downstream reservoirs using a bypass-line. The measurement of bi-directional permeability is designed in consideration of flow direction of fluid which can cause different results. These considerations suggest changes in both apparatus and procedure,
3. Determination of rock properties 3.1. Permeability The dimensionless differential pressure ( ΔPD ) between the upstream and downstream reservoirs is defined as:
ΔPD =
Pu (t ) − Pd (t ) Pu (0) − Pd (0)
(1)
If the experiment only involves very small change in pressure (i.e. o5%), the experimental dimensionless differential pressure at larger time becomes a single exponential function of time and can be approximated as (Dicker and Smits, 1988; Jones, 1997):
ln (ΔpD ) = ln (f0 ) + s1t where f0 is a constant and s1 is
(2)
6
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 8. Microfocus X-ray CT images of sample TS-1.
s1 = −
kf1 A (1/Vu + 1/Vd ) μLcg
(3)
where f1 = θ12/(a + b), θ1, the first solution of the transcendental equation, is
tan θ =
(a + b) θ θ 2 − ab
(4)
a and b , the ratio of the compressive storage of the sample's pore volume to that of the upstream and downstream reservoirs, respectively, are
a=
Vp (cg + cpv ) VP (cg + cpv ) and b = Vu (cg + cvu ) Vd (cg + cvd )
(5)
where cpv , cvu and cvd could be neglected because this factors were very smaller than cg . Using the experimental pulse-decay data, the slope ( s1) can be obtained by linear curve fitting. Then, permeability of the sample can be determined by simple rearrangement of Eq. (3):
k=
−s1μLcg f1 A (1/Vu + 1/Vd )
(6)
3.2. Porosity Boyle's Law and Gas Equation of State were used to determine porosity. For fully saturated core, gas was injected to downstream through tight core using a syringe pump. At that time, P1 and P2 are
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
7
Fig. 9. Microfocus X-ray CT images of sample TS-2.
pressure of the syringe pump before and after injection respectively. Also, V1 is volume of the syringe pump container before injection. V2 is the injected gas volume to tight core from a syringe pump.
P2 (V1 + V2 + Vp − Vb ) P1V1 = Z2 n2 RT2 Z1n1RT1
(7)
Then, the porosity of the sample can be determined with simple equation as:
ϕ = Vp/Vb
0.1 md to 0.01 μd. With the low-permeability, leak-tightness of the apparatus is of ultimate importance, and strict temperature control is critical as well (Haskett et al., 1988). Three sets of sample (TS-1, 2, and 3) from the Gyeongsang sedimentary basin in Korea were tested using the LPMA. Gyeongsang basin is the largest Cretaceous non-marine sedimentary basin in Korea and it is located in the southeastern part of the Korea (Fig. 4). The diameter and length of the samples are 38.1 mm and 45 mm respectively. 4.1. 1 Experimental results
(8)
4. Results and discussion The pulse-decay measurements using a gas or liquid are effective for determining the permeability of rock in the range from
The experimental results of three core samples are summarized in Table 1. To set initial pressure, equilibrium time takes about 84 h, 48 h, and 4.5 h for sample TS-1, TS-2, and TS-3 through conventional injection method, respectively. In other hand, the bidirectional injection spends 44 h, 25 h, and 3 h for each sample. Comparing to previous measurements, the apparatus reduces the time by approximately half until setting the initial condition of the
8
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 10. Microfocus X-ray CT images of sample TS-3.
core sample. The maximum of pulse-decay test takes about 14 h in sample TS-1. In case of sample TS-2 and TS-3, the measurements of porosity and bi-directional permeability take about 8 h and 1 h to complete respectively. The porosity ranges from 5.63% to 11% and the permeability measured in forward and reverse direction is 0.0004 md and 0.0005 md for TS-1, 0.0007 md and 0.0011 md for TS-2, and 0.0062 md and 0.007 md for TS-3, respectively. From the results, the differences due to heterogeneity of the core samples revealed as 0.0001 md, 0.0004 md, and 0.0008 md. Figs. 5–7 show the pressure behavior for TS-1, TS-2, and TS-3. The figures show that the pressure responses are different according to the forward and reverse directions. It is evident that each sample follows its own unique path of pore volume with direction although samples from the same set are of the same formation. For analysis of correlation among micro-crack, geological characteristic, and property, X-ray scan of a tight sand core is taken by Microfocus X-ray CT (SMX-225 CT). As the result, in case of TS-1, porosity is bigger than other so that samples the CT images show
that tight sand is alternated with sandstone (Fig. 8). However, micro-crack in the images of cross and plane section were undiscovered. Mostly, when the experimental gas flows in the sample, it moves through the easy route such as fracture. The reason why TS-1 has low-permeability is explained by comparison with other samples. In other samples, micro-crack was discovered in the lower surface of TS-2 and TS-3 as shown in Figs. 9 and 10. In case of TS-3, especially, its permeability is the highest among the three samples as micro-crack was larger than other samples. Therefore, it is shown that the micro-crack improves the permeability. This means that the micro-crack plays an important factor in terms of permeability variation by its direction and length in a tight gas reservoir. 4.2. Validation The measurements and its accuracy from the experimental equipment could be verified by comparison to analytical model.
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
9
Fig. 11. Comparison of experimental data on sample TS-1 to analytical model.
For the verification of measurement accuracy, Haskett et al.'s analytical model was used. The derivation of the final solution is analogous to the derivation presented by Hsieh et al. (1981). The linear flow of liquid in porous media can be described with
The equations were solved for dimensionless pseudo-pressure and adjusted pseudo-time for both the upstream and downstream reservoir volumes
∂ ⎡ P ∂P ⎤ ϕct ⎡ P ∂P ⎤ ⎢ ⎥= ⎢ ⎥ ∂x ⎣ μZ ∂x ⎦ k ⎣ Z ∂t ⎦
Ψu 1 = +2 Ψp 1+β+γ
(9)
For the flow of gas, Eq. (9) is not linear because μ and ct are functions of pressure. For gas flow, Eq. (9) can be linearized through the use of dimensionless pseudo-pressure (DPP) and adjusted pseudo-time
∂ ⎡ ∂Ψ ⎤ μ φct ⎡ ∂Ψ ⎤ ⎢ ⎥ ⎢ ⎥= ∂x ⎣ ∂x ⎦ k ⎣ ∂ta ⎦
(10)
Pseudo-pressure is defined as
Ψ=2
∫p
p 0
P dP μZ
And, adjusted pseudo-time is defined as
ta = μ ct
∫0
t
dt μct
Ψd 1 = +2 Ψp 1+β+γ
(13)
∞
2
e (−αθ n ) (β + γ 2θ n2/β ) ⎡ 2 4 2 ⎤ 2 2 2 2 n = 1 ⎣ γ θ n /β + (γ β + γ + γ + β ) θ n /β + (β + γβ + β ) ⎦ cosθ n
∑
(14)
For the downstream reservoir volume, where θn 's are the roots of the Eq. (4) and
kta 94, 812L2μ ϕct
(15)
and
β= (12)
2
e (−αθ n ) (β + γ 2θ n2/β ) ⎡ γ 2θ 4 /β 2 + (γ 2β + γ 2 + γ + β ) θ 2/β + (β 2 + γβ + β ) ⎤ n n n =1 ⎣ ⎦
For the upstream reservoir volume, and
α=
(11)
∞
∑
ALϕct Vu cgp
and
(16)
10
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
Fig. 14. Comparison of experimental data on sample TS-2 to analytical model. Fig. 12. Regression analysis of dimensionless pseudo-pressure for sample TS-1 in upstream reservoir.
Fig. 13. Regression analysis of dimensionless pseudo-pressure for sample TS-1 in downstream reservoir.
γ=
Vd Vu
(17)
The terms Ψu/Ψp and Ψd/Ψp are the upstream and downstream dimensionless pseudo-pressures, respectively. The calculated pressure from the analytical model was compared with the experimental results by pressure transient matching. The measured pressure data are converted to dimensionless pseudo-pressure with Eq. (11) and nondimensionalized by dividing the initial pseudo-pressure of the upstream reservoir. Time is converted to adjusted pseudo-time with Eq. (12). In the matching process, there are only two unknowns: porosity and permeability. All other parameters including upstream and downstream reservoir
Fig. 15. Regression analysis of dimensionless pseudo-pressure for sample TS-2 in upstream reservoir.
volumes, core dimensions, and fluid properties are known. As shown in Figs. 11, 14 and 17, the pressure transient is analyzed by matching the measured data to the analytical model. These results illustrate the accuracy and validity of experimental results obtained from the LPMA. A regression analysis of dimensionless pseudo-pressure by two methods for tight samples is shown in Figs. 12, 13, 15, 16, 18 and 19. As the result of a regression analysis, the values of correlation coefficient range from 0.96 to 0.99 in upstream and downstream reservoirs. From the result of a comparative analysis between analytical model and experiment results, it is found that both are approximately equal in terms of permeability and porosity.
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
11
Fig. 16. Regression analysis of dimensionless pseudo-pressure for sample TS-2 in downstream reservoir.
Fig. 18. Regression analysis of dimensionless pseudo-pressure for sample TS-3 in upstream reservoir.
Fig. 17. Comparison of experimental data on sample TS-3 to analytical model.
Fig. 19. Regression analysis of dimensionless pseudo-pressure for sample TS-3 in downstream reservoir.
5. Conclusions The experimental apparatus has been designed and set up so that low-permeability and porosity could be measured in unconventional gas reservoir such as tight gas reservoir. The experiments have been carried out to measure the low-permeability and porosity of tight core sample and to verify the accuracy of the measurement. From the result, the following conclusions have been drawn: (1) The new apparatus which is called LPMA has been developed to simultaneously measure the low-permeability and porosity. The LPMA can reduce the time by approximately half until
setting to initial condition of the core sample and efficiently measure the bi-directional permeability. (2) As the measurements, the porosity ranges from 5.63% to 11% and the permeability measured in forward and reverse direction is 0.0004 md and 0.0005 md for TS-1, 0.0007 md and 0.0011 md for TS-2, and 0.0062 md and 0.007 md for TS-3, respectively. (3) The differences due to heterogeneity of the core samples revealed as 0.0001 md, 0.0004 md, and 0.0008 md. It is evident that each sample follows its own unique path of pore volume with measurement direction although samples from the same set are of the same formation. (4) The X-ray scan of tight sand core samples was taken by Microfocus X-ray CT to investigate the effects of a micro-crack
12
H. Jang et al. / Journal of Petroleum Science and Engineering 142 (2016) 1–12
and geological characteristics inside core sample on rock properties. As the results, it is shown that the micro-crack plays an important factor in terms of permeability variation by its direction and length in a tight gas reservoir. (5) Comparative analysis between the experimental results and analytical model was performed to verify the accuracy of measurement. From the results, it is found that both are approximately equal in terms of permeability and porosity. Therefore, the LPMA can be efficiently applied to measure the rock properties of unconventional gas reservoir such as tight sand and shale gas.
Acknowledgments This work was supported by the Energy Efficiency and Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy (2011201030001B).
References Amaefule, J.O., Wolfe, K., Walls, J.D., Ajufo, A.O., 1986. Laboratory Determination of Effective Liquid Permeability in Low-Quality Reservoir Rocks by the Pulse Decay
Technique. SPE Paper 15149. SPE California Regional Meeting, Oakland, California, 2–4 April, 1986. Bourbie, T., Walls, J., 1982. Pulse decay permeability: analytical solution and experimental test. Soc. Pet. Eng. J. 22, 719–721. Brace, W.F., Walsh, J.B., Frangos, W.T., 1968. Permeability of granite under high pressure. J. Geophys. Res. 73, 2225. Chen, T., Stagg, P.W., 1984. Semilog analysis of the pulse decay technique of permeability measurement. Soc. Pet. Eng. J. 24, 639–642. Dicker, A.I., Smits, R.M., 1988. A practical approach for determining permeability from laboratory pressure pulse decay measurement. SPE Paper 17578. Presented at the SPE International Meeting in Petroleum Engineering. Tianjin, China, 1–4 November, 1988. Gai, S.H., Liu, H.Q., He, S.L., Lei, G., Mo, S.Y., Huang, X., Yang, Y., Chen, X., 2015. An improved particles model for stress sensitivity in low-permeability sandstones. Geosyst. Eng. 19 (2), 89–95. Haskett, S.E., Narahara, G.M., Holditch, S.A., 1988. A method for simultaneous determination of permeability and porosity in low permeability cores. Soc. Pet. Eng. Form. Eval. 3 (3), 651–658. Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E., 1981. A transient laboratory method for determining the hydraulic properties of tight rocks: I. Theory. Int. J. Rock Mech. Min. Sci. 18, 245–252. Jones, S.C., 1997. A technique for faster pulse-decay permeability measurement in tight rocks. Soc. Pet. Eng. Reserv. Eval. Eng. 12, 19–25. Kwan, M.Y., Okazawa, T., Fortier, R.A., 1988. Application of the Pulse-Decay Technique to the Measurement of Heavy Oil Core Fluid Mobilities and Porosity. J. Can. Pet. Technol. 27 (5), 92–98. Maini, B.B., Okazawa, T., 1986. On the use of pulse technique for minimizing damage during core tests in heavy oil system. Paper CIM 86-37-79 Presented at the 1986 Annual Technical Meeting of the Pet. Soc. Of CIM, Calgary, June 8–11, 1986. Rezaee, R., Saeedi, A., Clennell, B., 2012. Tight gas sands permeability estimation from mercury injection capillary pressure and nuclear magnetic resonance data. J. Pet. Sci. Eng. 88–89, 92–99.