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Experimental Study on Spontaneous Imbibition under Confining Pressure in Tight Sandstone Cores Based on Low-Field Nuclear Magnetic Resonance Measurements Yun Jiang, Yang Shi, Guoqing Xu, Chen Jia, Zhan Meng, Xianyou Yang, Hanqing Zhu, and Bin Ding Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03776 • Publication Date (Web): 14 Feb 2018 Downloaded from http://pubs.acs.org on February 14, 2018
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Experimental Study on Spontaneous Imbibition under Confining Pressure in Tight Sandstone Cores Based on Low-Field Nuclear Magnetic Resonance Measurements
5
Yun Jiang†, Yang Shi†, Guoqing Xu†, Chen Jia†, Zhan Meng†, Xianyou Yang†,
6
Hanqing Zhu† and Bin Ding*†
1 2 3
†
8
Research Institute of Petroleum Exploration & Development, PetroChina, Beijing 100083, P.R. China
9
ABSTRACT: Spontaneous imbibition (SI) is an important method to improve oil recovery in tight
10
sandstone reservoirs. Commonly, the physical simulation of SI is performed at atmospheric pressure
11
but the characteristics of spontaneous imbibition under confining pressure (SIUCP) is often
12
neglected. In this study, oil distribution in tight cores was obtained in combination of high pressure
13
mercury intrusion (HPMI) measurements and low-field nuclear magnetic (LF-NMR) measurements.
14
After that, oil recovery for SI and SIUCP of tight core samples with all faces open (AFO) were
15
obtained using LF-NMR measurements. Finally, a new scaling law for SIUCP was proposed to
16
predict shut-in time in field scale. The results showed that 95.94 - 98.12 wt% of the oil was
17
distributed in nano-pores (0.1 ms < T2 < 100 ms) of core samples, and the average amount of oil in
18
nano-micro-pores, nano-meso-pores and nano-macro-pores were 34.04 wt%, 40.15 wt% and 22.75
19
wt%, respectively. Ultimate oil recovery forcore samples were 22.41 wt%, 44.41 wt%, 57.27 wt%,
20
61.84 wt % and 62.82 wt%, respectively, as confining pressure increased from 0 psi to 2175 psi. The
21
improved oil recovery for SIUCP was associated with the decline of effective pore radius as a
22
function of confining pressure, which results in the effect of enhanced SI and compaction. Finally, a
23
modified dimensionless time model was proposed in combination of Mason’s dimensionless time
7
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model and effective pore radius as a function confining pressure.
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KEYWORDS: LF-NMR; oil distribution; oil recovery for SIUCP; effective pore radius;
26
dimensionless time model;
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1. INTRODUCTION
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Tight reservoir in Ordos Basin is characterized with ultralow permeability (less than 1 mD),
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porosity (less than 10%) and narrow flow channels (abundant nano-micro pores) 1. A series of
30
problems, including low formation pressure coefficient (0.6-0.8), fast decline of production and
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low oil recovery, are difficult to solve. One effective method to economically produce oil and gas
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is hydraulic fracturing stimulation, which is completed by injecting massive fracturing fluid to
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create complex fracture networks, to increase contact area with reservoirs and to improve pressure
34
coefficient of reservoirs2. After hydraulic fracturing, the well is commonly shut down for a period
35
to promote water uptake into shale/sandstone rocks, which has been proved to be a driving force
36
for enhanced oil recovery, especially for water wet reservoirs3-8. In several simulation studies,
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extended shut-in time might contribute to early-time production but decrease load recovery and
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late-time production9-11. Appropriated shut-in time becomes critical for understanding enhanced
39
oil recovery from water imbibition.
40
Qing. L et al.12 calculated shut-in time in field scale based on Ma’s dimensionless time (tD)
41
model 13, 14 and SI experiments of Horn River shale samples with AFO. B. Roychaudhuri et al. and
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K. Makhanov et al.15, 16 provided references for determining shut-in time by calculating water loss
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in both lab scale (SI of Marcellus shale samples and Horn River shale samples, respectively) and
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field scale (similarity criterion). In their studies, experiments of SI in lab scale were performed at
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atmospheric pressure and the corresponding scaling law considering confining pressure was
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neglected.
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One of the main difficulties in simulating SIUCP of tight cores is to record the amount of
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imbibed fluid since the cores are set in the closed and pressurized system and the imbibed amount
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is always limited. In SIUCP measurements, big error may occur by monitoring imbibed fluid
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volume using an Amott imbibition cell17 or weighting the core mass using a precision balance18.
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LF-NMR T2 distribution is a fast and non-destructive method to measure fluid distribution in
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pores and to provide information for pore size distribution (PSD) combined with HPMI
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measurements19-23. Furthermore, T2 distribution was also used to monitor uptake of liquid in shale
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samples and tight sandstone samples24, 25. Scaling equations for SI have been proposed in different
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forms based on capillary models26, 27, Buckley–Leverett equations13, 28-30. On the basis of these
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theoretical equations, factors influencing SI including viscosity ratios, initial water saturation,
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gravity, wettability, boundary conditions and tortuosity were discussed5,
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dimensionless time model considering the effect of confining pressure has not been presented.
7, 8, 31-35
. However,
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Gas flow in tight cores is usually affected by gas slippage effects as effective pore radius is
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ten times larger than the mean free path length of gas molecules. Then gas slippage factor and
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corresponding pore radius can be calculated according to Klinkenberg procedure36. As confining
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pressure increases, a series of parameters including porosity, permeability and pore radius, etc. are
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influenced, which is related to stress sensitivity phenomenon37-39.
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The objective of this study is to study the characteristics of SIUCP and construct a new
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scaling law for SIUCP. This study consisted of three sections. In the first section, PSD of core
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samples selected form Ordos Basin was obtained by combining HPMI and LF-NMR
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measurements and then oil distribution in tight cores was discussed. In the second section,
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recovery of SIUCP based on LF-NMR T2 distribution measurements was obtained and the result
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was compared with SI. Finally, a new scaling law for SPUCP based on Mason’s dimensionless
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time model32 was proposed to provide reference for calculating shut-in time in field scale.
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2. MATERIALS
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2.1. Core samples.
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Tight sandstone core samples were taken from Upper Triassic Yanchang formation in Ordos
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Basin, China. Core plugs (3-7 cm in length and 2.5 cm in diameter) were cut from larger materials
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and the fragments collected during cutting process were used for X-ray diffraction (XRD)
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analysis.
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The core samples were cleaned by exposing them to alternating vapor of toluene and
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methanol for 30 days to remove all residual oil in the core samples, and then dried under vacuum
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at 105 °C for 48 hours prior to measurements. Effective porosity was determined using a helium
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porosimeter and oil saturation method (measuring difference between oil saturated weight and dry
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weight), respectively. Helium gas permeability was determined using a pulse-decay permeametry,
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which was conducted at net confining pressure of 300 psi at 20 ºC.
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Permeability and porosity may differ significantly among tight cores as they are abundant
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with micro and nano pores. In this study, core samples with similar physical properties were
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carefully classified so that the effect of difference of permeability and porosity on imbibition can
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be minimized. More specifically, the prepared cores were classified into three sets (Table 1). Every
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core sample in the first set was cut into two slices and then all the cores were divided into two
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groups. They were used for HPMI measurements (A11, A12, A13, A14 and A15) and SIUCP
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measurements (A21, A22, A23, A24 and A25). Core samples used for SIUCP measurements were
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vacuumed at 20 to 50 mbar for 2 days and then saturated with oil at confining pressure of 4000 psi
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for 5 days prior to measurements. After that, they were equilibrated to 0 psi which lasted for 24
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hours. Similarly, core samples in the second set were also cut and divided into two groups and
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they were used for contact angle (CA) measurements (B11, B12 and B13) and oil mass calibration
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(OMC) measurements (B21, B22 and B23). The core samples used for OMC measurements were
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also saturated with oil (the step was same as core samples used for SIUCP measurements) prior to
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measurements. The last set of core samples (A1, A2, A3 and A4) were used to determine
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pulse-decay permeability (PDP), gas slippage factor and effective pore radius at different range of
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net confining pressures using a pulse-decay permeametry.
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2.2. Fluid properties.
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Oil (No.3 Jet Kerosene), purchased from Beijing Unicorn Company Limited, with a purity of
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99% was used in oil-saturation process. Deionized (DI) water, purchased from Cambridge Isotope
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Laboratories, with a purity of 99.9% was used in imbibition measurements. The physicochemical
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properties of the fluids used for imbibition experiments were listed in Table 2.
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3. METHODS
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3.1. XRD analysis.
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Bulk and clay mineralogies of core samples were investigated using an X’Pert X-ray
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diffractometer. The experimental procedure was following the Chinese Oil and Gas Industry
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Standard SY/T5163-2010 (Analysis Method for Clay minerals and Ordinary Non-clay Minerals in
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Sedimentary Rocks by the X-ray diffraction).
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3.2. HPMI measurements.
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PSD was determined using a mercury porosimeter (AutoPore IV 9520). Core samples were
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dried at 200 °C to remove all the water prior to measurements. After that, mercury was injected by
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applying uniform level of pressure, ranging from atmospheric pressure to 60,000 psi. PSD was
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calculated using Washburn’s equation26 based on the assumption of a bundle of connected
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capillary tubes.
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3.3. LF-NMR measurements.
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LF-NMR signal was measured using inversion and Carr-Purcell-Meiboom-Gill (CPMG)
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pulse sequences. T2 distributions was generated using SIRT (Simultaneous Iterative
119
Reconstruction Technique) inversion algorithms. The measurements were performed using a
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LF-NMR core analysis system (MesoMR-060H-HTHP-I) with a magnetic field intensity of 0.5 T.
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The major testing parameters included dominant frequency (21.326 MHz), echo spacing (TE = 0.2
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ms), polarization time (TW = 3000 ms) and echo number (NECH = 8000).
123 124
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LF-NMR transverse relaxation time (T2) in porous media is generally governed using the following equation:
1 1 1 1 = + + T2 T2,bulk T2,surface T2,diffusion
(1)
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Where the subscript “bulk”, “surface” and “diffusion” indicate bulk relaxation, surface
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relaxation and diffusion relaxation, respectively. Diffusion relaxation can be neglected when
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assuming a uniform magnetic field and a small field gradient. Moreover, bulk relaxation can also
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be neglected compared with surface-relaxation (bulk is commonly larger than 3000 ms). Thus, T2
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can be converted into pore size in the following equation:
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S C 1 1 = =ρ =ρ T2 T2, surface V R
(2)
Where, S is core surface area, cm2; V is pore volume, cm3; R is pore radius, µm; C is a
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constant parameter, C=1, 2 or 3 for planar, cylindrical and spherical model, respectively. ρ is
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surface relaxivity, which can be calculated by combining HPMI and LF-NMR measurements
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using the following equation40:
ρ=
136
T2 LM × Rp
(3)
C 200
∑ ln(T
2i
T2LM = exp(
137
) × Ai
i =1
200
∑A
)
(4)
i
i =1
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Rp =
139
2V A
(5)
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Where ρ is surface relaxivity, µm/ms; T2LM is the logarithmic mean value of T2 , ms; Ai is
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amplitude of LF-NMR T2 distribution spectrum at T2i, a.u.; Rp is average pore radius, µm; V is
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total intrusion volume, mL/g; A is total pore area, m2/g;
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3.4. CA measurements.
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CA measurement is the most widely used method to determine wettability between a single
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phase and a core sample. In this study, a sessile drop method using an automated goniometer
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(Drop shape analyzer, DSA-100) was performed to measure CA41. Prior to measurements, core
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samples were polished with 600-mesh diamond polisher and then aged in oil for at least 100 h at
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80 °C. After that, the core samples were dried in an oven at 80 °C for 20 min. After that, the core
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sample was set on the goniometer and a drop (10 - 20 µL) of DI water was dripped on the surface
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of it. Finally, the contact angle was calculated from a camera screenshot.
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3.5. OMC measurements.
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When the core sample is saturated with oil and DI water, LN-NMR T2 signal can reflect the
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statistical distribution of oil in pores as DI water has no response to hydrogen proton42-46. The
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integral area of T2 distribution along the axis of T2 is proportional to oil mass. Therefore, the main
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purpose of OMC is to transfer LF-NMR T2 signal into oil mass so that we can calculate oil mass
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in pores, especially initial oil mass. After that, oil recovery can be calculated and compared with
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previous studies. Moreover, overall T2 distribution is obtained using SIRT (Simultaneous Iterative
158
Reconstruction Technique) inversion algorithms which implies that the integral area of T2
159
distribution equals to the sum of amplitude of T2 distribution. Finally, a correlation between oil
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mass in pores and cumulative amplitude of T2 distribution can be built.
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Two methods were used for OMC in this study. The first method was to measure the T2
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cumulative amplitude of several bottles (without response to hydrogen proton) filled with different
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amount of oil (Figure 1a), and then the curve between T2 cumulative amplitude and oil mass was
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fitted. The second method was to measure T2 cumulative amplitude of tight core samples (Figure
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1b) before and after several centrifuge tests which were conducted to obtain a wide range of oil
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mass in pores to minimize the errors when using the fitting correlation to calculate oil mass. The
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oil mass was simultaneously measured using a precision balance (A & D GF-1000). The curve
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between T2 cumulative amplitude and oil mass was fitted. Centrifuge tests were performed using a
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high speed refrigerated centrifuge (CSC-12(S), Lu Xiangyi Centrifuge Company, Shanghai,
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China). The rotating speed were 3000 rpm, 4000rpm, 5000rpm, 6000rpm, 7000rpm, 8000rpm,
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respectively. Finally, oil mass was calculated using the following equation: 200
m = a + b ⋅ ∑ Ai
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(6)
i =1
Where m is oil mass in pores, g; Ai is amplitude of LF-NMR T2 distribution spectrum at T2i,
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a.u.;
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3.6. SI/ SIUCP measurements.
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SIUCP for oil-saturated core samples with all faces open (AFO) was simulated in a sealed
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and pressurized system (Figure 2). In the following, we briefly explained the experimental
178
procedure.
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(1) T2 distribution of oil-saturated the core samples was measured;
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(2) The core sample and 100 mL DI water were set in the floating piston accumulator, and
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valves in the upstream and downstream were kept open; (3) Distilled water was pumped to the bottom of floating piston accumulator continuously until all the gas in the accumulator was removed;
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(4) The valve in the upstream was closed and the ISCO pump started to work in the mode of
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constant pressure. The confining pressure in each accumulator was kept 0 psi, 362.5 psi,
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725 psi, 1450 psi and 2175 psi, respectively;
187 188 189 190
(5) Pressure in the accumulator was removed at selected time interval and the core sample was taken out; (6) Liquid in the surface of the core was dried with cotton yarn and then T2 distribution was measured;
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(7) Step 2 to 6 were repeated until the end of the experiment, which lasted for 25 days;
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(8) Oil recovery for SIUCP at different time interval was calculated using the following
193
194
195 196
equation:
Roil =
m0 − mi ×100% m0
(7)
Where Roil is oil recovery, %; m0 is oil mass in core samples before SI/ SIUCP measurements, g; mi is oil mass in pores measured for i th. time water at selected time, g;
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3.7. PDP measurements.
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PDP at different net confining pressures, ranging from 362.5 psi to 2175 psi, was measured
199
using a PDP system (PDP-200) at 20 ºC. Slippage factor was calculated from a linear regression
200
performed on the 1/Pp and PDP, which referred as Klinkenberg procedure. PDP, slippage factor
201
and effective pore radius were calculated using the following equations47:
ka =
202
αµ g Lcg 1 1 A( + ) Vu Vd
203
ka = k∞ (1 +
204
b= λ=
205
b ) Pp
4cλPp
r
µ
RgT π
Pp
2M
(8)
(9)
(10)
(11)
206
where ka is PDP, mD; α is slope of pressure decay curve in the semi-logarithmic plot; µg is
207
gas viscosity, mpa·s; cg is gas compressibility, psi-1; L is sample length, cm; A is sample cross
208
sectional area, cm2; Vu/d are upstream and downstream gas storage reservoirs volumes,
209
respectively, mL; k∞ is Klinkenberg gas permeability, mD; Pp is mean value of inlet pressure and
210
outlet pressure, psi; b is gas slippage factor, psi; λ is mean free path length of gas molecules, µm; c
211
is a constant parameter, in the order of 1; r is effective pore radius, µm; Rg is gas constant, J/K·mol;
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T is absolute temperature, K; M is molar mass of gas, mol-1;
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4. RESULTS
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4.1. Mineralogy.
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XRD analysis of bulk-rock mineralogy (Figure 3a) showed that twelve core samples mainly
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consisted of feldspar (42.0 - 53.3 wt%), quartz (28.1 - 33.9 wt%), and contained moderate amount
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of dolomite (11.0 - 15.0 wt%) and clays (10.8 - 17.2 wt%). Clay mineralogy (Figure 3b) of the
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core samples was categorized into three types: illite (9.2 - 18.5 wt%), chlorite (42.1 - 60.6%) and
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mixed layer illite/smectite (25.2 - 48.7 wt%).
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4.2. PSD.
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Pore diameter determined by HPMI (Figure 4a) was categorized into four groups, 1 - 10 nm,
222
10 - 100 nm, 100 - 1000 nm and > 1000 nm. According to pore size classification proposed by
223
Loucks48, nano-pores ranged from 1 nm to 1 µm and micro-pores ranged from 1 µm to 62.5 µm. In
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this study, average mercury intrusion saturation of nano-pores (Figure 4b) and micro-pores were
225
86.76 wt% and 13.24 wt%, respectively.
226
On the other hand, a wide range of T2 distribution (Figure 4b) was also observed
227
simultaneously, including ≤ 0.1 ms, 0.1 - 1 ms, 1 - 10 ms, 10 - 100 ms and ≥ 100 ms. The
228
correlation between T2 and pore radius can be built by calculating surface relaxivity using Eq.3 –
229
Eq.5.
230
The calculated surface relaxivity (Table 3) showed that surface relaxivity varied among core
231
samples with similar petrophysical properties, ranging from 2.75 µm/s to 10.68 µm/s. The result
232
was in accordance with Milad Saidian’s40 observation that a linear correlation (Eq. 11) between
233
surface relaxivity and illite content (Table 4) was satisfied. ρ = A × f illite + B
234 235 236
(12)
Where, ρ is surface relaxivity, µm/s; fillite is illite content, wt%; A, B are constant parameters, µm/s;
237
The calculated PSD using calculated relaxivity and measured HPMI PSD (Figure 5) showed
238
a good correlation with each other. Thus, using measured T2 distribution to obtain PSD is also an
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efficient method. The correlation between pore diameter and T2 can be roughly constructed in
240
Table 5.
241
4.3. CA.
242
E.J. Peters41 proposed that a system was defined as water-wet when CA was between 0 º to
243
60 º - 75 º. The system was defined as oil-wet when CA ranged from 105 º - 120 º to 180 º, and
244
neutral-wet was defined when CA was in the range of 75 º - 105 º. In this study, CA (Figure 6) was
245
22.7 º, 27.7 º and 25.8 º, respectively. Thus, the system was determined to be water-wet.
246
4.4. Oil mass calculation.
247
Two fitting curves (Figure 7) using different methods both showed strong positive linear
248
correlations between oil mass and T2 cumulative amplitude. But the calculated oil mass (Figure 8)
249
using method 2 was more close to authentic oil mass as the average error between calculated oil
250
mass and authentic oil mass was smaller (Table 6). Finally, the correlation between cumulative T2
251
distribution and oil mass was written as m = 0.125 × 10 × ∑ − 0.300 = 0.954
252
4.5. Oil recovery for SI and SIUCP.
253
Oil recovery with a wide range of imbibition time and different range of confining pressure was
254
obtained (Figure 9) through converting measured cumulative T2 distribution into oil mass using Eq.6 and
255
Eq.7. Clearly, oil recovery as a function imbibition time (Figure 9a) was divided into two phases for both
256
SI and SIUCP, each with its own slope. In phase 1, water uptake occurred rapidly and oil recovery
257
increased quickly with imbibition time. After that, little water was imbibed into core samples and oil
258
recovery tended to stabilize correspondingly. Two dash lines were placed on phase 1 and phase 2,
259
respectively, to represent for rate of water uptake. As confining pressure increased, the intersection of
260
two dash lines in the horizontal axis of Cartesian coordinate were 15 days, 10 days, 7 days, 5 days and 3
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days, respectively.
262
Similarly, oil recovery as a function of square root of imbibition time (Figure 9b) was also divided
263
into two phase. In phase 1, oil recovery for SIUCP was exponential to square root of imbibition time,
264
which was significantly from that of SI (linear correlation was observed). In phase 2, oil recovery for
265
both SI and SIUCP were linear to square root of imbibition time.
266
Furthermore, the ultimate oil recovery (Figure 10) as a function of confining pressure can also be
267
divided into two stages. Oil recovery increases significantly within confining pressure of 725 psi, and
268
then it slowly increased. The ultimate oil recovery for SIUCP enhanced by 21.98 wt%, 34.86 wt%, 39.43
269
wt% and 40.41 wt%, respectively, than that of SI.
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4.6. Gas slippage factor and effective pore radius.
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PDP measurements at different range of net confining pressure were performed on four tight core
272
samples, and then slippage factors were calculated from linear regression expressions. PDP as a function
273
of 1/Pp (reciprocal of mean value of inlet pressure and outlet pressure) of core sample C1 was plotted in
274
Figure 11 and results for three other core samples were obtained simultaneously. Gas slippage factor and
275
effective pore radius of four core samples were calculated and listed in Table 6.
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Effective pore radius as a function of net confining pressure was plotted in Figure 11. Clearly, the
277
drop of effective pore radius occurred in two different periods, each with its own distinct slope. It
278
decreased significantly in the first period with respect to net confining pressure, and then it slowly
279
decreased until it reaches a fixed value in the second period. The effective pore radius as a function of net
280
confining pressure can be expressed in the following equation:
281 282
r = 0.834 ⋅ exp( − P / 393.212) + 0.0792 Where, r is effective pore radius, µm; P is net confining pressure, psi.
ACS Paragon Plus Environment
(13)
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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5. DISCUSSION
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5.1. Oil distribution in tight cores.
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Oil distribution in the core sample was obtained according to measured T2 distribution (Figure 4b)
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before imbibition experiments. During the measurements of CPMG sequence, TE is required to bigger
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than 6*P2 (width of 180 degree radio frequency pulse). In this study, TE = 0.2 ms was optimized as the
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measured P2 was 24 µs. The optimized parameter may inevitably result in partially lost of authentic
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information from small pores less than T2=0.2 ms. In this study, the area of T2
