Simultaneous Measurement of Capillary Pressure and Dielectric Constant in Porous Media

Transcription

1 PIERS ONLINE, VOL. 3, NO. 4, Simultaneous Measurement of Capillary Pressure and Dielectric Constant in Porous Media W. J. Plug, L. M. Moreno, J. Bruining, and E. C. Slob Delft University of Technology, The Netherlands Abstract An experimental tool is presented with which the capillary pressure (P c ) and the dielectric constant (ε) of a porous medium are measured simultaneously. The equipment is designed to conduct measurements for the unconsolidated sand-distilled water-gas (CO 2 ) system for pressures up to 20 bar and constant temperature conditions. The bulk phase pressures of the gas and the water are measured at the top and bottom of the sample holder and we define the P c as the averaged pressure difference. The sample holder is a parallel plate capacitor with stainless steel plates, which also serve as support for the sample. The plates are kept separated by a plastic ring. A precision component analyzer is connected to the sample holder and measures the impedance as a function of frequency (f). The total impedance is directly related to the effective value of the complex permittivity. The aim of this paper is to describe the details and the calibration of the tool. The accuracy and the validity of both ε(s w ) and P c (S w ) are determined from reproducible data. Results are shown for a full capillary pressure cycle of drainage and imbibition at f = 3 MHz. DOI: /PIERS INTRODUCTION Both the capillary pressure and the electrical properties, e.g., the resistivity and the complex dielectric constant, can be expressed as function of the water saturation (S w ). These properties are used in subsurface flow engineering applications such as hydrocarbon production and soil remediation techniques. The electrical and capillary characteristics are used to determine the connate water saturation, resistivity logs, the height of the transition zone, monitoring of the remediation and to assist in modeling purposes [1]. In literature, numerous examples can be found which describe the hysteresis in capillary pressure. The term capillary hysteresis can be defined as the difference in capillary pressure value between drainage (decreasing S w ) and imbibition (increasing S w ). Hysteresis depends on the saturation history and can be ascribed to contact angle hysteresis [2], irreversible changes in pore-scale fluid distributions [3] and the interfacial area [4]. Experimental studies have shown that pore scale mechanisms have direct influence on several geophysical properties, such as the electrical resistivity and the dielectric constant [1, 5, 6]. In practice electromagnetic techniques become very popular. Therefore it is important to understand the relation of the dielectric properties with respect to the saturation history, the fluid saturation and the phase distribution. Knight and Nur [7] measured the dielectric constant of partially saturated sandstones in the frequency range of 60 khz to 4 MHz. They found that a coated water layer around the grains is the predominant reason for the dielectric response. Pronounced hysteresis effects in electrical resistivity are found by Longeron et al. [8] and Knight [9]. Both studies reported that the values during drainage process were higher than for imbibition process. Nguyen et al., [6] have measured the complex dielectric constant with the FDR technique for a water-wet sample during the drainage and imbibition cycle and found dielectric hysteresis. At S w < 0.6 the values of the permittivity for the imbibition is lower than those for the drainage. The opposite is found for S w > 0.6. The impact on surface interactions is explained by Knight and Abad [9]. In this study they concluded that the dielectric constant decreased when the sample altered from water-wet to oilwet. Similar results were obtained by Nguyen [10]. Combined measurements of capillary pressure and the dielectric constant, as found in the work of Nguyen and Longeron, provide important information to improve the interpretation of capillary hysteresis. Here we present a new method, with which the capillary pressure (P c ) and the dielectric constant (ε) of a porous medium are measured simultaneously. The capillary pressure is measured under quasi-static conditions using the set-up discussed by Plug et al., [11]. The sample holder is

2 PIERS ONLINE, VOL. 3, NO. 4, designed as a parallel plate capacitor, where the two stainless steel end-pieces act as electrodes. The advantage of this technique is that the sample remains intact during the measurements and the complex permittivity can be measured continuously as a function of the frequency. Calibration of the impedance tool is done using materials with known dielectric constants and the experimental technique is validated with reproducible data. 2. EXPERIMENTAL SET-UP 2.1. The Capillary Pressure Tool In this section we briefly describe the set-up that measures the capillary pressure as function of the water saturation under quasi-static conditions. The equipment, presented by Plug et al., [11], is based on the porous plate technique combined with the micro-pore membrane technique, discussed by Jennings et al., [12] and Longeron et al., [13]. A schematic diagram of the set-up is shown in Figure 1. Figure 1: Schematic lay-out of the experimental set-up. Figure 2: The sample-holder: 1. gas-inlet; 2. water-inlet; 3. stainless steel end piece 1; 4. stainless steel end piece 2; 5. PEEK ring; 6. porous medium; 7. Perforated plates; 8. SIPERM plates; 9. concentric grooves; 10. Water-wet filter; 11. O-rings (2.1 mm); 12. O-rings (4 mm); 13. Stainless steel bolts. Two syringe pumps (ISCO pump, 260D) are connected to the in- and outlet of the sample holder (see Figure 2) and can be set to a constant injection rate (accuracy of ml/h) or a constant pressure (accuracy ± 0.1 bar). The gas phase is injected (drainage) or produced (imbibition) at the top of the sample holder and the water is collected or injected at the bottom using the second

3 PIERS ONLINE, VOL. 3, NO. 4, (water) syringe pump. The gas pressure transducer (GPT) and the water pressure transducer (WPT) record the single phase pressures (range bar, accuracy ± 0.01 bar). The differential pressure between the gas and the water phase is measured by the pressure difference transducer (PDT, mbar, accuracy ± 0.1 mbar), which is placed at the middle of the sample, such that no correction for gravity effects is required. To maintain a constant temperature we cover the entire set-up with a Perspex box, sealed by polystyrene. We allow temperature equilibration for at least two days to ensure that the total set up is at equal temperature. The sample holder, see Figure 2, consists of a PEEK (Polyetheretherketone) ring which contains the unconsolidated sand sample. The height, H, of the sample is 27 mm and the diameter, D, is 84 mm. The grains are kept in place using a combination of plates at the top and bottom of the sample. At the bottom, two porous plates (SIPERM R, Cr-Ni-Steel basis) with a diameter of, D s,1 = 90 mm and D s,2 = 84 mm respectively, a permeability of m 2 and a porosity of 0.32, support the sample and protect the hydrophilic membrane (0.1 µm). Two stainless steel plates (D ss,1 = 90 mm and D ss,2 = 84 mm) both with 32 single perforations (D p = 5 mm) are used at the top directly above the sample in combination with a nylon filter with a pore size of 210 µm. To avoid leakage of gas or water over the hydrophilic membrane, we seal the outer perimeter with a rubber O-ring (thickness of 2.1 mm). Concentric flow grooves in the end-pieces redistribute the injected and produced phase over the total sample area to avoid preferential flow and fast breakthrough of the injected phase The Impedance Tool A precision component analyze (Precision Component Analyzer, 6640A) is connected to the sample holder and measures the impedance as a function of frequency (f). The analyzer supplies an AC potential difference of 990 mvac and the impedance and phase angle are measured. The total impedance is directly related to the effective value of the effective complex dielectric constant (ε) of the mixture of gas, water and grains. To measure correct values for the dielectric constant, the PEEK ring must separate the electrodes. In our design, the electrodes are the two end pieces (3 and 4, Figure 2), including the support plates (7 and 8, Figure 2). The PEEK material is nonconductive and the total sample holder will act as a parallel plate capacitor. As a result of this configuration a parallel circuit is established for the sample inside the PEEK ring and the PEEK ring itself. To keep the different parts of the sample holder together, 4 stainless steel bolts are used at the top and bottom of the sample holder. The placement of the bolts is such that no short-circuit for the electrical current occurs. To ensure total isolation of the sample holder, Teflon tubing are used for the in- and outlet. 3. CALIBRATION OF IMPEDANCE TOOL Different configurations of the sample holder are investigated to obtain the most accurate data for the dielectric constant and capillary pressure. It appears that the type and combination of the support plates, the presence and the number of the stainless steel bolts do not have an effect on the measurements. The use of the stainless steel bolts, the bolt holes (in the PEEK ring and the end-pieces) and the presence of electronic devices in the set-up, will introduce background noise. To account for this, we obtain the capacitance of the PEEK ring, where the sample holder is filled with air. Since ε of air is 1, we can derive the capacitance of the PEEK ring using Z = 1 iω (C sample + C PEEK RING ) where Z [Ω] is the complex impedance, iω is the complex frequency and C is the capacitance [F] expressed as C = ε 0 εa/d. Eq. (1) and the value for C PEEK RING is used in all of the derivations of the dielectric constant of the material inside the PEEK ring. Calibration is done at room temperature using materials with known dielectric properties. Figure 3 shows the straight calibration line (dashed line) and the values obtained for the different materials at f = 3 MHz. Good agreement is found between the experimental results and the theoretical values and the maximum relative error of 7% is measured for n-butanol. 4. EXPERIMENTAL RESULTS AND DISCUSSION In this section we describe the validity of the experimental technique. Two different experiments conducted for the CO 2 -sand-water system at 8 bar and 28 C. We use an unconsolidated sand sample with a grain-size fraction of 360 < D < 410 µm and a porosity of Reproducible (1)

4 PIERS ONLINE, VOL. 3, NO. 4, capillary pressure curves are obtained for both the drainage and imbibition process (see Figure 4). High precision is obtained for the saturation range between 0.15 and 0.9. Due to a power failure at A (Figure 4), the primary drainage data are missing near S w = 0.9. Non-monotonic behavior of the imbibition curve is observed at point B. These irregularities are attributed to summer temperatures in the laboratory, exceeding the upper limit of the temperature control system. Capillary pressure hysteresis is measured and is similar for both experiments. Figure 3: Calibration line for different materials obtained for the impedance tool for f = 3 MHz. Figure 4: Drainage and imbibition capillary pressure curves for the sand-co 2 -water system. In this case the capillary hysteresis is very pronounced. The corresponding dielectric constants as function of the water saturation for the drainage and imbibition experiments are presented in Figure 5 and Figure 6. As expected, the dielectric constant decreases during drainage and increases for imbibition. Comparison of the two experiments shows a small deviation, ε = ε ± 0.5, in dielectric constant for both drainage and imbibition. We ascribe these small differences to different sample packing. Figure 5: The real part of the dielectric constant as function of the water saturation during drainage for f = 3 MHz. Figure 6: The real part of the dielectric constant as function of the water saturation during imbibition for f = 3 MHz. As can be seen from our experimental results, the data can be modeled using the CRIM model [9]. As input model we use ε gas = 1 for gas, ε water = 77.5 for water and ε grains = 6.1 for the sample. For the drainage results the CRIM estimates the experimental data over the entire saturation range with an acceptable deviation. Figure 6 shows that the CRIM fits well for the experimental results for the imbibition experiment 2 and underestimates the results of experiment 1. Comparison of the dielectric constant for drainage and imbibition shows that dielectric hysteresis is measured. In contrast to resistivity measurements [5] the imbibition values for the dielectric constant are higher than the drainage values. The reasons of the dielectric hysteresis are found in the distribution of the water and gas phase as well as the surface area [7]. For a better understanding of this phenomenon, low frequency data must assist in the interpretation.

5 PIERS ONLINE, VOL. 3, NO. 4, CONCLUSIONS The experimental tool has proven to measure adequate dielectric constants for different fluids and materials. We have developed an experimental tool with which reproducible data for both the capillary pressure and the complex dielectric constant are measured. The dielectric values for drainage and imbibition are validated with CRIM, which indicates the correct measurement of the water saturation. Hysteresis is found for both the capillary pressure and the dielectric constant. The imbibition dielectric values are higher than the drainage values. Low frequency data is necessary for a better interpretation of the dielectric measurements. ACKNOWLEDGMENT The research presented in this work was carried out as part of the CATO program: CO 2 Capture, Transport and Storage in the Netherlands ( and the DIOC water project. The financial support is gratefully acknowledged. We thank L. Vogt, P. S. A. de Vreede and H. G van Asten for technical support. REFERENCES 1. Fleury, M. and D. Longeron, Combined resistivity and capillary pressure measurements using micropore membrane technique, J. Pet. Sci. Eng., Vol. 19, 73 79, Anderson, W. G., Wettability literature survey-part 2: wettability measurement, J. Pet. Sci. Technol., SPE 13933, , Morrow, N., Physics ad thermodynamics of capillary action in porous media, Ind. Eng. Chem., Vol. 62, No. 6, 32 56, Reeves, P. and M. A. Celia, Functional relationship between capillary pressure, saturation and interfacial area as revealed by a pore-scale network model, Water Resour. Res., Vol. 32, No. 8, , Knight, R., Hysteresis in the electrical resistivity of partially saturated sandstones, Geophysics, Vol. 56, No. 12, , Ngyuen, B.-L., J. Bruining, and E. C. Slob, Hysteresis in dielectric properties of fluidsaturated porous media, Proceedings of SPE Asia Pacific Improved Oil Recovery Conference, Kuala Lumpur, Malaysia, October Knight, R. J. and A. Nur, The dielectric constant of sandstones, 60 khz to 4 MHz, Geophysics, Vol. 52, No. 5, , Longeron, D. G., M. Argaurd, and J. P. Feraud, Effects of overburden pressure and the nature and microscopic distribution of fluids on electrical properties of rock samples, SPE Format. Eval., Vol. 4, , Knight, R. and A. Abad, Rock/water interaction in dielectric properties: experiments with hydrophobic sandstones, Geophysics, Vol. 60, No. 2, , Ngyuen, B-L., J. Bruining, and E. C. Slob, Effects of Wettability on dielectric properties of porous media, Proceedings of SPE Annual Technical Conference and Exhibition, Houston, Texas, October Plug, W. J., S. Mazumder, J. Bruining, N. Siemons, and K. H. Wolf, Capillary pressure and wettability behavior of the coal-water-carbon dioxide system at high pressures, Proceedings of International Coalbed Methane Symposium, Tusculoosa, Alabama, May Jennings, J. W., D. S. McGregor, and R. A. Morse, Simultaneous determination of capillary pressure and relative permeability by automatic history matching, SPE Format. Eval., , Longeron, D., W. L. Hammervold, and S. M. Skjaeveland, Water-oil capillary pressure and wettability measurements using micropore membrane technique, Proceedings of International Meeting on Petroleum Engineering, Bejing, China, November 1995.