On-chip porous media: Porosity and permeability measurements
Graphical abstract
Introduction
It is believed that the key driver to displace oil from the reservoir relies on the fact that the oil–water–gas co-exists in the pore-space of the reservoir and one needs to adopt suitable mechanisms to mobilize the oil from the pore space (Kaiser, 2009, Blunt et al., 2002, Jaber et al., 1999, Jamaloei and Kharrat, 2010, Blunt, 2001, Gunde et al., 2010). This brings to the focus of the present work, where a naturally occurring oil reservoir rock, i.e., porous medium, represented on a chip that can be exploited to provide the oil and gas industry with a better tool to understand the pore-scale displacement process relevant to a given geological formation.
It is a well known fact that the studies of transport mechanisms (Colombani et al., 2002, Talmon et al., 2010, Ellis and Bazylak, 2012, Ma et al., 2012, Miller and Fogler, 1995) at pore scale have been attempted because of their importance in many engineering applications in engineering. Such studies are highly relevant especially in the energy field since majority of the heavy/light oil is found in carbonate and sandstone formations which consist of solid matrix and pore space. Therefore, the researchers in the past have tried to create micro-models (Karadimitriou and Hassanizadeh, 2012) which consist of simple and regular geometric features, fractal patterns and irregular patterns with characteristic length-scale comparable with the average pore diameter, quite different than the pore geometry of a natural porous media (Jamaloei and Kharrat, 2010, Er et al., 2010, Wu et al., 2012a). However, recent microscopy techniques have made possible to characterize the pore space and the pore connectivity of such reservoir rocks (Rigby et al., 2002, Lindquist et al., 2000, Zhou et al., 2011, Spanne et al., 1994, Bera et al., 2012, Bera et al., 2011, Sok et al., 2002). In parallel, great advancement of micro/nanofabrication techniques has revolutionized the fabrication of micro-models for energy applications (Berejnov et al., 2008, Fadaei et al., 2011, Bowden et al., 2006). Building on these two advancements, Gunda et al. (2011a) fabricated the Reservoir-on-a-Chip (ROC), where for the first time the pore network of a naturally occurring oil reservoir rock was replicated on a silicon substrate covered with glass. They conducted oil recovery experiments by water flooding technique and were able to comprehensibly understand the displacement process of oil by water within the pore network. This concept of ROC has now been adopted in a recent paper by Karadimitriou et al. (2012), where they fabricated a similar pore network on a glass substrate. As ROC is becoming a popular tool to characterize a given reservoir, it is imperative that properties like porosity and permeability need to be calculated for such systems. Measurement of effective properties in such micro-systems has been difficult in the past due to challenges associated in the measurement techniques at such small length scales. Hence, in this paper, we have elaborated the technique of calculating relevant reservoir properties for on-chip porous medium, often coined as ROC (Gunda et al., 2011a),which can be adopted for other types of micro-models of different geological formations. The fabricated on-chip porous media used in the present work has resemblance with our previous work (Gunda et al., 2011a).
Typically, porosity and permeability are measured in a laboratory scale using core-flooding experimental systems. Porosity can be assessed through volumetric measurements of core samples, petrographic image analysis (PIA), or often geological logs. Mercury injection methods (Rigby et al., 2002) and fluid re-saturation method are often used to measure the pore volume of the porous samples. Other advanced and sophisticated techniques like X-ray tomography (Bera et al., 2011, Dong and Blunt, 2009, Okabe and Blunt, 2007, Rigby et al., 2006, Gunde et al., 2010), scanning electron microscopy (Clelland and Fens, 1991, Mattiello et al., 1997, Gunda et al., 2011b), Brunauer–Emmett–Teller (BET) for gas adsorption (Schull, 1948, Gan et al., 1972) and Nuclear Magnetic Resonance (Kenyon, 1992, Timur, 1969) of small sample sizes to estimate the pore distribution and surface area of porous samples. Often these techniques are expensive and are difficult to adopt for pore-scale micro-models.
The permeability estimation models in literature can be briefly classified into three classes: (a) Darcy's law (Whitaker, 1986, Vafai and Tien, 1981, Klinkenberg, 1941), (b) Non-linear Darcy's models, e.g. Darcy–Forchheimer equation (Pant et al., 2012, Nield, 1991, Alazmi and Vafai, 2001, Beckermann et al., 1986), and (c) Klinkenberg effect/Knudsen slip models, e.g. modified binary friction model (Pant et al., 2013, Kerkhof, 1996, Carnes and Djilali, 2006). However, the current work deals with liquids in micro-pores and therefore the Knudsen slip effects are negligible and hence the binary friction model is not applicable. The Forchheimer effect accounts for the non-liner effects of velocity in pressure drop measurements whereas Darcy's law accounts for linear effects. From physical perspective, Darcy's law accounts for viscous drag whereas the Forchheimer term accounts for the inertial effects of velocity on the pressure drop.
Also, there has been an emphasis in extracting pore network information from micro-CT images of sandstone (Al-Kharusi and Blunt, 2007) and carbonate (Okabe and Blunt, 2007, Bera et al., 2012) and then using numerical tools (Prodanovic et al., 2007, Bakke and Oren, 1997, Hazlett, 1995, Singh and Mohanty, 2003, Humby et al., 2002, Jaganathan et al., 2008, Gunda and Mitra, 2012) to calculate porosity and permeability of such extracted networks (Arns et al., 2001, Gervais et al., 2012, Singh and Mohanty, 2000, Wu et al., 2003). However, such technique is limited to the numerical reconstruction method and it is not feasible to visualize the pore-scale displacement process. On the other hand, on-chip porous media gives a tremendous flexibility in observing in situ pore-scale displacement processes and helps in characterizing the porosity–permeability relationship at the pore scale.
Thus to further extend the scope of ROC with application to reservoir characterization, effective porosity and permeability are measured for four different pore network structures fabricated on silicon substrates using dry etching. Fabrication procedure for producing such intricate pore network structure has been provided here, which will allow others to replicate the fabrication process relevant to any given extracted pore network. The complete microfluidic chip is fabricated with borofloat glass as covering layer for silicon substrate with proper inlet and outlet for fluidic connections. We characterize the single phase flow properties associated with this on-chip porous media consisting of different pore networks. Porosity is determined by processing the optical images when it is flooded by the dyed fluid. Permeability is calculated by measuring the pressure drop across the chip for different flow rates of deionized (DI) water injected into the chip. The methodology developed for calculating pressure drops in the present work has been adopted from the work reported by Gunda et al. (2013), where they have characterized the structured porous medium (microchannel with integrated micro-pillars).
The use of wetting fluid is important to achieve the single phase flow without having any trapped air for porosity and permeability measurements. The present device is made of silicon-glass material and shows water-wet characteristics. The methods for measuring the porosity and the permeability, developed in the present work, can be implemented in other types of micro-models made from different materials such as glass and/or PDMS. PDMS micro-models are easier to make, disposable and less expensive than glass micro-models, and they are widely used in the microfluidic community including porous media micro-models (Bhattacharya et al., 2005, Berejnov et al., 2008, Schneider et al., 2010, Ma et al., 2011, Zhao et al., 2012). The main problem in PDMS micro-models is the wettability, which is not an issue in glass micro-models. PDMS micro-models require some treatment like oxygen–plasma or UV–ozone to convert the surface of PDMS into water-wet (Bhattacharya et al., 2005, Ma et al., 2011). In addition to wettability problem, PDMS has several disadvantages of swelling and sagging when the liquid flows for a longer times or at higher flow rates (Bhattacharya et al., 2005, Berejnov et al., 2008, Schneider et al., 2010, Ma et al., 2011, Zhao et al., 2012).
The novelty of the present work lies in conducting experiments to show a detailed analysis of permeability measurement technique for on-chip porous media and to check the accuracy of the porosity measurements using image analysis and saturation methods, which is different compared to the material balance approach used in other published works (Gunda et al., 2011a, Jeong and Yavuz Corapcioglu, 2003, Wu et al., 2012b, Zhang et al., 2011). Other highlights of the present work are: (a) Determination of effective porosity using image analysis technique and (b) Estimation of the permeability by measuring the pressure drop across the pore network and applying Darcy's law. We justify the novelty of the present work by putting forward two important facts. First, the increasing popularity of on-chip porous medium or ROC has made it imperative that the flow properties of such pore networks be calculated and documented. Second, calculation of such properties would help in future studies related to the classic problem of pore-scale to reservoir scale modeling. As it is well known, the properties of any porous media are usually associated with three different length scales: pore scale, macroscopic or lab scale and field scale. An experimental determination of flow properties at the pore scale, in a realistic pore network, would help in documenting pore scale flow properties and can be used for such simulations or for theoretical work. At the same time, fabrication and knowledge of four different porous media geometries and their properties would help other researchers in performing future works related to enhanced oil recovery and multi-phase fluid flow phenomena in similar micro-models.
This present paper starts with a brief description of the technique employed for fabricating the four on-chip porous media. This is followed by a description of the experimental procedures for determination of effective porosity and absolute permeability. In the next section, results and discussion for the values of porosity and permeability obtained for different chips are presented. Further characterization of the chip in terms of flow resistance for different Darcy numbers is also presented here.
Section snippets
Pore network design
Four different pore networks are designed based on the typical sandstone microstructural information. Using Delaunay Triangulation routine (MATLAB, Mathworks Inc., Natick, MA, USA), a pore network of prescribed mean pore size is created for each chip. Mean pore size of these four networks varies from to . Network 1 and 2 contain mean pore size of , Network 3 contain mean pore size of and Network 4 containing mean pore size of . The aspect ratio (ratio of pore radius to the
Results and discussion
The porosity measurement data for the different chips are provided in Table 3. The four different networks that we created represent porous media over a wide range of porosity. Apart from calculating porosity from image analysis presented in the earlier section, the porosity of the networks were also calculated using the design images (AUTOCAD drawing file), one of which is shown in Fig. 1. This was done to distinguish between the true porosity of the network and the effective porosity after
Conclusion
In this work, a novel on-chip porous medium was fabricated and characterized using SEM and surface profilometer. Four different types of chips varying in number of pore bodies and pore throats were considered in this work. Properties like porosity and permeability were calculated to characterize such on-chip porous media. A very simple image analysis technique, as opposed to a complex material balance approach, was used to determine the porosity and it is found that the porosity values ranged
Acknowledgments
The authors thank Nikolaos K. Karadimitriou and Dr. S.M. Hassanizadeh, Department of Earth Sciences, Universiteit Utrecht, for providing the network design. The authors also thank Bijoyendra Bera for his help and support in developing the chip. The authors gratefully acknowledge Dr. Siddhartha Das and Lalit Pant, Department of Mechanical Engineering, University of Alberta, for their helpful comments and suggestions. Financial support from Natural Sciences and Engineering Council (NSERC) is
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