Elsevier

Chemical Engineering Science

Volume 99, 9 August 2013, Pages 274-283
Chemical Engineering Science

On-chip porous media: Porosity and permeability measurements

https://doi.org/10.1016/j.ces.2013.05.065Get rights and content

Highlights

  • Conducted experiments to calculate the effective porosity and permeability of on-chip porous media.

  • Effective porosity is determined by using image analysis technique.

  • Permeability is estimated by measuring the pressure drop across the pore network and applying Darcy's law.

  • The flow resistance in the networks is found to decrease with the increase in Darcy number.

  • Quantification of porosity and permeability would help in future studies of pore-scale transport in reservoir engineering.

Abstract

In porous media, accurate determination of petrophysical properties such as effective porosity and permeability are important to understand the porosity–permeability relationships that help in improving the oil extraction mechanisms. Measuring porosity and permeability for on-chip porous media is difficult due to their small length scales. Hence in the present work, we conduct experiments to calculate the effective porosity and permeability of on-chip porous media containing different pore-networks. Four different types of on-chip porous media varying in number of pore bodies and pore throats are fabricated in this work. Porosity for each on-chip porous media is determined by using image analysis technique. Absolute permeability is estimated by measuring the pressure drop across the pore network and applying Darcy's law. The pore sizes of the networks range from 40μm to 70μm and the porosity of the on-chip porous media varies from 0.39 to 0.67. The flow resistance in the networks, measured by the quantity ΔP/Q, is found to decrease with the increase in Darcy number (K/h2). The permeability values range between 2.66±0.06 and 15.93±0.55 Darcy (2.625×1012±0.059×1012 and 15.72×1012±0.542×1012m2). It is found that as the number of pores and throats in on-chip porous media increases, the porosity increases as expected resulting in approximately one order of permeability increase. The results of this study would help in understanding the porosity and the permeability values in on-chip porous media that are miniaturized versions of oil reservoirs, which can be effective in understanding pore scale porosity–permeability relationships.

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 40μm to 70μm. Network 1 and 2 contain mean pore size of 40μm, Network 3 contain mean pore size of 70μm and Network 4 containing mean pore size of 50μm. 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

References (80)

  • N.S.K. Gunda et al.

    Focused ion beam-scanning electron microscopy on solid-oxide fuel-cell electrodeimage analysis and computing effective transport properties

    J. Power Sources

    (2011)
  • A.C. Gunde et al.

    Investigation of water and CO2 (carbon dioxide) flooding using micro-CT (micro-computed tomography) images of berea sandstone core using finite element simulations

    Energy

    (2010)
  • V. Gurau et al.

    Characterization of transport properties in gas diffusion layers for proton exchange membrane fuel cells. 2. Absolute permeability

    J. Power Sources

    (2007)
  • S. Humby et al.

    Explicit numerical simulation of fluids in reconstructed porous media

    Chem. Eng. Sci.

    (2002)
  • J. Jaber et al.

    Evaluation of oil yield from jordanian oil shales

    Energy

    (1999)
  • S. Jaganathan et al.

    A realistic approach for modeling permeability of fibrous media3-D imaging coupled with CFD simulation

    Chem. Eng. Sci.

    (2008)
  • S.W. Jeong et al.

    A micromodel analysis of factors influencing NAPL removal by surfactant foam flooding

    J. Contaminant Hydrol.

    (2003)
  • M. Kaiser

    Hydrocarbon production forecast for committed assets in the shallow water outer continental shelf of the Gulf of Mexico

    Energy

    (2009)
  • P.J. Kerkhof

    A modified Maxwell–Stefan model for transport through inert membranesthe binary friction model

    Chem. Eng. J. Biochem. Eng. J.

    (1996)
  • K. Ma et al.

    Wettability control and patterning of PDMS using UV–ozone and water immersion

    J. Colloid Interface Sci.

    (2011)
  • M.J. Miller et al.

    Prediction of fluid distribution in porous media treated with foamed gel

    Chem. Eng. Sci.

    (1995)
  • D. Nield

    The limitations of the Brinkman–Forchheimer equation in modeling flow in a saturated porous medium and at an interface

    Int. J. Heat Fluid Flow

    (1991)
  • L.M. Pant et al.

    Absolute permeability and Knudsen diffusivity measurements in PEMFC gas diffusion layers and micro porous layers

    J. Power Sources

    (2012)
  • L.M. Pant et al.

    A generalized mathematical model to study gas transport in PEMFC porous media

    Int. J. Heat Mass Transfer

    (2013)
  • M. Prodanovic et al.

    3d image-based characterization of fluid displacement in a berea core

    Adv. Water Resour.

    (2007)
  • S.P. Rigby et al.

    Studies of the entrapment of non-wetting fluid within nanoporous media using a synergistic combination of MRI and micro-computed x-ray tomography

    Chem. Eng. Sci.

    (2006)
  • M. Singh et al.

    Permeability of spatially correlated porous media

    Chem. Eng. Sci.

    (2000)
  • M. Singh et al.

    Dynamic modeling of drainage through three-dimensional porous materials

    Chem. Eng. Sci.

    (2003)
  • K. Vafai et al.

    Boundary and inertia effects on flow and heat transfer in porous media

    Int. J. Heat Mass Transfer

    (1981)
  • F.J. Valdes-Parada et al.

    Validity of the permeability Carman–Kozeny equationa volume averaging approach

    Phys. A Stat. Mech. Appl.

    (2009)
  • W. Wu et al.

    Relationship of threshold diameter and Darcean permeability in unconsolidated porous structures

    Chem. Eng. Sci.

    (2003)
  • P. Xu et al.

    Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry

    Adv. Water Resour.

    (2008)
  • L.H. Zhao et al.

    Long-term retention of hydrophilic behavior of plasma treated polydimethylsiloxane (PDMS) surfaces stored under water and Luria–Bertani broth

    Sensors Actuators A Phys.

    (2012)
  • N. Zhou et al.

    Experimental study of capillary trapping on the pore scale for various sandstone cores

    Energy Procedia

    (2011)
  • M. Akbari et al.

    Pressure drop in rectangular microchannels as compared with theory based on arbitrary cross section

    J. Fluids Eng.

    (2009)
  • A.A. Alzaydi

    Flow of Gases through Porous Media

    (1975)
  • C. Arns et al.

    Accurate estimation of transport properties from microtomographic images

    Geophys. Res. Lett.

    (2001)
  • S. Bakke et al.

    3-d pore-scale modelling of sandstones and flow simulations in the pore networks

    SPE J.

    (1997)
  • C. Beckermann et al.

    A numerical study of non-darcian natural convection in a vertical enclosure filled with a porous medium

    Numer. Heat Transfer

    (1986)
  • B. Bera et al.

    Characterization of nanometer-scale porosity in reservoir carbonate rock by focused ion beam – scanning electron microscopy

    Microsc. Microanal.

    (2012)
  • Cited by (47)

    • In situ micro-emulsification during surfactant enhanced oil recovery: A microfluidic study

      2022, Journal of Colloid and Interface Science
      Citation Excerpt :

      The pore geometry was obtained by microscopic imaging of a cross section of a real core (the porous media image processed by AutoCAD software (Autodesk, USA) is shown in Fig. S2) and etched on a glass plate through plate-making, coating, optical imaging, chemical etching, sintering and wetting, with an effective area of 42 mm × 42 mm and average depth of approximately 100 µm. Its porosity (ϕ) was 44.3%, according to image analysis [42], and it permeability (K), characterized via water injection, was 8.8 Darcy [42]. The micromodel was fixed on the temperature-controlled stage, and linked to the injection system via a plastic pipeline (with 0.5 mm inner diameter).

    • A novel experimental investigation on the occurrence state of fluids in microscale pores of tight reservoirs

      2021, Journal of Petroleum Science and Engineering
      Citation Excerpt :

      Due to the lack of theoretical model and the complexity of crude oil, there are few researches can accurately describe the occurrence state of crude oil in microscale/nanoscale pores. As a popular means of micro scale experiment, microfluidics has the advantages of small sample consumption, fast analysis speed, high degree of automation, high heat mass transfer rate, easy integration and high security etc. (Li et al., 2012) The microfluidic chip materials used in the petroleum engineering include silicon (Joseph et al., 2013), glass (Boschan et al., 2003), PDMS (Glawdel and Ren, 2009), PMMA (Obuliraj et al., 2014) and rock slices (Chen et al., 2012) etc. Currently, it was mostly used for the investigation of the fluid phase characteristics, the distribution of residual oil and the flow behavior (Li et al., 2018).

    • Visualizing in-situ emulsification in porous media during surfactant flooding: A microfluidic study

      2020, Journal of Colloid and Interface Science
      Citation Excerpt :

      The average depth of the microchannel is ~100 µm, and the cross-section area of the porous media is 4.2 mm2. The porosity (ϕ) of the porous media was measured by image analysis according to a previously-reported work [31], and it was equal to 44.3%. The permeability (K) of the porous media was measured by injecting water at different flow rates and measuring the corresponding pressure drop between inlet and outlet, and found it was 8.8 Darcy.

    View all citing articles on Scopus
    View full text