Rock Physics Research Group

Movies of Data

Support Document for Manuscript entitled:

 Linking Pressure and Saturation through Interfacial Areas in Porous Media

J. Cheng1, L. J. Pyrak-Nolte1,2, D. D. Nolte1, and N. Giordano1

1Department of Physics, Purdue University,
West Lafayette, Indiana 47907-2036
2Department of Earth and Atmospheric Sciences, Purdue University,
West Lafayette, Indiana 47907

Linking Pressure and Saturation through Interfacial Areas in Porous Media  (J.-T. Cheng, L. J. Pyrak-Nolte, D. D. Nolte and N. J. Giordano, Geophysical Research Letters, vol. 31, L08502, doi:10.1029/2003GL019282, 2004)

All inquires should be sent to:  Laura J. Pyrak-Nolte,


Photoresist:  Shipley-type AZ photoresist [Shipley Co., 1982] 

Properties of Decane (J.T. Baker G143-07) AT 24.5 C

Specific gravity 0.727 gm/ml
Surface tension 24.74 mN/m
Viscosity 0.855 cp
Contact angle on glass 4.4 degrees
Contact angle on photoresist 4.1 degrees

Experimental Methods

Sample Preparation:

In optical lithography a pattern is transferred using a visible light image to a photo-sensitive polymer layer called photoresist. This layer acts essentially as photographic film.  When a region of the photoresist is exposed to a sufficiently large integrated intensity of blue light, a photochemical reaction within the photoresist makes the region soluble in a special developer solution (usually just a base).  The unexposed photoresist is not soluble, so after development the photoresist layer contains a negative image of the original light pattern.  In all of our work we have used Shipley photoresist types 1805 and 1827, and their standard developer (Shipley, 1982).  The image has been transferred to the photoresist in two different ways.  In one method, a photomask is put in direct contact with the photoresist and the exposing light is transmitted through the mask.  This mask is typically an opaque metal layer on a glass substrate, or a small portion of an ordinary video transparency sheet onto which the appropriate pattern has been printed.  With this contact configuration the mask pattern is transferred in a 1:1 fashion to the photoresist sample; i.e., without magnification or reduction in size.  We use this method for making the coarse (i.e., largest scale) features of the micro-models.  The smallest sample features are made by projecting the mask pattern onto the photoresist through a microscope objective.  We employ a specially modified optical microscope which enables the image of the mask to be focused onto the sample at the same time as the sample is in focus to the observer.  Projecting through a 50x objective yields a 50:1 reduction in the size of the image relative to the scale of the mask.  In this way we can routinely achieve sub-micron feature sizes at the sample.

Construction of a complete micro-model involves several steps (Figure 1).  The first is to transfer the pattern of the desired flow geometry into a photoresist layer.  This is accomplished using optical lithography as just described.  The resulting glass substrate/photoresist layer will form the bottom and sidewalls of the final micro-model.  The top wall (ceiling) of the micro-model is formed by a second glass coverslip.  This "top plate" is bonded to the bottom layer using another layer of photoresist ? this bonding is accomplished by bringing the two glass coverslips into contact with gentle pressure (approximately 1 atm, applied in a special holder in which a flexible plastic sheet is pulled against the sample by an applied vacuum) immediately after application of photoresist to the top plate (Figure 2a).  The top plate also contains two holes (approximately 1 mm in diameter, drilled ahead of time) that serve as inlet and outlet for the finished micro-model (Figure 2c).  The inlet and outlet regions are fairly open spaces (approximately 4 mm on a side) on the micro-model, and contain "pillars" which are approximately 0.5 mm in diameter to prevent collapse of the structure (Figure 2b).  The working region of the micro-model is the area labeled as "channel" in Figure 2b.  This is where a percolative pattern is created in the bottom photoresist layer. 

Figure 1.  Micro-model layout.  (a) Side view showing bottom plate containing micro-model pattern and top plate just prior to bonding.  The glass slides are cover glasses 200 microns thick.  The photoresist layers are 0.5 micron and 1.06 microns.   (b) Arrangement of inlet, outlet, and sample (channel) regions.  (c) Inlet and outlet holes are drilled in the top plate. 

Experimental Set-up

A schematic of the flow measurement apparatus for the micro-models is shown in Figure 2.  This apparatus is used for simultaneous measurements of flow rate and optical characterization of the geometries of the various phases within the sample.  This apparatus contains (1) two pressure sensors to monitor the input and output pressures, and (2) a video camera interfaced to an optical microscope to image the two-phase displacements experiments.

To perform a flow measurement on a micro-model, the micro-model is initially saturated with a fluid such as decane, which is inserted through the "outlet" region in Figure 2.  A second fluid, nitrogen gas, is then introduced through the inlet region.  All measurements are conducted at room temperature (temperature stability better than 0.5 degree Celsius during a measurement), with the apparatus located within one of the clean bench environments. 
The measurement of interfacial area per volume (IAV) is accomplished with our video microscopy setup.  For this we capture the image of the micro-model and do image processing with the computer interfaced to the camera.  The captured image is processed using thresholding techniques to determine the areas occupied by both fluids and the interfacial area, both of which are crucial for our studies. 

Figure 2.  Apparatus used for measurement of flow rates of decane and imaging of fluid geometry within a micro-model.  The pressure sensors are piezoelectric sensors (model PX550C1 from Omega Engineering) 

Supporting Results

The following animations of the data are presented to link the images of phase distribution within the porous medium micro-model with capillary pressure (Pcap), wetting-phase saturation (S), and interfacial area per volume (IAV).  


The movie Data is an animation of still images acquired with the CCD camera after the system reached equilibrium after an increment of pressure.  These images represent a subset of the raw data set.  The entire data set consists of 219 images.  In the images, white regions represent nitrogen, light gray regions represent decane and dark gray regions represent photoresist.  The images are shown at half the resolution (~ 1.2 microns per pixel).  The movie shows for two-saturation loops (i.e., two nitrogen imbibtion- drainage cycles). 

Movie #Data


Results from Image Analysis

In Movies #1 and #2 (see below), one quarter of the micro-model is shown because the full image would be too small to see the details of the interfaces. A pixel in the images of the micro-model is approximately 0.6 microns.  In the movies, black represents the photoresist, maroon represents voids filled with nitrogen, blue represents voids filled with decane, white represents capillary-dominated interfaces (interfaces between bulk fluid phases) and bright red represents all other interfaces.  Please note that the thickness of the interfaces are exaggerated to a thickness of 2 pixels for illustration purposes only.  All calculations based on the interfaces were based on interfaces one pixel in width. 

Movie #1 (PcapSatS8cmovie) shows one-quarter of the micro-model for two saturation loops from Figure 2 in the paper (not figure 2 above).  This helps illustrate the hysteresis in the capillary pressure (Pcap) - wetting phase saturation (S) relationship. For any given pressure, two values of sautration are possible, and conversely, for any value of saturation two capillary pressures are possible.  In the graph, Pcap has units of kPa.  Saturation ranges from 0.75 to 1.0 for the fraction of pore space saturated with the wetting phase (decane).

Movie #1


Movie #2 ( shows one-quarter of the micro-model and the three-dimensional surface that gives the relationship among capillary pressure (Pcap) - wetting phase saturation (S) and interfacial area per volume (IAV between the wetting and non-wetting phases).  In the animation, the same two saturation loops from Movie #1 are shown.  The points on the surface turn from red to green so a comparison between the fluid distribution in the micro-model and the values of IAV on the surface can be made. The axes for the three-dimensional surface are: z-axis represents IAV  and the axis ranges from 0 - 5000 inverse meters;  x-axis (hidden behind the surface) represents Pcap and ranges from 0.38 x 105 Pa to 0.46 x 105 Pa; y-axis (on the left) represents S and ranges from 0.7 - 1.0 fraction of pore space filled with the wetting phase (decane).

Movie #2