CHAPTER 4: POROSITY

Objective

To measure the porosity of rock samples using routine methods in petroleum industry and to measure porosity of glass bead packs to investigate the effect of grain size and sorting on porosity.

Introduction Porosity (  ) is defined as a ratio of pore volume ( V p ) to bulk volume ( V B ) of a reservoir rock (these volumes are sketched in Figure 4-1):



Vp VB

.......................................................................................................................(4-1)

V p  VB  VS ..............................................................................................................(4-2)

Where VS is volume occupied by the solid grains of the rock. The pore spaces in reservoir rocks are most frequently the intergranular spaces between the sedimentary particles. The void space is microscopic in scale, rarely exceeding a few, or very few, tens of microns. The porosity of the reservoir rocks may vary from 5% of the bulk volume to about 30% of bulk volume (values out of this range can be found).

Porosity is of primary importance in reservoir engineering because it is a measure of the space available for storage of commercial fluids within a reservoir rock. It is a measure of the volume of commercial fluids (and/or water) that a reservoir rock can store per unit of bulk volume. Note that if the dimensions of the reservoir are known (area and thickness), the total volume of fluids stored in the reservoir can be calculated.

4-1

Figure 4-1. Sketch of Cross Section of Reservoir Rock Porosity can be classified based on either its geological origin or pores connectivity. Based of geological origin, porosity can be primary (depositional, original) or secondary (postdepositional, induced).

The former is developed during the deposition of the sedimentary

material and the latter porosity develops by geological processes subsequent to original deposition. Based on pores connectivity, porosity can be total or effective. Total porosity includes all existing pores regardless of whether they are connected or not. Effective porosity only includes the interconnected pores.

Porosity Measurement Methods

Several techniques exist to measure rock porosity on plugs drilled from recovered cores. However, only two techniques that will be applied in our experiments are presented here. The first technique is Boyle’s Law method and the second is water saturation method. An additional experiment using glass bead packs to investigate the effect of grain size and sorting on porosity is also explained. Boyle’s Law Method: This method is a gas transfer technique that involves the compression of gas into the pores or the expansion of gas from the pores of a clean dry sample (Monicard-1980). Boyle’s law states that the volume of a gas varies inversely with pressure under isothermal conditions. Figure 4-2 shows a sketch of Boyle’s Law porosimeter.

4-2

Figure 4-2. Boyle's Law Porosimeter Suppose the rock sample is placed in the sample chamber at zero gauge pressure and the reference chamber is filled with gas at pressure P1, then the valve between the two chambers is open and the system is brought to equilibrium. The number of moles in both situations remains constant:

n1  n2 .......................................................................................................................(4-3) Using Boyle’s Law: P1VRef  P2 VRef  VSam  VS 

VS 

P2VRef  P2VSam  P1VRef ....................................................................................(4-4) P2

Where VS is the volume of solids in the rock, VRef is the volume of the reference chamber, VSam is the volume of the sample chamber, P1 is the pressure before opening the valve, and P2 is the pressure at equilibrium after opening the valve. Therefore, the technique as described here gives the solid volume of the sample (note that the gas fills only the effective volume of the rock). The bulk volume can be measured directly using a caliper. 4-3

Water Saturation Method: A dry rock sample is weigh and then vacuum-saturated with water. The water-saturated sample is weigh and the difference between both weights is the weight of water within the pores. Knowing the density of the water, the volume of water occupying the pore space of the rock is calculated. This technique also gives the effective pore space of the rock. Figure 4-3 shows a sketch of the apparatus to saturate the sample.

Figure 4-3. Saturation Device To saturate the sample, follow these steps: 

Place sample in a heavy-wall Erlenmeyer. Be sure the sample is horizontal and that the water does not drop directly on the sample.



Attach a burette with enough water on top of the erlenmeyer using a rubber stopper. Be sure valve 1 is closed and the stopper will preserve the vacuum.



Attach the vacuum pump to the Erlenmeyer. Open valve 2 and make vacuum.



Open valve 1 so the water will slowly run inside the container (drops instead of a continuous stream). Let the water run till the rock sample is completely covered



Close valve 1 and turn off the pump.

Glass Beads: For regular arrangements of uniform spheres the proportion of void space can be calculated theoretically. The porosity for cubical packing (least compact) is 47.6% (see Figure 4-4): 4-4

VB  (2r ) 3 and VS 



4r 3 3

VB  VS 2r 3  4r 3 / 3 8  1.33     0.476  47.6% VB 8 2r 3

Notice that the porosity of uniform sphere is independent of radius. For rhombohedral packing (most tight packing), porosity is 25.96%.

Figure 4-4. Groups of Spheres for Cubic and Rhombohedral Packing (Modified from Amyx et al, 1960) Sorting is a parameter describing the grain size distribution. Excellent sorting refers to packs of grains with the same size. Poor sorting refers to packs of grain with different sizes. Porosity increases as sorting improves. Therefore mixing glass beads of different sizes should reduce porosity compared to packs of same size glass beads.

Laboratory Experiments Part 1: Glass Beads

It is your job to design an experiment to investigate the effect of grain size and sorting on porosity using glass beads packs. Part 2: Water Saturation



Weigh a dry rock sample 4-5



Vacuum-saturate the rock sample with water as explained in this chapter



Weigh the saturated sample



Measure the water density



Calculate the weight of the water saturating the sample



Calculate the volume of the water saturating the sample

Part 3: Boyle’s Law (Reference 8)

The equipment is not in the laboratory yet. This procedure will be explained later. 

Place a clean and dry sample in the matrix cup



Set the helium source valve to a pressure of 120 psi



Turn valve sample to the VENT position



Open valve gas inlet to ON



Adjust the pressure regulator until the pressure gauge reads approximately 100 psi



Turn gas inlet valve to OFF position and record P1 given by the digital display



Turn sample valve to EXPAND position and record P2 given by digital display after reading has stabilized



Use the following correlation to directly calculate grain volume:

VGrain  0.0154 * P1 / P23  0.2609 * P1 / P22  4.6175* P1 / P2  51.042

References

1. Petroleum and Chemical Engineering Department, PETR 345 Lab Manual. Fall 1999. 2. API Recommended Practice for Core Analysis Procedure. API RP 40, American Petroleum institute, Dallas, 1960. 3. Monicard, R. P., Properties of Reservoir Rocks: Core Analysis.

Gulf Publishing Co.,

Houston, TX (1980). 4. Anderson, G., Coring and Core Analysis Handbook, Penwell, Tulsa, OK (1975) 5. Amyx, J.W., Bass, D.M., and Whiting R.L., Petroleum Reservoir Engineering, McGrawHill, New York, NY (1960).

4-6

6. Frick T.C., Petroleum Production Handbook, Vol II; Society of Petroleum Engineers, Dallas, TX (1962). 7. Keelan, D.K. and Donoheu D. A.T., Core Analysis, IHRDCVideo Product Sales, Boston, MA (1985). 8. Core Laboratories Operating Manual. Manually Operated Gas Porosimeter PORG-200TM. Core Laboratories Instruments, Houston, Texas. 2003.

4-7