Chapter 2 – Porosity 2.19 2.3 Measurement Porosity can be estimated through volumetric measurements of core samples, or from geophysical logs, which measure a property of the rock and infer porosity, or from Petrographic Image Analysis (PIA), which is pore level evaluation of a small sample size. This section is directed towards the measurement of porosity from rock samples or cores, because it provides the basic concepts for understanding. Equation (2.1) is derived from the volume balance of a given sample, i.e., pVgVbV  (2.15) where the sum of the grain and pore volumes is equal to the bulk volume. Measurement of any two of the three volumes allows for the calculation of the third, and subsequent determination of porosity. Therefore, the following measurement techniques are organized into their particular measurements taken. Bulk Volume Measurements Bulk volume measurements are classified into two types: linear measurement and displacement methods. Linear measurement is simply physically measuring the sample with a vernier caliper and then applying the appropriate geometric formula. This method is quick and easy, but is subject to human error and measurement error if the sample is irregularly shaped. Displacement methods rely on measuring either volumetrically or gravimetrically the fluid displaced by the sample. Gravimetric methods observe the loss in weight of the sample when immersed in a fluid, or observe the change in weight of a pycnometer filled with mercury and with mercury and the sample. Volumetric methods measure the change in volume when the sample is immersed in fluid. For all displacement methods, the fluid is prevented from penetrating into the pore space by coating the rock surface with paraffin, saturating the rock with the same fluid, or using mercury as the displacing fluid. Example 2.5 A clean, dry sample weighed 20 gms. This sample was saturated in water of density 1.0 gm/cc and then reweighed in air, resulting in an increase in weight to 22.5 gms. The saturated sample was immersed in water of the same density and subsequently weighed 12.6 gms. What is the bulk volume of the sample? 1. Weight of clean, dry sample: Wdry = 20 gms. 2. Weight of saturated sample in air: Wsat = 22.5 gmsChapter 2 – Porosity 2.20 3. Weight of saturated sample, immersed in water: Wimm = 12.6 gms. 4. Weight of water displaced: W displaced wtr = 22.5 – 12.6 = 9.9 gms. 5. Calculate the bulk volume: Vb =W displaced wtr /  wtr =9.9/1.0=9.9 cc. Grain Volume Measurements Several methods have been developed over the years to determine the grain volume. The simplest is to obtain the dry weight of the sample and then divide by the matrix density, Vg = Wdry/gr. Unfortunately, accurate matrix densities are not usually known and thus this method is not reliable. A second direct method of measuring grain volume is similar to the previous discussion on displacement methods. A crushed sample is placed in a pycnometer and the weight change is measured (Melcher-Nutting Method) or the volume change is measured (Russell Method). Example 2.6 The following sequence of measurements were obtained from the sample in Example 2.5 to determine the grain volume. Using the bulk volume from Ex. 2.6, calculate the porosity of the sample. 1. Weight of dry, crushed sample in air: Wdry = 16 gms 2. Weight of pycnometer filled with water: W py+wtr = 65 gms. 3. Add crushed sample to pycnometer and water: W py+wtr+sample = 75 gms. 4. Calculate weight of displaced water: W displaced wtr = 65 + 16 – 75 = 6 gms. 5. Calculate the grain volume: Vg =W displaced wtr /  wtr =6.0/1.0=6.0 cc. To determine the porosity of the original sample we must first determine the grain density of the sand. gr = Wdry/ Vg =16 gms/6 cc = 2.67 gm/cc Next the grain volume of the original sample must be calculated. Vg = Wdry/gr = 20 gms/2.67 gm/cc = 7.5 cc The porosity can now be determined, %2.249.95.79.9bVgVbVChapter 2 – Porosity 2.21 Several drawbacks of these methods have limited their application. First, it is a destructive method and therefore no further tests can be performed on the sample. Second, the crushing usually reduces the accuracy of the method. Therefore an alternative, reliable method has been developed which is based on Boyle’s Law. A Boyle’s Law porosimeter as shown in Figure 2.18 consists of two sample chambers. The first step is to calibrate the volumes of the sample chambers by injecting inert gas such as helium or nitrogen and recording the pressure differences when the valve between the two chambers is open and equalization occurs. The next step is to place the core sample in one chamber at some pressure, p1, which is isolated from the second chamber at p2. When the valve is opened pressure equilibrium occurs at some final pressure, pf. The pore space of the sample is penetrated by the gas; therefore the gas volume difference between the two tests is a measure of the grain volume. Mathematically, this procedure can be described as follows: - The total moles of gas is constant, thus 21nntn  - Substituting the ideal gas equation, RTVpRTVpRTfVfp2211 - Isothermal conditions prevail, 2211VpVpfVfp  - Substituting for the volumes, 22)1(1)21( VpgVVpgVVVfp  - Rearranging results in an expression for grain volume 1)2(2)1(1pfppfpVpfpVgV (2.16) where V1 and V2 are the calibrated chamber volumes. Example 2.7 A calibration procedure resulted in V1 = 100 cc and V2 = 80 cc, respectively. A core sample was placed in the first chamber at 0 kPa pressure. Gas was admitted to the second chamberChapter 2 – Porosity 2.22 to a pressure of 413.7 kPa. The valve was open and the final equalized pressure was recorded as 199.783 kPa. What is the grain volume? Substitution into Eq. (2.15) of the given parameters results in a Vg = 14.34 cc. .340.140783.199)7.413783.199(80)0783.199(100ccgV  The accuracy of this method has been estimated to be 0.1% to 0.5% of the grain volume [Jenkins,1960]. It is also nondestructive therefore the test can be repeated or the core sample can used for further tests. An inert gas is used to minimize any adsorption effects on the pore surfaces. Adsorption will cause