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., b (2.15) g p 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 olume 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. olumetric 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: W dry = 20 gms. 2. Weight of saturated sample in air: W sat = 22.5 gms 2.19
3. Weight of saturated sample, immersed in water: W imm = 12.6 gms. 4. Weight of water displaced: W displaced wtr = 22.5 12.6 = 9.9 gms. 5. Calculate the bulk volume: b =W displaced wtr / wtr =9.9/1.0=9.9 cc. Grain olume 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, g = W dry / 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: W dry = 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: g =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 = W dry / g =16 gms/6 cc = 2.67 gm/cc Next the grain volume of the original sample must be calculated. g = W dry / gr = 20 gms/2.67 gm/cc = 7.5 cc The porosity can now be determined, b g b 9.9 7.5 24.2% 9.9 2.20
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, p 1, which is isolated from the second chamber at p 2. When the valve is opened pressure equilibrium occurs at some final pressure, p f. 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 n t n 1 n 2 Substituting the ideal gas equation, p f f RT p 1 1 RT p 2 2 RT Isothermal conditions prevail, p f f p p 1 1 2 2 Substituting for the volumes, p f ( ) p ( ) p 1 2 g 1 1 g 2 2 Example 2.7 Rearranging results in an expression for grain volume g ( p p ) ( p p ) 1 f 1 2 f 2 (2.16) p f p 1 where 1 and 2 are the calibrated chamber volumes. A calibration procedure resulted in 1 = 100 cc and 2 = 80 cc, respectively. A core sample was placed in the first chamber at 0 kpa pressure. Gas was admitted to the second chamber 2.21
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 g = 14.34 cc. g 100(199.783 0) 80(199.783 413.7) 14.340cc. 199.783 0 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 erroneously low values of grain volume and subsequent overestimation of porosity. The Boyle s Law method yields effective porosity of the sample. An isolated pore, will not be penetrated by the gas, and therefore will act as if it is a portion of the grain volume. Pore olume Measurements Several methods have been developed to measure the pore volume of a sample. The original mercury injection methods such as Washburn-Bunting and Kobe (see Figure 2.18) are obsolete and seldom used. Their elimination was due to the destructive nature of mercury and the lack of accurate results. A second method is called the fluid resaturation method. A clean and dried sample is weighted, saturated with a liquid of known density, and then reweighed. The weight change divided by the density of the fluid results in the pore volume. Example 2.8 The following procedure was run to obtain pore and bulk volume of a sample and thus effective porosity. 1. Weight of clean, dry sample: W dry = 39.522 gms. 2. Evacuate core and saturate with liquid: W sat = 43.797 gms ( w =1.01 gm/cc) W sat W dry 3. Calculate the effective pore volume: 4. 233cc p w 3. Weight of sat. sample, immersed in water: W imm = 24.393 gms. 4. Weight of water displaced: W dis. wtr = 43.797-24.393 =19.404 gms. 5. Calculate the bulk volume: b =W dis wtr / wtr =19.404/1.01=19.212 cc. 6. Calculate the porosity: = p / b = 4.233/19.212 = 22% 2.22
This technique also yields effective porosity; however, complete saturation is seldom obtained and therefore porosity is commonly lower than that determined from the Boyle s Law method. Furthermore, if the sample is water sensitive then oil should be used as the saturating fluid. The procedure is slow, however numerous samples can be run simultaneously [Helander,1983]. A final method of determining pore volume is known as the summation of fluids or retort method. The basis for this method is the independent measurement of the volumes of oil, water and gas and then the summation of these volumes to obtain the pore volume, p = o + w + g. Unlike other methods, the samples are not clean and dried, but instead are used directly as received at the lab. The samples are split into two portions, which are adjacent to each other. The first sample is placed in a pycnometer and the bulk volume is measured. Next, the sample is placed in a mercury cell and injected with mercury at high pressures (750 psi), resulting in an estimation of the gas volume. The second sample is heated to evaporate the oil and water, which is condensed in a graduated cylinder and then oil and water volumes are measured. The gas volume (adjusted for sample 2) and the bulk volume from sample one are used to obtain the pore volume and porosity of the core. The advantages of this method are the fast speed of the measurements and the simultaneous determination of saturations. The disadvantages are the dependency on similarity of the adjacent samples, homogeneous formations are better suited for this method; a distinction is required between the pore water and the water of hydration, the high temperatures will coke some of the oil in the pore space, and the sample must be at insitu conditions to provide original reservoir saturations. Table 2.4 is a comparative study by Jenkins, 1960 of the various porosity measuring methods. Numerous samples from the United States, Canada and Iran were included in the study. Based on the trends indicated from this data, the conclusion was that the Boyle s Law, and summation of fluids methods yielded porosity values accurate to 0.5%. The Washburn- Bunting method normally exhibited an accuracy of 1% and the resaturation method routinely resulted in low porosity values of 2 to 10% than the other methods. 2.23
Number of samples Type Porosity Range, % Washburn Bunting, % Fluids, % Resat. % Boyle s Law, % Grain density, % 232 Clean sand 8-35 15.7 17.6 85 Sl. Shaly 4-28 17.5 19.5 29 Conglomerate 6-15 10.1 11.4 70 Carbonate 6-25 18.9 20.0 95 Clean sand 8-35 17.8 18.6 390 Sl. Shaly 4-28 21.1 20.4 15 Conglomerate 6-15 10.2 10.9 112 Carbonate 3-20 14.8 14.8 137 Sand 1-22 5.55 5.42 210 Sand 1-22 14.0 11.3 12.8 3220 ALL 2-35 14.6 14.6 Table 2.4 Comparison of porosity measuring methods [Jenkins, 1960] 2.24
Method Advantages Limitations Washburn-Bunting Low equipment costs. Equipment must be kept very clean; extremely careful techniques must be used in order to obtain acceptably accurate results. Sample cannot be used for further testing. Resaturation Grain density Summation of fluids Boyle s Law Accurate. Determination of porosity convenient while preparing samples for other tests. Samples can be used for further testing. Accurate. Measures total porosity. Accurate for most rock types encountered. Rapid - particularly when fluid saturations are also to be determined. Well suited for routine laboratory work. Allows porosity and saturation to be determined on the same sample. Utilizes relatively large sample, even for conventional type analyses. Elapsed time in the laboratory is shortest of all methods. Accurate Fairly rapid for majority of samples encountered. Samples can be used for further testing. Preparation and drying of sample are critical, as in the Boyle's Law method. Slow and fairly difficult. Wetting the rock surfaces with either brine or hydrocarbon saturants is difficult. Incomplete resaturation causes erroneously low porosity values. Preparation and drying of sample are critical, as in the Boyle's Law method. Slow and fairly difficult, requiring very careful laboratory techniques. Preparation and drying of sample are critical, as in the Boyle's Law method. Oil and water content determinations subject to calibration and corrections. Water calibration difficult when hydratable minerals are present. Conventional plug samples cannot be used for further tests. Slow for low permeability samples. Preparation of sample for test is important. Drying technique is critical when hydratable minerals are present. Measurement of bulk volume is critical in the grain volume determination type test. Adsorption of gas on the rock surfaces tends to give an erroneously high porosity value. Table 2.5 Comparison of porosity methods [Core Lab, 1983] 2.25
Figure 2.18 Illustration of porosity measuring apparatus [Core Lab, 1983] 2.26