Porosity analysis has two main parameters of interest that are typically used in further applications; pore volume (VP) and porosity (φ). Pore volume is the actual volume of pores within the sample and porosity is the ratio of empty space to total volume. From the American Petroleum Institute’s (API) Recommended Practice for Core Analysis (1998), these values can be calculated using equations 1 and 2 below using bulk volume (VB), which is the total volume of the sample, and grain volume (VG), which is the actual volume of the mass of the sample.
V_P=V_B-V_G (1) φ=(V_B-V_G )/V_B (2)
The two parameters can be related using equations 3 and 4 below. φ=V_P/(V_P+V_G) (3) φ=V_P/V_B (4)
Pore volume, bulk volume and grain volume can all be determined experimentally using various methods, the most common of which are listed in the following table from API’s Recommended Practice for Core Analysis (1998).
Table 1 - Methods for determining bulk, grain and pore volume
Bulk Volume
The Archimedes Buoyancy methods, as outlined by API (1998), apply the Archimedes Principle to determine the bulk volume of a sample via fluid displacement (most commonly mercury). The amount of mercury displaced can be related to bulk volume by the following equation.
V_B=(Mass of mercury displaced)/(Density of mercury) (5)
A typical setup for this method of measurement using mercury as the displaced fluid, shown in Figure X below, uses a mercury-filled container that rests upon a zeroed electronic scale. A core sample is then lowered and forced into the mercury until it is completely immersed. Due to the Archimedes Principle, which states that buoyancy force is equal to the weight of the displaced fluid, the weight changed on the scale is directly related to the...
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Where:
P1 = absolute initial reference volume pressure.
P2 = absolute expanded pressure.
Pa = absolute atmospheric pressure initially in sample.
Z1 = gas deviation factor at P1 and T1.
Z2 = gas deviation factor at P2 and T2.
Za = gas deviation factor at Pa and T1.
T1r = absolute temperature of reference volume at P1.
T1 = absolute temperature of sample pore volume at Pa.
T2 = absolute temperature of reference volume and sample after P2 is stabilized.
Vr = reference chamber volume.
VP = sample pore volume.
Vv = valve displacement volume
Vd = dead volume
The valve displacement volume, dead volume and reference chamber volume are all determined during the calibration process prior to testing. In an isothermal system, the equation can be simplified further:
V_P=(V_r ((P_1 Z_2)/(P_2 Z_1 )-1)-V_v)/(1-(P_a Z_2)/(P_2 Z_a ))-V_d (7)
High pressure porosity testing us
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