One method in which porosity is determined is by laboratory measurements of Core Samples brought to the surface during drilling. Measurement of porosity in the laboratory is part of Routine Core Analysis, sometimes referred to as PKS Analysis (porosity, permeability, and saturation analysis).
Core samples are rock samples that are cut from the reservoir formation using specialized Coring Bits. The extraction of core samples is a very complicated process and requires a lot of planning. When cutting a core, all phases of the coring process must be considered to ensure that the porosity is not altered prior to its delivery to the laboratory. These phases include core cutting, core handling, core preservation, core transport, core sampling, and core testing. Typically, a Formation Evaluation Specialist takes the lead role in designing the core program while working with a development geologist, a reservoir engineer, and a drilling engineer.
After retrieving representative core samples and delivering them to the laboratory, there are several methods that can be used to determine porosity. As shown in Equations 3.01 through 3.03, to determine porosity, we need to determine two of the three volumes, ${V}_{b}$, ${V}_{p}$, or ${V}_{g}$. Once these are determined, then the porosity and the third volume are known.
Bulk Volume, ${V}_{b}$, Determination
Bulk volume can be determined by one of two methods, physical measurement and displacement. The use of physical measurements is only applicable to core samples with regular geometric shapes. As the name implies, physical measurement involves the measurement of the dimensions of the core sample (typically a cylindrical core plug) and calculating the volume from standard volumetric formulae.
Displacement methods involve the immersion of the core sample in mercury inside of a pycnometer or graduated cylinder. Mercury is used in displacement methods to prevent invasion into the pore space. The bulk volume of the sample is the apparent volume change of the mercury in the pycnometer or graduated cylinder. Alternative, Archimedes’ Principle can be used to determine the bulk volume of the core sample from the apparent weight change due to buoyancy when fully immersed.
Grain Volume, ${V}_{g}$, Determination
The most direct method for determining grain volume is to measure the weight of a dried sample and to divide by the density of the rock matrix. Unfortunately, the rock densities are often not accurately known.
A second method, similar to the immersion method for bulk volume determination, can be used for grain volume determination. In this method, a core sample is crushed and the resulting rock grains are placed into a pycnometer or graduated cylinder along with a known volume of liquid. The volume of the rock grains can then be determined from the apparent volume change of the liquid (the Russell Method) after immersion or the apparent weight change (the MelcherNutting Method) of the immersed sample due to buoyancy using Archimedes’ Principle.
Unfortunately, the disadvantage of this method is that it is destructive. Once the sample is pulverized, it cannot be used for further testing. Since we have crushed the core sample to its constituent rock grains, the porosity determined from the immersion of these grains is the total porosity, ${\varphi}_{t}$.
A third method is the Boyle’s Law Method. As the name implies, it uses Boyle’s Law for the grain volume determination:
In this method, the core sample is placed into one chamber of an experimental apparatus containing two chambers of known volume connected by a closed valve. An inert gas (helium or nitrogen) is introduced into the chambers at different, but known, pressures. At this point, the total number of moles, n_{T}, in the apparatus can be determined from:
For isothermal conditions, this reduces to Boyle’s Law:
The valve between the chambers is opened and the pressure is allowed to stabilize to the final pressure, p_{f}, and is recorded. If we assume that the core sample was placed into Chamber 1, then we have:
Example 3.01
Given the following data:
 Weight of the crushed core sample in air: $W{t}_{dry}=20.0gm$
 Weight of the crushed core sample in water: $W{t}_{imm}=15.0gm$
 Density of water: ${\rho}_{w}=1.0gm/cc$
Use Archimedes’ Principle to calculate the grain volume of the sample.
SOLUTION:
The weight of the displaced water is simply the apparent change in weight of the sample due to buoyancy:
$$W{t}_{displaced}=W{t}_{dry}W{t}_{imm}$$
$$W{t}_{displaced}=20.0\text{}gm15.0\text{}gm=5.0gm$$
The volume of the rock grains then becomes the volume of the displaced water:
$${v}_{g}=\frac{W{t}_{displaced}}{{\rho}_{w}}=\frac{5.0\text{}gm}{1.0\text{}gm/cc}=5\text{}cc$$
Solving for ${v}_{g}$ :
The advantages of this method are that it is nondestructive and can be very accurate. The disadvantage of this method is that for low permeability core samples, it may take a long time for the pressures to stabilize. Since the gases can only enter or leave the connected pores, the porosity obtained from the Boyle’s Law Method is the effective porosity, ${\varphi}_{e}$.
Pore Volume, ${V}_{p}$, Determination
Early methods used for pore volume determination, such as the WashburnBunting Method, used mercury injection into the pore spaces of the core sample. In these Mercury Injection Methods, high pressure mercury was injected into the core sample and the volume of mercury entering the core was measured. These methods had several drawbacks, including the destructive nature of the test and the compression of any gases in the core sample retaining a residual volume, resulting in measurement inaccuracies.
Example 3.02
Given the data:
 ${V}_{1}=100cc$
 ${V}_{2}=100cc$
 ${p}_{1}=15.0psi$
 ${p}_{2}=60.0psi$
When the valve between Chamber 1 and Chamber 2 is opened, the pressure is found to stabilize at ${p}_{f}=39.0psi$ . What is the grain volume of the core sample?
SOLUTION:
From Equation 3.10, we have:
$${V}_{g}=\frac{100cc\left(39.0\text{}psi15.0\text{}psi\right)+100\text{}cc\left(39.0\text{}psi60.0\text{}psi\right)}{\left(39.0\text{}psi15.0\text{}psi\right)}$$
$${v}_{g}=12.5cc$$
A second method, the Resaturation Method, uses a clean dry core sample and resaturates it with a fluid of known density. The change in weight of the sample can then be used to determine the pore volume, V_{p}, of the sample
Since the fluid can only enter or leave the connected pores, the porosity obtained from the resaturation method is the effective porosity, ${\varphi}_{e}$.
A third method for the determination of the pore volume is the Summation of Fluids Method. In this method, a core sample in its native state (not cleaned or dried) is halved. In one of the halves, mercury injection is used to estimate the gas volume, while the second half is used in the retorting (distillation) process to determine the oil and water volumes. The pore volume is then set equal to the sum of the fluid volumes. The advantage of this method is that the Phase Saturations (fraction of the pore space occupied by each phase – oil, gas, and water) can be determined simultaneously with the porosity. The disadvantages of the method are the destructive nature of the test and the assumption that both halves of the core sample contain similar fluid volumes.
Again, in the summation of fluids method, fluids can only enter or leave the connected pores. Consequently, the porosity obtained from this method is the effective porosity, ${\varphi}_{e}$.
Example 3.03
Given the following data:
 Weight of the clean dried core sample in air: $W{t}_{dry}=20.0gm$
 Weight of the core sample saturated with water: $W{t}_{sat}=22.5gm$
 Density of water: ${\rho}_{w}=1.0gm/cc$
What is the pore volume of the core sample?
SOLUTION:
The weight of the water saturating the sample is:
$$W{t}_{water}=W{t}_{sat}W{t}_{dry}$$
$$W{t}_{water}=22.5gm20.0gm=2.5gm$$
The pore volume of the core sample then becomes the volume of the water saturating the core:
$${v}_{gp}=\frac{W{t}_{water}}{{\rho}_{w}}=\frac{2.5gm}{1.0gm/cc}=2.5cc$$
Method  Porosity Type  Advantages  Disadvantages 

Grain Determination by Immersion  Total Porosity, ${\varphi}_{t}$ 


Grain Determination by Boyles Law  Effective Porosity, ${\varphi}_{e}$ 


WashburnBunting (Mercury Injection)  Effective Porosity, ${\varphi}_{e}$ 


Resaturation  Effective Porosity, ${\varphi}_{e}$ 


Summation of Fluids  Effective Porosity, ${\varphi}_{e}$ 

