 Petroleum Reservoir Engineering Practice: Porosity of Reservoir Rocks

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1.3 Sources of Porosity Data

Rock porosity data are obtained by direct or indirect measurements. Laboratory measurements of porosity data on core samples are examples of direct methods. Determinations of porosity data from well log data are considered indirect methods.

1.3.1 Direct Methods for Measurement of Porosity

Direct measurements of porosity data on core samples in a laboratory typically require measurements of bulk and pore volumes of the core samples. For irregular-shaped core samples, the bulk volume is determined by gravimetric or volumetric methods. In gravimetric methods, the apparent loss in weight of the sample when immersed completely in a liquid of known density is measured. Volumetric methods measure the volume of liquid displaced by the rock sample when completely immersed in the liquid. These methods use specially designed equipment so that the liquid is not absorbed by the rock sample. For regular-shaped samples, the bulk volume is calculated from physical measurement of the dimensions of the core sample. For instance, if the core plug is cylindrical in shape, the bulk volume is calculated as:

Equation 1.6 In Eq. (1.6), VB = bulk volume; r = radius of the core plug; and l = length of the core plug.

Other direct methods for measuring the porosity of a rock sample include use of mercury porosimeter or gas expansion porosimeter. The use of mercury porosimeter or gas expansion porosimeter for measurement of porosity is not presented in this book because they are described in many introductory textbooks2 on petroleum reservoir engineering.

Most laboratory routines based on direct methods measure total porosity. It is important to remember to distinguish between total porosity data obtained from core samples and porosity data derived from well logs, which may include effective porosities. Porosity data obtained from core samples using direct methods are generally considered to be accurate and reliable. They are used to calibrate and validate log-derived porosity data which are based on indirect methods.

Example 1.1. Calculation of Porosity from Gravimetric Data

• Problem

The dimensions of a cylindrical core sample are 10.16 cm long and 3.81 cm in diameter after it was thoroughly cleaned and dried. The dried core sample weighed 365.0 g. The core sample was then completely (100%) saturated with brine that has specific gravity of 1.04. The weight of the saturated core sample is 390.0 g. Calculate the porosity of the core sample.

Solution

Using Eq. (1.6), the bulk volume of the core sample is: The pore volume of the core sample is given by: Using Eq. (1.2), porosity of the core sample is: 1.3.2 Indirect Methods for Derivation of Porosity

Indirect methods for derivation of porosity data are based on well log data. The well logs generally used for this purpose are density, sonic, neutron, and nuclear magnetic response (NMR) logs. In most formation evaluation programs, density, sonic, and neutron logs are routinely acquired. The NMR log is frequently run in many wells because of its capability of providing other data for formation evaluation, in addition to porosity data. In most deepwater wells, it is common practice to run NMR logs, in addition to density, sonic, and neutron logs. It is important to note that density, sonic, and neutron logs are lithology-dependent, while the NMR logs are lithology-independent for derivation of porosity.3 NMR data are very sensitive to environmental conditions. It is recommended that NMR tools should be run together with conventional logs, such as density logs or neutron logs for quality control and validation of the NMR data. A summary of the basic principles, data requirements, advantages, and disadvantages of all the porosity tools is provided in Table 1.1.

 Type of Porosity Log Attributes Density Neutron Sonic NMR Basic principle Gamma ray attenuation "Slowed" neutrons or Gamma ray capture Transit times Excitation of hydrogen in pore spaces Required data Matrix and fluid densities Calibration Matrix and fluid transit times Hydrogen index Advantages Little effect of presence of gas in formation Ability to detect presence of gas in formation; can be used in cased hole Good compensation for environmental effects; combinable with induction logs Lithology independent Disadvantages Shallow depth of investigation; affected by wellbore washouts Sensitive to irregular borehole; requires calibration Depth of investigation dependent on type of formation Environmental corrections; tool run speed affects results

1.3.2.1 Density Logs

Density logs are based on the attenuation of gamma rays in the formation.3 Density logging tools measure the attenuation of gamma rays produced by a gamma source of known strength. The attenuation caused by the interaction between gamma ray photons and electrons on the outer shell of electrons (called Compton scattering) is directly proportional to the bulk density (r b ) of the formation. The formation bulk density is related to formation matrix density (r ma )and formation fluid density (r f ) as:

Equation 1.7 Re-arranging Eq. (1.7), density-derived porosity is given by:

Equation 1.8 In Eq. (1.8), f d = density-derived porosity; r ma = matrix density; r b = bulk density; and r f = fluid density. The porosity data obtained from density logs are considered to be total porosity. This relationship can be represented as:

Equation 1.9 For density logs, effective porosity is derived from Eq. (1.3) as:

Equation 1.10 In Eq. (1.10), f dsh is the shale porosity derived from the density logs. The depth of investigation of density logging tools is shallow and typically within the zone invaded by mud filtrate. For this reason, it is sometimes appropriate to assume that the density of formation fluid is equal to the density of the mud filtrate. However, this assumption may cause errors in the density-derived porosity data, if virgin formation fluid remains within the depth of investigation of the density tool.4 The matrix density can be determined from elemental capture spectroscopy (ECS) log, if available.

Example 1.2. Calculation of Porosity from Density Logs

• Problem

The bulk density of a clean, sandy interval saturated with water was measured by the density logging tool to be 2.4 g/cm3. Assuming that the density of the formation water is 1.04 g/cm3 and the density of the matrix is 2.67 g/cm3, calculate the density porosity of this interval.

Solution

Using Eq. (1.8), density porosity is calculated to be: 1.3.2.2 Sonic (acoustic) Logs

In sonic (acoustic) logging, the formation is probed with sound waves. The time it takes the sound waves to travel a given distance is measured. This interval transit time depends on the elastic properties of the rock matrix, the properties of the fluid in the rock, and the porosity of the rock. Wyllie et al.5 proposed that the interval transit time (Dt) can be represented as the sum of the transit time in the matrix fraction (Dtma ) and the transit time in the liquid fraction (Dtf ) thus:

Equation 1.11 Re arranging Eq. (1.11), sonic-derived porosity is given by:

Equation 1.12 In Eq. (1.12), f s = sonic-derived porosity; Dt = transit time; Dtf = fluid transit time; and Dtma = transit time for the rock matrix. Total porosity is related to porosity derived from sonic logs as:

Equation 1.13 In Eq. (1.13), Vclay = the volume of clay; and f scl = sonic porosity derived in the clay. Effective porosity as calculated from sonic logs as:

Equation 1.14 In Eq. (1.14), Vsh = volume of shale; and f ssh = sonic porosity derived for shale. Analysis of sonic logs based on Eq. (1.12) gives reliable porosity data only for consolidated formations. For unconsolidated sandstones and carbonates, Eq. (1.12) gives porosity values that are too high. Other equations similar to Eq. (1.12) have been proposed for calculation of porosity for unconsolidated formations and carbonates by Raymer et al.6 These equations should be used for calculations of sonic porosities on unconsolidated formations and carbonates. Note that sonic logs are well-compensated for environmental effects such as mud velocity, borehole diameter, etc. and that its depth of investigation is dependent on the compactness of the formation.

Example 1.3. Calculation of Porosity from Sonic Logs

• Problem

The transit time for a well-consolidated sandstone interval saturated with brine was measured to be 82 x 10–6 sec/ft. The matrix transit time is 55.5 x 10–6 sec/ft and the brine transit time is 189 x 10–6 sec/ft. Calculate the sonic porosity for the interval.

Solution

Applying Eq. (1.12), sonic porosity is calculated to be: 1.3.2.3 Neutron Porosity Logs

The first logging tool that was used for the estimation of formation porosity is the neutron logging tool, which was introduced around 1940. The neutron porosity logging tool consists of either a chemical source or an electrical source of fast neutrons, and detectors located some distance from the source. The fast neutrons from the neutron source are slowed down by successive collisions with individual nuclei in the rock, thereby losing most of their energy. The detectors in the neutron tool record either the "slowed" down neutrons directly or capture gamma radiation generated when the neutrons are captured by nuclei. The neutron porosity log is sensitive to the amount of hydrogen in the formation because the neutrons interact most effectively with hydrogen due to the closeness of their masses. Neutron logs estimate the amount of hydrogen in the rock, and relate it to the amount of fluid in the formation. From the amount of fluid in the formation, the porosity of the rock is estimated after calibration for different lithologies (sandstone, dolomite, and limestone). Neutron porosity tools are sensitive to borehole conditions, especially variations in the size of the borehole. In combination with density porosity logs, neutron porosity logs can be used to detect the presence of gas in some formations. This known crossover of density porosity log and neutron porosity log in gas-filled formation intervals results from the apparent increase of density-derived porosities and apparent decrease of neutron-derived porosities in gas-filled formation intervals (Figure 1.2).

For neutron porosity logs, correction for total porosity is applied as:

Equation 1.15 In Eq. (1.15), f n = porosity from neutron logs; and f ncl = neutron porosity for clay. Effective porosity is defined as:

Equation 1.16 In Eq. (1.16), f nsh is the neutron porosity for shale.

1.3.2.4 Nuclear Magnetic Resonance (NMR) Porosity Logs

Nuclear magnetic resonance (NMR) porosity tools have a clear advantage over other porosity tools (density, sonic, and neutron) because their determination of porosity is independent of lithology of the rock. Porosities calculated from density, sonic, and neutron logs depend on "knowing" or estimating the properties of the rock matrix. NMR porosities are calculated from the number of hydrogen atoms in the fluids (hydrocarbon and water) within a specific measurement volume of the tool, and are independent of the lithology of the rock formation.7 For reservoirs with highly heterogeneous rocks consisting of mixed or unknown lithology, porosity data derived from NMR logs are more consistent and reliable than porosity data from the other porosity tools.8 NMR logs report porosities in terms of total porosity, bound-fluid porosity, and free-fluid porosity (Figure 1.1). Free-fluid porosity (also termed free-fluid index) is a qualitative measure of effective porosity and is linked to the hydrocarbon storage potential of the formation. A comparison of porosities measured with NMR in the laboratory to porosities measured by direct methods on core samples from a reservoir is shown in Figure 1.3. The porosity data plotted in Figure 1.3 show close agreements between NMR porosities and core porosities measured on core samples. It demonstrates a method for calibrating NMR porosities with core porosities, which can then be used to calculate porosities from NMR data in other wells. In addition to measurement of porosity, NMR tools are used for determination of pore size distributions, measurements of permeability (Chapter 2), and fluid saturations (Chapter 3). NMR tools have become standard in most wireline logging operations because they can quickly provide qualitative data on formation porosity, permeability, pore size distributions, and fluid saturations.9,10 These data are very valuable and useful. They are frequently used to make decisions on selection of fluid sampling points and formation intervals to be tested in discovery, appraisal, and development wells. Figure 1.3 NMR porosity versus core porosity based on core samples from a reservoir.