Estudio de la dureza de un sustrato antes y después del depósito

The porosity of reservoir rocks can be determined essentially by two different methods: routine core analysis (laboratory measurements on core plugs drilled from whole core samples) and well logging techniques. Between these two methods, routine core analysis is probably the most common method used in the determination of porosity of reservoir rocks. Rock samples used in porosity mea-surements are called core plugs. Sometimes subsamples called end trims sliced from core plugs are used in routine core analysis (porosity, absolute permeability, and saturation measurement). See Chapter 6 for a discussion on core plugs and end trims.

Well logging techniques are somewhat indirect in nature, and usually poros-ity is measured in situ (in the vicinporos-ity of the wellbore), that is, actual physical samples of the reservoir rock are not tested in laboratories like routine core analysis. Porosity determination using well logging techniques (porosity logs) is not discussed here; the reader is referred to the works of Brock⁶ and Bassiouni⁷ that cover this subject in great details. In addition to the two methods of routine core analysis and well logging, other nonconventional techniques of porosity determination exist, such as x-ray computerized tomography (CT) scanning that is discussed in Section 3.6.

The routine core analysis method of porosity determination is discussed in the following sections.

25 Porosity

3.5.1 POROSITYDETERMINATIONUSING ROUTINE COREANALYSIS

A given reservoir rock sample basically comprises three different volumes: bulk volume (BV), pore volume (PV), and grain volume (GV). These three volumes are related by the following simple relationship:

BV=PV GV+ (3.6)

Therefore, in the laboratory measurement of porosity, it is necessary to determine only two of the three volumes: BV, PV, or GV. The various methods described in the following text for determining BV, PV, or GV are mainly for dry, cleaned reservoir rock samples.

3.5.1.1 Bulk Volume Measurement

The most common types of samples used in routine core analysis are cylindrical core plugs which allow the determination of BV from the dimensions of the sample (L = length and D = diameter; BV = (π/4)D²L). This is the easiest and simplest method of determining the BV of a reservoir rock sample. Although this method works well for perfectly cylindrical samples, inaccuracies in the computed BV are evident in the case of chipped samples or slight geometric irregularities, usually resulting in a nonrepresentative BV and incorrect porosities. Therefore, in order to avoid such uncertainties in the BV measurement, a procedure that utilizes the observation of the volume of fluid displaced by the sample is employed (Archimedes principle).

The fluid displaced by a sample is generally obtained gravimetrically. This proce-dure has obvious advantages because the BV of irregular-shaped samples as well as geometrically well-defined or symmetric samples can be determined with the same accuracy and speed. However, it is very important to prevent the penetration of the fluid used in observing the displacement into the pore space of the rock specimen because this affects the BV measurement. This can be accomplished by either coat-ing the sample with paraffin wax or presaturatcoat-ing the sample with the same fluid used for observing the displacement, or using mercury, which, owing to its wetting characteristics, does not tend to enter the pore spaces unless it is forced. If the sample is coated, then corrections are required to determine the displaced volume.

If mercury is used, then three different weights are recorded: (a) dry core sample in air, (b) mercury-filled pycnometer, and (c) mercury-filled pycnometer containing the core sample. Based on the recorded weights, the volume of mercury displaced is simply (a) + (b) − (c)/ρmercury= BV. Note that (c) will be lower than the summation of (a) and (b) due to buoyancy effects. Saturating the sample with the fluid that is used for observing the displacement has a clear advantage, in that as part of the BV measurement, PV is also measured, which actually allows the determination of sample porosity.

3.5.1.2 Pore Volume Measurement

All methods used for determining pore volume are based on either extraction of a fluid from the rock sample or reintroduction of a fluid in the pore spaces of the rock sample. It is noteworthy that all methods measuring pore volume yield effective

26 Petroleum Reservoir Rock and Fluid Properties

porosity simply because the fluid either extracted from the pore spaces of the rock sample or introduced into the pore spaces of the rock sample will always be from interconnected and dead-end or cul-de-sac pores. It should also be mentioned here that since pore spaces in reservoir rocks are quite small (of the order of 20–200 μm), the determination of pore volumes of such samples involves measuring the volume of literally thousands of pores.

In the extraction methods, the rock sample (in most cases saturated with native or original reservoir fluids) is subjected to an extraction procedure that uses suit-able solvents to recover the fluids contained in the pore spaces. The total volume of the extracted fluids is determined and that in itself theoretically represents the pore volume. This particular technique is in fact part or basis of the fluid saturation deter-mination of as-received core plug samples and is discussed in detail in Chapter 6.

When introducing fluids into the pore spaces of the rock sample, a number of meth-ods are used for the determination of pore volume of reservoir rocks. These methmeth-ods typically use three different types of fluids: helium, water or synthetic oil, and mer-cury. The porosity measured is, however, effective porosity because the saturating fluids only penetrate the interconnected and dead-end pore spaces. Although mercury has some distinct advantages, its use in laboratory testing is accompanied with the associated health hazards and, additionally, the rock sample is rendered unusable. The various methods that employ these saturating fluids are described in the following text.

3.5.1.2.1 Helium Porosimeter

The use of helium in the determination of porosity has certain obvious advan-tages over other gases and liquids: Helium is a clean inert gas and does not cause any unwanted rock–fluid interactions that may affect/change the original poros-ity; molecules are small that can rapidly penetrate the small pores, and it can be considered an ideal gas (compressibility factor = 1) for pressures and temperatures usually employed in the procedure. Additionally, porosity measurements can be completed in a short amount of time. The use of helium in desktop-type porosim-eters, commonly available in the market, is by far the most common technique for measuring porosities of plug size core samples.

All helium porosimeters actually employ the principles of Boyle’s law, that is, PV = constant, where P is the pressure and V the volume, for the determination of porosity of rock samples. Figure 3.6 shows a general arrangement of the helium porosimeter. In principle, the apparatus consists of two equal-volume chambers or cells called the reference chamber and the sample chamber. The reference chamber has a volume V₁ at initial pressure P₁ (usually 100 psig), and the sample chamber has an unknown volume V₂ and initial pressure P₂ (normally atmospheric). The system is then brought to equilibrium by opening the valve to the sample chamber, allow-ing the determination of the unknown volume V₂ by noting the resultant equilibrium pressure P. The application of Boyle’s law allows the equalization of pressures (for iso-thermal conditions) before and after the opening of the valve to the sample chamber, as per the following equation:

PV_{1 1}+P V_{2 2}=P V( ₁+V₂) (3.7)

27 Porosity

or by rearrangement

V V P P P P

2= 1 1−

−

( )

( ₂) (3.8)

The calculated unknown volume V₂ can in fact be expressed as

V₂= −V₁ BV PV+ (3.9)

which allows the calculation of PV or porosity φ =V₂− +V₁ BV

BV (3.10)

where

BV is the bulk volume of the sample measured (e.g., from sample dimensions) V₁ is known, and V₂ is determined from Equation 3.8

The sample porosity calculated in Equation 3.10 can be multiplied by 100 to report the value in percentage.

3.5.1.2.2 Vacuum Saturation

The vacuum saturation method is in fact one of the very basic methods of obtaining the pore volume of a rock sample. One of the advantages is the fact that pore volumes of multiple samples can be determined in one step. The method uses a large enough vacuum flask or a beaker, filled with a degassed liquid, normally water, in which dry rock samples are placed. Subsequently, as soon as the evacuation of the vacuum flask

Pressure gauges

Reference chamber Sample chamber

Core sample

Valves

Helium supply

V₂ V₁

FIGURE 3.6 Schematic illustration of a helium porosimeter.

28 Petroleum Reservoir Rock and Fluid Properties

is initiated, air bubbles are seen in the saturating liquid as it replaces air from the pore spaces of the rock samples. The disappearance of the air bubbles gives an indi-cation that the saturation is complete and at this point the evacuation is terminated, and porosity is calculated as follows:

φ=(WW DW)−ρ ×

BV %

w

100 (3.11)

where

WW is the wet weight of the sample, after vacuum saturation DW is the dry weight of the sample, before vacuum saturation ρw is the saturating fluid (water) density

The time required for completion of the saturation is directly proportional to the sample size and pore sizes. This simple method may work well for small samples and those having reasonably large pore spaces.

3.5.1.2.3 Liquid Saturation by Other Methods

The other methods of introduction of a liquid into the pore spaces of a rock sample include forced saturation by either water or synthetic oil. The rock sample is held in a special device called a core holder, and a given liquid is injected through the sample by use of a pump. This method, however, requires advanced apparatus called a core flooding rig or a displacement apparatus (see Figure 4.7), compared to the techniques discussed earlier.

A volume balance, based on the injection rate and total time between the injected liquid and the produced liquid from the rock sample, can give an indication of the saturation of the sample. In some cases, the vacuum saturation technique discussed earlier may be used as a forerunner for this technique to speed up the saturation process. On completion of the saturation, sample porosity is determined using Equation 3.11.

3.5.1.3 Grain Volume Measurement

All methods measuring grain volume usually yield total or absolute porosity, sim-ply because the rock samples are normally crushed for grain volume measurements which actually destroy all pores, thus resulting in total porosity as grain volume is subtracted from the bulk volume. Although only the effective pore space has direct application in most reservoir engineering calculations, knowledge of the magnitude and distribution of the isolated pore spaces can reveal other characteristics of reservoir rocks.

Grain volume of rock samples is sometimes calculated from dry sample weight and knowledge of average density. For example, in the case of sandstone, average density of quartz (2.65 g/cm³) can be used as the sand grain density to calculate the grain volume, and for carbonates the grain density is of the order of 2.70 g/cm³. However, formations of varying lithology and grain density limit the applicability of this method.

29 Porosity

The Boyle’s law technique for pore volume measurement that was discussed earlier can in fact also be construed as a method that determines the grain volume.

This is clear from Equations 3.8 and 3.9; that is, the volume, V₂, occupied by helium in the sample chamber is equal to the difference between the overall chamber volume V₁ because both reference and sample chambers have equal volume and the vol-ume of solids in the sample chamber. This particular volvol-ume of solids in the sample chamber is nothing but the grain volume, which allows Equation 3.9 to eventually permit the determination of porosity:

V₂= − GVV₁ (3.12)

The measurement of the grain volume of a cleaned and dried crushed core sample may also be based on the loss in weight of a saturated sample plunged in a liquid, which is similar to the bulk volume measurement using the principle of buoyancy.

3.6 NONCONVENTIONAL METHODS