Petrography and Texture of Petroleum' Bearing Formations
The petrographical parameters are facilitated to quantitatively describe the texture or appearance of the rock minerals and the pore structure. The fundamental parameters used for this purpose are described in the following.
Fabric and Texture
Lucia (1995) emphasizes that "Pore space must be defined and classified in terms of rock fabrics and petrophysical properties to integrate geological and engineering information." Fabric is the particle orientation in sedimentary rock (O'Brien et al., 1994). Defarge et al. (1996) defined: "Texture, i.e., the size, shape, and mutual arrangement of the constitutient elements at the smaller scale of ... sedimentary bodies, is a petrological feature that may serve to characterize and compare" them.
Lucia (1995) points out that: "The pore-size distribution is controlled by the grain size in grain-dominated packstones and by the mud size in mud-dominated packstones." Lucia (1995) explains that: "Touching-vug pore systems are defined as pore space that is:
(1) significantly larger than the particle size, and
(2) forms an interconnected pore system of significant extent"
Porosity, (j), is a scalar measure of the pore volume defined as the volume fraction of the pore space in the bulk of porous media. The porous structure of naturally occurring porous media is quite complicated. The simplest of the pore geometry is formed by packing of near-spherical grains. When the formation contains different types of grains and fractured by stress and deformation, pore structure is highly complicated. For convenience in analytical modeling, the porous structure of a formation can be subdivided into a number of regions. Frequently, a gross classification as micropores and macropores regions according to Whitaker (1999) and Bai et al. (1993) can be used for simplification. However, in some cases, a more detailed composite description with multiple regions may be required (Cinco-Ley, 1996; Guo and Evans, 1995). Such descriptions may accommodate for natural fractures and grain packed regions of different characteristics. The various regions are considered to interact with each other (Bai et al., 1995).
Spherical Pore Space Approximation
For simplification and convenience, the shapes of the pore space and grains of porous media are approximated and idealized as spheres. The pore volume can be approximated in terms of the mean pore diameter, D, as:
The specific pore surface in terms of the pore surface per pore volume is given by:The expressions given above for a spherical shape can be corrected for irregular pore space, respectively, as (Civan, 1996):
Area Open for FlowAreosity or areal porosity is the fractional area of the bulk porous media open for flow (Liu and Masliyah, 1996). Liu and Masliyah (1996) point out that, frequently, the areal porosity has been taken equal to the volumetric porosity of porous media.
They emphasize that Equation 3-11 performs well for models considering a bundle of straight hydraulic flow pathways and nonconnecting constricted pathways. Whereas, for isotropic porous media, Liu et al. (1994) recommend that the areal porosity should be estimated as:
Tortuosity is defined as the ration of the lengths, Lt and L, of the tortuous fluid pathways and the porous media:
Liu and Masliyah (1996a, b) recommend the Bruggeman (1935) equation for consolidated porous media of porosity (|) < 0.45. They point out that the latter may have a variable accuracy and, therefore, tortuosity should be measured.
Interconnectivity of Pores
Davies (1990) classified the pore types in four groups:
Pore Type 1: Microspores, generally equant shape, less than 5 microns in diameter. These occur in the finest grained and shaly portions of the sand.
Pore Type 2: Narrow, slot like pores, generally less than 15 microns in diameter, commonly slightly to strongly curved. These represent reduced primary intergranular pores resulting from the reduction of original primary pores by extensive cementation.
Pore Type 3: Primary intergranular pores, triangular in shape, twenty-five to fifty microns maximum diameter. These are the original primary intergranular pores of the rock which have been affected only minimally by cementation.
Pore Type 4: Solution enlarged primary pores: oversized primary pores, fifty to two hundred microns maximum diameter produced through the partial dissolution of rock matrix.
Frequently, for convenience, pore space is perceived to consist of pore bodies connecting to other pore bodies by means of the pore necks or throats as depicted. Many models facilitate a network of pore bodies connected with pore throats.
However, in reality, it is an informidable task to distinguish between the pore throats and pore bodies in irregular porous structure (Lymberopoulos and Payatakes, 1992). Interconnectivity of pores is a parameter determining the porosity of the porous media effective in its fluid flow capability. In this respect, the pores of porous media.
The sketched are classified in three groups:
1. Connecting pores which have flow capability or permeability (conductor),
2. Dead-end pores which have storage capability (capacitor), and
2 Non-connecting pores which are isolated and therefore do not contribute to permeability (nonconductor).
The interconnectivity is measured by the coordination number, defined as the number of pore throats emanating from a pore body. Typically, this number varies in the range of 6 < Z < 14 (Sharma and Yortsos, 1987). For cubic packing, Z = 6 and <J> = 1 - n/6. The coordination number can be determined by nitrogen sorption measurements (Liu and Seaton, 1994).
Pore and Pore Throat Size Distributions
Typical measured pore body and pore throat sizes, given by Ehrlich and Davies (1989) The mathematical representation of the distribution of the pore body and pore throat sizes in natural porous media can be accomplished by various statistical means. The three of the frequently used approaches are the following:
1. Log-Normal Distribution (not representative)
2. Bi-Model Distribution (fine and course fractions)
3. Fractal Distribution
Because of is simplicity, the log-normal distribution function given below has been used by many, including Ohen and Civan (1991):
Typically, the pore body and pore throat sizes vary over finite ranges and the size distributions can display a number of peaks corresponding to various fractions of pore bodies and pore throats in porous media. If only two groups, such as the fine and coarse fractions, are considered, a bi-modal distribution function according to Popplewell et al. (1989) can be used for mathematical representation of the size distribution:
where D denotes the diameter, f\(D) and /2(^) are the distribution functions for the fine and coarse fractions, and w is the fraction of the fine fractions. Popplewell et al. (1988, 1989) used the p-distribution function to represent the skewed size distribution, because the diameters of the smallest and the largest particles are finite in realistic porous media. For convenience, they expressed the P-distribution function in the following modified from:
Chang and Civan (1991, 1992, 1997) used this approach successfully in a model for chemically induced formation damage.
Fractal Distribution: Fractal is a concept used for convenient mathematical description of irregular shapes or patterns, such as the pores of rocks, assuming self-similarity. The pore size distributions measured at different scales of resolution have been shown to be adequately described by empirically determined power law functions of the pore sizes (Garrison et al., 1993; Verrecchia, 1995; Karacan and Okandan, 1995; Perrier et al., 1996). The expression given by Perrier et al. (1996) for the differential pore size distribution can be written in terms of the pore diameter as:
where, D denotes the pore diameter, V represents the volume of pores whose diameter is greater than D, d is the fractal dimension (typically 2 < d < 3), e is the Euclidean space dimension (e = 3) and (3 is a positive constant. Thus, integrating Equation 3-23, Perrier et al. (1996) derived the following expression for the pore size distribution.
Nolen et al. (1992) have described the textual appearance of reservoir formation by four parameters:
1. Median grain size, defined as:
and the surface area and surface area based diameter, dA, are given, respectively, by:
2. Grain shape factor, defined as:
3. Sorting, defined by:
4. Packing, which is the volume fraction of the solid matrix, given by:
density, cement, and intergranular volume at various locations of reservoir formations. Such diagrams provide useful insight into the heterogeneity of reservoirs. Coskun et al. (1993) shows the relationships between composition, texture, porosity, and permeability for a typical sandstone reservoir.
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