Effective elastic properties of cracked solids . Friction stir welding and processing - ScienceDirect
In this chapter, we will tabulate important mineral and rock properties, and provide many of the mathematical models used to describe and predict properties. Much of this summary is drawn upon the extensive work and compellations already available. As examples, Clark provides an extensive list of mineral and rock properties; Birch presents tables of compressional velocities, and Gregory gives a detailed overview of the use of rock property information in seismic interpretation.
Castagna et al.  focused on rock properties for use in amplitude versus offset analyses. Useful handbooks on this topic include Carmichael and Lama and Vutukuri.  Probably the best reference covering a wide range of rock property formulas and models is Mavko et al.  These references can be consulted for details not presented here. Knowledge of Rock Properties Is Largely EmpiricalMany theoretical models have been developed to predict or correlate specific physical properties of porous rock.
Most theoretical models are built on simplified physical concepts: what are the properties of an ideal porous media. However, in comparison with real rocks, these models are always oversimplified (they must be, to be solvable). Most of these models are capable of forward modeling or predicting rock properties with one or more arbitrary parameters. However, as is typical in Earth science, our models cannot be inverted from measurements to predict uniquely real rock and pore-fluid properties. Many efforts have been made and will continue to be made to build porous rock models, but progress is very limited.
Some of the most fundamental questions are still unanswered. To establish the basic relationships between physical properties and rock parameters, laboratory investigations are made. Laboratory measurements of rock samples can provide controlled conditions and high data quality (hard data). These relationships can be extended to a larger scale, or can even be made scaleless. Typically, models and relations based on laboratory data are then applied to in-situ measurements to derive the parameters we actually need (say, permeability) from information we can actually collect (say, density and gamma ray radiation). The relative merits and problems associated with several rock and fluid measurement techniques are presented in Table 13.1.
Table 13.1Although many empirical relationships already have been established, when facing a frontier basin, new development areas, or untested portions of known formations, valid prediction of rock properties usually requires core data (including sidewall plugs). For many applications, standard trend data may not be adequate. A broad investigation is needed. Philosophy for Rock PropertiesMany of the factors affecting rock properties are incompletely ascertained.
For example, acoustic velocities can be affected by numerous parameters, many of which cannot be measured. In addressing a rock physics problem, the following aspects should be remembered:There may be no exact solution. Rock properties are controlled by rock parameters, and these physical correlations can be examined and recognized (although perhaps not understood). Often nature gives us a break. At certain conditions, relationships between the rock properties and rock parameters can be simplified (such as Archies Law).
We usually must settle on imperfect solutions with some uncertainty. Statistical trends or high and low bounds might be used to handle the uncertainty. Every measurement is, to some degree, wrong.
The question is: Can we tolerate the errors and understand how they propagate through our analyses? We will begin this chapter with a suite of definitions and examples, then move on to data and models of individual properties. By necessity, we will be restricted in the material we can cover in a single chapter. As a result, we will not go into many details of rock fabrics and petrography. Also, with a few exceptions, the information provided here assumes that rocks are homogeneous and isotropic.
Rocks are defined for our purposes as aggregates or mixtures of minerals plus pores. The three general rock types are classified as igneous, metamorphic, and sedimentary. Although hydrocarbon reservoirs have been found in all three rock types, we will consider here primarily sedimentary rocks, by far the most common rocks associated with hydrocarbons. Minerals are defined as naturally occurring solids: They have a definite structure, composition, and suite of properties that are either fixed or vary systematically within a definite range. Although there are dozens of elements and hundreds of described minerals available in the Earths crust, the actual number that we must concern ourselves with for reservoir engineering purposes is remarkably small.
Classification can be broken into silicates, carbonates, sulfates, sulfides, and oxides. In addition, solid organic mixtures such as coal or bitumen can be abundant. Common sedimentary silicates include quartz, feldspars, micas, zeolites, and clays. Carbonates usually consist of calcite and dolomite, although siderite may be present.
Gypsum and anhydrite are the most common sulfates, with pyrite the typical sulfide. Oxides are usually materials such as magnetite and hematite. For most of our purposes, we can further restrict our attention to the subset of quartz, feldspars, clays, calcite, dolomite, and anhydrite. A working knowledge of six or so minerals fulfills most engineering needs.
Clays represent an entire family of minerals with widely differing properties. This situation is compounded by the fact that clays are among the most abundant minerals in the sedimentary section. Clays are also problematic because their properties can vary with the in-situ pressure, temperature, and chemical environment. These issues have led to an unfortunate bias against clays when measuring or describing rocks. A clean sand, for example, is one that has little or no clay. Dirty sandstones or limestones have significant amounts of clay.
Clays and their influence on rock properties remain poorly understood and continue to be an area requiring intensive research. The properties of primary engineering interest are often controlled more by the rock fabric than by the bulk composition. The holes are usually more important than the mineral frame. With the following few examples, we will see many of the most common sedimentary rock forms and textures. Numerous attempts have been made to extract rock properties from images of the rock and pore space.  These techniques often work well, but depend on the observation scale, representative nature of the image, and internal heterogeneity.
A thin section of clean sandstone is shown in Fig. 13.1. Under plane-polarized light, quartz grains appear white and pores are stained blue.
This is a high-porosity, friable sample that has not undergone substantial consolidation. Silica cement can be seen coating the individual grains and bonding the largely unchanged, rounded quartz grains. Grain-to-grain stress is indicated by the fractures radiating from points of grain contact. Although these fractures have a relatively small volume, they have a disproportionately large influence on the mechanical properties, particularly the pressure dependence. With continued diagenesis, quartz grains typically would become intergrown, and large amounts of cement would develop, reducing the pore volume. Fig.
13.1 Common sandstone textures include point contacts, cements, and microfractures. These microstructures determine the properties of the rock on a whole. A Scanning Electron Microscope (SEM) image of another sandstone is seen in Fig. 13.2. A higher degree of compaction is indicated here by the intergrown, sutured contacts of the quartz grains (gray areas). A grain undergoing alteration (a) as well as some of the matrix quartz (b) contain isolated, ineffective porosity.
Fractures are again present, particularly near point of grain contact. Many of these fractures, however, may be caused by stress relief as the sample was cored, or by the cutting and polishing. The most obvious features are the contorted and rotated mica grains (d). These micas were crushed due to compaction, and now host numerous sets of parallel fractures. Some diagenetic clays are also beginning to grow in the pore spaces and act as a cement. Fig.
13.2 Scanning electron microscope (SEM) image of sandstone AT49 showing numerous compaction features. Some grains are either altering (a) or have internal, ineffective porosity (b). Fractures (c) cut numerous grains. Mica plates (d) are rotated and crushed, forming parallel sets of microfractures. A cementation front is visible in Fig. 13.3.
Cements come in a wide variety of forms. Open pores are black in the SEM image. In this case, the lighter gray calcite has filled the pores in the lower portion of the image.
Unlike the dispersed silica and clay cements seen in the previous figures, the calcite is deposited with an abrupt front. This kind of texture is common for carbonate cements in sands and is probably caused by the availability of crystal nucleation sites available to a slightly supersaturated pore fluid. We would obviously expect vastly different properties of the uncemented vs.
cemented portions separated by only a few grain diameters. This rock is an example of the extreme heterogeneity that can frequently occur even within the same small geologic unit of the same formation. Fig.
13.3 SEM image of sandstone AT41 showing a progressing calcite cementation front. Carbonates can have extremely complex textures resulting form the mixture of fossils and matrix building the rock. In Fig. 13.4, an optical image demonstrates the multitude of forms that can be present. Shell fragments appear as crescent shapes in cross section.
Much of the material between fragments can be filled with carbonate mud, reducing the porosity substantially. In this sample, bulk porosity is dominated by the larger disconnected vugs. Such vugs can occur as parts of fossils or as a result of chemical dissolution after deposition. Here, a coating of crystals has grown on the vug surfaces.
Because of the wide range of sizes, shapes, and compositions that can occur in carbonate rocks, they are often difficult to characterize with core or even log sampling. Fig. 13.4 Thin-section image of carbonate textures; in this limestone, numerous curved shell fragments [e.g., at (a)] are packed together and bound by a fine-grained lime mud. Calcite crystals (b) are growing into the pore spaces.
Dolomites are usually formed by recrystallization of original aragonite or calcite crystals in sediments. Magnesium in the pore fluids replace some of the calcium, forming a Mg-Ca carbonate structure. Because of the greater density of dolomite, this transformation can include a porosity increase. Sometimes, the replacement can be subtle, and original sedimentary structures and fossil forms can be preserved. Often, however, the recrystalliztion largely destroys the original rock fabric and rhombohedral dolomite crystals appear, as at (a) in Fig.
13.5. The other intergrown dolomite crystals form porosity that is polygonal. In this sample, many of the pores are coated (b) with pyrobitumin, a complex organic material similar to coal. This pyrobitumen is sometimes incased within dolomite crystals.
In this case, it will lower the apparent grain density and strength of the rock. Fig. 13.5 Thin-section image of a dolomite.
Dolomite rhombohedra (a) are common. Within the pore space and between grains are black layers of phyrobitumen (b and c). As mentioned, clays are among the most abundant minerals. These minerals can influence or control physical properties to a major degree. In addition, many clays are sensitive to the environment and will change properties and forms under different conditions.
An example of such sensitive clay fabrics is shown in Fig. 13.6. Note that the scale is much finer here than in previous figures.
In Fig. 13.6a, chlorite originally coats the quartz grains. On top of the chlorite, a smectite coating was developed. This core sample was allowed to dry, and the smectite collapsed, forming long slender columns in the pore space.
Resaturating the rock with distilled water allowed the smectite coating to expand and fill the pore space ( Fig. 13.6b). The closed pores will obviously have different fluid-flow characteristics. In this case, we cannot assume the mineral in is a passive, inert solid.
This rock will change properties according to pore fluid chemistry. Fig. 13.6 SEM images of a smectite-rich sandstone. When dry (a), the smectites have collapsed.
After saturation with distilled water, the smectites have expanded (b) to plug the pore space. The most common sedimentary rock types are shales and silts. In Fig. 13.7, white quartz grains float in the surrounding clay matrix.
Black organic material in thin layers indicates the horizontal bedding. As a result, this rock has properties that vary strongly with direction and are thus anisotropic. This material could serve as both a source rock and reservoir seal. This sample demonstrates how a mudstone or shale could have a complex composition.
Although clays typically make up a large portion of fine-grained rocks, terms such as clay and shale are not synonymous. Fig. 13.7 Thin-section image of an organic-rich siltstone.
Quartz grains (white) are surrounded by silt and clay (brown). Thin organic layers (black) are aligned to give the rock a strong anisotropy. Most sedimentary rocks have porosities under 0.50 (fractional). This is easy to understand, particularly with coarser clastic sediments, in which open grain packings that can support a matrix framework have maximum porosities around 0.45. Exceptions to this and other generalizations can occur, and an example is shown in Fig. 13.8.
This globigerina ooze is composed largely of the small shells or tests of organisms. The matrix mud fills the region between tests, but interiors remain empty. In addition, the tests themselves are porous. As a result, porosities can be as high as 0.8. Despite these huge porosities, because of the isolated nature of the pores, permeability can be in the microdarcy range. A similar situation often occurs in shallow clay-rich sediments where the open clay plate structure results in initial very high porosities.
In the remainder of this chapter, however, these types of sediments will be considered exceptional and will not be included in our analyses. Fig. 13.8 Thin-section image of fossil-rich globigerina ooze. Because of the porosity of the individual fossil tests, the total rock porosity reaches 80%.
Much of this is microporosity. Despite the high porosity and soft nature of this rock, a fracture has formed across the sample. The rock images shown in these several figures are meant to convey a feel for the types of textures common in sedimentary rocks, and that influence physical properties.
We will refer back to these images later in the chapter. These few images can in no way be considered a complete description of rock textures. For a more thorough treatment, the reader should consult one of the standard petrography texts or pertinent papers. Basics and DefinitionsDensity is defined as the mass per volume of a substance.
....................(13.1)typically with units of g/cm3 or kg/m3. Other units that might be encountered are lbm/gallon or lbm/ft3 (see Table 13.2). Table 13.2For simple, completely homogeneous (single-phase) material, this definition of density is straightforward. However, Earth materials involved in petroleum engineering are mixtures of several phases, both solids (minerals) and fluids. Rocks, in particular, are porous, and porosity is intimately related to density.
For rocks, porosity ( ) is defined as the nonsolid or pore-volume fraction. ....................(13.2)Porosity is a volume ratio and thus dimensionless, and