Petrophysical Rocks: Electrofacies and Lithofacies

Many years ago, the classification of sedimentary rocks was largely descriptive and relied primarily on petrographic methods for composition and granulometry for particle size. The compositional aspect broadly matches the goals of the previous chapter in estimating mineral content from petrophysical logs. With the development of sedimentology, sedimentary rocks were now considered in terms of the depositional environment in which they originated. Uniformitarianism, the doctrine that the present is the key to the past, linked the formation of sediments in the modern day to their ancient lithified equivalents. Classification was now structured in terms of genesis and formalized in the concept of “facies.” A widely quoted definition of facies was given by Reading (1978) who stated, “A facies should ideally be a distinctive rock that forms under certain conditions of sedimentation reflecting a particular process or environment.” This concept identifies facies as process products which, when lithified in the subsurface, form genetic units that can be correlated with well control to establish the geological architecture of a field. The matching of facies with modern depositional analogs means that dimensional measures, such as shape and lateral extent, can be used to condition reasonable geomodels, particularly when well control is sparse or nonuniform. Most wells are logged rather than cored, so that the identification of facies in cores usually provides only a modicum of information to characterize the architecture of an entire field. Consequently, many studies have been made to predict lithofacies from log measurements in order to augment core observations in the development of a satisfactory geomodel that describes the structure of genetic layers across a field. The term “electrofacies” was introduced by Serra and Abbott (1980) as a way to characterize collective associations of log responses that are linked with geological attributes. They defined electrofacies to be “the set of log responses which characterizes a bed and permits it to be distinguished from the others.” Electrofacies are clearly determined by geology, because physical properties of rocks. The intent of electrofacies identification is generally to match them with lithofacies identified in the core or an outcrop.

Porosity Volumetrics and Pore Typing

The primary objective of porosity estimations based on measurements made either from petrophysical logs or core is the volume of pore space within the rock, given simply by the equation: . . . Φ = Vp/Vb . . . The Greek letter, phi, is the standard symbol for porosity and is expressed in this equation as the ratio of the volume of void space (Vp) to the bulk volume of the rock (Vb). The simplest concepts of porosity are generally explained in terms of the packing of spheres as the sum of the pore volume of the space between the spheres. There are five basic arrangements of uniform-sized spheres that can be constructed: simple cubic, orthorhombic, double-nested, face-centered cubic, and rhombohedral packing (Hook, 2003). Each has a geometrically defined pore volume that represents an upper limit for granular rocks whose constituent grains have a variety of sizes and shapes and whose pore volumes have been reduced by compaction and diagenetic cements. This intergranular model is a useful starting point for the characterization of pores in clastic rocks and will be considered first, before reviewing the additional complexities of pore geometry introduced by dissolution in carbonate rocks. The solid framework of a sandstone consists of a nonconductive “matrix” dominated by quartz, but commonly with accessory nonconductive minerals, and conductive clay minerals, whose electrical properties are caused by cation exchange with ions in saline formation water. It is important to distinguish between connected and unconnected pores, as well as larger pores that sustain fluid movement in contrast to smaller pores filled with capillary-bound water. A graphic presentation of these components is widely used in the petrophysical literature as a reference basis to disentangle terminology that can be confusing and contradictory. In particular, the term “effective porosity” has different meanings that vary from one technical discipline to another. In their review of porosity terms, Wu and Berg (2003) concluded that many core analysts considered all porosity to be effective, log analysts excluded clay-bound water, while petroleum engineers excluded both clay-bound and capillary-bound from porosity consideration, thereby restricting effective porosity to pores occupied by mobile fluids.

Saturation-Height Functions

As observed by Worthington (2002), “The application of saturation-height functions forms part of the intersection of geologic, petrophysical, and reservoir engineering practices within integrated reservoir description.” It is also a critical reference point for mathematical petrophysics; the consequences of deterministic and statistical prediction models are finally evaluated in terms of how closely the estimates conform to physical laws. Saturations within a reservoir are controlled by buoyancy pressure applied to pore-throat size distributions and pore-body storage capacities within a rock unit that varies both laterally and vertically and may be subdivided into compartments that are not in pressure communication. Traditional lithostratigraphic methods describe reservoir architecture as correlative rock units, but the degree to which this partitioning matches flow units must be carefully evaluated to reconcile petrofacies with lithofacies. Stratigraphic correlation provides the fundamental reference framework for surfaces that define structure and isopach maps and usually represent principal reflection events in the seismic record. In some instances, there is a strong conformance between lithofacies and petrofacies, but all too commonly, this is not the case, and petrofacies must be partitioned and evaluated separately. Failure to do this may result in invalid volumetrics and reservoir models that are inadequate for fluid-flow characterization. A dynamic reservoir model must be history matched to the actual performance of the reservoir; this process often requires adjustments of petrophysical parameters to improve the reconciliation between the model’s performance and the history of production. Once established, the reservoir model provides many beneficial outcomes. At the largest scale, the model assesses the volumetrics of hydrocarbons in place. Within the reservoir, the model establishes any partitioning that may exist between compartments on the basis of pressure differences and, therefore, lack of communication. Lateral trends within the model trace changes in rock reservoir quality that control anticipated rates and types of fluids produced in development wells. Because the modeled fluids represent initial reservoir conditions, comparisons can be made between water saturations of the models and those calculated from logs in later wells, helping to ascertain sweep efficiency during production.

Compositional Analysis of Mineralogy

Formation lithologies that are composed of several minerals require multiple porosity logs to be run in combination in order to evaluate volumetric porosity. In the most simple solution model, the proportions of multiple components together with porosity can be estimated from a set of simultaneous equations for the measured log responses. These equations can be written in matrix algebra form as: . . . CV = L . . . where C is a matrix of the component petrophysical properties, V is a vector of the component unknown proportions, and L is a vector of the log responses of the evaluated zone. The equation set describes a linear model that links the log measurements with the component mineral properties. Although porosity represents the proportion of voids within the rock, the pore space is filled with a fluid whose physical properties make it a “mineral” component. If the minerals, their petrophysical properties, and their proportions are either known or hypothesized, then log responses can be computed. In this case, the procedure is one of forward-modeling and is useful in situations of highly complex formations, where geological models are used to generate alternative log-response scenarios that can be matched with actual logging measurements in a search for the best reconciliation between composition and logs. However, more commonly, the set of equations is solved as an “inverse problem,” in which the rock composition is deduced from the logging measurements. Probably the earliest application of the compositional analysis of a formation by the inverse procedure applied to logs was by petrophysicists working in Permian carbonates of West Texas, who were frustrated by complex mineralogy in their attempts to obtain reliable porosity estimates from logs, as described by Savre (1963). Up to that time, porosities had been commonly evaluated from neutron logs, but the values were excessively high in zones that contained gypsum, caused by the hydrogen within the water of crystallization. The substitution of the density log for the porosity estimation was compromised by the occurrence of anhydrite as well as gypsum.

Pore-System Facies: Pore Throats and Pore Bodies

When Archie (1950) first introduced the term “petrophysics,” he outlined a tentative petrophysical system “. . . which revolves mainly around pore-size distribution which defines the capillary pressure curve, permeability, and porosity.” As such, a pore distribution does not necessarily coincide with a specific rock type. Different lithologies might contain similar pore distributions and a single lithology might be characterized by several distinctive pore distributions. In the latter case, these differences could be used as the basis for a lithofacies subdivision, where the criteria were defined by pore-network properties rather than more conventional fabric observations. Often, there will be a substantial commonality between the two approaches, because the pore network and rock framework are complementary. The term “petrofacies” (which comes from “petrophysical facies”) extends the facies concept to pore networks. Although this name is commonly (but not exclusively) used for this purpose, the range of published definitions is fairly broad, as pointed out by Sullivan et al. (2003). Some authors intermingle notions of petrofacies with electrofacies and lithofacies, which is understandable, because in many reservoirs there are strong intercorrelations between them. In this text, we distinguish between electrofacies, either seemingly natural petrophysical log associations found by unsupervised methods, or those determined from lithofacies by supervised methods. Lithofacies are generally recognized by standard visual observations of a core, although they may be defined by reference to distinctive porosity-permeability associations (petrofacies) in core measurements. The two fundamental reservoir components of pore microarchitecture are essentially the same as the spatial elements of conventional architecture: the relative sizes and arrangement of the pore bodies (rooms) and the pore throats (doors between rooms). In an oil or gas reservoir, the volume of pore space contained in the pore bodies dictates the total storage capacity, while the access of hydrocarbon to the pore bodies is regulated by the size of the linking pore throats. Realistic pore-network models for characterizing hydrocarbon recovery from reservoirs are, appropriately, labyrinthine in their intricacy. However, the key pore attributes that are the focus of petrophysical applications are the size distributions of the pore bodies and pore throats, together with the aspect ratio of pore-body size to pore-throat size.

Permeability Estimation

Because it is a measure of flow, permeability is a vector quantity, as contrasted with conventional petrophysical log data, which are responses to static properties of the rock. In the absence of a direct measurement of permeability, predictions must be inferred from the rock framework characteristics that control the ability of fluids to move through the rock. In this chapter, we consider methods that predict absolute permeability, that is, permeability with respect to a single fluid. This is the most widely used meaning of the term and would be immediately applicable to aquifers. In engineering applications to reservoirs, a relative permeability is assigned to each fluid phase, so that relative fluid rates and volumes can be characterized explicitly. Although the fundamental physics of permeability in tubes has been understood for many years, reliable estimations are difficult to make in all but the simplest rock types. As we shall see, one approach attempts to adapt modifications to a tube model to accommodate the complexity of pore-system geometry. This model-driven methodology tends to be favored by engineers and contrasts with a data-driven geological approach that applies empirical relationships from core data from mercury porosimetry measurements. The most fundamental property used to predict permeability is that of pore volume. Both porosity and permeability are routine measurements from core analysis. If a useable relationship can be developed to predict permeability from porosity, then predictions of permeability can be made in wells that were logged with conventional measurements but not cored. The simplest quantitative methods used to predict permeability from logs have been keyed to empirical equations of the type: . . . log k = P +Q.Φ or log k = P +Q.log Φ. . . where P and Q are constants determined from core measurements and applied to log measurements of porosity (Φ) to generate predictions of permeability (k). These equations are the basis for statistical predictions of permeability in regression analysis, where porosity is the independent variable and logarithmically scaled permeability is the dependent variable. The fitted function minimizes the sum of the squared deviations of the permeability about the trend line.

Fluid Saturation Evaluation

In his treatise on electricity and magnetism, Maxwell (1873) published an equation that described the conductivity of an electrolyte that contained nonconducting spheres as: . . . Ψ = co/cw = 2Φ/(3-Φ) . . . where the “meaning” of Ψ (psi) has been most commonly interpreted as some expression of tortuosity, Co and Cw are the conductivity of the medium and the electrolyte, respectively, and Φ is the proportion of the medium that is occupied by the electrolyte. Since that time, considerable efforts have been devoted to elucidation of the electrical properties of porous materials, particularly with the advent of the first resistivity log in 1927, which founded an entire industry focused on estimating fluid saturations in hydrocarbon reservoirs from downhole measurements. To some degree, spirited discussions in the literature reflect two schools of thought, one that considers the role of the resistive framework from a primarily empirical point of view, and the other that models the conductive fluid phase in terms of electrical efficiency. Clearly, the two concepts are intertwined because resistivity is the reciprocal of conductivity and the pore network is the complement of the rock framework. If the solid part of the rock is nonconductive, then the ability of a rock to conduct electricity is controlled by the conductive phase in the pore space, which should make the case for equations to be formulated from classical physical theory. This approach is typically developed using electrical flow through capillary tubes as a starting point. Unfortunately, the topological transformation of a capillary tube model to a satisfactory representation of a real pore network is a formidable challenge, so that mathematical solutions may not be acceptable, even though they are grounded in basic physics. The most successful model along these lines has been proposed by Herrick and Kennedy (1994), who maintain that while the Archie equation is a useful parametric function, it has no physical basis. Some of their conclusions are reviewed at the end of this chapter.