The Origins of Anisotropy (includes associated papers 18394 and 18458 )
- Larry W. Lake
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- April 1988
- Document Type
- Journal Paper
- 395 - 396
- 1988. Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 5.4.7 Chemical Flooding Methods (e.g., Polymer, Solvent, Nitrogen, Immiscible CO2, Surfactant, Vapex), 5.6.2 Core Analysis, 4.1.2 Separation and Treating, 4.1.5 Processing Equipment, 5.6.4 Drillstem/Well Testing, 5.2.1 Phase Behavior and PVT Measurements, 4.3.4 Scale, 5.4.1 Waterflooding, 5.4.3 Gas Cycling, 5.3.2 Multiphase Flow, 1.2.3 Rock properties, 5.5.2 Core Analysis, 5.7.2 Recovery Factors
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Lake, Larry W., SPE, U. of Texas
A property is anisotropic if its value depends on the direction in which it is measured; otherwise, the property is said to be isotropic. Both terms are usually applied only to intrinsic properties of permeable media. Only flow or transport properties, which have a specific direction associated with their measurement, can be anisotropic: permeability, relative permeability, resistivity, thermal conductivity, and dispersivity, Static properties are intrinsically isotropic: density, porosity, and capillary pressure, Static properties apparently exhibiting anisotropy in homogeneous media are probably manifesting size effects. Here we deal mainly with permeability anisotropy. A property is nonuniform if its values form a single distribution with a nonzero variance-i.e., if there is a range of values about some average. Heterogeneity, is a description that refers to a property having values that form two or more distributions. Both definitions are quite distinct from anisotropy, but as we shall see below, heterogeneity in particular is the major source of anisotropy.
The Effects of Anisotropy
Permeability anisotropy causes fluid to flow in a direction different from that in which it is pushed. Fig. 1 illustrates that the flow and isopotential (isopressure if single-phase horizontal flow) lines in an isotropic medium are perpendicular to each other. Because in a waterflood we normally impose the isopotential lines, the behavior illustrated means that we have a good deal of control over the direction in which fluids are flowing. In an anisotropic medium, flow is not perpendicular to isopotential lines. Here, there is much less control over where the fluid will go, with a consequent loss in sweep efficiency. Of course, the right panel of Fig. 1 is only schematic because, as the isopotential lines accommodate themselves to the anisotropy, they will no longer be straight vertical lines.
The illustration in Fig. 1 is of single-phase flow through a two-dimensional (2D) medium. The anisotropic nature of permeability can affect any process in which there is a substantial density difference between fluids: primary production below the bubblepoint, gas cycling, gas and/or water coming, some waterfloods, some solvent floods, and many steam and in-situ combustion processes. It also can influence fluid injection and production rates if the anisotropy is severe.
A medium property that causes the redirection of flow requires six independent scalar values to represent it fully in three dimensions (three values in two dimensions). Mathematicians call such representations tensors. Finding accurate values for these quantities represents an immense challenge in data collection. Many of our normal tools yield estimates that are usually (1) too integrated over a wide range of variation (single-well tests) and hence do not give good definition or (2) too local (core analysis) to be of much use by themselves. Moreover, the number of scalar quantities is so large in three dimensions, particularly when heterogeneity is included, that complete representation is a considerable challenge even for numerical simulation. For these reasons, nearly all numerical simulators include only three principal components (horizontal, lateral, and vertical permeability) of anisotropy. Because the representation of anisotropy in simulators is coarse, we cannot fully appreciate the effects this phenomenon can have.
Sand grains with typical packing and shape can exhibit anisotropy ratios (largest/smallest permeability in two perpendicular directions) of no more than 2 to 3. Yet measurements of anisotropy in the field and on whole cores indicate that horizontal permeability can be several factors of 10 larger than vertical permeability. The origin of such extreme values lies in the existence of heterogeneity on a scale smaller than the measuring device. Two geologic features in particular will account for this type of anisotropy: crossbedding and shales. Crossbedding is the alternate layering of sands of differing grain sizes and/or textures at an acute angle with major depositional features. Crossbedding is an extremely common feature of sedimentary media, but unfortunately it is also highly irregular and usually intermittent. The right panel of Fig. 1 is a schematic of flow through a crossbedded sand. The spacing between the layers usually is only a centimeter or two. There frequently is little difference between the mineral composition of the alternating layers. Shales, on the other hand, usually have a mineral composition distinct from the adjoining media, being most closely related to clays, which because of an extremely small grain size usually have a very low permeability. Dispersed shales reduce the permeability of most media, but do not impart significant anisotropy. Continuous segregated shales reduce or, under extreme conditions, eliminate flow through the shale. Fig. 2 shows a synthetic generation of discontinuous shales in a 2D cross section. In this figure, it is easy to see how the horizontal permeability, which is an arithmetic average of the shale and sand permeabilities, is affected very little by the shales, while the vertical permeability, which is closer to a harmonic average, can be greatly reduced. The calculated mean horizontal-to-vertical-permeability ratio in Fig. 2 is between 103 and 105. Fig. 2 also illustrates three important points about anisotropy. First, severe anisotropy is the result of local heterogeneity. In the case of Fig. 2, the heterogeneity is separate, uniform distributions of shale and sand permeabilities.
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