PERMEABILITY CONSIDERATION, DEFINITION, DARCY’S EQUATION, ESTIMATION, EFFECTIVE AND RELATIVE PERMEABILITY

Introduction – the consideration of permeability in petroleum geology

Recovery of hydrocarbons from the reservoir is an important process in petroleum engineering and estimating permeability can aid in determining how much hydrocarbons can be produced from a reservoir. Permeability is a measure of the ease with which a formation permits a fluid to flow through it. To be permeable, a formation must have interconnected porosity (inter-granular or inter-crystalline porosity, interconnected vugs, or fractures).

To determine the permeability of a formation, several factors must be known: the size and shape of the formation, its fluid properties, the pressure exerted on the fluids, and the amount of fluid flow. The more pressure exerted on a fluid, the higher the flow rate. The more viscous the fluid, the more difficult it is to push through the rock. Viscosity refers to a fluid’s internal resistance to flow, or it’s internal friction. For example, it is much more difficult to push honey through a rock than it is to push air through it. Permeability is measured in darcies. Few rocks have a permeability of 1 darcy, therefore permeability is usually expressed in millidarcies or 1/1000 of a darcy. Permeability is usually measured parallel to the bedding planes of the reservoir rock and is commonly referred to as horizontal permeability. This is generally the main path of the flowing fluids into the borehole. Vertical permeability is measured across the bedding planes and is usually less than horizontal permeability. The reason why horizontal permeability is generally higher than vertical permeability lies largely in the arrangement and packing of the rock grains during deposition and subsequent compaction. For example, flat grains may align and overlap parallel to the depositional surface, thereby increasing the horizontal permeability, see Figure 25. High vertical permeabilities are generally the result of fractures and of solution along the fractures that cut across the bedding planes. They are commonly found in carbonate rocks or other rock types with a brittle fabric and also in clastic rocks with a high content of soluble material. As seen in Figure 25, high vertical permeability may also be characteristic of uncemented or loosely packed sandstones. Examples of variations in permeability and porosity, some fine-grained sandstone can have large amounts of interconnected porosity; however, the individual pores may be quite small. As a result, the pore throats connecting individual pores may be quite restricted and tortuous; therefore, the permeabilities of such fine-grained formations may be quite low.

Shales and clays¾ which contain very fine-grained particles¾ often exhibit very high porosities. However, because the pores and pore throats within these formation are so small, most shales and clays exhibit virtually no permeability. Some limestones may contain very little porosity, or isolated vuggy porosity that is not interconnected. These types of formations will exhibit very little permeability. However, if the formation is naturally fractured (or even hydraulically fractured), permeability will be higher because the isolated pores are interconnected by the fractures.

Definition – Permeability

Permeability is the attribute of the rock that permits the passage of fluids through it. It is, an general, a measure of the degree of interconnectedness of the pore space, but some reservoirs (e.g. in massive limestone deposits, or in igneous intrusions) depend for fluid flow – and to a greater or lesser extent for the space in which the fluids may accumulate - on a network of fractures within the rock. The quantitative definition of permeability, K, is by means of a transport equation, similar in form to equations used in the definition of thermal or electrical conductivity. It is known as Darcy’s equation in honor of the nineteenth century French civil engineer, H. Darcy, who carried out and published the result of a series of experiments on the flow of water through a filter bed. The equation itself may be written in the form –

Where,

q/A is the flow rate per unit area through the rock

ρ is the fluid density

dΦ/dl is the potential gradient in the direction of the flow (the minus sign indicaing that flow occurs in the direction of decreasing potential),

μ is the fluid viscosity

It is found that for flow in a particular rock sample in a given direction, K is a constant, independent of the fluid used, provided that flow rates are not so high that turbulence is encountered. If the rock sample is the reservoir itself, the potential may be replaced by p/ρ where p is the pressure corrected to some common datum level. In such a case take on the form –

In order to emphasized the statistical nature of this equation and of permeability, consider a horizontal reservoir containing oil only, the overall movement of the oil being horizontal also (i.e. a fully penetrating well). At the scale of the pores the oil movement is by no means strictly horizontal as the liquid follows various tortuous paths through the pore structure. But since, on the larger scale, the flow is horizontal the equipotential surface are – on this scale – vertical. Let A be the area of intersection of one of these vertical surceases with the reservoir. If the neighboring equipotential surface is at an average distance δl and the flow rate across A is q, defines the average reservoir permeability across the area. Over the area of intersection of the

reservoir and a different equipotential surface, the average reservoir permeability defined in this way is usually different. Moreover, if attention is confined, not to the entire area A, but to some part of that area, the permeability is again different.

It is evident that the permeability must depend upon the continuity of the pores within the rock as well as on their geometry. It is also evident that it is a ‘large-scale’ or ‘statistical’ property because of the heterogeneous nature of the pores and their connections to each other. Although there is no direct and general relationship between permeability and porosity, it may be said that higher (interconnected) porosities usually result in higher permeabilities; and that for rocks of similar lithology subject to similar conditions of sedimentation it may be possible to establish an approximate relationship between the two parameters, but that this is likely to be of local validity only.

The dimensions of K are –

[L3 T-1] / [L2] = |K| / [ M L-1 T-1] x [M L-1 T-2] / [L]

Estimation of permeability

I. The radial diffusivity (conti)