Introduction

Fluids such as water, steam, petroleum, and natural gas often migrate through the Earth's crust. If these flows occur through open fractures, they can be studied using the channel flow theory developed in Chapter 6. In many cases, however, flows in the Earth's crust occur through a matrix of interconnecting passages provided by large numbers of small fractures or through the voids of naturally porous rocks. If the scale of the flow system is large compared with the scale of the interconnected passages, it is often appropriate to consider flow through a uniform porous medium.

Sand is an example of a naturally porous material. Because of the irregular shapes of sand particles there is a considerable void or pore space between them. The fraction of the volume made up of pore space is known as the porosity ϕ. Loose sand is particularly porous, ϕ ≈ 40%, while oil sands have porosities in the range of 10 to 20%. Values of ϕ for some porous rocks, for example, sandstone and limestone, are listed in Table 2–2. As noted before, rocks that are not naturally porous can still be approximated as porous media if they are extensively fractured. The distribution of fractures must be reasonably uniform and the separation of fractures small compared with the scale of the overall flow.

Fluids can flow through a porous medium under the influence of an applied pressure gradient. In Chapter 6 we showed that, for laminar flow, the flow rate in channels and pipes is linearly proportional to the pressure gradient and inversely proportional to the viscosity.