Chapter 5: One-Dimensional Immiscible Water-Oil Flow Calculations

This chapter presents the theory and basic equations for two-phase immiscible flow in homogeneous porous media. The development of the mathematical constructs included here is limited to 1D flow without capillary or gravity effects. At the end of this chapter, the modifications of the 1D flow equations for capillary pressure and gravity effects are discussed. Subsequent chapters will address 2D cross section (X–Z), 2D areal (X–Y), and 3D (XYZ) flow.

Topics addressed in this chapter:

In Chapter 3, the principal concepts of oil-water interactions within a porous and permeable reservoir rock that relate to waterflooding were discussed, as well as capillary pressure and relative permeability phenomena. In this section, the mathematics describing the physics of water-oil displacement for homogeneous linear systems is presented, first for steady-state flow and then for unsteady-state flow. This review is brief and does not include the intermediate steps of the mathematical derivation of the key equations; details of these mathematical derivations are available in Appendix D or in Willhite’s SPE Waterflooding textbook (Willhite 1986).