Unsaturated Flow (Richards Equation)

  • Akpofure E. Taigbenu


We pay attention in this chapter to the solution to the problem of flow in variably saturated soils because of its importance in many fields of engineering such as drainage, irrigation, environmental, soil and petroleum engineering. The flow in unsaturated soils is essentially a two-phase flow of two immiscible fluids — air and water. The physical processes that give rise to this kind of flow are infiltration of surface water through the upper layers of soil which enriches the soil moisture, and subsurface flow through soils which are partially filled with air. The interaction of roots of plants with this flow, and the advection and dispersion of fertilizers and pesticides within the unsaturated zone make this flow phenomenon of considerable interest to soil scientists, agronomists, and irrigation engineers. In petroleum explorations of underground reservoirs where immiscible fluid flows are also encountered, the fluids involved are water, oil, and gas. Although the partial differential equations that govern the two-phase immiscible flow in unsaturated formations are similar to those that govern the three-phase immiscible flow in underground reservoirs, it is usual in the case of the former to assume that the dynamics of flow within the air phase play an insignificant role in determining water movement and storage in the unsaturated zone. In the absence of this assumption, the solution would have required a simultaneous solution of two partial differential equations, each of which describes the flow in each fluid phase.


Hydraulic Conductivity Soil Column Unsaturated Zone Unsaturated Soil Green Element 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Akpofure E. Taigbenu
    • 1
  1. 1.Department of Civil and Water EngineeringNational University of Science and TechnologyBulawayoZimbabwe

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