This assumption is that time variations of all variables are neglected in a time increment. The equations of mass and momentum conservation are solved subject to the assumption of steady flow. For instance, for flow in a tube, the frictional pressure drop is formulated in terms of the average velocity, density, and viscosity. ![]() The assumption of 1D flow means that the flow variables, such as density, velocity, viscosity, etc., are given as their average values over the cross-sectional area of the flow stream. The flow streams are treated as 1D constant area flow but with recognition of the effects of discontinuous area changes, such as nozzles. Here, the whole problem is set out, with appropriate assumptions made for special, simplified cases as they are considered. In the usual treatment of these equations, the mass conservation equations are not stated explicitly, and the temperatures are given, rather than calculated from the energy equation. These problems are considered in the following order:Ī complete fluid mechanics analysis of wellbore flow solves the equations of mass, momentum, and energy for each flow stream and the energy equation for the wellbore and formation. The wellbore flow problems listed below are examined in detail, starting from the simplest and progressing to the most complicated. ![]() ![]() This page first presents a general overview of one-dimensional (1D) fluid flow so that the common features of all these problems can be studied. Fluid mechanics problems range from the simplicity of a static fluid to the complexity of dynamic surge pressures associated with running pipe or casing into the hole. 5 General steady flow wellbore pressure solutionsĭrilling fluids range from relatively incompressible fluids, such as water and brines, to very compressible fluids, such as air and foam.
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