Changes

==Radial flow==

==Radial flow==

Darcy's law can be applied to an ideal well model producing a constant steady-state production rate. The model assumes cylindrical flow in the reservoir where flow across the formation is horizontal and fluid moves radially toward the wellbore. It also assumes constant pay zone thickness, constant isotropic permeability, and an ideal liquid (homogeneous incompressible liquid in which viscosity is pressure independent).

Darcy's law can be applied to an ideal well model producing a constant steady-state production rate. The model assumes cylindrical flow in the reservoir where flow across the formation is horizontal and fluid moves radially toward the wellbore. It also assumes constant pay zone thickness, constant isotropic permeability, and an ideal liquid (homogeneous incompressible liquid in which viscosity is pressure independent).

:<math>p = p_{\rm wf} + \frac{141.2q_{\rm o}\mu_{\rm o}B_{\rm o}}{kh} \ln (r/r_{\rm w})</math>

:<math>p = p_{\rm wf} + \frac{141.2q_{\rm o}\mu_{\rm o}B_{\rm o}}{kh} \ln (r/r_{\rm w})</math>

That is, for every radius ''r'' there is a corresponding pressure ''p'' that increases logarithmically with ''r'' (Figure 4).

That is, for every radius ''r'' there is a corresponding pressure ''p'' that increases logarithmically with ''r'' ([[:file:fundamentals-of-fluid-flow_fig4.png|Figure 4]]).

 

[[file:fundamentals-of-fluid-flow_fig4.png|thumb|{{figure number|4}}Pressure distribution in a radiai reservoir.]]

Pressure distribution in radial bounded reservoirs is similar to the infinite case for the most of the drainage volume. It is different, however, near the boundaries, as shown in Figure 4.

Pressure distribution in radial bounded reservoirs is similar to the infinite case for the most of the drainage volume. It is different, however, near the boundaries, as shown in [[:[[:file:fundamentals-of-fluid-flow_fig4.png|Figure 4]].

===Units of Darcy's law formulas===

===Units of Darcy's law formulas===

===Restricted entry into the wellbore (Skin Effect)===

===Restricted entry into the wellbore (Skin Effect)===

The actual pressure distribution differs in most cases from the ideal pressure distribution derived for the ideal model. The following additional pressure drop at the wellbore results from near wellbore phenomena (Figure 5):

 

The actual pressure distribution differs in most cases from the ideal pressure distribution derived for the ideal model. The following additional pressure drop at the wellbore results from near wellbore phenomena ([[:file:fundamentals-of-fluid-flow_fig5.png|Figure 5]]):

:<math>\Delta p_{\rm skin} = p_{\rm wf(ideal)} - p_{\rm wf(actual)}</math>

:<math>\Delta p_{\rm skin} = p_{\rm wf(ideal)} - p_{\rm wf(actual)}</math>

The most important phenomena are usually flow convergence due to limited penetration of the pay zone (partial penetration), impaired permeability adjacent to the wellbore (formation damage), and flow restrictions in the perforations.

The most important phenomena are usually flow convergence due to limited penetration of the pay zone (partial penetration), impaired permeability adjacent to the wellbore (formation damage), and flow restrictions in the perforations.