Page tree

Versions Compared

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.

...

LaTeX Math Inline
bodyp_i = p(0)

initial formation pressure

LaTeX Math Inline
body\phi_e(p)

effective porosity as function of formation pressure 

LaTeX Math Inline
bodyp(t)
 

LaTeX Math Inline
bodyc_t(p)

total compressibility as function of formation pressure 

LaTeX Math Inline
bodyp(t)
 

LaTeX Math Inline
bodyA_e

drainage area

LaTeX Math Inline
bodyh_e

effective formation thickness averaged over drainage area

LaTeX Math Inline
bodyQ^{\uparrow}_t(t)

cumulative offtakes by the time moment

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyQ^{\downarrow}_t(t)

cumulative intakes by the time moment

LaTeX Math Inline
bodyt


For low compressibility fluid 

LaTeX Math Inline
body\{ \phi_e = {\rm const}, \ c_t = {\rm const} \}
the 
LaTeX Math Block Reference
anchorMatBal
 equation can be explicitly integrated:

LaTeX Math Block
anchorQ6XP7
alignmentleft
\phi_e (p_i) \, c_t(p_i) \, p_i - \phi_e(p) \, c_t(p) \, p(t)  = \frac{Q^{\uparrow}_t(t) - Q^{\downarrow}_t(t)}{A_e \cdot h_e}

...