Equivalent Time (te)

Equivalent time is essentially a time transformation which is used in order to apply drawdown analysis techniques to buildup data.  The transformation takes shut-in time, or delta time, and converts it into an equivalent time using the following equation:

 

image267.gif

 

Note that this can also be defined as the flow time (tc) divided by the Horner time as follows:

 

image268.gif

 

This definition is derived for radial flow and thus works very well for analyzing wellbore storage and radial flow regimes, but breaks down in heterogeneous reservoirs or when boundaries come into play.  When analyzing bilinear or linear flow regimes, corresponding definitions of bilinear or linear equivalent time are used.  Equivalent time has little effect on early time data but compresses late time shut-in data significantly.  The maximum value of equivalent time is flow time (tc) as shut-in time (Dt) approaches infinity.  Thus no matter how long the well is shut-in, equivalent time cannot be greater than tc.  Thus the behavior of a buildup depends heavily on the flow time.

 

The preceding definition of equivalent time assumes a constant rate before shut-in.  When the rate has been variable, a complex superposition equivalent time function should be used.