Buildup Following a Two-Rate Drawdown Test

The analysis of a buildup that follows a two-rate drawdown can yield values of kh that provide a check on the results of a drawdown analysis. The flow rate and time sequences used to develop multirate drawdown analysis still apply, but with a slight modification. A well is flowed at a rate q _{sc 1} up to time t ₁, at a rate q _{sc 2} up to time, t, and then shut in. The shut-in time is represented, as before, by ?t. Using this notation, Eq. 4 50 may be modified to represent the buildup period as

Combining these terms and simplifying Eq. 6 56 gives

Hence a plot of

on arithmetic coordinates should give a straight line of slope m from which permeability is calculated as

Calculate the skin factors from

The following equations can be used to estimate the pressure drop across the skin at rates q _{sc 1} and q _{sc 2}, respectively. Thus, at q _{sc 1},

and at q _{sc 2},

Having found values for k and s, one may now proceed to determine p*. The flowing bottom-hole pressure in a well at a time t ₁ can be expressed as

By setting ?( p _i) = ? and rearranging Eq. 6 63, we have

For a bounded reservoir, ? may be used...