Questions arise whether bottomhole pressures (BHPs), derived from their wellhead counterpart (WHP), lend themselves to transient analysis. That is because considerable heat exchange may affect the wellbore-density profile, thereby making the WHP translation a nontrivial exercise. In other words, gas density is dependent on both spatial locations in the wellbore and time during transient testing. Fully coupled wellbore/reservoir simulators are available to tackle this situation. However, they are not readily adaptable for their numeric formulations.
This paper presents analytic expressions, derived from first principles, for computing time-dependent fluid temperature at any point in the wellbore during both drawdown and buildup testing. The simplicity of the analytic expressions for Tf (z, t) is profound in that one can compute flowing or shut-in BHPs on a spreadsheet.
Two tests were considered to verify the new analytic formulae. In one case, measurements were available at both sandface and surface, and partial wellhead information was available in the other case. We explored a parametric study to assess whether a given wellbore/reservoir system will lend itself to wellhead measurements for valid transient analysis. Reservoir flow capacity (kh) turned out to be the most influential variable.