Horner Analysis for Negative Inflow Tests of Well Barriers

Negative tests, or inflow tests, are conducted to verify the integrity of well barriers in the direction of potential flow, subjecting a barrier to a negative pressure differential, while monitoring for signs of a leak. A common practice is to observe the rate of flowback from the well. Flowback may be a sign of a leak due to an influx of formation fluids into the well. However, even when there is no leak, flowback is commonly observed due to thermal expansion of wellbore fluids. Heat transfer will occur between the wellbore fluids in each annulus and with the surrounding formation until temperatures reach an equilibrium. This behavior is described by the process of thermal diffusion, with the resulting temperature increase causing expansion of wellbore fluids and flowback from the well. Industry guidelines state “Horner” analysis may be used when monitoring flowback or pressure buildup during an inflow test. In doing so, engineers and wellsite supervisors may use a “Horner plot” to determine if flowback or pressure buildup is attributable to thermal effects. Those without a reservoir engineering background may not be aware the method was originally derived from a radial flow equation for the purpose of monitoring pressure buildup in a well when shut in after a period of production. The apparent similarity of the radial flow and thermal diffusion equations is what led Horner's technique to subsequently be applied to the prediction of static formation temperature from well logs. However, although thermal expansion is a function of formation temperature, Horner analysis of flowback or pressure buildup during an inflow test has remained a black box that is poorly understood. For the first time, with support from empirical data from offshore wells, we reveal that Horner analysis of thermal expansion is a practice without theoretical justification. The radial equation on which Horner analysis depends, along with the constraints implied by the boundary conditions, fails to accurately account for the conditions of an inflow test. As a result, the method should not be used for analyzing flowback or pressure buildup during an inflow test. Instead, a new method is proposed to interpret a trend of flowback when monitoring well barriers. The findings of this study can help improve understanding Horner analysis and techniques for interpreting inflow tests.