Diagnostic fracture injection testing or DFIT has gained widespread usage in the evaluation of unconventional reservoirs. The DFIT entails injection of water above the formation-parting pressure, followed by a long-duration pressure falloff test. This test is a pragmatic way of gaining critical reservoir information, such as the formation-parting pressure, fracture-closure pressure, and initial-reservoir pressure, leading to fracture-completion design and reservoir-engineering calculations.
In typical field operations, pressure is measured at the wellhead, not at the bottomhole, because of cost considerations. The bottomhole pressure (BHP) is obtained by simply adding a constant hydrostatic head of the water column to the wellhead pressure (WHP) at each timestep. Questions arise whether this practice is sound because of significant changes in temperature that occur in the wellbore, leading to changes in density and compressibility throughout the fluid column. The paper explores this question and offers an analytical model for estimating the transient temperature at a given depth and timestep for computing the BHP. Furthermore, based on the premise of line-source well, we showed that the early-time data can be represented by the square-root of time formulation, leading to the new modified-Hall relation for the injection period.