Diagnostic fracture-injection testing (DFIT) has gained widespread usage in the evaluation of unconventional reservoirs. DFIT entails injection of water above the formation-parting pressure, followed by a long-duration pressure-falloff test. This test is a pragmatic method of gaining critical reservoir information (e.g., 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 bottom of the hole, 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. This 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, on the basis of the premise of a line-source well, we have shown 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.

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