## Modeling Transient Wellbore Temperature During Diagnostic Fracture Injection Tests

Fig. 1—BHP, bottomhole-temperature (BHT), and WHP data gathered during a falloff test.

Diagnostic fracture injection tests (DFITs) have gained widespread usage in the evaluation of unconventional reservoirs. In typical field operations, pressure is measured at the wellhead, not at the bottom of the hole. The bottomhole pressure (BHP) is obtained by adding a constant hydrostatic head of the water column to the wellhead pressure (WHP) at each timestep. One can question the soundness of this practice because of significant changes in temperature that occur in the wellbore, leading to changes in density and compressibility throughout the fluid column. This paper offers an analytical model for estimating the transient temperature at a given depth and timestep, for computing the BHP.

## Temperature Model During Pressure-Falloff Test

After a well is shut in at the surface, afterflow at the sandface is negligible because of low formation permeability. Upon cessation of injection, the cold injection water begins to gain heat from the surroundings. Heat transfer during flowing and shut-in conditions has been modeled with an energy-balance equation, accounting for various resistances to heat transfer. The resulting differential equations are solved numerically. However, with robust assumptions, an analytical expression can be developed for transient fluid temperature during falloff. The heat flow from the formation into the wellbore raises the internal energy of the fluid and of the composite tubing/casing/cement material. Please see the complete paper for the quantitative expression.

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 166120, “Modeling Wellbore Transient Fluid Temperature and Pressure During Diagnostic Fracture Injection Testing in Unconventional Reservoirs,” by B. Nojabaei, SPE, The Pennsylvania State University, A.R. Hasan, SPE, Texas A&M University, and C.S. Kabir, SPE, Hess, prepared for the 2013 SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. The paper has not been peer reviewed.
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Modeling Transient Wellbore Temperature During Diagnostic Fracture Injection Tests

01 February 2015

Volume: 67 | Issue: 2

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