Precision in Defining Diagnostic Plots Optimizes Well-Test Results
Authors: Carpenter Chris 
Published: March 2023

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This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 206108, “Diagnostic Plots of Pressure-Transient, Rate-Transient, and Diagnostic Fracture Injection/Falloff Tests,” by David Craig, SPE, Occidental, and Thomas Blasingame, SPE, Texas A&M University. The paper has not been peer reviewed.

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All transient-test interpretation methods use diagnostic plots for the identification of wellbore or fracture storage distortion, flow regimes, and other parameters. The associated diagnostic plots are not interchangeable between such tests. The objective of this work is to clearly define the appropriate diagnostic plots for each type of transient test.

Introduction
In the complete paper, the authors review constant-rate drawdown solutions for a few specific cases of interest and the plotting function used to match buildup data to the drawdown solutions. They extend their review to the cases of buildup or falloff analysis following short flow periods and illustrate the differences between analysis of buildup or falloffs following short and long flow periods. After covering pressure-transient testing, they discuss rate-transient diagnostic plots and the ambiguity observed during analysis of multifractured horizontal well diagnostic plots and the uncertainty of analyst straight lines. Finally, they discuss and demonstrate the correct plotting functions and flow-regime interpretation for diagnostic fracture injection and falloff tests. Multiple examples from the literature are included as part of the discussion.

Pressure-Transient Diagnostic Plots
Pressure-transient-testing diagnostic plots evolved from the solutions to constant-rate drawdown problems. The authors’ intent is to review infinite-acting solutions for radial flow with wellbore storage and skin and flow through an infinite-conductivity fracture. On a log-log plot, the characteristic slopes, detailed in the complete paper, are unit slope, ½ slope, and zero slope.
Many authors have proposed plotting functions for overlaying the observed pressure response from transient tests other than a constant-rate drawdown on the drawdown solutions. In many cases, the slopes identifying storage distortion and flow regimes from drawdown solutions will match and can be used to identify storage and flow regimes from pressure-buildup tests.
A situation in which pressure-buildup or falloff test plotting functions fail to match the drawdown solution is when the flow period before shut-in is short. Short-flow transient tests have been reviewed by multiple authors. In lower-permeability reservoirs, pressure-transient tests with short flow periods are very common, and, in unconventional reservoirs, short-flow transient tests are the most-common transient test. Diagnostic plots constructed based on the characteristic shapes of the dimensionless pressure and the dimensionless pressure derivative with respect to the natural logarithm of dimensionless time for constant-rate drawdown solutions cannot be applied in the same manner for short-flow transient tests.
With short-flow transient tests, the observed derivative of pressure difference with respect to the natural logarithm of time matches the negative product of dimensionless time and the second derivative of dimensionless pressure with respect to dimensionless time.
Additionally, the commonly known impulse derivative, which is defined as the product of time and the derivative of pressure difference with respect to the natural logarithm of time, will match the negative product of dimensionless time squared and the second derivative of dimensionless pressure with respect to dimensionless time.