During wellbore storage flow regime, what is the slope of the pressure derivative?

During wellbore storage flow regime, what is the slope of the pressure derivative?

• A. One
• B. Zero
• C. Infinity
• D. Two

Answer: (A)

In wellbore storage, the pressure response is governed by the amount of fluid that can be released from the wellbore into the formation, which leads to a logarithmic-in-time behavior for pressure change. When time is non-dimensionalized and we look at the pressure derivative plotted against the logarithm of time, this region produces a line with unit slope. Put simply, the dimensionless pressure derivative grows in direct proportion to log time, giving a slope of one. This unit-slope behavior on the log-time derivative plot is a hallmark of the storage-dominated early-time regime. The other slopes would imply either no time dependence, an unphysical infinite rate, or a steeper-than-log growth, none of which match the storage-dominated response.

In wellbore storage, the pressure response is governed by the amount of fluid that can be released from the wellbore into the formation, which leads to a logarithmic-in-time behavior for pressure change. When time is non-dimensionalized and we look at the pressure derivative plotted against the logarithm of time, this region produces a line with unit slope. Put simply, the dimensionless pressure derivative grows in direct proportion to log time, giving a slope of one. This unit-slope behavior on the log-time derivative plot is a hallmark of the storage-dominated early-time regime. The other slopes would imply either no time dependence, an unphysical infinite rate, or a steeper-than-log growth, none of which match the storage-dominated response.