How much rate history to use in pressure transient analysis ?
This is a common question and a source of error. The rate data will affect the derivative plot, the selection of the interpretation model and the calculated well and reservoir parameters.
Accuracy in the rate measurement
The derivative is rate-normalized. As a result, the derivative of the PBU tests should share the same stabilization level, provided the well performance doesn’t change.
Note the y-axis is rate-normalized (“/STB/D”).
This derivative stabilization level is proportional to :
(independent of the rate)
If the rate before the PBU is wrong or incorrectly estimated, the derivative will be shifted. Additional erroneous features may also be introduced.
The example below uses a rate that is over-estimated by 20 %.
The resulting permeability will then be over-estimated by 20% in this case.
This is why it is critical to perform routine production flow tests so as to reduce the uncertainty on the rate data. (By the way, these are sometimes called “well tests” to add some confusion…)
The impact of rate history on the derivative
To analyze a PBU test from a production shut-in, the derivative is defined by deriving the pressure with respect to the superposition time. This time function is shown below:
The superposition time takes the rate history into account. As a result, an error in the rate history may have some negative impact on the derivative.
Input some rate data…
Once a production PBU or an injection PFO is detected, the pressure data are uploaded into the well testing software, along with some rate data. In general, the rate history gets truncated and simplified.
Some “rules of thumb” are sometimes being used, but these vary according to whom you ask… Some use a rate history of duration 1.5 or 2 times the shut-in duration.
However, this is a rule of thumb, and as such, it doesn’t work all the time. It can introduce some erroneous features in the derivative and lead to some wrong results. An example is shown below.
In the above case, using a rate history of duration equal to 2 times the shut-in duration will result in a 25 % error in permeability KH. Since this is a vertical well with limited perforations, that mistake will impact the perforation height, vertical permeability, skin and the distances to the boundaries. All the calculated reservoir parameters will be wrong.
Truncating the rate history is likely to bring some errors, especially when under transient period. A pressure transient “disappears” once it reaches the boundary. As a result, the rate history should at least extend to a duration equal to the time to reach pseudo-steady state.
Equivalent Horner time
Sometimes the equivalent Horner time is used to account for the total cumulative production volume Q. The rate history is reduced to a single constant rate production period of duration equal to the equivalent Horner time Tpe= Q/q with q being the last rate just before the PBU test. However, this technique may also introduce some errors in the derivative.
The figure below shows the original rate history in red and the new rate in blue over a time period equal to the equivalent Horner time.
When using the equivalent Horner time, it is preferable to use it only for the first 60% (or less) of the cumulative production, as demonstrated in SPE 63077.