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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 3 – P ressure Transient Analysis (PTA) -p121/743
As soon as we have a pressure gradient in the reservoir, the diffusion term, and especially the
product
c
t
, will become different from one reservoir block to the next.
Although one could consider that it also happens during any well test, this becomes critical
when the reservoir average pressure declines in the reservoir and/or in the well drainage area.
It is therefore necessary to adjust the models or the data.
Fig. 3.J.3 – Match without a material balance correction
If we look at a real gas simulation for a long term limit test, or a production survey using
permanent gauges, and use it to match with an analytical model where the diffusion was taken
at initial pressure, we can see a divergence between the simulated pressure and the measured
data, even though the reservoir geometries and the PVT used are strictly the same.
There are again three ways to handle this problem:
3.J.3.a
Using pseudotime functions
The pseudotime function is calculated with the reservoir, or drainage area, average pressure:
See more details in the chapter ‘13.E - The use of pseudofunctions’.
This method was useful at the time when one only had type-curves as models. Today
computers can do much better and faster. The main shortcoming was that the initial estimate
of the volume and the initial pressure was made before the model was matched. The model
would give a value of initial pressure and volume, which might not be the same as the initial
guess, hence requiring another modification of the data, another match, and so on. The
process would however, converge quickly.
3.J.3.b
Integrating the material balance correction in the analytical model
The theory behind this solution is the same, but the use of a model makes the process simpler
and more coherent. The model includes a reservoir size and an initial pressure. So the initial
gas in place can be calculated as an integral part of the model. At any time step the algorithm
calculates the average pressure from the cumulative production using p/Z, and replaces the
viscosity and total compressibility in the superposition by the one coming from the average
pressure. So at any time step the simulated pressure is coherent with the material balance of
the model. The optional derivation is shown below: