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Fig. 3.J.4 – Match with a material balance correction
3.J.3.c
Using a numerical model
The use of a numerical model is, conceptually, even simpler. As the gas equation is entered at
the level of each cell, the material balance is automatically honoured, not only globally, as
above, but at the level of each cell. Solving the problem numerically is by far the most rigorous
approach.
As the problem is nonlinear, this requires Saphir NL and the use of a nonlinear solver, but in
the case of single gas this will rarely require more than one iteration. So this sort of model, for
reasonably simple geometries, will be both fast and accurate.
For information, the case presented above is an actual simulation using Saphir NL.
3.J.4
Non-Darcy flow
As mentioned previously, there are two main options to address non-Darcy flow: using a rate
dependent skin model or integrating the Forchheimer equation in a numerical model.
3.J.4.a
Simulating non-Darcy flow with a rate dependent skin model
There are two complimentary approaches to determine the rate dependency caused by high
flow velocities and turbulence using the simplified assumption that the relationship is linear. In
an analytical model the non-Darcy flow effect is simulated by an additional skin using the
linear function of the rate.
D dq ds
qdq ds
S S
total
/
) / (
0
This is illustrated in the figure above. D is called the (linear) non-Darcy flow coefficient.
In order to access the rate dependency it is necessary to conduct a multi flowrate test, these
tests are described in the chapter Well Performance Analysis.