Page 12 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation

VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation p 11/23
4. Numerical examples
In order to properly assess the validity of the proposed methodology, we consider four
examples with fractures in low permeability medium and restrict the simulation to the linear
PVT case. In this context, we can compare to analytical solutions computed using Ozkan and
Raghavan methodology [8].
Case a) 2D Single Fracture constant pressure production
We first consider a case with a single fracture (see parameters on Table 2) which has a
complete penetration in a homogeneous layer. In this case the potential is purely 2D. The well
is set to produce at constant bottom-hole pressure for 27 years.
Reservoir data
Initial Reservoir Pressure, psia 5000
Net pay, ft 100
Porosity, % 10
Permeability, mD 1E-3
Well data
Number of Fractures 1
Fractures half-length Xf, ft 400
Fractures position centered
Fractures penetration full
Fractures conductivity Fc, md.ft infinite
Production duration, years 27
Table 2 – Reservoir and well properties
Figure 10 displays the production rate and cumulative production obtained with and without
the proposed transmissibility corrections, compared to that obtained from the reference
solution. Figure 11 displays the cumulative relative production error with and without
transmissibility corrections.
It is clear that the solution obtained without transmissibility corrections leads to an increasing
error with time (we extended it to 100 years and obtained 5% error on the standard
cumulative). On the contrary, the proposed solution leads to a bounded error, which in this
case is always lower than 1 percent in terms of cumulative production.