Page 3 - Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation

VA - DF: Transmissibility Corrections and Grid Control for Shale Gas Numerical Simulation p 2/23
At each step of the workflow, the results of the last analysis are used as a starting point for the
next model, which includes additional physical effects. At each stage, results and forecasts are
checked, and the validity/influence of any new sophistication can be analyzed in order to
ensure proper update of the different parameters.
It is obvious that at each stage, the results of the different methods must be coherent in order
to ensure the overall robustness of the complete analysis. In particular, under the same
assumptions, different methods should give similar results.
The objective of this paper is to focus on the comparison between the analytical, multiple
fractures horizontal well model and the numerical model, trying to explain and correct existing
differences. We show that the transient, non-linear nature of the pressure field around
fractures can challenge the classical assumptions of the numerical model. As a consequence,
both the transmissibility derivations and the automatic gridding procedure were adapted.
This validation step under simplistic assumptions (simple PVT and geometry, no desorption,
etc…) is essential to the integration of the numerical model in the workflow, i.e. just before
adding further complexity. This should prevent tuning fudge parameters in the full-physics
model to compensate for uncontrolled, purely numerical effects…
1. Pressure transient and non-linear effects
Reservoir data
Initial Reservoir Pressure, psia 5000
Reservoir temperature, ºF 112
Reservoir radius, ft 10,000
Net pay, ft 100
Porosity, % 10
Swi, % 0
Gas specific gravity 0.65
Well data
Horizontal well length, ft 4000
Horizontal well position centered
Horizontal well skin factor 0
Number of Fractures 20
Fractures half-length Xf, ft 250
Fractures position centered
Fractures penetration full
Fractures conductivity Fc, md.ft 1000
Well flowing pressure, psia 250
Completion type cased hole
Table 1 – Reservoir and well properties
Let us consider a simple reservoir, as described in Table 1 and Figures 1 and 2. For the
numerical model, we use a finite-difference simulator with a Voronoi grid, allowing smooth grid
refinement close to the fractures. By default, the size of the finest cells is automatically set to
a couple of times the width of the fracture and a default cell size progression ratio of 1.4 is
applied as one moves away from the fracture, until the constant size ‘back grid’ cells
(hexagons) are reached.