Journal of Canadian Petroleum Technology
Volume 48,
Number 7,
July 2009,
54-65
Abstract
A semi-analytical model is presented to study transient pressure behaviour of
vertical wells in a dual porosity reservoir under the influence of non-Darcy
flow inside the reservoir (Forchheimer number), formation damage around the
wellbore (mechanical skin factor), and their combined effect (near-wellbore
non-Darcy skin factor). Unique transient pressure behaviour is presented in
both semi-log pressure and log-log pressure derivative plots. Semi-log pressure
plots suggest that for a vertical well producing with a constant sandface flow
rate, its pressure responses exhibit two linear portions for Darcy flow, even
with non-Darcy skin factor (i.e. the near-wellbore non-Darcy skin factor is
larger than zero). However, the first linear portion will dismiss if non-Darcy
flow presents inside the reservoir (i.e. the Forchheimer number is larger than
zero). Further pressure derivative analyses in a log-log plot suggest that: 1)
both Forchheimer number and nearwellbore non-Darcy skin factor lead to a
narrower and steeper transition region between pure wellbore storage and radial
flow region for build up tests and a wider and gentler one for drawdown tests;
and 2) the derivative curves under the effect of the Forchheimer number always
exhibit a slight convex shape in the radial flow region, rather than a
horizontal line with a constant value of 0.5 for Darcy flow.
The type curves presented may be applied to estimate mechanical skin factor,
Forchheimer number and near-wellbore non- Darcy skin factor from a single rate
test. Synthetic cases show that ignoring the globally distributed non-Darcy
flow causes errors of up to 300% in interpreting dual porosity characteristic
parameters. Both synthetic and field case studies suggest that the non-Darcy
flow has a significant effect on the interpretation of the inter-porosity flow
coefficient, λ, and less effect on the interpretation of the storativity ratio,
ω.
Introduction
The Forchheimer equation suggests that high velocity gas flow in porous media
obeys the following quadratic equation:
Equation (available in full paper)
It has been recognized that Forchheimer non-Darcy flow is introduced by gas
inertial effects; thus, β?is called the inertial factor. Forchheimer non-Darcy
flow is a universal phenomenon in gas reservoir development. It could affect
reservoir parameter estimations, well productivity evaluation and production
performance analysis. Observations in the field(1) and the
laboratory(2, 3) have suggested that, in the fracture system of a
naturally fractured reservoir, the pressure loss is dominated by the square
term in the Forchheimer equation.
Studies on modelling non-Darcy flow in naturally fractured reservoirs are
limited. The first attempt was reported by Villalobos-L. et al.(4).
Based on numerical results of a radial liquid flow model with the Forchheimer
non-Darcy flow, these authors derived an expression of a rate-dependent
pseudo-skin term similar to that in homogeneous single porosity
reservoirs.
Wu(5) modelled non-Darcy flow in a naturally fractured system using
the Multiple Interacting Continua (MINC) method by applying the results of
Darcy flow to approximate the characteristic length of non-Darcy flow distance
between fractures and the matrix crossing the interface for the dual porosity
formation. He observed that semi-log plots of pressure drop versus time are
extremely sensitive to the values of non-Darcy coefficient.
© 2009. Petroleum Society of Canada (now Society of Petroleum Engineers)
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History
- Original manuscript received:
2 April 2007
- Meeting paper published:
12 June 2007
- Revised manuscript received:
2 April 2009
- Manuscript approved:
8 June 2009
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