Abstract
Despite the economics and environmental benefits of PWRI (Produced Water
Re-Injection) projects, the permeability reduction due to deposited particles
is a persistent problem. Various models for permeability damage calculation are
available. Most of them are based on one-dimensional laboratory parameters and
have not considered the anisotropy of the media. In previous attempts at
anisotropy modelling, the initial anisotropy of the media has been considered.
However, when it comes to the damage intensity calculation, isotropic
parameters have been used for the entire media. As a result, the relative
damage in these models is isotropic.
In this paper, a robust approach for anisotropic permeability impairment is
developed based on micromechanical considerations. The damage mechanics is
coupled with numerical flow code. The model formulation has been successfully
tested in 1D flow against the core flood tests from the Masila Block onshore
Yemen. Then, the damage model has been extended to 3D using pseudo directional
parameters to capture the anisotropy. A dynamic anisotropic mathematical
formulation for damage intensity has been derived, implemented in a 3D
numerical code and successfully tested on a field case study. The new model
exhibits the expected anisotropy of damage.
Introduction
Anisotropic formation damage has been studied by many researchers, especially
for horizontal wells. However, in all previous work it has been assumed that
the damage intensity in different directions (defined as a ratio of the damaged
permeability to the original permeability) would remain the same in all
directions(1, 2). This assumption (sometimes clearly stated, sometimes not)
means that, although the damage profile and front would be dissimilar in
different directions (sometime considered to be anisotropic damage), the ratio
of the damaged permeabilities in the horizontal and vertical direction
kh/kv (called "anisotropy ratio") stays constant. The
common result of this assumption for a horizontal well is to have an elliptical
cross-sectional damage profile, which will grow with time proportionally in
both directions.
The hypothesis for the mechanics of real anisotropic damage is obtained by
starting with an elliptical cross-section for the damage profile. The following
phenomenon is plausible. Since we have a higher velocity (and volume) of
damaging water flowing in the direction of higher permeability (horizontal), we
would continue to have a deeper invasion in this direction compared to the
direction of lower permeability. Therefore, the anisotropy persists as the
damage grows. However, we would expect the intensity of damage to be higher in
the vertical direction because of lower initial permeability and, therefore,
smaller pore throats. Hence, the anisotropy ratio (kh/kv)
is expected to increase with time, rather than to stay constant.
To be able to model the anisotropy phenomenon, consider the velocity-based
damage model(3) (VDM). First, we note that in isotropic
permeability, it was proven that the use of the vector of velocity would create
the correct solution for a multidimensional case(4). In an
anisotropic situation, the original model produces a constant anisotropy ratio.
We therefore need to have different initial damage coefficients a for different
directions and they need to be changed with time in a different fashion.
© 2009. Petroleum Society of Canada (now Society of Petroleum Engineers)
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History
- Original manuscript received:
19 March 2007
- Meeting paper published:
12 June 2007
- Revised manuscript received:
23 May 2008
- Manuscript approved:
3 March 2009
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