New Solution for Anisotropic Formation Damage Due to Produced Water Re-Injection

Abstract Despite the economics and environmental benefits of PWRI 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 1D laboratory parameters and have not considered the anisotropy of the media. In previous attempts at anisotropy modeling, the initial anisotropy of the media has been considered, but 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 1-D flow against the core flood tests from 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 remains the same in all directions. This assumption (sometimes clearly stated, sometimes not) means that, although the damage profile and front would be dissimilar in different direction (sometime considered to be anisotropic damage), the ratio of the damaged permeabilities in horizontal and vertical direction Kh/Kv (which will be 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 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, the intensity of damage would expect 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(2) (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 multidimensional case(9). In an anisotropic situation, the original model produces constant anisotropy ratio. We therefore need to have different initial damage coefficients α for different directions and those need to change with time in different fashion.

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