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Mathematical modeling of formation damage effect during underbalanced drilling operations

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Abstract

Formation damage during underbalanced drilling is created due to the spontaneous counter-current imbibition when drilling mud is in contact with saturated formations. Therefore, it should be appropriately recognized and investigated. The objective of this study is to develop a numerical model to simulate the penetration rate of drilling mud in the formation during underbalanced drilling. Modeling of this phenomenon is done by implementing its formulation through implicit pressure–explicit saturation (henceforth, IMPES) method. To validate the results of the developed model with a pilot study in this field, it is demonstrated that the model performs effectively in determining the penetration range of muds and finding the distribution of drilling mud saturation across the core. Consequently, the degree of damage to the formation through laboratory studies is usually time-consuming and therefore, the developed model can be employed for initial studies. Increasing the unbalanced pressure difference, oil viscosity and porosity will reduce the amount of drilling mud penetration in the formation during underbalanced drilling operations.

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Abbreviations

ρ :

Density of each phase

u :

Velocity of each phase

φ :

Cross-section porosity

S :

Saturation of each phase

x :

Location

\(\rho_{\text{osc}}\) :

Oil density in the surface conditions

\(\rho_{\text{msc}}\) :

Drilling mud density in the surface conditions

K :

Absolute permeability

\(k_{\text{r}}\) :

Relative permeability for each phase

μ :

Viscosity for each phase

P :

Pressure of each phase

\(S_{\text{wc}}\) :

Connate water saturation

\(P_{\text{i}}\) :

Formation initial pressure

\(S_{\text{or}}\) :

Residual oil saturation

\(P_{\text{wellbore}}\) :

Wellbore pressure

\(K_{{{\text{i}} \pm \frac{1}{2}}}\) :

Obtained from the harmonic average

\(k_{\text{rw}}^{0}\) :

Water maximum relative permeability

\(k_{\text{ro}}^{0}\) :

Oil maximum relative permeability

B :

Capillary pressure parameter

D m :

The maximum value of the penetration coefficient

c :

Coefficients of the penetration

n :

Coefficients of the penetration

m:

Stands for drilling mud

o:

Stands for oil

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Authors and Affiliations

  1. Department of Petroleum Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Erfan Aghashahi Ardestani, Afshin Davarpanah, Ghasem Zargar & Behnam Mirshekari

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  1. Erfan Aghashahi Ardestani
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  2. Afshin Davarpanah
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  3. Ghasem Zargar
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  4. Behnam Mirshekari
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Correspondence to Afshin Davarpanah.

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Aghashahi Ardestani, E., Davarpanah, A., Zargar, G. et al. Mathematical modeling of formation damage effect during underbalanced drilling operations. Model. Earth Syst. Environ. 5, 1651–1661 (2019). https://doi.org/10.1007/s40808-019-00617-8

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