Abstract
Long down-time and colossus economic loss associated with frequent well shut down required for proper well test analysis near oil wellbore damages has necessitated the use of numerical models for simulating change in reservoir properties. In the current study, change in reservoir properties has been simulated by formulating models involving modification of Darcy equation in an attempt to optimize reservoir pressure for improved reservoir properties. The coupled transient linear partial differential equations (CTLPDE) models developed for predicting reservoir properties such as porosity, permeability and water saturation profile were numericallysolved using finite difference method implemented in MATLAB and solution validated using field data perturbed with Gaussian noise of 10%.
The results obtained for CTLPDE models indicated initial decreasein both water and oil pressure from 4550 psi and 350 psi to 4525 psi and 320 psi respectively. Both water and oil pressure subsequently increased to 4530 psi and 325 psi and then remained constant. However, while water saturation (Sw) increased throughout the pressure regime; 0.730 through 0.735 to 0.739, oil saturation (So) decreased from 0.320 through 0.268 to 0.263. The results of the corresponding auxiliary equation indicated increase in relative permeability of water (Krw) with Sw but decreased with increase in So, while relative permeability of oil (Kro) decreased with increase in Swbut increased with So. Generally however, for every value of either So or Sw ,krw≫kro
Numerical simulation proved to be effective in predicting reservoir behaviour. The formulated models indicate drop in oil saturation as pressure depleted over time.

Key words: Long down-time, Shut down, Formation damage, Gaussian noise, Oil pressure, Water saturation