Abstract:
This paper investigates a numerical model of non-stationary fluid filtration in
the vertical well vicinity after a short-term disturbance of a formation taking into account
the skin effect and wellbore storage effect. The numerical solution to the problem is
compared with an approximate solution to the Muskat problem, which is obtained by the
method of sequentially changing stationary states. The influence of formation permeability
and skin factor on the bottomhole pressure build-up is studied. The wellbore storage
effect has been shown to completely mask indications of the bottomhole zone. For low-permeability formations, the pressure build-up process is time-consuming. Hence, the
flow-over techniques should be used to investigate them.
A method for interpreting pressure-transient data based on the theory of solving ill-posed
inverse problems is proposed. The method determines the formation permeability, skin
factor, and formation pressure values using the measured bottomhole pressure profile
after a short-term disturbance of the formation. Estimates of the well productivity index
and formation pressure are in good agreement with those obtained using the integral and
Muskat methods. In contrast to the methods based on the Muskat solution, the proposed
method allows the assessment of the skin factor.
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