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The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different “thickness”, the N-order approximate expansion of perturbed solution concerning small parameter is obtained, and the “multiple layer” phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well. [ABSTRACT FROM AUTHOR]

Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained. It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridblocks away from the well. When an initial pressure gradient existent sensitivity coefficients in the region are closer to the active well than to the observation well. Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient. [ABSTRACT FROM AUTHOR]