4. Conclusions

Property Value Unit Property Value Unit qt 3000 RB/DAY Bo 1.003 RB/STB h 60 ft Bw 1.002 RB/STB rw 0.35 ft co <sup>8</sup> <sup>10</sup><sup>6</sup> 1/psi re <sup>6800</sup> ft cw <sup>3</sup>:<sup>02</sup> <sup>10</sup><sup>6</sup> 1/psi <sup>k</sup> <sup>300</sup> ft cr <sup>5</sup> <sup>10</sup><sup>6</sup> 1/psi s 0 mD μ<sup>o</sup> 3.0 cp Siw 0.10 μ<sup>w</sup> 0.5 cp

pi 2500 psi pt 0.5 psi

Figure 13. Comparison of the wellbore pressure response from analytical solution and IMEX during water injection test

Figure 14. The log-log diagnostic plots for wellbore pressure data (blue curve) and its derivative with respect to time (red

Sor 0.25 λ 2

134 Perturbation Methods with Applications in Science and Engineering

Table 1. Reservoir, rock, and fluid properties for simulation and analytical solution.

ϕ 0.22

with capillary pressure (a).

curve) during water injection (b).

In this work, an accurate approximate analytical solution was constructed for wellbore pressure during water injection test in a reservoir containing oil and immobile water. Our solution was validated by comparing the bottom hole pressure calculated from the analytical model with the data obtained from a commercial numerical simulator. Our solution presented here for water injection together with the wellbore pressure and flow rate history for subsequent tests as shut-in and flowback can be used as forward model in a nonlinear regression in order to estimate relative permeabilities and capillary pressure curves in addition to the rock absolute permeability, the skin zone permeability, and the water endpoint relative permeability.
