Dear Yusri,

From the late time region of my pressure derivative plot, two boundary effect was apparent which was closed boundary (upward curve) and a constant pressure boundary (downward curve). The constant pressure boundary appears just after the closed boundary so my pressure derivative plot curves upwards then downwards in the late time region.

About your querry of boundary effect on pressure derivative, if the derivative goes up during late times it shows the presence of a boundary/fault. If the test is for sufficient time for the derivative to stabilize then the derivative stablizes at twice the value that of the radial homogeneous, in case of single fault.
Now for closed boundary case, the derivative and the del P curve both goes up with a slope of +1 and that too only in the drawdown case. This is pseudo steady state case. the reason for the derivative to go up is that since the volume of the closed reservoir is fixed and the pressure transient has seen all the boundaries, so the pressure continues to decline, thats why dP and its derivative increases in drawdown.
And for constant pressure case, the change in pressure, after the transient reaches the constant pressure is negligible so the derivative falls. This is visible in both drawdown and build up.