Derivative Logs (Pressure Transient Analysis)

Key Takeaways

• The flat derivative plateau identifies radial flow and directly yields reservoir permeability — the most important single feature on a pressure derivative plot is the flat (zero-slope) plateau that indicates infinite acting radial flow: the region where the pressure disturbance has propagated past the near-wellbore effects (skin, wellbore storage, fracture effects) and is flowing radially in an effectively unbounded reservoir; during this flat plateau, the derivative value equals m/2.303 where m is the slope of the Horner straight line, and the permeability-thickness product (kh) is directly calculated from the derivative level; identifying the flat derivative plateau is the fundamental objective of pressure transient data quality assessment — if no flat plateau develops during the test, the test duration was insufficient to reach radial flow and the reservoir permeability cannot be reliably determined; well test designers specify minimum test durations based on estimated permeability and expected drainage radius to ensure the derivative plateau is reached before the test ends.
• Derivative signature shapes are diagnostic of specific flow geometries that cannot be identified from pressure alone — the power of the derivative plot lies in its sensitivity to flow regime transitions that appear only as subtle inflections in the pressure-time curve but create distinct, mathematically characteristic slopes on the derivative plot; a half-slope (0.5) on the derivative indicates linear flow (pressure transient propagating in one dimension) characteristic of hydraulically fractured wells during the fracture linear flow period, and the slope duration and level allow estimation of fracture half-length; a quarter-slope (0.25) indicates bilinear flow (simultaneous linear flow in the fracture and the formation matrix feeding the fracture) and allows estimation of fracture conductivity; a unit slope (1.0) on both the pressure change and derivative curves at early time indicates wellbore storage (compressible fluid in the wellbore dominating the pressure response), which must end before formation properties can be read; a "hump" in the derivative followed by a second flat plateau indicates dual porosity behavior (naturally fractured formation) with interporosity flow parameters visible from the hump geometry.
• Numerical differentiation of field pressure data requires smoothing to produce interpretable derivative plots — field pressure measurements contain noise from gauge resolution, vibration, fluid movement, and other sources; taking the derivative of noisy data amplifies the noise dramatically, producing a jagged derivative curve that masks the diagnostic flow regime signatures; the Bourdet algorithm smooths the derivative by computing it over a logarithmic time window (the L-factor) that averages the pressure difference over a span of log-time rather than at each point; larger L-factors produce smoother derivative curves but may smooth out real features; smaller L-factors preserve real features but may show noise as false diagnostic signatures; optimal L-factor selection is a judgment call that requires experience — too smooth, and you may miss a real feature; too noisy, and you may invent a feature; modern pressure transient software automatically applies and allows interactive adjustment of the smoothing parameter, and the analyst must evaluate the resulting derivative critically rather than accepting the software's default output without examination.
• Derivative analysis has revolutionized hydraulic fracture characterization in tight formations — in low-permeability gas and oil wells with hydraulic fractures, the derivative plot reveals the sequence of flow regimes that characterize the complex fracture system: early fracture storage (unit slope if the fracture itself is compressible), bilinear flow (quarter slope) when the fracture has finite conductivity and the formation is feeding the fracture, linear flow (half slope) when the fracture is fully conductive and flow is linear from the matrix to the fracture, and compound linear or pseudo-radial flow if the test continues long enough for the drainage area to expand beyond the fracture; quantifying the fracture half-length from the transition between linear and pseudo-radial flow requires tests lasting weeks to months in tight formations, which is why DFITs (diagnostic fracture injection tests) with carefully designed shut-in periods and high-resolution gauge data are used to generate derivative plots that can be interpreted for fracture and reservoir properties before the main fracturing program proceeds.
• Boundary identification on the derivative plot guides reservoir model construction and field development planning — when the pressure transient has propagated far enough to reach the boundaries of the drainage area (fault, pinchout, water contact, or producing edge of an aquifer), the derivative plot deviates from the flat radial flow plateau; a fault or sealing boundary causes the derivative to rise with a slope of 1.0 (unit slope) after a period of flat radial flow, while an aquifer (pressure support boundary) causes the derivative to fall below the radial flow plateau; the time at which boundary effects appear on the derivative allows estimation of the distance from the wellbore to the boundary, and the nature of the boundary deviation (sealed or open) indicates the type of boundary; this boundary characterization from derivative plots is particularly valuable in exploration wells where the reservoir limits are unknown and the test is one of the primary tools for establishing the size and connectivity of the accumulation before development drilling commences.