Middle-Time Transient Data

Key Takeaways

• The pressure derivative log-log plot is the standard diagnostic tool for identifying the MTR boundary (where ETR ends and MTR begins, and where MTR ends and LTR begins), because the derivative amplifies the subtle rate-of-change differences between flow regimes that are often invisible on the pressure versus time plot itself — in the ETR dominated by wellbore storage, the derivative is rising (approximately proportional to time on a log-log plot, giving a unit slope); at the transition from ETR to MTR, the derivative curves over from the rising storage signature and flattens to a horizontal plateau representing the constant dp/d(lnt) that characterizes radial flow; in the LTR with boundary effects, the derivative departs upward from the plateau (for a no-flow boundary or closed reservoir) or downward from the plateau (for a constant-pressure boundary like an aquifer or a gas cap); the flat portion of the derivative between these two departures is the MTR, and its duration on the log-log time axis determines how many data points are available for the semilog analysis and how confidently the slope can be estimated; a well-developed flat derivative plateau spanning at least one log cycle (a factor of ten in time) provides an unambiguous MTR that supports a reliable semilog analysis, while a short plateau of less than half a log cycle requires careful assessment of whether the data are truly in radial flow or represent a transition between regimes.
• Formation permeability-thickness product (kh) is extracted from the MTR semilog slope by the relationship kh = 162.6 * q * B * mu / (m * h) where m is the slope of the semilog straight line in psi/log cycle, q is the production rate, B is the formation volume factor, mu is the fluid viscosity, and h is the net pay thickness — the inverse proportionality between slope and permeability means that a tight formation (low permeability) produces a steep MTR slope while a high-permeability formation produces a shallow slope; for a given test design and analysis pressure range, the steeper the slope the easier it is to identify and measure, meaning that MTR analysis is actually more straightforward for tight formations than for high-permeability formations where the slope may be nearly flat and difficult to distinguish from background noise; the MTR slope is the fundamental permeability measurement in a well test and is more reliable than any log-derived permeability estimate because it directly samples the in-situ flow behavior of formation fluids through the formation as it exists in the subsurface, without the calibration uncertainties inherent in log-to-core comparisons and permeability transforms.
• Near-wellbore skin is calculated from the MTR data using the intercept of the semilog straight line at a specific reference time (typically one hour of shut-in on the Horner scale, or at the zero-flow time on the production drawdown scale) — the skin factor S is proportional to the difference between the extrapolated MTR straight-line value at the reference time and the actual wellbore pressure; a positive skin indicates that the measured pressure at the wellbore is lower than the undamaged formation prediction (the near-wellbore permeability is lower than the bulk formation permeability, representing damage), while a negative skin indicates that the measured pressure is higher than predicted (the near-wellbore connection is better than the bulk formation, representing natural fractures or stimulation); the MTR data must extend over at least one to two log cycles in the semilog straight-line region to give a well-constrained slope for the skin calculation, and the skin calculation is meaningless if the identified MTR time window is incorrect — applying the semilog analysis during the ETR gives a skin that reflects wellbore storage rather than formation damage, and applying it during the LTR gives a skin that includes boundary effects in the apparent damage signal.
• Permeability anisotropy within the drainage area can be inferred from MTR data collected in multiple wells at different distances and azimuths from each other through interference testing — if the MTR pressure derivative from an observation well (which is recording the pressure response to production in an active well) is analyzed along with the active well's own MTR data, the combination gives the directional permeability components that the single-well buildup cannot reveal; in naturally fractured reservoirs where the fracture orientation creates a preferred flow direction, the permeability in the fracture direction is much higher than perpendicular to the fractures, and the MTR slope from different source-observation well geometries varies systematically with the angle between the line connecting the wells and the fracture orientation; mapping the MTR permeability estimates from multiple interference tests across a field provides a permeability anisotropy map that informs directional well placement, hydraulic fracture azimuth selection, and waterflood pattern design to optimize sweep efficiency in the preferred permeability direction.
• Test design for guaranteeing adequate MTR data capture requires estimating the start time and end time of the MTR before the test is run, using available information about the formation permeability (from logs, analogue wells, or preliminary production data), the wellbore storage coefficient (from the planned tubing size and fluid), and the reservoir boundaries (from seismic, well control, and geological maps) — the estimated start of MTR (end of wellbore storage) can be approximated as 50 * C / (kh/mu) where C is the wellbore storage coefficient, and the estimated end of MTR (start of boundary effects) can be approximated from the tD/r² relationships that give the time for the pressure transient to reach the drainage boundary at a specific radius; if the estimated MTR window is shorter than the minimum required duration for a reliable semilog analysis (typically at least 0.5 to 1.0 log cycles), the test design must be adjusted by changing the shut-in pressure gauge accuracy, extending the test duration, or accepting that only a partial MTR will be available and planning the interpretation uncertainty accordingly; systematic test design that explicitly targets an adequate MTR window is the difference between a well test investment that returns reliable formation parameters and one that produces ambiguous results requiring additional testing.