Transient Pressure Response

Key Takeaways

• The infinite-acting radial flow (IARF) regime is the most commonly analyzed transient pressure response, occurring after wellbore storage effects have dissipated and before reservoir boundaries are encountered, during which the pressure at the wellbore decreases (during drawdown) or increases (during buildup) as a semi-logarithm of time in a diagnostic straight-line segment on the semilog plot whose slope m is related to formation transmissibility (kh/mu) by the relationship m = 162.6 qBmu / kh for field units with q in STB/day, B as formation volume factor in RB/STB, mu in centipoise, k in millidarcies, and h in feet: the slope m of the IARF straight line is the primary calculation input for reservoir permeability, with kh determined from the slope and h known from the net pay interval identified on the log; the skin factor S (quantifying the near-wellbore damage or stimulation relative to the undamaged ideal) is calculated from the position of the IARF line at a specific time relative to the theoretical position expected for an undamaged well, with positive skin indicating near-wellbore damage that reduces productivity and negative skin indicating stimulation (fracturing or acidizing) that enhances productivity beyond the undamaged level; the identification of the IARF straight line on the pressure or Horner derivative plot is the central diagnostic challenge in well test analysis, because deviations from IARF at early time (wellbore storage, partial penetration, fracture linear flow) and at late time (boundary effects, dual porosity, heterogeneity) can mask or distort the IARF segment and lead to incorrect permeability or skin calculations if not properly diagnosed.
• Wellbore storage effect dominates the early transient pressure response by masking the formation response behind the pressure change associated with fluid compressibility changes in the wellbore volume during the rate change that initiated the test: when a flowing well is shut in for a pressure buildup test, the wellbore continues to produce at a declining rate from the wellbore fluid compressibility as the wellbore pressure rises (afterflow), and this afterflow means that the formation is not actually shut in immediately even though the surface valve has been closed, causing the early buildup to reflect wellbore physics rather than formation properties; the wellbore storage coefficient (C, in barrels per psi) quantifies the volume of fluid produced from wellbore storage per unit pressure change, with C = Vwb cwb for a wellbore full of single-phase fluid (where Vwb is wellbore volume and cwb is fluid compressibility) and C = 25.65 Awb/rho for a rising liquid level wellbore; the log-log plot of delta P versus delta t shows a unit slope straight line during pure wellbore storage (indicating that delta P is proportional to delta t, since all the rate change is being absorbed by wellbore storage rather than formation flow), with the storage-dominated unit slope line transitioning to the formation-dominated response (a half-slope for fracture linear flow or a flatter slope for radial flow) after the wellbore storage effect has dissipated at a time determined by the storage coefficient and the formation transmissibility.
• Hydraulic fracture transient response produces diagnostic straight-line segments on the log-log pressure derivative plot that identify the fracture geometry and conductivity, allowing post-fracture well testing to quantify the effectiveness of the hydraulic fracture treatment in creating the intended near-wellbore permeability enhancement: a high-conductivity (infinite conductivity) hydraulic fracture produces a half-slope (0.5) straight line on the log-log derivative plot during the linear flow period when fluid flows linearly from the formation into the fracture face before the flow geometry transitions to radial flow; a finite-conductivity fracture produces a quarter-slope (0.25) straight line during bilinear flow, when fluid flows linearly along the fracture from the fracture tip toward the wellbore simultaneously with linear flow from the formation into the fracture face; the slopes, durations, and transitions between these diagnostic straight-line segments allow the well test analyst to calculate the fracture half-length (xf), the fracture conductivity (kf wf, the product of fracture permeability and width), and the dimensionless fracture conductivity (FCD = kf wf / k xf) that characterizes the fracture performance relative to the formation permeability; post-fracture well testing is particularly important in unconventional tight reservoir completions where the fracture network (rather than the matrix permeability) controls production, and where the production log and pressure transient analysis together characterize how many of the hydraulic fracture stages created in a multi-stage completion are actually contributing to production.
• Dual porosity and naturally fractured reservoir transient responses exhibit characteristic dips or transitions on the pressure derivative plot that reflect the two-porosity nature of the system, where the fracture network and the matrix blocks that feed the fractures have different storage capacities and interporosity flow characteristics: in a dual porosity system, the early transient response reflects the fracture system alone (high permeability fractures respond rapidly to the rate change and exhibit an early IARF segment on the derivative plot), followed by a transition period where fluid transfer from the matrix to the fracture system distorts the response (causing a characteristic trough or minimum on the pressure derivative plot in transient interporosity flow models), and finally a late IARF segment representing the total system (fractures plus matrix) when the matrix-fracture transfer has reached equilibrium; the depth of the trough in the derivative plot and the time at which it occurs are related to the interporosity flow coefficient (lambda, characterizing how easily fluid transfers from matrix to fractures) and the storativity ratio (omega, the ratio of fracture storage to total system storage), which together characterize the dual porosity behavior of the reservoir; identifying dual porosity behavior from the transient pressure response is important for reservoir simulation and development planning because dual porosity reservoirs produce differently than homogeneous matrix reservoirs, with the fracture network initially providing high productivity that declines as fracture storage depletes and then partially recovers as slower matrix drainage replenishes the fractures.
• Composite reservoir transient responses identify radial variations in formation properties at different distances from the wellbore, including near-wellbore damage zones, altered zones from injection flooding, and natural heterogeneity boundaries that create concentric rings of different permeability or mobility in the investigated volume: a damaged near-wellbore zone (positive skin) causes the early transient to reflect a higher apparent skin (lower initial permeability) that transitions to the undamaged formation permeability at a later time when the investigation radius has expanded past the damage zone into the undamaged formation; conversely, an acidized or fractured stimulated zone causes the early transient to reflect a higher apparent permeability that transitions to the lower native formation permeability when the investigation radius expands past the stimulated region; in waterflooded reservoirs, the water-invaded zone near an injector has different mobility than the oil-bearing uninvaded zone, creating a composite system boundary effect visible on pressure transient tests as a slope change on the semilog derivative plot at the time corresponding to the investigation radius reaching the water-oil contact; the analysis of composite reservoir transient responses requires specialized type curve matching or numerical simulation because the two-zone composite system does not have the simple analytical solutions that apply to homogeneous or simple boundary-dominated systems, but it provides uniquely valuable information about the effective permeability and mobility distribution within the flooded zone that is not obtainable from any other measurement method.