In horizontal wells, an estimate of permeability perpendicular to the well can be made if the productive well length open to flow is known.Īn equation that models linear flow in a channel reservoir of width w isįor a hydraulically fractured well with fracture half-length L f, Data from linear flow regimes can be used to estimate channel width or fracture half-length if an estimate of permeability is available. Linear flow is also common and occurs in channel reservoirs, hydraulically fractured wells, and horizontal wells. 3 – Radial flow appears as a horizontal derivative on the diagnostic plot. 3), radial flow is indicated by a horizontal derivative.įig. The equation used to model radial flow for a well producing at constant rate is the familiar logarithmic approximation to the line-source solution,Įquations modeling radial flow have the general form Common situations in which radial flow occurs include flow into vertical wells after wellbore storage distortion has ceased and before boundary effects, hydraulically fractured wells after the transient has moved well beyond the tips of the fracture, horizontal wells before the transient has reached the top and bottom of the productive interval, and horizontal wells after the transient has moved beyond the ends of the wellbore. Infinite-acting radial flow is common in reservoirs, and data in the radial flow regime can be used to estimate formation permeability and skin factor. 2 – Volumetric flow produces derivative with unit slope. During pseudosteady-state flow or recharge, the pressure change and pressure derivative plots will not coincide.įig. In wellbore storage, b v is zero, and the derivative and pressure change plots will lie on top of one another. The implication is that the derivative plot will have unit slope (up one log cycle as it moves over one log cycle) on log-log coordinates, and the pressure change plot will approach unity at long times when b v is not equal to zero ( Fig. The equation modeling pseudosteady-state flow in a cylindrical drainage area is The equation modeling wellbore storage (derived from a mass balance on the wellbore) is As a final example, in a test the reservoir may behave like a tank with recharge (fluid influx) entering from a secondary source of pressure support, such as a large supply of hydrocarbons in a lower-permeability medium in pressure communication with the reservoir being tested. In this case, the reservoir is the tank pressure is changing at the same rate throughout (although it is not the same at all points), and fluid is leaving the reservoir through the producing well. Another example is pseudosteady-state (boundary-dominated) flow in a closed reservoir during constant-rate production. Fluid either leaves this tank (earliest times in a flow test, before the reservoir begins to respond) or enters the tank (earliest times in a buildup test). The "tank" is the wellbore, in which the pressure is uniform. The most common example of volumetric behavior is wellbore storage, which dominates during the early-time region. Volumetric behavior is defined as that pressure response time dominated by the wellbore, reservoir, or part of the reservoir acting like a uniform-pressure "tank" with fluid entering or leaving the tank. Several common flow regimes and the diagnostic plots associated with these flow regimes are discussed here. The types of boundaries that may affect the pressure response include sealing faults, closed reservoirs, and gas/water, gas/oil, and oil/water contacts. At the latest times in a test (the late-time region), boundary effects dominate curve shapes. Data in this region lead to the most accurate estimates of formation permeability. For a homogeneous reservoir, the pressure derivative will be horizontal during this time region. At intermediate times (the middle-time region), a reservoir will ordinarily be infinite acting. These effects include wellbore storage, formation damage, partial penetration, phase redistribution, and stimulation (hydraulic fractures or acidization). At the earliest times on a plot (the early-time region), wellbore and near-wellbore effects dominate. The diagnostic plot can be divided into three time regions: early, middle, and late. The diagnostic plot is a log-log plot of the pressure change and pressure derivative (vertical axis) from a pressure transient test vs.
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