The equations originally developed by Nolte and Lee for the interpretations of a pump-in/shut-in test were modified and successfully used in the pump-in/flow-back tests. A new graphical technique has been developed for physical interpretation of the fracture closure pressure from a pump-in/ flow back test. The methodology developed in this paper has been successfully used in the field for the determination of the needed fracture parameters such as, fracture closure pressure, fluid loss properties, and fracture geometry from mini- or micro-fracturing tests.


Mini- or Micro-fracturing tests such as pump-in/shut-in and pump-in/flow-back tests are commonly conducted for on-site evaluation of fracture parameters. Generally, the former is used to determine the fluid loss of the formation and the fracture geometry, while the latter is normally used to determine the fracture closure pressure.

Conventionally, in a pump-in/shut-in test, a log-log plot of the pressure difference versus shut-in time is usually used to identify the existence or of linear or bi-linear flow. In which an one-half slope normally indicates the existence of linear flow and a quarter slope for bi-linear flow. In the case of linear flow, a log-log plot of the bottom hole pressure versus square root time is then made and the fracture closure pressure is determined from the point where the curve deviates from the straight line. Similarly, the fracture closure pressure for a bi-linear flow can also be determined from a log-log plot of the bottom hole pressures versus one fourth-root of the shut-in time.

However, due to the inconclusive nature of the transient pressure decline during shut-in, the log-log plot sometimes may exhibit multiple straight lines with inconsistent slopes, which makes proper identification of the flow region impossible. Moreover, it normally requires excessively long period of time to reach the point of deflection where the closure pressure can be determined, especially in the case of high fluid efficiency. A fluid efficiency of 95 percent, for instance, it requires a shut-in time of approximately 240 folds that of pump-in time to reach the point of inflection.

The pump-in/flow-back test is normally conducted separately or in concurrent with the pump-in/shut-in test. In this test, the well is allowed to flow back at a low, constant rate through a surface choke after shut-in. The flow-back process will normally enhance the rate of pressure decline, causing a continuous change of the curvature on a pressure versus flow-back time plot. There are four techniques which are normally applied to interpret the closure pressure from a Cartesian plot of bottom-hole pressure versus cumulative time including shut-in. Unfortunately, their differences are normally in the order of hundreds of psi, which add substantial uncertainties in the field applications.

In this paper, the equations originally developed by Nolte and Lee for pump-in/shut-in test were modified and adopted for the pump-in/flow-back tests. A new graphical technique was also developed to resolve the difficulties involved in the conventional methods in determining the fracture closure pressure.

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