Hydraulic fracturing has generally been limited to relatively low-permeability reservoirs. In recent years, the use of hydraulic fracturing has expanded significantly to high permeability reservoirs. The objectives of fracturing low permeability reservoirs and high permeability reservoirs are different and defined by reservoir parameters.

The estimation of reservoir permeability, a variable of great importance in hydraulic fracturing design is frequently unknown because candidate wells either do not flow or a pretreatment pressure transient test is required. Consequently, Nolte has introduced a new method for adding after-closure fracturing analysis to the pretreatment calibration testing sequence that defines fracture geometry and fluid loss characteristics. The exhibition of the radial flow is ensured by conducting a specialized calibration test called mini-fall test. The derivations by Nolte, based on the theory of impulse test and principle of superposition, allow the identification of radial flow and thus the determination of reservoir transmissibility and reservoir pressure.

This study presents a review of the after-closure radial flow analysis. A modified method is proposed to complete the Nolte's method for the determination of the reservoir transmissibility and reservoir pressure based on the pressure derivative.

The application of the modified method is demonstrated on actual field data from calibration tests performed on several oil and gas wells. The reservoir parameters determined with this method are verified by comparison with results obtained from buildup tests.


Hydraulic fracturing has been recognized to be an effective means for enhancing well productivity and recoverable reserves, especially for low permeability reservoirs, by reducing the resistance to flow area between the wellbore and formation.

The appropriate fracturing treatment for a given well has been hard to design because of the numerous variables involved. The use of inaccurate reservoir variables to design treatments may lead to poor production estimates.

In wells that are to be hydraulically fractured, minifracture treatment, called also calibration test, frequently is performed to determine parameters needed for the stimulation design. It is generally performed without proppant and therefore, retains negligible conductivity when it closes.

Fracture pressure analysis was pioneered by Nolte1,2. The basic principles are analogous to those for pressure analysis of transient fluid in the reservoir. Both provide a means to interpret complex phenomena occurring underground by analyzing the pressure response resulting from fluid movement in rock formation.

The analysis of fracturing pressure, during injection, during closing and after closure period, provide powerful tools for understanding and improving the fracture process.

Advances in minifracture analysis techniques have provided methods for determination of fracturing treatment design parameters such as leak-off, fracture dimensions, fluid efficiency, closure pressure and reservoir parameters. These parameters can then be used to determine the pad volume required, best fluid loss additives to be used, and most importantly, to achieve the optimum fracturing treatment design.

Fig. 1 shows a typical history of the calibration test from the beginning of pumping until the reservoir disturbance from the fracture decays back to the initial reservoir pressure.

Fracturing pressures during each stage of fracture evolution (i.e. growth, closing and after-closure) provide complementary information pertinent to the fracture design process. Therefore, Fracturing pressure analysis may be reduced to three distinct types of analysis.

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