Production from unconventional reservoirs plays a key role in supplying hydrocarbon to the world's increasing energy demand. Hydraulic fracturing is one of the most advancing technologies in producing hydrocarbon from low-permeability reservoirs, especially in tight and shale formations. The geometric properties of a hydraulic fracture affect significantly the production rate from these stimulated reservoirs. Therefore, it is of utmost importance to characterize the geometric features of hydraulically-inducedfractures during stimulation processes.

The geometric properties of a hydraulic fracture change with fracture evolution due to stress propagation along the cracks. We have modeled such a system based on the analogy between fluidic and electric circuits. The model takes into account the dynamic alteration of hydrodynamic impedance of the fracture. The hydrodynamic impedance controls the relation between the fracture fluid flow rate and pressure drop during stimulation process. The proposed model incorporates the effects of both hydrodynamic capacitance and resistance of the fracture and the wellbore to compute the fracture impedance.

Downhole measurements of pressure and flow rate can explicitly determine the hydrodynamic impedance of the fracture. Fracture impedance can also be implicitly inferred from wellhead pressure and flow rate measurements. The pulsatile nature of hydraulic fracturing treatment makes it sensible to utilize the wellhead data for the purpose of impedance monitoring based on the electromagnetic transmission line theory.

We have performed extensive sensitivity analyses on the most important parameters of a single hydraulic fracture for assessing fracture impedance. These parameters include fracture thickness, fracture radial extent, and fracture shape. Through sensitivity analyses results and real-time measurement of fracture impedance, we infer the basic geometric properties of a hydraulic fracture.

This research has led to an analytical approach for evaluating hydraulic fractures geometric characteristics. The approach builds an intuition toward better understanding how to design hydraulic fractures in a more efficient fashion.

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