Effect of Non-Darcy Flow on the Interpretation of Transient Pressure Responses of Hydraulically Fractured Wells
Authors: Umnuayponwiwat S. , Ozkan E. , Pearson C.M. , Vincent M. 
Published: December 2007

Abstract
This paper discusses the effect of non-Darcy flow on transient pressure analysis of hydraulically fractured wells. Common oversight of the results that exist in the literature is noted. It is emphasized that non-Darcy flow in the fracture affects the estimates of fracture conductivity and fracture-half-length. The limitations of buildup analysis under non-Darcy flow conditions in the fracture are discussed. Synthetic and field examples are presented to demonstrate the errors caused by neglecting the non-Darcy flow in the fracture. It is shown that, for the examples considered here, traditional pressure transient analysis neglecting non-Darcy flow may lead to errors up to 78% and 54% in the estimates of the fracture conductivity and fracture half-length, respectively. The examples also show that even the fractures with moderate production rates may be subject to the effects of non-Darcy flow.

Introduction
The effect of non-Darcy flow on the transient pressure responses of hydraulically fractured wells has been investigated in several papers.1–5 It, however, appears that the results obtained in these papers have not been effectively conveyed to the practicing engineers and utilized especially in the design and assessment of hydraulic fracturing treatments.6 As a result of negligence in accounting for non-Darcy flow effects in the fracture, conflicts between the well-test estimates and design values of fracture conductivity and/or fracture half-length continue to cause confusion and debate. The objective of this paper is, therefore, to emphasize the importance of non-Darcy flow effects in the evaluation of hydraulically fractured well responses, especially with a view to communicate with completion engineers.
We start with presenting the background of the subject matter. Here, we note some of the relevant literature and highlight their fundamental findings. Following the background section, we present two examples for high and low fracture conductivities to demonstrate that non-Darcy flow alters the distributions of flux and pressure along the fracture length and thus changes the interaction between the fracture and reservoir. We, then, discuss the effect of non-Darcy flow on drawdown and buildup responses. We emphasize that non-Darcy flow during the producing period also affects the buildup responses. The consequences of using the conventional models that do not take into account the non-Darcy flow effects are also discussed. Finally, we present a field example to discuss and demonstrate the appropriate use of the available theory and methods in the evaluation of fractured well responses. This example also helps us highlight the problems and pitfalls in the analysis of transient pressure analysis of finite-conductivity fractures. In summary, our expectation from this communication is to provide the bridge especially between the -mostly unappreciated- well testing literature on the subject and the practicing completion engineers.
Background
As we noted in the introduction, considerable effort has been made in the well testing literature1–5 to understand the effects of non-Darcy flow on the transient pressure behavior of finite-conductivity fractures. These efforts have led to the development of comprehensive semi-analytical transient flow models for hydraulically fractured wells with non-Darcy flow effects.3,4 These developments, however, have been ignored, overlooked, or completely forgotten in the field practices.6