A New Model of Fluid Leak-off in Naturally Fractured Gas Fields and Its Effects on Fracture Geometry
Authors: Li Y. , Guo J. , Zhao J. , Yue Y. 
Published: July 2010

Abstract
In investigations of tectonic stress fields, natural fractures are often found in low-permeability formations. Fracturing wells in naturally fractured gas fields can differ dramatically from those in conventional isotropic formations. Fluid leak-off is the pri-mary difference. To take account of fracturing fluid leaking into the formation through natural fractures and the matrixes, this paper presents a new model that describes fluid leak-off in naturally fractured gas fields and its exact solution is given by or-thogonal transformation. We studied the effects of some sensitive parameters to fluid leak-off. From the cases studied, fluid leak-off in naturally fractured gas fields should not use the classic leak-off theory which states that leak-off velocity is inversely proportional to the exponent 0.5 of leak-off time. Based on numerous calculations, the equation V = C.t ∧ b (b &lt; 0) is presented to describe fluid leak-off in naturally fractured gas fields, and the constant C is defined as the equivalent leak-off coefficient. If b is equal to -0.5, the new model can be simplified according to the classic model. The model has been applied to investigate fracture propagation in naturally fractured gas fields.

Introduction
Fluid loss can be described as leakage of the fracturing fluid leaking out of the main fracture. The rate of fluid leaking into the formation is one of the critical factors involved in the treatment design and in determining the fracture geometry. Moreover, in naturally fractured reservoirs, fluid loss is the key factor affecting the treatment success. Therefore, many investigators have studied the simulation of fluid loss and a number of mathematic models were developed to accurately model fluid loss.
Classic theory(1, 2) considers the combined effect of the phenomena as a material property, so that leak-off velocity is given by the Carter equations. To date, it is still extensively used in fracturing simulation and fracturing design. In fact, the net fracturing pressure changes with an increase in pumping time, which has an important effect on fluid loss. Therefore, the pressure-dependent leak-off model was derived(3, 4), which is used for studying hydraulic fracture propagation(5). More recently, van den Hoek(6) developed a nonlinear fluid leak-off model for high-permeability fracturing. But the effects of natural fractures on fluid loss are not considered in the existing models. However, the fluid leak-off rate in naturally fractured reservoirs is typically excessive and completely dominated by the natural fractures(7). Vinod et al.(8) studied dynamic fluid loss in low-permeability formations with natural fractures by room experiments, which has some useful implications for fracturing design in naturally fractured reservoirs. Dietzel and Koehler(9) and Rodgerson(10) offered some key considerations in the hydraulic fracturing of naturally fractured reservoirs. Whereas, the leak-off model with natural fractures has not been reported, the objective of this paper is to set up a new theoretical leak-off model for natural fractures and analyze the effect on fracture propagation.

Leak-off Model for Natural Fractures
Basic Assumptions
Figure 1 illustrates the leak-off of fracturing fluid in naturally fractured gas fields. The following are the basic assumptions for deriving the leak-off model: