With the effects of tectonic stress field, natural fractures are widely developed in low-permeability formations. Fracturing of wells in naturally-fractured gas fields can differ dramatically from that in conventional isotropic formations. Fluid leakoff is the primary difference. To take account of fracturing fluidleaking into the formation through natural fractures and the matrixes, this paper has presented a new model that describes fluid leakoff in naturally-fractured gas fields and its exact solution is given by orthogonal transformation. We studied the effects of some sensitive parameters to fluid leakoff. From casestudying, fluid leakoff in naturally-fractured gas fields should not use the classic leakoff theory that leakoff velocity is inverse proportional to the exponent 0.5 of leakoff time. Basing on a great deal of calculations, the equation of V=C.t^b(b<0) is firstly presented to describe fluid leakoff in naturally-fractured gas fields and we define the constant C as equivalent leakoff coefficient. If b equals to −0.5, the new model can be simplified to the classic model. The model has been applied to investigate fracture propagation in naturally-fractured gas fields.


Fluid loss can be described as leakage of the fracturing fluid out of the main fracture. The rate of fluid leakoff(fluid loss) to the formation is one of the critical factors involved in treatment design and determining the fracture geometry. Moreover, in the naturally fractured reservoirs, fluid loss is the key factors affecting the treatment success. Therefore, many investigators have studied the simulation of fluid loss and a lot of mathematic models were developed to accurately model fluid loss.

The classic theory[1,2] considers the combined effect of the phenomena as a material property that the leakoff velocity is given by the Carter equations. To date, it is still extensively used in fracturing simulation and fracturing design. In fact, thenet fracturing pressure changes with the increase of pumping time, which has important effects on fluid loss. Therefore, the pressure-dependent leakoff model was derived by the researchers[3,4], which is used for studying hydraulic fracture propagation[5]. The latest advance of leakoff model, is accomplished by P.J.van den Hoek[6], who set up a nonlinear fluid leakoff in high-permeability fracturing. But the effects of natural fractures on fluid loss are not considered in all the existing models. However, the fluid leakoff rate in naturally fractured reservoirs is typically excessive and completely dominated by the natural fractures[7]. P.S. Vinod[8] studied the dynamic fluid loss in low-permeability formations with natural fractures by room experiments, which has some instructive meanings for fracturing design in naturally fractured reservoirs. H.J. Dietzel[9] and James L. [10] gave some key considerations in hydraulic fracturing of naturally fractured reservoirs. Where as the leakoff model with natural fractures has not been reported. The objective of this paper is to set up a new theoretical leakoff model with natural fractures and analyze its effects on fracture propagation.

Leakoff Model with Natural Fractures

Basic Assumptions Fig.1 illustrates the leakoff of fracturing fluid in naturally fractured gas fields. The followings are the basic assumptions for deriving the leakoff model:

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