This work introduces a new model for the production-decline analysis (PDA) of hydraulically fractured wells on the basis of the concept of the induced permeability field. We consider the case when the hydraulic-fracturing operation—in addition to establishing the fundamental linear-flow geometry in the drainage volume—alters the ability of the formation to conduct fluids throughout, but with varying degrees depending on the distance from the main fracture plane. We show that, under these circumstances, the reservoir response departs from the uniform-permeability approach significantly.
The new model differs from the once promising group of models that are inherently related to power-law-type variation of the permeability-area product and thus are burdened by a mathematical singularity inside the fracture. The analysis of field cases reveals that the induced permeability field can be properly represented by a linear or exponential function characterized by the maximal induced permeability k0 and the threshold permeability k*. Both these permeabilities are induced (superimposed on the formation) by the hydraulic-fracturing treatment; thus, the model can be considered as a simple, but nontrivial, formalization of the intuitive stimulated-reservoir-volume (SRV) concept.
It is quite reasonable to assume that the maximum happens at the fracture face and that the minimum happens at the outer boundary of the SRV. The contrast between maximal and minimal permeability, SR = k0/k*, will be of considerable interest, and thus, we introduce a new term for it: stimulation ratio (SR). Knowledge of these parameters is crucial in evaluating the effectiveness of today's intensively stimulated well completions, especially multifractured horizontal wells in shale gas. The approach describes, in a straightforward manner, the production performance of such wells exhibiting transient linear flow and late-time boundary-dominated flow affected also by a skin effect (i.e., by an additional pressure drop in the system characterized by linear dependence on production rate).
This work provides the induced-permeability-field model within the single-medium concept, and shows that some features widely believed to require a dual-medium (double-porosity) representation are already present. Advantages and drawbacks related to applying the concept in a dual-medium approach will be discussed in an upcoming work. We present the model and its analytical solution in Laplace space. We provide type curves for decline-curve analysis, closed-form approximate solutions in the time domain, field examples, and practical guidelines for the analysis of commonly occurring production characteristics of massively stimulated reservoirs.