Abstract
Multifractured horizontal wells have gained significant attention within the petroleum industry for commercial development. Despite considerable developments of transient pressure analysis or flow rate behaviors for horizontal wells in naturally fractured reservoirs, some significant problems are yet to be resolved, including high heterogeneity of reservoirs, pressure sensitivity of hydraulic fractures, and non-Darcy flow effect, which may occur during the production life. This paper presents a more pragmatic mathematical model for multifractured horizontal wells in naturally fractured reservoirs based on the fractal system, the theory of permeability modulus, and the time-fractional calculus correspondingly as an extension of the classic trilinear flow model. This new model comprises three modules: high heterogeneity of the reservoir based on the fractal system, the permeability modulus typically showing the pressure sensitivity of hydraulic fractures, and the anomalous diffusion describing non-Darcy flow turbulence. This investigation evaluates a trilinear dual-permeability dual-porosity flow model, with the dual-porosity model for the unstimulated outer reservoir flow region, the dual-permeability model for the stimulated inner reservoir flow region, and the permeability modulus for the flow region of hydraulic fractures. The comprehensive sensitivity analysis conducted indicates how the key parameters, such as fractal dimension, hydraulic fracture permeability modulus and conductivity, interporosity flow coefficient, storativity ratio, etc., affect the transient pressure behaviors, along with their reasons for the change in behavior. Application to a field case study further demonstrates the validity of the mathematical model, and the results presented may play a guiding role in well test interpretation.
Highlights
Increasing demand for oil and gas resources while being economical has significantly accelerated the development of multifractured horizontal wells (MFHWs)
We introduce the theory of anomalous diffusion; the modified pseudo-interporosity flow rate qom→f from the matrix system to the fracture system in the outer reservoir flow region is typically concerned with the time-fractional derivative of the pressure difference between these two systems
Model analysis, based on the dimensionless theoretical parameters, aims to observe how the well test curves are influenced by the hydraulic permeability modulus, the fractal dimension, the fractal connectivity index, the interporosity flow coefficient, the storativity ratio, the hydraulic fracture conductivity, the choking skin factor, and the wellbore storage coefficient separately
Summary
Increasing demand for oil and gas resources while being economical has significantly accelerated the development of multifractured horizontal wells (MFHWs). Previous researchers evolved their work from case studies to the field data analysis of transient pressure behaviors of MFHWs.[5−8] Previous investigations have incorporated computational methods to show the main flow regimes in the closed reservoir where the transversely fractured horizontal well completed, including the fracture linear flow, the bilinear flow, the early radial flow, the pseudo-radial flow, and the formation linear flow regimes respectively.[9,10] It is evident that linear flow patterns are dominant in the whole production life of the reservoir, which is the basic premise of the trilinear flow model.[11] To cope with such a situation, Brown et al.[12] first put forward a practical trilinear dual-porosity flow model for MFHW and took into account the effect of the outer reservoir flow region and the influence of natural fractures on fluid flowing behaviors using the dual-porosity model.[13] Figure 1 presents the outer reservoir flow region, regarded as an unstimulated homogeneous area with one single porosity and permeability; the stimulated inner reservoir flow region incorporates pseudo/transient interporosity flow from the matrix system to the fracture system; the region of hydraulic fractures comprises multiple equidistant transverse singlepermeability/porosity hydraulic fractures with finite conductivity
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