A Semianalytical Approach To Model Pressure Transients in Heterogeneous Reservoirs

Abstract

Summary Pressure-transient responses of wells in a heterogeneous reservoir are usually computed with numerical models by using fine gridding and very short timesteps. An exceptions to this practice has been the use of analytical, semianalytical, and boundary-element methods for relatively simpler forms of heterogeneity, such as layering or the existence of natural fractures. This paper presents a semianalytical approach to compute pressure transients for more-complex forms of heterogeneity including composite, layered, and compartmentalized reservoirs. In this approach, the reservoir is divided into blocks corresponding to locally homogeneous substructures, and analytical pressure-transient solutions for adjacent blocks are coupled at the boundaries. This approach is consistent with the averaging effect of pressure transients and provides an alternative to full numerical modeling of pressure-transient responses in heterogeneous formations. The validation of the approach is demonstrated in comparison to the analytical solution for horizontal wells in a homogeneous reservoir. Application examples highlight the physical consistency of the approach and demonstrate its capability to model different types of reservoir heterogeneity.

Analysis of Production Data From Hydraulically Fractured Horizontal Wells in Shale Reservoirs

“…The first aspect is the use of a semianalytical model that incorporates the important features of reservoir heterogeneity and hydraulic fractures without elaborate numerical computations. The model has been built on the basis of the semianalytical simulation approach presented by Medeiros et al (2010). The computational advantage of the semianalytical simulation approach over full finite-difference simulation is that gridding is required only at the interfaces of the blocks.…”

A Decomposed Fracture Network Model for Characterizing Well Performance of Fracture Networks on the Basis of an Approximated Flow Equation

“…Analytical and semianalytical approaches, such as the multiple-porosity model, Green function method, and stimulated reservoir volume (SRV) model, have been extensively used to model the production of fracture networks. In the multiple-porosity model, the fractures are upscaled into the multiple-porosity model to take hydraulic fractures and natural fractures into consideration [11,[18][19][20]. But this model cannot reflect the real configurations of the fracture networks.…”

“…The reservoir heterogeneity was characterized by assigning different permeabilities to different layers. Medeiros et al [18] divided the reservoir into blocks to model the pressure transient behavior in compartmentalized reservoirs. However, these methods can only model simple cases involving reservoir heterogeneity.…”

Pressure Transient Behavior of Horizontal Wells Intersecting Multiple Hydraulic Fractures in Naturally Fractured Reservoirs

“…In the first paper published on this subject, de Carvalho and Rosa (1988) used the pseudosteady-state flow conditions in matrix blocks with the s → s f (s) transformation to derive the pressure transient solution for a horizontal well in a naturally fractured reservoir. After the de Carvalho and Rosa (1988) solution, many more solutions have been published in the petroleum literature using the → s f (s) transformation, while varying the matrix block shape and matrix block flow condition, and adding the interporosity skin factor for the matrix (Aguilera and Ng 1991;Du and Stewart 1992;Williams and Kikani 1990), in addition to the more recent papers by Abdulal et al (2011), Brohi et al (2011), Guo et al (2012, Ketineni and Ertekin (2012), Lu et al (2009), Medeiros et al (2007, 2008, 2010, Nie et al (2012a, b), Torcuk et al (2013).…”