On a Well-Test Pressure Theory of Analysis for Naturally Fractured Reservoirs, Considering Transient Interporosity Matrix, Microfractures, Vugs, and Fractures Flow

Abstract

Constant flow, rate solutions are presented for a fractured reservoir with transient interporosity flow in a convolution form, considering matrix, microfractures, vugs and fractures flow. New solutions are presented for two cases, where there is no primary flow through the microfractures and where the compressive and distensive strength process has created an interconnected system of microfractures. In both cases there is an interaction between matrix, microfractures, and fracture systems. The numerical inversion was carried out with Stehfest's algorithm. In addition, approximate analytical solution for short and long dimensionless time are obtained and compared with the solution calculated by numerical inversion, providing satisfactory results. The values of the numerical inversion were used to generate the results, presented in terms of the dimensionless groups derived from the approximate analytical solution. Introduction In areas without cores, open-hole wireline logs may be used to help identify vugs zones; however, vugs are not always recognized by conventional logs because of their limited vertical resolution. Vugs porosity is common in many reservoirs and its importance in the petrophysical and productive characteristics of a rock has been recognized in several works. Vugs porosity can be subdivided into small and large types. Vugs effect on permeability is related to their connectivity3. One purpose of our work is to present a technique to identify high secondary porosity, mainly vugs porosity. When dealing with NFR, it is important to study its origin and main characteristics, such as the regularity of their distribution, and morphology, aperture, width, etc. Figs. 1 and 2 presents photographs of whole cores taken in highly productive naturally fractured carbonate vuggy and fractured formations. Fig. 1.a shows two fracture system, one being vertical and the other inclined, connected through vugs. Fig. 1.b illustrates a fracture system that has a main vertical direction. Fig. 1.c shows a system of vertical and conjugate fractures; some vugs can be observed and an open fracture of aperture of about 3mm. Fig. 2 shows three additional images of carbonate whole cores. Fig. 2.a illustrates the case of fractures filled by calcite. Fig 2.b presents the important physical condition of fracture planes affected by dissolution, which increases both secondary porosity and bulk permeability. Finally, Fig. 2.c exhibits vertical fractures, enhanced by dissolution vugs, which improve the formation bulk conductivity. It has been observed in the literature that vugs zones strongly influence production performance3, 4. Recently two papers have discussed results strictly related to the presents study. Camacho etal1. developed a new way to model the secondary porosity of naturally reservoirs (NFR), mainly vuggy porosity the authors derived solutions for two cases, one where there is no primary flow through the vugs (which is an improvement of the Warren and Root model), and second in which the dissolution process of the pore volume has resulted in an interconnected system of vugs and caves. Thus, this is a triple-porosity / dual permeability model. Rodriguez et al 2. developed a nested - triple -porosity single - permeability model for the pressure transient behavior of a well producing in a NFR, there porosity systems, acting at different scales, are assumed to coexist in these reservoirs: matrix, small scale and large scale secondary porosity media, flow in series among these media is considered; the matrix exchanges fluids whit the small - scale secondary porosity, which in turn feeds the large - scale secondary porosity. The first two media are assumed to have a local effect on fluid flow, and are considered as discontinuous, while the third, the large - scale secondary porosity medium, is considered to affect fluid flow at the reservoir scale and it is consequently continuous.

Variability of Double-Porosity Flow, Interporosity Flow Coefficient λ and Storage Ratio ω in Dolomites

“…The double-porosity concept was later extended to triple-porosity systems [6,7], where the porosities include the common porosities of the matrix and fractures, as well as the vugs, microfractures and any other cavities occurring in the rock. The original doubleporosity model of Warren and Root [2] has been updated by other authors [8], such as Water 2024, 16, 1072 2 of 10 Odeh [9], Kazemi [10,11], de Swaan-O [12] and Serra et al [13], with the introduction of well storage, skin effects [4,14], and other approaches.…”

Fluid Flow Behavior Prediction in Naturally Fractured Reservoirs Using Machine Learning Models

“…Tis examined some of the factors afecting the leakage of fuids by making a model for analyzing the leakage of fuids in naturally fractured gas felds. Turn to Warren and Root [11], the authors have provided a suitable solution to this problem and were able to arrive at these parameters, the actual shape, dimensions, and fuid fow properties of the reservoir, where the same scenario had been adopted later in [20,21].…”

Dual permeability flow behavior for modeling horizontal well production in fractured-vuggy carbonate reservoirs

“…Izadi and Yildiz (2007) examined transient flow in discretely fractured porous media, and Jalali and Ershaghi (1987) investigated pressure transient analysis of heterogeneous naturally fractured reservoirs, and formulated a pressure vs. time log curve. Additionally, Leveinen (2000) established a composite model with fractional flow dimensions for well test analysis in fractured rocks, Nie et al (2011) investigated a flow model for triple porosity carbonate reservoirs by conceptualizing vugs as spherical shapes, Wu et al (2004Wu et al ( , 2007Wu et al ( , 2011) studied a triple continuum pressure transient model for a naturally fractured vuggy reservoir, and Pulido et al (2006) established a well-test pressure theory of analysis for naturally fractured reservoirs, considering transient interporosity matrix, micro fractures, vugs, and fractures flow.…”

“…In Pulido et al (2006) and Nie et al (2011), the pathway connected to the wellbore was a fracture system where flow from the matrix system to the wellbore was ignored and the fracture system was treated as the main pathway, thus considering inter-porosity flows from the matrix and vug systems to the fracture system; (2) triple porosity and dual permeability models for vertical well production in fractured-vuggy reservoirs. Camacho-Velázquez et al (2005) considered the vug system as a continuum medium.…”