A Novel Trilinear Flow Model for Capturing Dynamic Behavior of Water Flooding in Core Plug with Different Fracture Inclinations in Carbonate Reservoirs

The purpose of this study is to introduce a new three-linear flow model for capturing the dynamic behavior of water flooding with different fracture occurrences in carbonate reservoirs. Low-angle and high-angle fractures with different occurrences are usually developed in carbonate reservoirs. It is difficult to simulate the water injection development process and the law of water flooding is unclear, due to the large variation of the fracture dip. Based on the characteristics of water flooding displacement streamlines in fractured cores with different occurrences, the matrix is discretized into a number of one-dimensional linear subregions, and the channeling effect between each subregion is considered in this paper. The fractures are divided into the same number of fracture cells along with the matrix subregion, and the conduction effect between the fracture cells is considered. The fractured core injection-production system is divided into three areas of linear flow: The injected fluid flows horizontally and linearly from the matrix area at the inlet end of the core to the fracture and then linearly diverts from the fracture area. Finally, the matrix area at the outlet end of the core also presents a horizontal linear flow pattern. Thus, a trilinear flow model for water flooding oil in fractured cores with different occurrences is established. The modified BL equation is used to construct the matrix water-flooding analytical solution, and the fracture system establishes a finite-volume numerical solution, forming a high-efficiency semianalytical solution method for water-flooding BL-CVF. Compared with traditional numerical simulation methods, the accuracy is over 86%, the model is easy to construct, and the calculation efficiency is high. In addition, it can flexibly portray cracks at any dip angle, calculate various indicators of water flooding, and simulate the pressure field and saturation field, with great application effect. The research results show that the greater the fracture dip angle, the higher the oil displacement efficiency. When the fracture dip angle is above 45°, the fracture occurrence has almost no effect on the oil displacement efficiency. The water breakthrough time of through fractures is earlier than that of nonthrough fractures, and the oil displacement efficiency and injection pressure are more significantly affected by the fracture permeability. With the increase of fracture permeability, the oil displacement efficiency and the injection pressure of perforated fractured cores dropped drastically. The findings of this study can help for better understanding of the water drive law and optimizing its parameters in cores with different fracture occurrences. The three-linear flow model has strong adaptability and can accurately solve low-permeability reservoirs and high-angle fractures, but there are some errors for high-permeability reservoirs with long fractures.

Effective Continuum Approximations for Permeability in Brown-Coal and Other Large-Scale Fractured Media

The stability of open-pit brown-coal mines is affected by the manner in which water is transmitted or retained within their slopes. This in turn is a function of the in-situ fracture network at those mines. Fracture networks in real mines exhibit significant degrees of heterogeneity; encompassing a wide range of apertures, inter-fracture separations, and orientations. While each of these factors plays a role in determining fluid movement, over the scale of a mine it is often impractical to precisely measure, let alone simulate, the behaviour of each fracture. Accordingly, effective continuum models capable of representing the bulk effects of the fracture network are needed to understand the movement of fluid within these slopes. This article presents an analysis of the fracture distribution within the slopes of a brown coal mine and outlines a model to capture the effects on the bulk permeability. A stress-dependent effective-fracture-permeability model is introduced that captures the effects of the fracture apertures, spacing, and orientation. We discuss how this model captures the fracture heterogeneity and the effects of changing stress conditions on fluid flow. The fracture network data and the results from the effective permeability model demonstrate that in many cases slope permeability is dominated by highly permeable but low-probability fractures. These results highlight the need for models capable of capturing the effects of heterogeneity and uncertainty on the slope behaviour.

Discrete Fracture Model for Hydro-Mechanical Coupling in Fractured Reservoirs

The process of coupled flow and mechanics occurs in various environmental and energy applications, including conventional and unconventional fractured reservoirs. This work establishes a new formulation for modeling hydro-mechanical coupling in fractured reservoirs. The discrete-fracture model (DFM), in which the porous matrix and fractures are represented explicitly in the form of unstructured grid, has been widely used to describe fluid flow in fractured formations. In this work, we extend the DFM approach for modeling coupled flow-mechanics process, in which flow problems are solved using the multipoint flux approximation (MPFA) method, and mechanics problems are solved using the multipoint stress approximation (MPSA) method. The coupled flow-mechanics problems share the same computational grid to avoid projection issues and allow for convenient exchange between them. We model the fracture mechanical behavior as a two-surface contact problem. The resulting coupled system of nonlinear equations is solved in a fully-implicit manner. The accuracy and generality of the numerical implementation are accessed using cases with analytical solutions, which shows an excellent match. We then apply the methodology to more complex cases to demonstrate its general applicability. We also investigate the geomechanical influence on fracture permeability change using 2D rock fractures. This work introduces a novel formulation for modeling the coupled flow-mechanics process in fractured reservoirs, and can be readily implemented in reservoir characterization workflow.

Parameter Optimization of Segmental Multicluster Fractured Horizontal Wells in Extremely Rich Gas Condensate Shale Reservoirs

For economic and efficient development of extremely high-condensate shale gas reservoirs, a numerical model of segmental multicluster fractured horizontal well was established considering the effect of condensate and desorption, and the optimization of fracturing segments, fracturing clusters, half-length of main fracture, fracture permeability, fracture mesh density, and fracture distribution patterns were studied. It is indicated that the horizontal well whose design length is 2,700 m performs best when it has 43 fracturing segments with three clusters in each segment and the fracture permeability is 300 mD. The production capacity of horizontal wells is positively linearly correlated with the half-length of fractures. Increasing fracture half-length would be an effective way to produce condensate oil near wellbore. An effective fractured area can be constructed to remarkably improve productivity when the half-length of the fracture is 50 m and the number of secondary fractures is four in each segment. On the basis of reasonable fracture parameters, the staggered type distribution pattern is beneficial to the efficient development of shale gas-condensate reservoirs because of its large reconstruction volume, far pressure wave, small fracture interference, and small precipitation range of condensate.

CBM exploration: Permeability of coal owing to cleat and connected fracture

Coalbed methane (CBM) resources cannot be efficiently explored and exploited without a robust understanding of the permeability of fracture-size heterogeneities in coal. In this study, two sister coal samples were imparted with pre-developed cleat and connected fractures, and the permeability of the coal samples was measured under different conditions of controlled confining and gas pressures. Furthermore, the implications of the results for CBM exploration and exploitation were discussed. The permeability of coal with cleat development ranged from 0.001–0.01 mD, indicating ultra-low permeability coal. The gas migration in this coal changed from a linear flow to a non-linear flow, with the increase in gas pressure (>1 MPa). Thus, the permeability of the coal initially increased and then decreased. However, the Klinkenberg effect does not exist in this ultralow-permeability coal. For the coal sample with connected fracture, permeability ranged from 0.1–10 mD, which is larger by hundred orders of magnitude than that of the sample with cleat. For this coal, with a decrease in gas pressure (<1 MPa), the Klinkenberg effect significantly increased the permeability of the coal. With an increase in the applied confining pressure, both the Klinkenberg coefficient and permeability of the coal presented a decreasing trend. It is suggested that field fracture investigation is a prerequisite and indispensable step for successful CBM production. The coal beds that cleat network is well conductive to the connected fracture can be an improved target area for CBM production. During CBM production, a variety of flow regimes are available owing to the decrease in CBM reservoir pressure. In particular, under the low CBM reservoir pressure and low in situ geo-stress conditions, the gas migration in the CBM reservoir with connected facture development exhibits remarkable free-molecular flow. Thus, the reservoir permeability and predicted CBM production will be enhanced.

Application Investigation of Light Proppant in Hydraulic Fracturing of Marcellus Shale

Slickwater-sand fracturing design is widely employed in Marcellus shale. The slickwater- sand creates long skinny fractures and maximizes the stimulated reservoir volume (SRV). However, due to the fast settling of sand in the water, lots of upper and deeper areas are not sufficiently propped. Reducing sand size can lead to insufficient fracture conductivity. This study proposes to use three candidate ultra-lightweight proppants ULWPs to enhance the fractured well performance in unconventional reservoirs. In step 1, the current sand pumping design is input into an in-house P3D fracture propagation simulator to estimate the fracture geometry and proppant concentrations. Next, the distribution of proppant concentration converts to conductivity and then to fracture permeability. In the third step, the fracture permeability from the second step is input into a reservoir simulator to predict the cumulative production for history matching and calibration. In step 4, the three ULWPs are used to replace the sand in the frac simulator to get new frac geometry and conductivity distribution and then import them in reservoir model for production evaluation. Before this study, the three ULWPs have already been tested in the lab to obtain their long-term conductivities under in-situ stress conditions. The conductivity distribution and production performance are analyzed and investigated. The induced fracture size and location of the produced layer for the current target well play a fundamental effect on ultra-light proppant productivity. The average conductivity of ULWPs with mesh 40/70 is larger and symmetric along the fracture except for a few places. However, ULWPs with mesh 100 generates low average conductivity and create a peak conductivity in limited areas. The ULW-3 tends to have less cumulative production compared with the other ULWPs. For this Marcellus Shale study, the advantages of ultra-lightweight proppant are restricted and reduced because the upward fracture height growth is enormous. And with the presence of the hydrocarbon layer is at the bottom of the fracture, making a large proportion of ULWPs occupies areas that are not productive places. The current study provides a guidance for operators in Marcellus Shale to determine (1) If the ULWP can benefit the current shale well treated by sand, (2) what type of ULWP should be used, and (3) given a certain type of ULWP, what is the optimum pumping schedule and staging/perforating design to maximize the well productivity. The similar workflow can be expanded to evaluate the economic potential of different ULWPs in any other unconventional field.

Numerical Simulation of Proppant Transport in Hydraulically Fractured Reservoirs

An existing equation-of-state compositional simulator is extended to include proppant transport. The simulator determines the final location of the proppant after fracture closure, which allows the computation of the permeability along the hydraulic fracture. The simulation then continues until the end of the production. During hydraulic fracturing, proppant is injected in the reservoir along with water and additives like polymers. Hydraulic fracture gets created due to change in stress caused by the high injection pressure. Once the fracture opens, the bulk slurry moves along the hydraulic fracture. Proppant moves at a different speed than the bulk slurry and sinks down by gravity. While the proppant flows along the fracture, some of the slurry leaks off into the matrix. As the fracture closes after injection stops, the proppant becomes immobile. The immobilized proppant prevents the fracture from closing and thus keeps the permeability of the fracture high. All the above phenomena are modelled effectively in this new implementation. Coupled geomechanics simulation is used to model opening and closure of the fracture following geomechanics criteria. Proppant retardation, gravitational settling and fluid leak-off are modeled with the appropriate equations. The propped fracture permeability is a function of the concentration of immobilized proppant. The developed proppant simulation feature is computationally stable and efficient. The time step size during the settling adapts to the settling velocity of the proppants. It is found that the final location of the proppants is highly dependent on its volumetric concentration and slurry viscosity due to retardation and settling effects. As the location and the concentration of the proppants determine the final fracture permeability, the additional feature is expected to correctly identify the stimulated region. In this paper, the theory and the model formulation are presented along with a few key examples. The simulation can be used to design and optimize the amount of proppant and additives, injection timing, pressure, and well parameters required for successful hydraulic fracturing.

A Hybrid Model for Simulating Fracturing Fluid Flowback in Tight Sandstone Gas Wells considering a Three-Dimensional Discrete Fracture

Two-phase (gas+water) flow is quite common in tight sandstone gas reservoirs during flowback and early-time production periods. However, many analytical models are restricted to single-phase flow problems and three-dimensional fracture characteristics are seldom considered. Numerical simulations are good choices for this problem, but it is time consuming in gridding and simulating. This paper presents a comprehensive hybrid model to characterize two-phase flow behaviour and predict the production performance of a fractured tight gas well with a three-dimensional discrete fracture. In this approach, the hydraulic fracture is discretized into several panels and the transient flow equation is solved by the finite difference method numerically. A three-dimensional volumetric source function and superposition principle are deployed to capture the flow behaviour in the reservoir analytically. The transient responses are obtained by coupling the flow in the reservoir and three-dimensional discrete fracture dynamically. The accuracy and practicability of the proposed model are validated by the numerical simulation result. The results indicate that the proposed model is highly efficient and precise in simulating the gas/water two-phase flow and evaluating the early-time production performance of fractured tight sandstone gas wells considering a three-dimensional discrete fracture. The results also show that the gas production rate will be overestimated without considering the two-phase flow in the hydraulic fracture. In addition, the influences of fracture permeability, fracture half-length, and matrix permeability on production performance are significant. The gas production rate will be higher with larger fracture permeability at the early production period, but the production curves will merge after fracturing fluid flows back. A larger fracture half-length and matrix permeability can enhance the gas production rate.