Semi-analytical model for the transient analysis of the pressure in vertically fractured wells in reservoirs considering the influence of natural fractures

2021 ◽  
pp. 1-12
Author(s):  
Yiming Chen ◽  
Qiushi Zhang ◽  
Zhiming Zhao ◽  
Cunlei Li ◽  
Bo Wang
Keyword(s):  
Fluid Flow ◽  
Analytical Model ◽  
Fluid Flows ◽  
Transient Behavior ◽  
Natural Fracture ◽  
Natural Fractures ◽  
Flow Process ◽  
Main Fracture ◽  
The Matrix ◽  
Flow Stage

Abstract In addition to artificial fractures generated by hydraulic fracturing technology, natural fractures distributed in reservoirs will also affect the fluid flow process. To study the transient behavior of the pressure in fluid flows in reservoirs containing natural fractures, a semi-analytical model for vertically fractured wells with complex natural fracture networks was established. This model was based on the linear source function theory and the fracture discretization and coupling methods. It was solved by the Stehfest numerical inversion and the matrix transformation. The results of the study on the fluid flow stages in a reservoir with natural fractures indicated that the presence of natural fractures increased natural fracture flows. These flows were dominated by natural fractures and fracture interference stages and were different from the fluid flows observed in vertically fractured wells with a single main fracture. The sensitivity analysis on the influences of the fluid flow factors in the reservoirs with three types of natural fractures could provide a more detailed reference for the identification of the reservoir parameters and the transient characteristics of the flow stage. The different characteristic curves of the fluid flow in the reservoirs with different scale natural fractures could also provide a theoretical basis for determining the distribution of natural fractures in reservoirs.

Pressure-Transient Behavior of Partially Penetrating Inclined Fractures With a Finite Conductivity

SPE Journal ◽  
2018 ◽  
Vol 24 (02) ◽  
pp. 811-833 ◽  
Author(s):  
Bailu Teng ◽  
Huazhou Andy Li
Keyword(s):  
Fluid Flow ◽  
Transient Flow ◽  
Flow Behavior ◽  
Transient Behavior ◽  
Finite Conductivity ◽  
Linear Flow ◽  
Pressure Transient ◽  
Proposed Model ◽  
Elliptical Flow ◽  
The Matrix

Summary Field studies have shown that, if an inclined fracture has a significant inclination angle from the vertical direction or the fracture has a poor growth along the inclined direction, this fracture probably cannot fully penetrate the formation, resulting in a partially penetrating inclined fracture (PPIF) in these formations. It is necessary for the petroleum industry to conduct a pressure-transient analysis on such fractures to properly understand the major mechanisms governing the oil production from them. In this work, we develop a semianalytical model to characterize the pressure-transient behavior of a finite-conductivity PPIF. We discretize the fracture into small panels, and each of these panels is treated as a plane source. The fluid flow in the fracture system is numerically characterized with a finite-difference method, whereas the fluid flow in the matrix system is analytically characterized on the basis of the Green's-function method. As such, a semianalytical model for characterizing the transient-flow behavior of a PPIF can be readily constructed by coupling the transient flow in the fracture and that in the matrix. With the aid of the proposed model, we conduct a detailed study on the transient-flow behavior of the PPIFs. Our calculation results show that a PPIF with a finite conductivity in a bounded reservoir can exhibit the following flow regimes: wellbore afterflow, fracture radial flow, bilinear flow, inclined-formation linear flow, vertical elliptical flow, vertical pseudoradial flow, inclined pseudoradial flow, horizontal-formation linear flow, horizontal elliptical flow, horizontal pseudoradial flow, and boundary-dominated flow. A negative-slope period can appear on the pressure-derivative curve, which is attributed to a converging flow near the wellbore. Even with a small dimensionless fracture conductivity, a PPIF can exhibit a horizontal-formation linear flow. In addition to PPIFs, the proposed model also can be used to simulate the pressure-transient behavior of fully penetrating vertical fractures (FPVFs), partially penetrating vertical fractures (PPVFs), fully penetrating inclined fractures (FPIFs), and horizontal fractures (HFs).

scholarly journals Analytical and Computational Modeling of Sustained-Release Drug Implants in the Vitreous Humor

2021 ◽  
Author(s):  
Anahid Khoobyar ◽  
Amin Naghdloo ◽  
Anita Penkova ◽  
Mark S. Humayun ◽  
Satwindar Singh. Sadhal
Keyword(s):  
Fluid Flow ◽  
Sustained Release ◽  
Analytical Model ◽  
Drug Transport ◽  
Transfer Problem ◽  
Vitreous Humor ◽  
Convective Transport ◽  
Time Dependent ◽  
Flow Process ◽  
Dependent Mass

Abstract Sustained ocular drug delivery systems are necessary for patients needing regular drug therapy since frequent injection is painful, undesirable and risky. One type of sustained-release systems includes pellets loaded with the drug, encapsulated in a porous shell that can be injected into the vitreous humor. There the released drug diffuses while the physiological flow of water provides the convective transport. The fluid flow within the vitreous is described by Darcy's equations for the analytical model and Brinkman flow for the computational analysis, while the drug transport is given by the classical convection-diffusion equation. Since the timescale for the drug depletion is quite large, for the analytical model we consider the exterior surrounding the capsule to be quasi-steady and the interior is time dependent. In the vitreous, the fluid-flow process is relatively slow, and meaningful results can be obtained for small Peclet number whereby a perturbation analysis is possible. For an isolated capsule, with approximately uniform flow in the far-field around it, the mass-transfer problem requires singular perturbation with inner and outer matching. The computational model, besides accommodating the ocular geometry, allows for a fully time-dependent mass-concentration solution and also admits moderate Peclet numbers. As expected, the release rate diminishes with time as the drug depletion lowers the driving potential. The predictive results are sufficient general for a range of capsule permeability values and are useful for the design of the sustained-release microspheres as to the requisite permeability for specific drugs.

Mechanism for Network Fracturing in Natural Fractured Reservoir

2013 ◽  
Vol 868 ◽  
pp. 718-724 ◽  
Author(s):  
Hong Liu ◽  
Jiang Xin Feng ◽  
Ya Long Zhang ◽  
Yi Xing Yue ◽  
Tao Zhang ◽  
...  
Keyword(s):  
Fracture Initiation ◽  
Natural Fracture ◽  
Fractured Reservoir ◽  
Natural Fractures ◽  
Crustal Stress ◽  
Fracture Width ◽  
Fracturing Process ◽  
Main Fracture ◽  
Secondary Fractures ◽  
The Difference

By the methods of in-house experiment and theory analysis, the fracture initiation, stretch and interconnected mechanism of natural fracture is studied in the fracturing process of main fracture and branch fracture extending. The results have shown that, the hydraulic fracture in fractured formation is composed of a few main fractures in large size and many s secondary fractures in small size. The main fracture has the extending trend with the maximum crustal stress direction. The direction of sub fracture is network along the maximum crustal stress. The higher the degree of natural fractures, the difference between maximum and minimum crustal stress smaller. And the natural fracture is easier to form larger fracture. Fracture orientation and fracture width are determined by different combinations of natural fractures and the relative orientation with the maximum crustal stress.

scholarly journals A new methodology to train fracture network simulation using Multiple Point Statistic

2018 ◽  
Author(s):  
Pierre-Olivier Bruna ◽  
Julien Straubhaar ◽  
Rahul Pranhakaran ◽  
Giovanni Bertotti ◽  
Kevin Bisdom ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Fracture Network ◽  
Natural Fracture ◽  
Multiple Point ◽  
Fracture Aperture ◽  
Strong Impact ◽  
Data Sampling ◽  
Natural Fractures ◽  
Training Images ◽  
Network Geometry

Abstract. Natural fractures have a strong impact on flow and storage properties of reservoirs. Their distribution in the subsurface is largely unknown mainly due to their sub-seismic scale and to the scarcity of available data sampling them (borehole). Outcrop can be considered as analogues where natural fracture characteristics can be extracted. However, acquiring fracture data on outcrops may produce a large amount of information that needs to be processed and efficiently interpreted to capture the key parameters defining fracture network geometry. Outcrops thus become a natural laboratory where the interpreted fracture network can be tested mechanically (fracture aperture, distribution of strain/stress) and dynamically (fluid flow simulations (Bisdom et al., 2017). The goal of this paper is to propose the multiple point statistics (MPS) method as a new tool to quickly predict the geometry of a fracture network in both surface and subsurface conditions. This sequential simulation method is based on the creation of small and synthetic training images representing fracture distribution parameters observe in the field. These training images represent the complexity of the geological object or processes to be simulated and can be simply designed by the user. In this paper we chose to use multiple training images and a probability map to represent the fracture network geometry and its potential variability in a non-stationary manner. The method was tested on a fracture pavement (2D flat surface) acquired using a drone in the Apodi area in Brazil. Fractures were traced manually on images of the outcrop and constitute the reference on which the fracture network simulations will be based. A sensitivity analysis emphasizing the influence of the conditioning data, the simulation parameters and the used training images was conducted on the obtained simulations. Stress-induced fracture aperture calculations were performed on the best realisations and on the original outcrop fracture interpretation to qualitatively evaluate the accuracy of our simulations. The method proposed here is innovative and adaptable. It can be used on any type of rocks containing natural fractures in any kind of tectonic context. This workflow can also be applied to the subsurface to predict the fracture arrangement and its fluid flow efficiency in water, heat or hydrocarbon reservoirs.

Numerical Simulation of Heat Transfer from Hot Dry Rock to Water Flowing through a Circulation Fracture

2014 ◽  
Vol 852 ◽  
pp. 831-834
Author(s):  
Bin Dou ◽  
Hui Gao ◽  
Gang Zhou ◽  
Lei Ren
Keyword(s):  
Fluid Flow ◽  
Fracture Network ◽  
Natural Fracture ◽  
Heat Extraction ◽  
Natural Fractures ◽  
Fracture Networks ◽  
Pumping Rate ◽  
Hydraulic Stimulation ◽  
Hot Dry Rock ◽  
Well Spacing

This paper presents an advanced computational modeling of natural fracture networks in hot dry rock (HDR) reservoirs. A mathematical model is developed for describing the heat energy extracted from a HDR in a multi-well system. The model stochastically simulates discrete properties of natural fractures, utilizing multi-set orientation and fractal mathematics. The simulated fracture networks are essential for further stimulation and fluid flow studies. The results show that the heat extraction effectiveness is affected significantly by the well spacing, well radius, reservoir thickness, and pumped flow rate in a multi-well system. The water temperature decreases with increasing pumping rate and increases with the well spacing, well radius, and reservoir thickness. This paper also examines the detrimental effects of the simulated natural fracture network on the stimulated fluid flow capacity. The effective permeability enhancement (due to hydraulic stimulation) is found almost proportional to the density of the reservoir natural fractures.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

scholarly journals The impact of natural fractures on heat extraction from tight Triassic sandstones in the West Netherlands Basin: a case study combining well, seismic and numerical data

2021 ◽  
Vol 100 ◽  
Author(s):  
Quinten D. Boersma ◽  
Pierre Olivier Bruna ◽  
Stephan de Hoop ◽  
Francesco Vinci ◽  
Ali Moradi Tehrani ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Heat Production ◽  
Positive Impact ◽  
Heat Extraction ◽  
Natural Fractures ◽  
Negative Power ◽  
Petrophysical Analysis ◽  
Production Values ◽  
Geostatistical Inversion ◽  
The Impact

Abstract The positive impact that natural fractures can have on geothermal heat production from low-permeability reservoirs has become increasingly recognised and proven by subsurface case studies. In this study, we assess the potential impact of natural fractures on heat extraction from the tight Lower Buntsandstein Subgroup targeted by the recently drilled NLW-GT-01 well (West Netherlands Basin (WNB)). We integrate: (1) reservoir property characterisation using petrophysical analysis and geostatistical inversion, (2) image-log and core interpretation, (3) large-scale seismic fault extraction and characterisation, (4) Discrete Fracture Network (DFN) modelling and permeability upscaling, and (5) fluid-flow and temperature modelling. First, the results of the petrophysical analysis and geostatistical inversion indicate that the Volpriehausen has almost no intrinsic porosity or permeability in the rock volume surrounding the NLW-GT-01 well. The Detfurth and Hardegsen sandstones show better reservoir properties. Second, the image-log interpretation shows predominately NW–SE-orientated fractures, which are hydraulically conductive and show log-normal and negative-power-law behaviour for their length and aperture, respectively. Third, the faults extracted from the seismic data have four different orientations: NW–SE, N–S, NE–SW and E–W, with faults in proximity to the NLW-GT-01 having a similar strike to the observed fractures. Fourth, inspection of the reservoir-scale 2D DFNs, upscaled permeability models and fluid-flow/temperature simulations indicates that these potentially open natural fractures significantly enhance the effective permeability and heat production of the normally tight reservoir volume. However, our modelling results also show that when the natural fractures are closed, production values are negligible. Furthermore, because active well tests were not performed prior to the abandonment of the Triassic formations targeted by the NLW-GT-01, no conclusive data exist on whether the observed natural fractures are connected and hydraulically conductive under subsurface conditions. Therefore, based on the presented findings and remaining uncertainties, we propose that measures which can test the potential of fracture-enhanced permeability under subsurface conditions should become standard procedure in projects targeting deep and potentially fractured geothermal reservoirs.

scholarly journals A numerical investigation on the performance of hydraulic fracturing in naturally fractured gas reservoirs based on stimulated rock volume

2020 ◽  
Vol 10 (8) ◽  
pp. 3333-3345
Author(s):  
Ali Al-Rubaie ◽  
Hisham Khaled Ben Mahmud
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Natural Fracture ◽  
Shear Stresses ◽  
Individual Element ◽  
Natural Fractures ◽  
Gas Reservoirs ◽  
Stimulated Reservoir Volume ◽  
Reservoir Volume ◽  
Naturally Fractured

Abstract All reservoirs are fractured to some degree. Depending on the density, dimension, orientation and the cementation of natural fractures and the location where the hydraulic fracturing is done, preexisting natural fractures can impact hydraulic fracture propagation and the associated flow capacity. Understanding the interactions between hydraulic fracture and natural fractures is crucial in estimating fracture complexity, stimulated reservoir volume, drained reservoir volume and completion efficiency. However, because of the presence of natural fractures with diffuse penetration and different orientations, the operation is complicated in naturally fractured gas reservoirs. For this purpose, two numerical methods are proposed for simulating the hydraulic fracture in a naturally fractured gas reservoir. However, what hydraulic fracture looks like in the subsurface, especially in unconventional reservoirs, remain elusive, and many times, field observations contradict our common beliefs. In this study, the hydraulic fracture model is considered in terms of the state of tensions, on the interaction between the hydraulic fracture and the natural fracture (45°), and the effect of length and height of hydraulic fracture developed and how to distribute induced stress around the well. In order to determine the direction in which the hydraulic fracture is formed strikethrough, the finite difference method and the individual element for numerical solution are used and simulated. The results indicate that the optimum hydraulic fracture time was when the hydraulic fracture is able to connect natural fractures with large streams and connected to the well, and there is a fundamental difference between the tensile and shear opening. The analysis indicates that the growing hydraulic fracture, the tensile and shear stresses applied to the natural fracture.

A Suction Device Using Air Under Pressure

1956 ◽  
Vol 23 (2) ◽  
pp. 269-272
Author(s):  
L. F. Welanetz
Keyword(s):  
Fluid Flow ◽  
Flow Rate ◽  
Fluid Flows ◽  
Central Hole ◽  
Fluid Flow Rate ◽  
Circular Plates ◽  
Suction Device ◽  
Holding Power ◽  
Plate Separation

Abstract An analysis is made of the suction holding power of a device in which a fluid flows radially outward from a central hole between two parallel circular plates. The holding power and the fluid flow rate are determined as functions of the plate separation. The effect of changing the proportions of the device is investigated. Experiments were made to check the analysis.

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