Modeling and Numerical Analysis of Mud Filtration for a Well with a Finite-Conductivity Vertical Fracture: Based on Convection-Dispersion Filtrate Transport

2011 ◽  
Author(s):  
M. Pordel Shahri ◽  
M. Mosleh Tehrani ◽  
M. Namvar
Keyword(s):  
Numerical Analysis ◽  
Finite Conductivity ◽  
Vertical Fracture ◽  
Mud Filtration

A hybrid analytic solution for a well with a finite-conductivity vertical fracture

2020 ◽  
Vol 188 ◽  
pp. 106900
Author(s):  
Cao Wei ◽  
Shiqing Cheng ◽  
Kun Tu ◽  
Xiaoping An ◽  
Dan Qu ◽  
...  
Keyword(s):  
Analytic Solution ◽  
Finite Conductivity ◽  
Vertical Fracture

scholarly journals Numerical well test for well with finite conductivity vertical fracture in coalbed

2014 ◽  
Vol 35 (6) ◽  
pp. 729-740 ◽  
Author(s):  
Yue-wu Liu ◽  
Wei-ping Ou-Yang ◽  
Pei-hua Zhao ◽  
Qian Lu ◽  
Hui-jun Fang
Keyword(s):  
Finite Conductivity ◽  
Well Test ◽  
Vertical Fracture ◽  
Numerical Well Test

Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture

1978 ◽  
Vol 18 (04) ◽  
pp. 253-264 ◽  
Author(s):  
Heber Cinco L. ◽  
F. Samaniego V. ◽  
N. Dominguez A.
Keyword(s):  
Early Time ◽  
Curve Analysis ◽  
Hydraulic Fractures ◽  
Finite Conductivity ◽  
Pressure Data ◽  
Transient Pressure ◽  
Type Curve ◽  
Fracture Characteristics ◽  
Vertical Fracture ◽  
Pressure Behavior

Abstract A mathematical model was developed to study the transient behavior of a well with a finite-conductivity vertical fracture in an infinite slab reservoir. For values of dimensionless time of interest, to >10, the dimensionless wellbore pressure, p, can be correlated by the dimensionless group; wk / x k, where w, k, and x are the width, permeability, and half length of the fracture, respectively, and k represents the formation permeability. Results when plotted as a function of P vs log to give, for large t, a 1.151-slope straight line; hence, semilogarithmic pressure analysis methods can be applied. When plotted in terms o/ log P vs log t, a family of curves of characteristic shape result. A type-curve matching procedure can be used to analyze early time transient procedure can be used to analyze early time transient pressure data to obtain the formation and fracture pressure data to obtain the formation and fracture characteristics. Introduction Hydraulic fracturing is an effective technique for increasing the productivity of damaged wells or wells producing from low permeability formations. Much research has been conducted to determine the effect of hydraulic fractures on well performance and transient pressure behavior. The results have been used to improve the design of hydraulic fractures. Many methods have been proposed to determine formation properties and fracture characteristics from transient pressure and flow rate data. These methods have been based on either analytical or numerical solutions of the transient flow of fluids toward fractured wells. Recently, Gringarten et al. made an important contribution to the analysis of transient pressure data of fractured wells. They presented a type-curve analysis and three basic presented a type-curve analysis and three basic solutions: the infinite-fracture conductivity solution (zero pressure drop along a vertical fracture the uniform flux solution for vertical fractures, and the uniform flux solution for horizontal fractures. Although the assumption of an infinite fracture conductivity is adequate for some cases, we must consider a finite conductivity for large or very low flow capacity fractures. Sawyer and Locke studied the transient pressure behavior of finite-conductivity vertical fractures in gas wells. Their solutions cannot be used to analyze transient pressure data because only specific cases were presented. In this study, we wanted to prepare general solutions for the transient pressure behavior of a well intersected by a finite-conductivity vertical fracture. The solutions sought should be useful for short-time or type-curve analysis. We also wanted to show whether conventional methods could be applied to analyze transient pressure data for these conditions. A combination of both methods, as pointed out by Gringarten to al., should permit an pointed out by Gringarten to al., should permit an extraordinary confidence level concerning the analysis of field data. STATEMENT OF THE PROBLEM AND DEVELOPMENT OF FLOW MODELS The transient pressure behavior for a fractured well can be studied by analyzing the solution of the differential equations that describe this phenomenon with proper initial and boundary conditions. To simplify the derivation of flow models, the following assumptions are made.An isotropic, homogeneous, horizontal, infinite, slab reservoir is bounded by an upper and a lower impermeable strata. The reservoir has uniform thickness, h, permeability, k, and porosity, which are independent of pressure.The reservoir contains a slightly compressible fluid of compressibility, c, and viscosity, mu, and both properties are constant.Fluid is produced through a vertically fractured well intersected by a fully penetrating, finite-conductivity fracture of half length, x, width, w, permeability, k, and porosity, phi . These fracture permeability, k, and porosity, phi . These fracture characteristics are constant. Fluid entering the wellbore comes only through the fracture. A system with these assumptions is shown in Fig. 1. In addition, we assume that gravity effects are negligible and also that laminar flow occurs in the system.

A Semianalytic Solution for Flow in Finite-Conductivity Vertical Fractures by Use of Fractal Theory

SPE Journal ◽  
2013 ◽  
Vol 18 (01) ◽  
pp. 83-96 ◽  
Author(s):  
M.. Cossio ◽  
G.J.. J. Moridis ◽  
T.A.. A. Blasingame
Keyword(s):  
Fluid Flow ◽  
Numerical Study ◽  
Fractal Theory ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Finite Conductivity ◽  
Reservoir Heterogeneity ◽  
Vertical Fracture ◽  
Diffusivity Equation ◽  
First Time

Summary The exploitation of unconventional reservoirs complements the practice of hydraulic fracturing, and with an ever-increasing demand in energy, this practice is set to experience significant growth in the coming years. Sophisticated analytic models are needed to accurately describe fluid flow in a hydraulic fracture, and the problem has been approached from different directions in the past 3 decades—starting with the work of Gringarten et al. (1974) for an infinite-conductivity case, followed by contributions from Cinco-Ley et al. (1978), Lee and Brockenbrough (1986), Ozkan and Raghavan (1991), and Blasingame and Poe (1993) for a finite-conductivity case. This topic remains an active area of research and, for the more-complicated physical scenarios such as multiple transverse fractures in ultratight reservoirs, answers are currently being sought. Starting with the seminal work of Chang and Yortsos (1990), fractal theory has been successfully applied to pressure-transient testing, although with an emphasis on the effects of natural fractures in pressure/rate behavior. In this paper, we begin by performing a rigorous analytical and numerical study of the fractal diffusivity equation (FDE), and we show that it is more fundamental than the classic linear and radial diffusivity equations. Thus, we combine the FDE with the trilinear flow model (Lee and Brockenbrough 1986), culminating in a new semianalytic solution for flow in a finite-conductivity vertical fracture that we name the “fractal-fracture solution (FFS).” This new solution is instantaneous and comparable in accuracy with the Blasingame and Poe solution (1993). In addition, this is the first time that fractal theory is used in fluid flow in a porous medium to address a problem not related to reservoir heterogeneity. Ultimately, this project is a demonstration of the untapped potential of fractal theory; our approach is flexible, and we believe that the same methodology could be extended to different applications. One objective of this work is to develop a fast and accurate semianalytical solution for flow in a single vertical fracture that fully penetrates a homogeneous infinite-acting reservoir. This would be the first time that fractal theory is used to study a problem that is not related to naturally fractured reservoirs or reservoir heterogeneity. In addition, as part of the development process, we revisit the fundamentals of fractals in reservoir engineering and show that the underlying FDE possesses some interesting qualities that have not yet been comprehensively addressed in the literature.

Non-Darcy Flow in Wells With Finite-Conductivity Vertical Fractures

1982 ◽  
Vol 22 (05) ◽  
pp. 681-698 ◽  
Author(s):  
K.H. Guppy ◽  
H. Cinco-Ley ◽  
H.J. Ramey ◽  
F. Samaniego-V.
Keyword(s):  
Hydraulic Fracturing ◽  
Turbulent Flow ◽  
High Flow ◽  
Darcy Flow ◽  
Finite Conductivity ◽  
Gas Wells ◽  
Fracture Conductivity ◽  
Flow Rates ◽  
Vertical Fracture ◽  
Constant Rate

Abstract Several methods have been proposed in the literature for analyzing drawdown data for the determination of fracture conductivity of vertically fractured wells. These techniques have paved accurate, but in some cases the fracture conductivity calculated is much smaller than anticipated. This study shows that producing fractured wells at high flow rates will cause nondarcy effects in the fracture, resulting in a pessimistic fracture conductivity.Numerical and semianalytical models were developed to analyze the unsteady flow behavior of finite conductivity fractures producing at high flow rates. Two methods are presented for determining the true fracture conductivity when drawdown data are available at two different flow rates. The amount of turbulent effects also is quantified by the techniques. Examples are presented to illustrate the solution methods. Introduction The increasing use of hydraulic fracturing as a means of improving the productivity of oil and gas wells in low-permeability formations has resulted in many research efforts aimed at increasing fracturing capabilities as well as evaluating the characteristics of the fracture in the postfracturing period. With the advent of the massive postfracturing period. With the advent of the massive hydraulic fracturing (MHF) treatment in recent years, the need for new solutions for evaluating these systems has increased. The problem with the older solutions was the need for many assumptions to arrive at a simple solution. One of the more common assumptions made in these systems was the use of linear flow to describe the flow within the fracture. In gas wells with finite-conductivity fractures producing at high flow rates, the non-Darcy effect is created within the fracture. Hence, new solutions must be developed for these systems. The objective of this paper is to present a new semianalytical solution to this problem that can be applied both to the linear and to the nondarcy flow regimes within the fracture.Over the years. several methods have been developed to analyze postfracture data. Gringarien et al. first solved the fracture system analytically for three special cases: infinite-conductivity vertical fracture, uniform flux vertical fracture, and horizontal fracture. At that time, its application became quite useful. But since not all systems behaved in this manner, the need for further solutions was warranted. Cinco-L. et al. investigated the general case of finite-conductivity vertical fractures, which included the above solution. as well as fracture conductivities as low as 0.1. This research also led to the need to analyze short-time data to obtain unique solutions. Similar results were obtained by Agarwat et al., who presented a finite-difference solution to this problem, considering both the constant rate as well as the problem, considering both the constant rate as well as the constant pressure cases.One of the first papers written on the effects of non-Darcy flow in fractured systems was by Wattenbarger and Ramey. They investigated the effects of non-Darcy flow in the formation and concluded that these effects cannot be felt if the fracture is long or intermediate in size. They further concluded that the effects of turbulent flow within the fracture were more significant.Holditch and Morse investigated the effect of turbulent flow in a fracture and analyzed the transient behavior of specific conductivities (low, medium, and high), giving a qualitative approach to the solution. They stressed the need for greater detail on these solutions and showed that there was indeed a large reduction in the fracture conductivity when non-Darcy flow was included. Although Holditch and Morse gave a detailed descriptive insight into the flow regime problem, they did not develop any general methods for determining the actual conductivity of the fracture. SPEJ P. 681

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