Pressure Transient Analysis for a Finite-Conductivity Fractured Vertical Well Near a Leaky Fault in Anisotropic Linear Composite Reservoirs

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Junjie Ren ◽  
Yangyang Gao ◽  
Qiao Zheng ◽  
Delong Wang
Keyword(s):  
Numerical Solutions ◽  
Superposition Principle ◽  
Analytical Models ◽  
Finite Conductivity ◽  
Vertical Wells ◽  
Pressure Behavior ◽  
Linear Composite ◽  
Composite Models ◽  
Multiple Reservoir ◽  
Almost All

Abstract Geologic discontinuities usually exist in subsurface permeable formations, where multiple reservoir regions with distinct properties are separated by linear leaky faults. This kind of heterogeneous reservoir is usually called a linear composite reservoir. Although many analytical/semi-analytical linear composite models have been established to investigate the pressure behavior for linear composite reservoirs, almost all of these models were aimed at vertical wells without hydraulic fracturing and there are few analytical/semi-analytical models of fractured vertical wells in linear composite reservoirs. This paper first derives the Laplace-space point source solution for anisotropic linear composite systems separated by a partially communicating fault. Then, superposition principle and fracture discrete scheme are employed to acquire the semi-analytical solution for finite-conductivity fractured vertical (FCFV) wells in anisotropic linear composite reservoirs with a fault. The proposed solution is validated against numerical solutions under different reservoir scenarios. The characteristic of the pressure behavior for an FCFV well in anisotropic linear composite reservoirs with a fault is discussed in detail. The proposed model can be employed to obtain accurate pressure response with high computational efficiency. It is a good start to further develop analytical/semi-analytical models for other complex well types in an anisotropic linear composite reservoir with a fault.

New Analytical Approach to Operational Assessment of Fractured Well Productivity with Variable Permeability

2021 ◽  
Author(s):  
Evgeniy Viktorovich Yudin ◽  
George Aleksandrovich Piotrovskiy ◽  
Maria Vladimirovna Petrova ◽  
Alexey Petrovich Roshchektaev ◽  
Nikita Vladislavovich Shtrobel
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Free Parameter ◽  
Numerical Solutions ◽  
Analytical Models ◽  
Productivity Index ◽  
Finite Conductivity ◽  
Well Productivity ◽  
Fracture Conductivity ◽  
Variable Permeability

Abstract Requirements of targeted optimization are imposed on the hydraulic fracturing operations carried out in the conditions of borderline economic efficiency of fields taking into account geological and technological features. Consequently, the development of new analytical tools foranalyzing and planning the productivity of fractured wells, taking into account the structuralfeatures of the productive reservoir and inhomogeneous distribution of the fracture conductivity, is becoming highly relevant. The paper proposes a new approach of assessing the vertical hydraulic fracture productivityin a rectangular reservoir in a pseudo-steady state, based on reservoir resistivity concept described in the papers of Meyer et al. However, there is a free parameter in the case of modeling the productivity of a hydraulic fracture by the concept. The parameter describes the distribution of the inflow along the plane of the fracture. This paper presents a systematic approach to determining of the parameter. The resulting model allows to conduct an assessment of the influence of various complications in the fracture on the productivity index. During the research a method of determining the free parameter was developed,it was based on the obtained dependence of the inflow distribution on the coordinate along the fracture of finite conductivity. The methodology allowed to refine existent analytical solution of the Meyer et al. model, which, in turn, allowed to assess the influence of different fracture damages in the hydraulic fracture on the productivity index of the well. The work includes the cases of the presence of fracture damages at the beginning and at the end of the fracture. A hydraulic fracture model was built for each of the types of damages, it was based on the developed method, and also the solution of dimensionless productivity ratio was received. The results of the obtained solution were confirmed by comparison with the numerical solutions of commercial simulators and analytical models available in the literature. The advantage of the methodology is the resulting formulas for well productivity are relatively simple, even for exotic cases ofvariable conductivity fractures. The approaches and algorithms described in the paper assume the calculation of the productivity of a hydraulic fracture with variable conductivity and the presence of other complicatingfactors.The methodology of the paper can be used for analysis and diagnosis problems with formation hydraulic fracturing. The efficiency of the calculations allows using the presented methodology to solve inverse problems of determining the efficiency of the hydraulic fracturing operation.

scholarly journals A Practical Solution Model for Transient Pressure Behavior of Multistage Fractured Horizontal Wells with Finite Conductivity in Tight Oil Reservoirs

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pin Jia ◽  
Defeng Wu ◽  
Hengfei Yin ◽  
Zhuang Li ◽  
Linsong Cheng ◽  
...  
Keyword(s):  
Superposition Principle ◽  
Horizontal Wells ◽  
Oil Reservoirs ◽  
Finite Conductivity ◽  
Tight Oil ◽  
Transient Pressure ◽  
Transient Model ◽  
Pressure Behavior ◽  
Tight Oil Reservoirs ◽  
Fractured Horizontal Wells

Fractured horizontal wells have been widely used to develop unconventional oil and gas reservoirs. In previous studies, most studies on the transient pressure behavior of multistage horizontal wells were based on the assumption of single porosity medium, in which the coupling relationship of natural fractures and artificial fractures was not taken into account or artificial fractures were assumed to be infinitely conductive. In this paper, the fracture is finite conductive, which means that there is flow resistance in the fracture. Based on point-source method and superposition principle, a transient model for multistage fractured horizontal wells, which considers the couple of fracture flow and reservoir seepage, is built and solved with the Laplace transformation. The transient pressure behavior in multistage fractured horizontal wells is discussed, and effects of influence factors are analyzed. The result of this article can be used to identify the response characteristic of fracture conductivity to pressure and pressure differential and provide theoretical basis for effective development of tight oil reservoirs. The findings of this study can help for better understanding of transient pressure behavior of multistage fractured horizontal wells with finite conductivity in tight oil reservoirs.

scholarly journals Semi-analytical model of multiple fractured horizontal well across a discontinuity in a linear composite reservoir

2021 ◽  
Vol 18 (6) ◽  
pp. 845-861
Author(s):  
Junjie Ren ◽  
Xiaoxue Liu ◽  
Qingxing Wu ◽  
Shuai Wu
Keyword(s):  
Analytical Model ◽  
Horizontal Well ◽  
Superposition Principle ◽  
Hydraulic Fractures ◽  
Inversion Algorithm ◽  
Type Curves ◽  
Pressure Behavior ◽  
Linear Composite ◽  
Well Location ◽  
Production Wells

Abstract Many geologic settings can be treated as linear composite (LC) reservoirs, where linear discontinuities divide the formation into multiple zones with different properties. Although there have been many studies on pressure behavior of production wells in an LC reservoir, most of the studies focus on vertical wells. The modeling of multiple fractured horizontal (MFH) wells in an LC reservoir remains limited. The goal of the present work is to propose a general semi-analytical model of an MFH well situated anywhere in a two-zone LC reservoir. This model can take into account the situation where the horizontal well intersects with the discontinuity and hydraulic fractures are distributed in both the two zones. According to the point-source function method, the semi-analytical solution for an MFH well in LC reservoirs is derived by using superposition principle, fracture discrete scheme and numerical inversion algorithm of Laplace transformation. Type curves of MFH wells far away from a discontinuity and across a discontinuity in an LC reservoir are drawn and analysed, respectively. Furthermore, the effects of some parameters on pressure behavior and rate response of an MFH well across a discontinuity are studied. This research finds that the pressure behavior and rate response of an MFH well across a discontinuity are significantly affected by the well location, properties of hydraulic fractures and formation properties.

Characteristics of Dimensionless Pressure Gradients and Derivatives of Horizontal and Vertical Wells Completed within Inclined Sealing Faults

2021 ◽  
Author(s):  
A V Ogbamikhumi ◽  
E S Adewole
Keyword(s):  
Pressure Drop ◽  
Horizontal Well ◽  
Superposition Principle ◽  
Early Time ◽  
Pressure Gradients ◽  
Vertical Wells ◽  
Pressure Derivative ◽  
Vertical Well ◽  
Dimensionless Pressure ◽  
Horizontal And Vertical Wells

Abstract Dimensionless pressure gradients and dimensionless pressure derivatives characteristics are studied for horizontal and vertical wells completed within a pair of no-flow boundaries inclined at a general angle ‘θ’. Infinite-acting flow solution of each well is utilized. Image distances as a result of the inclinations are considered. The superposition principle is further utilized to calculate total pressure drop due to flow from both object and image wells. Characteristic dimensionless flow pressure gradients and pressure derivatives for the wells are finally determined. The number of images formed due to the inclination and dimensionless well design affect the dimensionless pressure gradients and their derivatives. For n images, shortly after very early time for each inclination, dimensionless pressure gradients of 1.151(N+1)/LD for the horizontal well and 1.151(N+1) for vertical well are observed. Dimensionless pressure derivative of (N+1)/2LD are observed for central and off-centered horizontal well locations, and (N+1)/2 for vertical well are observed. Central well locations do not affect horizontal well productivity for all the inclinations. The magnitudes of dimensionless pressure drop and dimensionless pressure derivatives are maximum at the farthest image distances, and are unaffected by well stand-off for the horizontal well.

scholarly journals Importance of on-time decision making in energy sector based on perspectives: Case study new Stavalj project

2017 ◽  
Vol 21 (5) ◽  
pp. 1925-1935
Author(s):  
Dragan Zlatanovic ◽  
Lato Pezo ◽  
Aleksandar Sedmak ◽  
Snezana Kirin
Keyword(s):  
Decision Making ◽  
Sustainable Development ◽  
Swot Analysis ◽  
Numerical Solutions ◽  
Thermal Power ◽  
Assessment Model ◽  
Strategic Decision ◽  
Underground Mines ◽  
Practical Experiences ◽  
Almost All

Expression "Development conditions and perspectives" became important for numerous analyses in various industrial and social areas. Several strategic documents and studies in last two decades analysed projects with topics on perspectives of future development in Serbia. Various tools are used for development of such documents, based on recent scientific and numerical solutions, thus providing reliable assessment for strategic decision making. Almost all analyses tried to implement the theories and practical experiences through the prism of "sustainable development", which included establishment of most important sustainability parameters. Analysis and ranking presented in this paper considered the potential of the Stavalj coal deposit, near city of Sjenica in Serbia, and feasibility of construction project of new mine and thermal power plant. Basis for analysis was a hybrid assessment model which takes into account principles of sustainable development. The model incorporates quantified SWOT analysis, which applies to active underground mines in Serbia. Special attention was given to the parameters describing potential for development.

Effect of Non-Darcy Flow on the Constant-Pressure Production of Fractured Wells

1981 ◽  
Vol 21 (03) ◽  
pp. 390-400 ◽  
Author(s):  
K.H. Guppy ◽  
Heber Cinco-Ley ◽  
Henry J. Ramey
Keyword(s):  
Constant Pressure ◽  
Darcy Flow ◽  
Flow In Porous Media ◽  
Graphical Form ◽  
Finite Conductivity ◽  
Fracture Conductivity ◽  
Type Curves ◽  
Pressure Behavior ◽  
Apparent Conductivity ◽  
Constant Rate

Abstract In many low-permeability gas reservoirs, producing a well at constant rate is very difficult or, in many cases, impossible. Constant-pressure production is much easier to attain and more realistic in practice. This is seen when production occurs into a constant-pressure separator or during the reservoir depletion phase, when the rate-decline period occurs. Geothermal reservoirs, which produce fluids that drive backpressure turbines, and open-well production both incorporate the constant-pressure behavior. For finite-conductivity vertically fractured systems, solutions for the constant-pressure case have been presented in the literature. In many high-flow-rate wells, however, these solutions may not be useful since high velocities are attained in the fracture, which results in non-Darcy effects within the fracture. In this study, the effects of non-Darcy flow within the fracture are investigated. Unlike the constant-rate case, it was found that the fracture conductivity does not have a constant apparent conductivity but rather an apparent conductivity that varies with time. Semianalytical solutions as well as graphical solutions in the form of type curves are presented to illustrate this effect. An example is presented for analyzing rate data by using both solutions for Darcy and non-Darcy flow within the fracture. This example relies on good reservoir permeability from prefracture data to predict the non-Darcy effect accurately. Introduction To fully analyze the effects of constant-bottomhole-pressure production of hydraulically fractured wells, it is necessary that we understand the pressure behavior of finite-conductivity fracture systems producing at constant rate as well as the effects of non-Darcy flow on gas flow in porous media. Probably one of the most significant contributions in the transient pressure analysis theory for fractured wells was made by Gringarten et al.1,2 In the 1974 paper,2 general solutions were made for infinite-conductivity fractures. Cinco et al.3 found a more general solution for the case of finite-conductivity fractures and further extended this analysis in 1978 to present a graphical technique to estimate fracture conductivity.4 For the case of constant pressure at the wellbore, solutions were presented in graphical form by Agarwal et al.5 In his paper, a graph of log (1/qD) vs. log (tDxf) can be used to determine the conductivity of the fracture by using type-curve matching. Although such a contribution is of great interest, unique solutions are difficult to obtain. More recently, Guppy et al.6 showed that the Agarwal et al. solutions may be in error and presented new type curves for the solution to the constant-pressure case assuming Darcy flow in the fracture. That paper developed analytical solutions which can be applied directly to field data so as to calculate the fracture permeability-width (kfbf) product.

One-dimensional consolidation of multilayered aquifer systems with viscoelastic properties induced by time-dependent groundwater drawdown

2021 ◽  
pp. qjegh2021-073
Author(s):  
Weitao Yang ◽  
Jin Xu
Keyword(s):  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Time Dependent ◽  
Analytical Models ◽  
Consolidation Process ◽  
One Dimensional ◽  
Groundwater Drawdown ◽  
Aquifer Systems

Most analytical and semi-analytical models for pumping-induced land subsidence invoke the simplifying assumptions regarding characteristics of geomaterials, as well as the pattern of drawdown response to pumping. This paper presents an analytical solution for one-dimensional consolidation of the multilayered soil due to groundwater drawdown, in which viscoelastic property and time-dependent drawdown are taken into account. The presented solution is developed by using the boundary transformation techniques. The validity of the proposed solution is verified by comparing with a degenerated case for a single layer, as well as with the numerical solutions and experimental results for a two-layer system. The difference between the average consolidation degree Up defined by hydraulic head and that Us defined by total settlement is discussed. The detailed parametric studies are conducted to reveal the effects of viscoelastic properties and drawdown patterns on the consolidation process. It is revealed that while the effect of different drawdown response patterns is significant during the early-intermediate stages of consolidation, the viscoelastic properties may have a more dominant influence on long-term consolidation behavior, depending on the values of the material parameters, which are reflected in both the deformation process of soil layers and the dissipation of excess pore-water pressure.

Models of non-Boussinesq lock-exchange flow

2011 ◽  
Vol 675 ◽  
pp. 1-26 ◽  
Author(s):  
R. ROTUNNO ◽  
J. B. KLEMP ◽  
G. H. BRYAN ◽  
D. J. MURAKI
Keyword(s):  
Free Boundary ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Water System ◽  
Analytic Solutions ◽  
Analytical Models ◽  
Navier Stokes ◽  
Exchange Flow

Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.

scholarly journals Mathematical modeling of groundwater contamination with varying velocity field

2017 ◽  
Vol 65 (2) ◽  
pp. 192-204 ◽  
Author(s):  
Pintu Das ◽  
Sultana Begam ◽  
Mritunjay Kumar Singh
Keyword(s):  
Groundwater Contamination ◽  
Analytical Solutions ◽  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Time Dependent ◽  
Analytical Models ◽  
Retardation Factor ◽  
Hydrodynamic Dispersion ◽  
The Impact

Abstract In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).

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