A Semianalytical Model for Evaluating the Performance of a Refractured Vertical Well With an Orthogonal Refracture

SPE Journal ◽  
2019 ◽  
Vol 24 (02) ◽  
pp. 891-911 ◽  
Author(s):  
Bailu Teng ◽  
Huazhou Andy Li
Keyword(s):  
Production Rate ◽  
Horizontal Stress ◽  
Fracture Flow ◽  
Vertical Well ◽  
Flow Equations ◽  
Stress Reversal ◽  
Reservoir Flow ◽  
Proposed Model ◽  
Stress Changes ◽  
Initial Fracture

Summary Production from a fractured vertical well will lead to a redistribution of the stress field in formations. If the induced stress changes are sufficiently large to overcome the effect of the initial horizontal-stress deviator, the direction of the minimum horizontal stress can be turned into the direction of the maximum horizontal stress within an elliptical region around the initial fracture, resulting in a stress-reversal region near the wellbore. In such cases, a refracturing treatment can create a refracture that propagates orthogonally to the initial fracture because of the stress reversal. As such, the high-pressure area of the formation can be stimulated by the refracture, and the productivity of the refractured well can be improved. In this work, we develop a semianalytical model to evaluate the performance of a refractured vertical well with an orthogonal refracture. To simulate the well performance throughout the entire production period, we divide the well production into three stages: the first stage, when the well is producing oil with the initial fracture; the second stage, when the well is shut down for the refracturing treatment; and the third stage, when the well is producing oil with both the initial fracture and the refracture. In addition, by discretizing the initial fracture and the refracture into small segments, the conductivity of the fractures can be taken into account, and the geometry of the fracture system can be captured. We use the Green-function method to analytically simulate the reservoir flow and use the finite-difference method to numerically simulate the fracture flow; therefore, a semianalytical model can be constructed by coupling the reservoir-flow equations with the fracture-flow equations. This proposed model is applied to different wellbore and reservoir conditions. The calculated results show that this proposed model is versatile because it can simulate various wellbore constraints, including the conditions of constant bottomhole pressure (BHP), varying BHP, constant production rate, and varying production rate. The permeability anisotropy of the reservoir system, as well as the nonuniform conductivity distribution along the fracture, can also be incorporated into this proposed model. In addition, we demonstrate that this proposed model can be used to simulate other types of refractured vertical wells with minor modifications.

A stress sensitivity model for the permeability of porous media based on bi-dispersed fractal theory

2018 ◽  
Vol 29 (02) ◽  
pp. 1850019 ◽  
Author(s):  
X.-H. Tan ◽  
C.-Y. Liu ◽  
X.-P. Li ◽  
H.-Q. Wang ◽  
H. Deng
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stress Sensitivity ◽  
Maximum Diameter ◽  
Proposed Model ◽  
Fractal Parameters ◽  
Stress Changes ◽  
Capillary Bundle ◽  
Definition Of

A stress sensitivity model for the permeability of porous media based on bidispersed fractal theory is established, considering the change of the flow path, the fractal geometry approach and the mechanics of porous media. It is noted that the two fractal parameters of the porous media construction perform differently when the stress changes. The tortuosity fractal dimension of solid cluster [Formula: see text] become bigger with an increase of stress. However, the pore fractal dimension of solid cluster [Formula: see text] and capillary bundle [Formula: see text] remains the same with an increase of stress. The definition of normalized permeability is introduced for the analyzation of the impacts of stress sensitivity on permeability. The normalized permeability is related to solid cluster tortuosity dimension, pore fractal dimension, solid cluster maximum diameter, Young’s modulus and Poisson’s ratio. Every parameter has clear physical meaning without the use of empirical constants. Predictions of permeability of the model is accordant with the obtained experimental data. Thus, the proposed model can precisely depict the flow of fluid in porous media under stress.

An explicit analytical solution for calculating horizontal stress changes and displacements around an excavated diaphragm wall panel

2003 ◽  
Vol 40 (4) ◽  
pp. 780-792 ◽  
Author(s):  
C WW Ng ◽  
G H Lei
Keyword(s):  
Analytical Solution ◽  
Uniaxial Stress ◽  
Horizontal Stress ◽  
Ease Of Use ◽  
Elastic Solution ◽  
Diaphragm Wall ◽  
Wall Panel ◽  
Principle Of Superposition ◽  
Explicit Analytical Solution ◽  
Stress Changes

A new, simple, and explicit analytical solution has been derived for calculating horizontal stress changes and displacements caused by the excavation for a diaphragm wall panel. The theoretical solution is obtained by applying the principle of superposition appropriately to model diaphragm wall construction using a basic elastic solution to the problem of an infinite horizontal plate with a rectangular opening subjected to a uniaxial stress at infinity. The basic elastic solution can be obtained by using the method of complex variables with a simplified conformal transformation function. Key parameters governing the magnitude of horizontal stress changes and displacements are identified. Computed results are given in a normalized form in terms of aspect ratio (length to width) of a diaphragm wall panel. Two extreme cases for diaphragm wall panels with dimensions 1 m × 1 m and 10 m × 1 m have been analysed to investigate the distributions of stress changes and deformations around the panels during the bentonite stage. By performing a parametric study, calculation charts have been developed for computing horizontal stress changes and displacements for practising engineers and researchers to carry out preliminary designs and for numerical modellers to verify their sophisticated predictions. The ease of use of the charts is illustrated by two examples, and the limitations of the derived solutions are discussed.Key words: diaphragm wall, elasticity, stress change, displacement, stress analysis, earth pressure.

scholarly journals Numerical and Experimental Analysis of Horizontal Stress Changes and Soil Collapse During Chemical Dissolution in a Modified Oedometer Cell

2016 ◽  
pp. 19-27
Author(s):  
Cecilia Lins ◽  
Nayra Silva ◽  
Leonardo Guimarães ◽  
Analice Lima ◽  
Igor Gomes
Keyword(s):  
Unsaturated Soils ◽  
Horizontal Stress ◽  
Sample Volume ◽  
General Purpose ◽  
Dissolution Process ◽  
Solid Matrix ◽  
Soil Behavior ◽  
Mineral Concentration ◽  
Basic Model ◽  
Stress Changes

The purpose of this paper is to investigate the horizontal stress evolution and soil collapse during the cement dissolution process using a combination of experimental and numerical methods. The experimental procedure was carried out using a modified oedometer cell with horizontal stress measurements and synthetic samples in order to simulate simultaneous cement dissolution, stress changes and sample deformation. The samples were loaded at a constant vertical stress and exposed to a reactive fluid which dissolved the cementation of the artificial soil. During the dissolution process, sample volume decreased and horizontal stress changes were observed. Initially the horizontal stress decreased due to grain mass loss and then increased due to solid matrix rearrangement. Numerical simulation of these coupled chemical and mechanical processes was performed using a general purpose finite element code capable of performing numerical analysis of engineering problems. The constitutive model adopted to reproduce the soil behavior is an extension of the Barcelona Basic Model for unsaturated soils including the cement mineral concentration as state variable. Some new features were incorporated to the original elasto-plastic model in order to represent the results observed in the experiments. In this paper a good agreement between experimental and numerical results was achieved.

scholarly journals Fatique durability of smooth cylindrical rods under uniaxial symmetric stretch – compression

2019 ◽  
pp. 82-85
Author(s):  
Ju. M. Kobzar
Keyword(s):  
Elastic Limit ◽  
Mass Density ◽  
Gray Iron ◽  
Half Cycle ◽  
Software Environment ◽  
Volume Deformation ◽  
High Tension ◽  
Proposed Model ◽  
Stress Changes ◽  
Model Algorithm

The paper proposes a model of fatigue, that is based on the reduction of the carrier mass of the substance at half-cycle compression and its density increase by half-cycle stretching. High tension and volume deformation are linearly related by Hooke's law. Mass and density changes and stress changes depending on the elastic properties of the rod, its initial mass, density and volume are received analytically for each cycle. The model usage limit is a cycle in which amplitude values stress reaches the elastic limit. The proposed model algorithm is implemented in software environment with which the destruction is determined fatigue limit and fatigue. The resulting design value curve is different from the curve of fatigue of gray iron that was investigated. This is due to the fact that scattering of the applied energy on internal friction and heating is not included in the model.

A Strongly Coupled, Fully Implicit, Three-Dimensional, Three-Phase Well Coning Model

1981 ◽  
Vol 21 (04) ◽  
pp. 454-458 ◽  
Author(s):  
Russell H. Trimble ◽  
A.E. McDonald
Keyword(s):  
Strong Coupling ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Stable Model ◽  
Data Input ◽  
Strongly Coupled ◽  
Flow Equations ◽  
Regulatory Constraints ◽  
Reservoir Flow ◽  
Three Phase

Abstract WELCOS is a robust, three-dimensional, three-phase well coning simulator that couples the well rate equation to the reservoir flow equations. This strong coupling allows well rate to be determined simultaneously with reservoir pressures and saturations. The flexibility obtained permits the use of dynamic constraints on well rates, resulting in a highly stable model. The model may be used to obtain the maximum well productivity for a given set of physical limitations and regulatory constraints e.g., minimum surface pressure, maximum allowed GOR, WOR, water rate, gas rate, etc. The model can function either as a production well or an injection well and, in general, may be used to study any single-well behavior. This paper describes a strongly coupled formulation and discusses its utility in relation to other implicit models. The linearization of the nonlinear finite difference equations and solution of the resulting linear equations are discussed. Example field applications are included to show the utility of user-supplied production constraints in determining well performance. Introduction A number of well coning simulators have been reported in the literature. 1–6 This paper describes a three-dimensional, three-phase well coning simulator that has been in extensive use in our company since 1972. A primary consideration in the development of WELCOS was easy usage by inexperienced users working difficult problems. This demands freedom from stability problems and algorithmic parameters requiring user intervention. This paper emphasizes stability and flexibility of a strongly coupled algorithm. Strong coupling of the production and reservoir flow terms requires simultaneous solution for all unknowns, without auxiliary side calculations or approximations to bring the well rate terms to a desired level of accuracy. This algorithm is computationally more expensive than a sequential formation7,8 but it has several offsetting advantages. Increased stability permits larger time steps than sequential methods, especially for difficult problems. The coupling of the well constraints yields a very reliable model. The user can forecast well potential under assigned operating conditions with a single simulation run. Several trial-and-error runs may be required when operating constraints are uncoupled from the flow equations. The utility of WELCOS is enhanced further by modern concepts of well flow equations.9,10 These include the pseudogas potential function,11 skin factor to account for damage or improvement, non-Darcy flow effect, flow restriction due to restricted entry such as partial penetration, flash surface separation, gas lift calculations, and tubing string pressure losses. Simplicity and flexibility are key features of the data input and output systems. Data input has free-field formatting with a standard structure for all cards. Each card has a mnemonic field for data identification, a control field for processing instructions, and six data fields. Data need not appear in specific columns within fields. All input cards are read and checked for validity (proper mnemonic card names, valid numbers, etc.) and for inconsistencies (such as monotonic table values, negative numbers, etc.). A data processing run will not be aborted when the first error is detected. Processing will continue until as many errors as possible have been found.

Structural Controls on Alteration Stages at the Chuquicamata Copper-Molybdenum Deposit, Northern Chile

2020 ◽  
Author(s):  
Jorge Skarmeta
Keyword(s):  
Local Stress ◽  
Horizontal Stress ◽  
Hydrothermal Activity ◽  
Fault Reactivation ◽  
Far Field ◽  
Field Stress ◽  
Stress Reversal ◽  
Stress Orientation ◽  
Fracture Development ◽  
Far Field Stress

Abstract All existing bench and tunnel vein and fault structural data with identified mineral infill, acquired in Chuquicamata, were georeferenced, digitized, and, according to their mineralogy, assigned to one or more of the major alteration events developed between 35 and 31 Ma. Veins and faults were separated into two main stages: (1) the late magmatic and potassic stage that comprises the background potassic and the propylitic alteration and (2) the hydrothermal stage composed by early (intense potassic), main (principal and late sericite; hydrothermal stages H1 through H4), and late (advanced argillic alteration) hydrothermal events. The spatial distribution of the propylitic to late-hydrothermal events that plotted within the major fault framework indicate these had either permeable or impermeable (±barrier) behavior through time. The area of the deposit was divided into 600 square grids measuring 100 × 100 m, and a stress orientation analysis was carried out for every propylitic to late-hydrothermal alteration event. The analysis indicates that the local principal horizontal stress (σH) trajectories are nonlinear and noncoaxial through the successive alteration events, differing from the previous and following stages, and in the majority of cases do not coincide with the approximate east-northeast orientation of the inferred tectonic far-field stress orientation. The differences between the stress trajectories, away from the far-field stress orientation throughout the evolution of the system, are considered to be principally related to the dynamic variations experienced by the stress components, such as thermal-magmatic stresses linked to temperature fluctuations due to cooling or heating by progressive igneous/hydrothermal activity and/or elastic, overburden-related stresses associated with reaccommodations developed during uplift and erosion. The estimated stresses resulting after erosional unroofing and decreasing temperature indicate that the maximum horizontal stress varied as the system evolved from the commonly accepted depth of emplacement of ~6 km. During the late magmatic, background potassic, and intense potassic stages, the calculated differential stress was contractional, decreasing to an isotropic state at the contraction-extension stress reversal that hosted the main hydrothermal H1 through H3 events, to finally become extensional at the shallow late-hydrothermal event. The most significant mineralization occurred at the time of stress reversal, coincidental with the sericite and quartz-sericite events (H1-H4), associated with hydrothermal fluid accumulation, overpressuring, and multiple-orientated hydraulic fracture development. The Chuquicamata study suggests that the local stress control involved in the emplacement of porphyry copper systems is fundamentally related to variable and progressive heat energy release, associated with igneous and hydrothermal activity, and to the elastic stresses derived from uplift and unloading, rather than to a constant far-field tectonic stress. The continuous local stress fluctuations led to bulk stress readjustments and cyclical stress-fluid interactions for local fault reactivation, damage zone modification, brecciation, permeability creation/destruction, and fluid focusing, as well as the discharge of hydrothermal fluids throughout the evolution of the system.

Radionuclide Migration: Laboratory Experiments with Isolated Fractures

1981 ◽  
Vol 6 ◽  
Author(s):  
R. S. Rundberg ◽  
J. L. Thompson ◽  
S. Maestas
Keyword(s):  
Laboratory Experiments ◽  
Field Experiments ◽  
National Laboratory ◽  
Test Site ◽  
Matrix Diffusion ◽  
Fracture Flow ◽  
Flow Equations ◽  
Welded Tuff ◽  
The Matrix ◽  
Element Migration

ABSTRACTLaboratory experiments examining flow and element migration in rocks containing isolated fractures have been initiated at the Los Alamos National Laboratory. Techniques are being developed to establish simple fracture flow systems which are appropriate to models using analytical solutions to the matrix diffusion - flow equations, such as those of I. Neretnieks [1]. These experiments are intended to be intermediate steps toward larger scale field experiments where it may become more difficult to establish and control the parameters important to nuclide migration in fractured media.Laboratory experiments have been run on fractures ranging in size from 1 to 20 cm in length. The hydraulic flow in these fractures was studied to provide the effective apertures. The flows established in these fracture systems are similar to those in the granite fracture flow experiments of Witherspoon et al. [2]. Traced solutions containing 85Sr and 137Cs were flowed through fractures in Climax Stock granite and welded tuff (Bullfrog and Tram members, Yucca Mountain, Nevada Test Site). The results of the elutions through granite agree with the matrix diffusion calculations based on independent measurements of Kd. The results of the elutions through tuff, however, agree only if the Kd values used in the calculations are lower than the Kd values measured using a batch technique. This trend has been previously observed in chromatographic column experiments with tuff.

Experimental Investigation of Reservoir Stress Path Hysteresis During Production-Injection Periods

2014 ◽  
Author(s):  
Mojtaba P. Shahri ◽  
Stefan Z. Miska
Keyword(s):  
Pore Pressure ◽  
Poisson’S Ratio ◽  
Stress Path ◽  
Horizontal Stress ◽  
Poisson's Ratio ◽  
Injection Process ◽  
Fracture Pressure ◽  
Industry Standards ◽  
Depletion Period ◽  
Stress Changes

There has been an increasing consciousness regarding stress changes associated with reservoir depletion as the industry moves towards more challenging jobs in deep-water or depleted reservoirs. These stress changes play a significant role in the design of wells in this condition. Therefore, accurate prediction of reservoir stress path, i.e., change in horizontal stresses with pore pressure, is of vital importance. In this study, the current stress path formulation is investigated using a Tri-axial Rock Mechanics Testing Facility. The reservoir depletion scenario is simulated through experiments and provides a better perspective on the currently used formulation and how it’s applicable during production and injection periods. The effect of fluid re-injection into reservoirs on the horizontal stress is also analyzed using core samples. According to the results, formation fracture pressure would not be equal to its initial value if pressure builds up using re-injection. The irrecoverable formation fracture pressure has a power law relation with pore pressure drawdown range. In order to avoid higher permanent fracture pressure reduction, it’s recommended to start the injection process as soon as possible during the production life of reservoirs. According to the experimental results, rocks behave differently during production and injection periods. Poisson’s ratio is greater during pressure build-up as compared to the depletion period. According to the current industry standards, Poisson’s ratio is usually obtained using fracturing data; i.e., leak-off test or mini-fracture test, or well logging methods. However, we are not able to use the same Poisson’s ratio for both pressure drawdown and build-up scenarios according to the experimental data. Corresponding to Poisson’s ratio values, the change in horizontal stress with pore pressure during drawdown (production) is higher than during build-up (injection) period. The outcomes of this study can significantly contribute to well planning and design of challenging wells over the life of reservoirs.

Sign in / Sign up

Export Citation Format

Share Document