Estimation of Fracture Properties by Combining DAS and DTS Measurements

2022 ◽  
Author(s):  
Shohei Sakaida ◽  
Iuliia Pakhotina ◽  
Ding Zhu ◽  
A. D. Hill
Keyword(s):  
Fluid Flow ◽  
Acoustic Signal ◽  
Input Parameter ◽  
Temperature Inversion ◽  
Volume Of Fluid ◽  
Fluid Volume ◽  
Hydraulic Fractures ◽  
Volume Distribution ◽  
Time Step ◽  
Interpretation Method

Abstract Distributed Temperature Sensing (DTS) and Distributed Acoustic Sensing (DAS) measurements during hydraulic fracturing treatments are used to estimate fluid volume distribution among perforation clusters. DAS is sensitive to the acoustic signal induced by fluid flow in the near-well region during pumping a stage, while DTS is sensitive to temperature variation caused by fluid flow inside the wellbore and in the reservoir. Raw acoustic signal has to be transferred to frequency band energy (FBE) which is defined as the integration of the squared raw measurements in each DAS channel location for a fixed period of time. In order to be used in further interpretation, FBE has to be averaged between several fiber-optic channels for each cluster on each time step. Based on this input, DAS allows us to consider fluid flow through perforation stage by stage during an injection period, and to evaluate the volume of fluid pumped in each cluster location as a function of time, and therefore to estimate the cumulative volume of fluid injected into each cluster. This procedure is based on a lab-derived and computational dynamics model confirmed correlation between the acoustic signal and the flow rate. At each time step, we apply the perforation/fracture noise correlation to determine the flow rate into each cluster, constrained by the requirement that the sum of the flow rates into individual clusters must equal the total injection rate at that time. On the other hand, the DTS interpretation method is based on the transient temperature behavior during the fracturing stimulation. During injection, the temperature of the reservoir surrounding the well is cooled by the injection fluid inside the well. After shut-in of stage pumping, temperature recovers at a rate depending on the injected volume of fluid at the location. The interpretation procedure is based on the temperature behavior during the warm-back period. This temperature distribution is obtained by solution of a coupled 3-D reservoir thermal model with 1-D wellbore thermal model iteratively. Once we confirm that the DAS and DTS interpretation methods provide comparable results of the fluid volume distribution, either of the interpretation results can be used as a known input parameter for the other interpretation method to estimate additional unknown such as one of the fracture properties. In this work, the injected fluid volume distribution obtained by the DAS interpretation is used as an input parameter for a forward model which computes the temperature profile in the reservoir. By conducting temperature inversion to reproduce the temperature profile that matches the measured temperature with the fixed injection rate for each cluster, we can predict distribution of injected fluid for hydraulic fractures along a wellbore. The temperature inversion shows that multiple fractures are created in a swarm pattern from each perforation cluster with a much tighter spacing than the cluster spacing. The field data from MIP-3H provided by the Marcellus Shale Energy and Environmental Laboratory is used to demonstrate the DAS/DTS integrated interpretation method. This approach can be a valuable means to evaluate the fracturing treatment design and further understand the field observation of hydraulic fractures.

The Effects of Direction and Velocity of Movement, and Intra-Articular Fluid Volume on Intra-Articular Pressue

1988 ◽  
Vol 01 (03/04) ◽  
pp. 113-121 ◽  
Author(s):  
S. F. Straface ◽  
P. J. Newbold ◽  
S. Nade
Keyword(s):  
Dynamic Pressure ◽  
Volume Of Fluid ◽  
Joint Capsule ◽  
Fluid Volume ◽  
Structural Configuration

levels. In joints with simulated acute effusion the effect of position on IAP was dependent upon the volume of fluid in the joint. The results indicate that dynamic pressure levels in the moving knee are related to the movements of the joint. The characteristic and reproducible patterns of pressure may reflect changes in the structural configuration of the joint capsule and surrounding tissues during movement, and are influenced by the amount of fluid in the joint.

Fluid-Structure Interaction Approach for Numerical Investigation of a Flexible Hydrofoil Deformations in Turbulent Fluid Flow

2018 ◽  
Author(s):  
M. Benaouicha ◽  
S. Guillou ◽  
A. Santa Cruz ◽  
H. Trigui
Keyword(s):  
Fluid Flow ◽  
Numerical Model ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Time Step ◽  
Fluid Structure ◽  
Turbulent Fluid Flow ◽  
Turbulent Fluid ◽  
Structure Interaction ◽  
Ale Formulation

The study deals with a 3D Fluid-Structure Interaction (FSI) numerical model of a rectangular cantilevered flexible hydrofoil subjected to a turbulent fluid flow regime. The structural response and dynamic deformations are studied by analyzing the oscillations frequencies and amplitudes, under a hydrodynamics loads. The obtained numerical results are confronted with experimental ones, for validation. The numerical model is performed in the same geometric, physical and material conditions as the experimental set-up carried out in a hydrodynamic tunnel. A polyacetal (POM) flexible hydrofoil NACA0015 with an angle of attack of 8° is considered to be immersed in a fluid flow at a Reynold number of 3 × 105. The structure is initially at rest and then moved by the action of the fluid flow. The numerical model is based on a strong coupling procedure for solving the Fluid-Structure Interaction problem. The Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations is used and an anisotropic diffusion equation is solved to compute the fluid mesh velocity and position at each time step. The finite volume method is used for the numerical resolution of the fluid dynamics equations. The structure deformations are described by the linear elasticity equation which is solved by the finite elements method. The Fluid-Structure coupled problem is solved by using the partitioned FSI implicit algorithm. A good agreement between numerical and experimental results for the hydrodynamics coefficients and hydrofoil deformations, maximum deflection and frequencies is obtained. The added mass and damping are analyzed and then the FSI effect on the dynamic deformations of the structure is highlighted.

Non-Orthogonal Transformation of Irregular Geometry for Particle Based Simulation

2010 ◽  
Author(s):  
Anurag Kumar ◽  
Eiyad Abu-Nada ◽  
Toru Yamada ◽  
Yutako Asako ◽  
Mohammad Faghri
Keyword(s):  
Fluid Flow ◽  
Fluid Dynamic ◽  
Orthogonal Transformation ◽  
Maximum Deviation ◽  
Physical Domain ◽  
Time Step ◽  
Velocity Change ◽  
Irregular Boundary ◽  
Contraction Ratio ◽  
Irregular Geometry

Simulations of irregular geometries using non-orthogonal transformation is widely used in grid based methodology such as computational fluid dynamics. However, this approach is not utilized for particle based models. In this paper we introduce non-orthogonal transformation to simulate fluid flow in irregular geometry using dissipative particle dynamics (DPD). Applying boundary condition is not trivial in DPD methodology and problem becomes more complicated for irregular boundary. In the present work, irregular (physical) domain is transformed into a rectangular domain and boundary particles are frozen along the wall. Transformation for position and velocity is used to relate physical and computational domains. As particle’s position and velocity change with time, transformation matrices are determined for each DPD particle at every time step. In DPD, forces are function of actual distance between the particles and acts within a cutoff radius, which change in transformed domain at every location. To solve this problem, firstly, interacting particles are identified in the physical domain and then forces are calculated in the transformed domain. This approach is described by simulating fluid flow inside a convergent-divergent nozzle, whose geometry is controlled by the contraction ratio (CR) in the middle of the nozzle. The DPD results were validated against in-house computational fluid dynamic (CFD) finite volume code based on the stream function vorticity approach. The range of Reynolds number and CR, under study here, is Re = 10–200 and CR = 0.8 and 0.6, respectively. The results revealed an excellent agreement between the DPD and CFD. The maximum deviation between the DPD and CFD results is within 2%. It is found that using large values of dissipative force parameter velocity fluctuations are less.

Sources of error in determinations of carnitine and acylcarnitine in plasma.

1984 ◽  
Vol 30 (2) ◽  
pp. 316-318 ◽  
Author(s):  
R C Fishlock ◽  
L L Bieber ◽  
A M Snoswell
Keyword(s):  
Perchloric Acid ◽  
Volume Of Fluid ◽  
Fluid Volume ◽  
Free Carnitine ◽  
Short Chain ◽  
Distilled Water ◽  
Plasma Samples ◽  
Long Chain ◽  
Total Fluid

Abstract Radioactive and nonradioactive L-carnitine and acyl-L-carnitine were used to evaluate the washing procedures used during the determination of free, total, short-chain, and long-chain acylcarnitine in human and sheep plasma. The volume of fluid trapped by the protein precipitated by perchloric acid is approximately 24% of the total fluid volume and thus contains 24% of free carnitine and short-chain acylcarnitine. Washing twice with distilled water removes about 25% of the long-chain acylcarnitine along with the trapped free carnitine and short-chain acylcarnitines. Washing the pellet twice with a 60 g/L solution of perchloric acid completely removes the trapped free carnitine and short-chain acylcarnitine but does not remove the bound long-chain acylcarnitines. Thus washing with perchloric acid is essential for accurate measurement of long-chain acylcarnitines in plasma samples.

Investigation of Rupture and Slip Mechanisms of Hydraulic Fractures in Multiple-Layered Formations

SPE Journal ◽  
2019 ◽  
Vol 24 (05) ◽  
pp. 2292-2307 ◽  
Author(s):  
Jizhou Tang ◽  
Kan Wu ◽  
Lihua Zuo ◽  
Lizhi Xiao ◽  
Sijie Sun ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Hydraulic Fracture ◽  
Fracture Propagation ◽  
Propagation Model ◽  
Rock Deformation ◽  
Hydraulic Fractures ◽  
Fracture Geometry ◽  
Fracture Width ◽  
Hydraulic Fracture Propagation ◽  
Fracture Height

Summary Weak bedding planes (BPs) that exist in many tight oil formations and shale–gas formations might strongly affect fracture–height growth during hydraulic–fracturing treatment. Few of the hydraulic–fracture–propagation models developed for unconventional reservoirs are capable of quantitatively estimating the fracture–height containment or predicting the fracture geometry under the influence of multiple BPs. In this paper, we introduce a coupled 3D hydraulic–fracture–propagation model considering the effects of BPs. In this model, a fully 3D displacement–discontinuity method (3D DDM) is used to model the rock deformation. The advantage of this approach is that it addresses both the mechanical interaction between hydraulic fractures and weak BPs in 3D space and the physical mechanism of slippage along weak BPs. Fluid flow governed by a finite–difference methodology considers the flow in both vertical fractures and opening BPs. An iterative algorithm is used to couple fluid flow and rock deformation. Comparison between the developed model and the Perkins–Kern–Nordgren (PKN) model showed good agreement. I–shaped fracture geometry and crossing–shaped fracture geometry were analyzed in this paper. From numerical investigations, we found that BPs cannot be opened if the difference between overburden stress and minimum horizontal stress is large and only shear displacements exist along the BPs, which damage the planes and thus greatly amplify their hydraulic conductivity. Moreover, sensitivity studies investigate the impact on fracture propagation of parameters such as pumping rate (PR), fluid viscosity, and Young's modulus (YM). We investigated the fracture width near the junction between a vertical fracture and the BPs, the latter including the tensile opening of BPs and shear–displacement discontinuities (SDDs) along them. SDDs along BPs increase at the beginning and then decrease at a distance from the junction. The width near the junctions, the opening of BPs, and SDDs along the planes are directly proportional to PR. Because viscosity increases, the width at a junction increases as do the SDDs. YM greatly influences the opening of BPs at a junction and the SDDs along the BPs. This model estimates the fracture–width distribution and the SDDs along the BPs near junctions between the fracture tip and BPs and enables the assessment of the PR required to ensure that the fracture width at junctions and along intersected BPs is sufficient for proppant transport.

Development of single fluid volume element method for simulation of transient fluid flow in self-siphons

2014 ◽  
Author(s):  
S. Viridi ◽  
Novitrian ◽  
Nurhayati ◽  
W. Hidayat ◽  
F. D. E. Latief ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Volume Element ◽  
Fluid Volume ◽  
Element Method

Isothermal Displacement Processes With Interphase Mass Transfer

1967 ◽  
Vol 7 (02) ◽  
pp. 205-220 ◽  
Author(s):  
H.W. Price ◽  
D.A.T. Donohue
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Mathematical Models ◽  
Predictive Models ◽  
Time Step ◽  
Two Phase ◽  
Simplifying Assumptions ◽  
Energy Equations ◽  
Displacement Processes

Abstract The system of equations describing displacement of a hydrocarbon liquid by a hydrocarbon vapor in a porous medium where mass transfer takes place between the phases is solved numerically for a variety of gas injection processes. Even though the method of solution is quite general, only systems with three hydrocarbon components are considered. Computer simulations of displacement processes wherein mass transfer between phases is both considered and neglected are compared, and it is shown that neglecting mass transfer can give pessimistic displacement efficiencies. Introduction The role of the gas displacement process in the recovery of petroleum has been subjected to a series of detailed analyses; as a result, a number of predictive models have been published in the literature. However, because of major simplifying assumptions, most of these models do not completely represent the physical system. As a result, the effect of making the simplifying assumptions is unknown. Therefore, a complete representation of this process one without major simplifying assumptions should lead to a full understanding of the process, and perhaps to methods of improving it. The general method of developing a model for two-phase fluid flow in a porous medium is to solve simultaneously the continuity equation, the energy equations and the equation-of-state for each phase under the prescribed initial and boundary conditions. For an isothermal system, the energy equations reduce to the momentum equation, Darcy's law. However, since natural gas is the vapor state of the reservoir liquid, interphase mass transfer may take place with concomitant changes in both the intensive and extensive thermodynamic properties of each phase. It is this phenomenon that has often been omitted in previous mathematical models. An additional relation, then, which accounts for mass transfer between the phases, must be included with the other equations to specify a complete model. Completely formulating the equations to be solved is not a difficult task but obtaining their solution has been intractable up to now. Availability of large-memory, high-speed digital computers now makes an attack on this formidable problem possible. This paper presents a preliminary study of the problem. Since this investigation is intended to be exploratory, it is restricted to the linear, horizontal, isothermal, two-phase viscous flow of oil and gas in an oil reservoir. In the early development of predictive models of this process, the reservoir system was considered as a unit and various forms of the material balance equation were proposed. Pressure and saturation gradients were than added in the Buckley-Leverett model. The Buckley-Leverett formulation considered the fluids to be incompressible; thus, the mathematical model reduces to a steady-state system. In the 1950's, studies incorporating numerical techniques were being published. These mathematical models differed in the efficiency of finite difference techniques, the inclusion or exclusion of capillarity or the number of space dimensions considered. To solve these nonlinear, partial differential equations, each phase was considered to be homogeneous with time; therefore, mass transfer between phases was neglected. The effect of mass transfer on the gas displacement process was first reported by Attra. He simulated the one-dimension flow system by a series of cells in each of which the fluids were equilibrated during a time step. In addition, the pressure throughout the system during each time step was predetermined and constant phase velocities were calculated according to the Buckley-Leverett incompressible fluid flow model. Welge et al. developed a model for the displacement of oil by an enriched gas where composition is considered to be a dependent variable. SPEJ P. 205ˆ

In-Situ Combustion Model

1980 ◽  
Vol 20 (06) ◽  
pp. 533-554 ◽  
Author(s):  
Keith H. Coats
Keyword(s):  
Fluid Flow ◽  
Input Data ◽  
Computing Time ◽  
Three Dimensions ◽  
Maximum Efficiency ◽  
Combustion Model ◽  
Model Formulation ◽  
Time Step ◽  
In Situ Combustion

Abstract This paper describes a numerical model forsimulating wet or dry, forward or reverse combustionin one, two, or three dimensions. The formulation isconsiderably more general than any reported to date.The model allows any number and identities ofcomponents. Any component may be distributed inany or all of the four phases (water, oil, gas, andsolid or coke.The formulation allows any number of chemicalreactions. Any reaction may have any number ofreactants, products, and stoichiometry, identifiedthrough input data. The energy balance accounts forheat loss and conduction, conversion, and radiationwithin the reservoir.The model uses no assumptions regarding degreeof oxygen consumption. The oxygen concentration iscalculated throughout the reservoir in accordancewith the calculated fluid flow pattern and reactionkinetics. The model, therefore, simulates the effectsof oxygen bypassing caused by kinetic-limitedcombustion or conformance factors.We believe the implicit model formulation resultsin maximum efficiency (lowest computing cost), andrequired computing times are reported in the paper.The paper includes comparisons of model resultswith reported laboratory adiabatic-tube test results.In addition, the paper includes example field-scalecases, with a sensitivity study showing effects on oilrecovery of uncertainties in rock/fluid properties. Introduction Recent papers by Ali, Crookston et al., andYoungren provide a comprehensive review of earlierwork in numerical modeling of the in-situcombustion process.The trend in this modeling has been toward morerigorous treatment of the fluid flow and interphasemass transfer; inclusion of more components, morecomprehensive reaction kinetics, and stoichiometry;and more implicit treatment of the finite differencemodel equations.The purpose of this work was to extend thegenerality of previous models while preserving orreducing the associated computing-time requirement.The most comprehensive or sophisticated combustionmodels described to date appear to be thoseof Crookston et al. and Youngren. Therefore, wecompare our model formulation and results here withthose models.A common objective of different investigators'efforts in modeling in-situ combustion is developmentof more efficient formulations and methods ofsolution. This is especially important in thecombustion case because of the large number ofcomponents and equations involved. For a given numberof components and reactions, computing time pergrid block per time step will increase rapidly as theformulation is rendered more implicit. However, increasing implicitness tends to allow larger timesteps, which in turn reduces overall computingexpense. To pursue the above objective, then, authorsshould present as completely as possible the details oftheir formulations and the associatedcomputing-time requirements.The thermal model described here simulateswet or dry, forward or reverse combustion in one, two, or three dimensions. The formulation allowsany number and identities of components and anynumber of chemical reactions, with reactants, products, and stoichiometry specified through input products, and stoichiometry specified through input data. SPEJ P. 533

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