Implementation of a Two-Phase Simulator Based on the Brinkman's Equation for Vuggy-Karstified Reservoirs

2019 ◽  
Author(s):  
Daniel Metanias Carvalho Hallack ◽  
Jose Sergio De Araujo Cavalcante Filho ◽  
Paulo Couto
Keyword(s):  
Two Phase ◽  
Brinkman’S Equation

scholarly journals Darcy model with optimized permeability distribution (DMOPD) approach for simulating two-phase flow in karst reservoirs

2021 ◽  
Author(s):  
Mohammad S. Jamal ◽  
Abeeb A. Awotunde
Keyword(s):  
Single Phase ◽  
Two Phase Flow ◽  
Complex Problem ◽  
Phase Flow ◽  
Two Phase ◽  
Darcy Model ◽  
Model Flow ◽  
Alternative Approach ◽  
Brinkman’S Equation ◽  
Permeability Distribution

AbstractDarcy model fails to accurately model flow in karst reservoirs because the flow profiles in free-flow regions such as vugs, fractures and caves do not conform to Darcy’s law. Flows in karsts are often modelled using the Brinkman model. Recently, the DMOPD approach was introduced to reduce the complexity of modelling single-phase flow in Karst aquifers. Modelling two-phase flow using the Brinkman’s equation requires either a method of tracking the front or introducing the saturation component in the Brinkman’s equation. Both of these methods introduce further complexity to an already complex problem. We propose an alternative approach called the two-phase Darcy’s Model with optimized permeability distribution (TP-DMOPD) to model pressure and saturation distributions in karst reservoirs. The method is a modification to the DMOPD approach. Under the TP-DMOPD model, the caves are initially divided into zones and the permeability of each zone is estimated. During this stage of the TP-DMOPD model, the fluid inside the reservoir is assumed to be in a single-phase. Once the permeability distribution is obtained, the two-phase Darcy model is used to simulate flow in the reservoir. The example applications tested showed that the TP-DMOPD approach was able to model two-phase flow in karst reservoirs.

A New Two Phase Extension of Modified Brinkman Formulation for Fluid Flow through Porous Media

2005 ◽  
Author(s):  
Hadi Belhaj ◽  
Shabbir Mustafiz ◽  
Fuxi Ma ◽  
M. R. Islam
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Petroleum Reservoirs ◽  
Two Dimensional ◽  
Transient Pressure ◽  
Two Phase ◽  
Phase Saturation ◽  
Brinkman’S Equation ◽  
The Difference ◽  
Relative Permeability Curves

In porous media research, Modified Brinkman’s equation is a very recent development. It is important as it incorporates the concept of viscous effect to inertial effect in a fluid flow system when Darcy’s, Forchheimer’s and Brinkman’s terms are brought all together. So far, researchers have developed the modified equation in its two-dimensional forms; however, limited to only one phase. In reality, petroleum reservoirs experience the multiphase conditions. Therefore, the simulation of a multidimensional, multiphase scenario is mostly desired, the highlight of this paper. The paper presents the formulation of two-dimensional, transient pressure and saturation equations for oil and water phases, one equation for each phase. The difference between phases is noticeable explicitly in their respective saturation, permeability, viscosity and velocity terms. The equations are then solved numerically to generate relative permeability curves. The simultaneous solution of pressure and saturation terms in the governing equations required additional relationships: the phase saturation constraint and capillary pressure as function of saturation. Finally, the numerical results are compared and validated with the experimental results. The implication of this study is manifold. The formulated equations including the solution part for the multiphase conditions are new. The new comprehensive model will describe fluid flow in reservoirs prone to high velocity or fractures more accurately than ever described by Darcy’s or other aforementioned equations.

Effect of Shock Loading on the Microstructure of Uniloy 326

1974 ◽  
Vol 32 ◽  
pp. 504-505
Author(s):  
K. P. Staudhammer ◽  
L. E. Murr
Keyword(s):  
Grain Size ◽  
Shock Loading ◽  
Current Investigation ◽  
Two Phase ◽  
05 C ◽  
Shock Deformation ◽  
Heat Treated

The effect of shock loading on a variety of steels has been reviewed recently by Leslie. It is generally observed that significant changes in microstructure and microhardness are produced by explosive shock deformation. While the effect of shock loading on austenitic, ferritic, martensitic, and pearlitic structures has been investigated, there have been no systematic studies of the shock-loading of microduplex structures.In the current investigation, the shock-loading response of millrolled and heat-treated Uniloy 326 (thickness 60 mil) having a residual grain size of 1 to 2μ before shock loading was studied. Uniloy 326 is a two phase (microduplex) alloy consisting of 30% austenite (γ) in a ferrite (α) matrix; with the composition.3% Ti, 1% Mn, .6% Si,.05% C, 6% Ni, 26% Cr, balance Fe.

Exsolution and inversion in pigeonite from the Whin Sill, Northern England

1978 ◽  
Vol 36 (1) ◽  
pp. 474-475
Author(s):  
P.P.K. Smith
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Homogeneous Nucleation ◽  
Silicate Mineral ◽  
Antiphase Boundaries ◽  
Two Phase ◽  
Primitive Form ◽  
The Core ◽  
Nucleation Mechanisms ◽  
And Inversion

Grains of pigeonite, a calcium-poor silicate mineral of the pyroxene group, from the Whin Sill dolerite have been ion-thinned and examined by TEM. The pigeonite is strongly zoned chemically from the composition Wo8En64FS28 in the core to Wo13En34FS53 at the rim. Two phase transformations have occurred during the cooling of this pigeonite:- exsolution of augite, a more calcic pyroxene, and inversion of the pigeonite from the high- temperature C face-centred form to the low-temperature primitive form, with the formation of antiphase boundaries (APB's). Different sequences of these exsolution and inversion reactions, together with different nucleation mechanisms of the augite, have created three distinct microstructures depending on the position in the grain.In the core of the grains small platelets of augite about 0.02μm thick have farmed parallel to the (001) plane (Fig. 1). These are thought to have exsolved by homogeneous nucleation. Subsequently the inversion of the pigeonite has led to the creation of APB's.

Shock consolidation of Ni-Ti alloy powder

1986 ◽  
Vol 44 ◽  
pp. 430-431
Author(s):  
Naresh N. Thadhani ◽  
Thad Vreeland ◽  
Thomas J. Ahrens
Keyword(s):  
Alloy Powder ◽  
Amorphous Material ◽  
Ti Alloy ◽  
Two Phase ◽  
Near Surface ◽  
Optical Micrograph ◽  
Shock Compaction ◽  
Powder Particles ◽  
Ti Powder ◽  
Rapidly Solidified

A spherically-shaped, microcrystalline Ni-Ti alloy powder having fairly nonhomogeneous particle size distribution and chemical composition was consolidated with shock input energy of 316 kJ/kg. In the process of consolidation, shock energy is preferentially input at particle surfaces, resulting in melting of near-surface material and interparticle welding. The Ni-Ti powder particles were 2-60 μm in diameter (Fig. 1). About 30-40% of the powder particles were Ni-65wt% and balance were Ni-45wt%Ti (estimated by EMPA).Upon shock compaction, the two phase Ni-Ti powder particles were bonded together by the interparticle melt which rapidly solidified, usually to amorphous material. Fig. 2 is an optical micrograph (in plane of shock) of the consolidated Ni-Ti alloy powder, showing the particles with different etching contrast.

A Comparison of Tem and Apfim to the Interpretation of Modulated Microstructures

1985 ◽  
Vol 43 ◽  
pp. 70-71
Author(s):  
M.G. Burke ◽  
M.K. Miller
Keyword(s):  
Low Temperature ◽  
Microstructural Characterization ◽  
Superlattice Reflection ◽  
High Volume ◽  
Atom Probe ◽  
Dark Field ◽  
Miscibility Gap ◽  
Second Phase ◽  
Two Phase ◽  
Probe Field

Interpretation of fine-scale microstructures containing high volume fractions of second phase is complex. In particular, microstructures developed through decomposition within low temperature miscibility gaps may be extremely fine. This paper compares the morphological interpretations of such complex microstructures by the high-resolution techniques of TEM and atom probe field-ion microscopy (APFIM).The Fe-25 at% Be alloy selected for this study was aged within the low temperature miscibility gap to form a <100> aligned two-phase microstructure. This triaxially modulated microstructure is composed of an Fe-rich ferrite phase and a B2-ordered Be-enriched phase. The microstructural characterization through conventional bright-field TEM is inadequate because of the many contributions to image contrast. The ordering reaction which accompanies spinodal decomposition in this alloy permits simplification of the image by the use of the centered dark field technique to image just one phase. A CDF image formed with a B2 superlattice reflection is shown in fig. 1. In this CDF micrograph, the the B2-ordered Be-enriched phase appears as bright regions in the darkly-imaging ferrite. By examining the specimen in a [001] orientation, the <100> nature of the modulations is evident.

A TEM study of the influence of microstructure on the superplastic behavior of a U-5.8 wt.% Nb alloy

1986 ◽  
Vol 44 ◽  
pp. 568-569
Author(s):  
G. Mackiewicz Ludtka
Keyword(s):  
Grain Size ◽  
Heating Rate ◽  
Phase Field ◽  
Single Phase ◽  
Superplastic Behavior ◽  
Two Phase ◽  
Single Phase Field

Historically, metals exhibit superplasticity only while forming in a two-phase field because a two-phase microstructure helps ensure a fine, stable grain size. In the U-5.8 Nb alloy, superplastici ty exists for up to 2 h in the single phase field (γ1) at 670°C. This is above the equilibrium monotectoid temperature of 647°C. Utilizing dilatometry, the superplastic (SP) U-5.8 Nb alloy requires superheating to 658°C to initiate the α+γ2 → γ1 transformation at a heating rate of 1.5°C/s. Hence, the U-5.8 Nb alloy exhibits an anomolous superplastic behavior.

Transition alpha structure in beta-isomorphous Nb-Hf alloys

1987 ◽  
Vol 45 ◽  
pp. 232-233
Author(s):  
R.W. Carpenter ◽  
Changhai Li ◽  
David J. Smith
Keyword(s):  
Solid Solution ◽  
Solution Phase ◽  
Miscibility Gap ◽  
Large Strains ◽  
Solid Solution Phase ◽  
Two Phase ◽  
Diffuse Intensity ◽  
Metastable Form ◽  
The Matrix ◽  
Equilibrium Morphology

Binary Nb-Hf alloys exhibit a wide bcc solid solution phase field at temperatures above the Hfα→ß transition (2023K) and a two phase bcc+hcp field at lower temperatures. The β solvus exhibits a small slope above about 1500K, suggesting the possible existence of a miscibility gap. An earlier investigation showed that two morphological forms of precipitate occur during the bcc→hcp transformation. The equilibrium morphology is rod-type with axes along <113> bcc. The crystallographic habit of the rod precipitate follows the Burgers relations: {110}||{0001}, <112> || <1010>. The earlier metastable form, transition α, occurs as thin discs with {100} habit. The {100} discs induce large strains in the matrix. Selected area diffraction examination of regions ∼2 microns in diameter containing many disc precipitates showed that, a diffuse intensity distribution whose symmetry resembled the distribution of equilibrium α Bragg spots was associated with the disc precipitate.

Using crystallographic symmetry in diffraction and contrast analysis

1989 ◽  
Vol 47 ◽  
pp. 504-505
Author(s):  
U. Dahmen ◽  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
High Symmetry ◽  
Two Phase ◽  
Tem Analysis ◽  
Crystallographic Symmetry ◽  
The Matrix ◽  
Contrast Analysis ◽  
Practical Tool ◽  
Convergent Beam ◽  
Beam Diffraction

Despite the increased use of convergent beam diffraction, symmetry concepts in their more general form are not commonly applied as a practical tool in electron microscopy. Crystal symmetry provides an abundance of information that can be used to facilitate and improve the TEM analysis of crystalline solids. This paper draws attention to some aspects of symmetry that can be put to practical use in the analysis of structures and morphologies of two-phase materials.It has been shown that the symmetry of the matrix that relates different variants of a precipitate can be used to determine the axis of needle- or lath-shaped precipitates or the habit plane of plate-shaped precipitates. By tilting to a special high symmetry orientation of the matrix and by measuring angles between symmetry-related variants of the precipitate it is possible to find their habit from a single micrograph.

Chapter 7 Pyroclastic surges and compressible two-phase flow

1998 ◽  
Vol 4 ◽  
pp. 247-312 ◽  
Author(s):  
K WOHLETZ
Keyword(s):  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Pyroclastic Surges
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