scholarly journals One-dimensional model equations for hyperbolic fluid flow

2016 ◽  
Vol 140 ◽  
pp. 1-11 ◽  
Author(s):  
Tam Do ◽  
Vu Hoang ◽  
Maria Radosz ◽  
Xiaoqian Xu
Keyword(s):  
Fluid Flow ◽  
Dimensional Model ◽  
One Dimensional ◽  
Model Equations

scholarly journals Land subsidence and hydrodynamic compaction of sedimentary basins

1998 ◽  
Vol 2 (2/3) ◽  
pp. 159-171 ◽  
Author(s):  
H. Kooi ◽  
J. J. de Vries
Keyword(s):  
Response Time ◽  
Land Subsidence ◽  
Sedimentary Basins ◽  
Sediment Loading ◽  
Dimensional Model ◽  
One Dimensional ◽  
Model Equations ◽  
Sediment Layers ◽  
The Relationship

Abstract. A one-dimensional model is used to investigate the relationship between land subsidence and compaction of basin sediments in response to sediment loading. Analysis of the model equations and numerical experiments demonstrate quasi-linear systems behaviour and show that rates of land subsidence due to compaction: (i) can attain a significant fraction (>40%) of the long-term sedimentation rate; (ii) are hydrodynamically delayed with respect to sediment loading. The delay is controlled by a compaction response time τc that can reach values of 10-5-107 yr for thick shale sequences. Both the behaviour of single sediment layers and multiple-layer systems are analysed. Subsequently the model is applied to the coastal area of the Netherlands to illustrate that lateral variability in compaction-derived land subsidence in sedimentary basins largely reflects the spatial variability in both sediment loading and compaction response time. Typical rates of compaction-derived subsidence predicted by the model are of the order of 0.1 mm/yr but may reach values in excess of 1 mm/yr under favourable conditions.

scholarly journals Filament bifurcations in a one-dimensional model of reacting excitable fluid flow

2003 ◽  
Vol 327 (1-2) ◽  
pp. 59-64 ◽  
Author(s):  
Emilio Hernández-Garcı́a ◽  
Cristóbal López ◽  
Zoltán Neufeld
Keyword(s):  
Fluid Flow ◽  
Dimensional Model ◽  
One Dimensional

Numerical Three-Phase Model of the Two-Dimensional Steamflood Process

1970 ◽  
Vol 10 (04) ◽  
pp. 405-417 ◽  
Author(s):  
N.D. Shutler
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Oil Recovery ◽  
Vertical Cross Section ◽  
Recovery Efficiency ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Oil Water ◽  
Three Phases

Abstract This paper describes a numerical mathematical model that is a significant extension of a previously published one-dimensional model of the steamflood published one-dimensional model of the steamflood process. process. The model describes the simultaneous flow of the three phases - oil, water and gas - in two dimensions. Interphase mass transfer between water and gas phases is allowed, but the oil is assumed nonvolatile and the hydrocarbon gas insoluble in the liquid phases. The model allows two-dimensional heat convection within the reservoir and two-dimensional heat conduction in a vertical cross-section spanning the oil sand and adjacent strata. Example calculations are presented which, on comparison with experimental results, tend to validate the model. Steam overriding due to gravity effects is shown to significantly reduce oil recovery efficiency in a thick system while jailing to do so in a thinner system. A study of the effect of capillary pressure indicates that failure to scale capillary forces in laboratory models of thick sands may lead to optimistic recovery predictions, while properly scaled capillary forces may be sufficiently low as to play no important role in oil recovery. Calculations made with and without vertical permeability show that failure to account for vertical fluid flow can lead to predictions of pessimistic oil recovery efficiency. pessimistic oil recovery efficiency Introduction Mathematical tools of varying complexity have been used in studying the steamflood process. A "simplified" class of mathematical models has served primarily as aids in engineering design. A more comprehensive class of models has improved understanding of the nature of the process. The model described in this report is of the latter class, but it is more comprehensive than any previously published model. published model. All previously available calculations of the steamflood process are confined to one space dimension in their treatments of fluid flow. Thus all previous models necessary ignore all effects of gravity reservoir heterogeneity, and nonuniform initial fluid-phase distributions on fluid flow in a second dimension. This model, an extension of a previously published model accounts for heat and previously published model accounts for heat and fluid transfer in two space dimensions and, hence, can evaluate these effects on simultaneous horizontal and vertical flow. While the model can describe the areal performance of a steamflood (in which case the heat transfer is described in three dimensions), this aspect will not be considered in this paper. Rather, this paper will describe the model in its application to a vertical cross-section through the reservoir and will consider some preliminary investigations to demonstrate the importance of being able to simultaneously account for horizontal and vertical fluid flow. Mathematical details are given in appendices. MATHEMATICAL DESCRIPTION OF STEAMFLOODING Darcy's law provides expressions for the velocities of the three phases (oil, water and gas), which, when combined with oil, water and gas mass balances give the partial differential equations governing Now of the three phases within a reservoir sand: OIL PHASE ..(1) WATER PHASE ..(2) SPEJ P. 405

On the well-posedness of various one-dimensional model equations for fluid motion

2017 ◽  
Vol 160 ◽  
pp. 25-43 ◽  
Author(s):  
Hantaek Bae ◽  
Dongho Chae ◽  
Hisashi Okamoto
Keyword(s):  
Fluid Motion ◽  
Well Posedness ◽  
Dimensional Model ◽  
One Dimensional ◽  
Model Equations

A One-Dimensional Numerical Model of a Drop-On-Demand Ink Jet

1986 ◽  
Vol 53 (1) ◽  
pp. 193-197 ◽  
Author(s):  
R. L. Adams ◽  
J. Roy
Keyword(s):  
Numerical Model ◽  
Lagrangian Coordinates ◽  
Dimensional Model ◽  
Dimensional Approach ◽  
One Dimensional ◽  
On Demand ◽  
Drop On Demand ◽  
Ink Jet ◽  
Model Equations ◽  
Predictor Corrector

MacCormack’s predictor-corrector algorithm is used to solve one-dimensional model equations of drop development from a drop-on-demand ink jet. The calculation is done in Lagrangian coordinates, and the results are compared with calculations reported in which an axisymmetric marker-and-cell algorithm is used. The comparison indicates that, although drop velocities differ in the two cases, good qualitative results can be obtained with the less complex one-dimensional approach.

Choking Phenomena in a Lung-Like Model

1987 ◽  
Vol 109 (1) ◽  
pp. 1-9 ◽  
Author(s):  
David Elad ◽  
Roger D. Kamm ◽  
Ascher H. Shapiro
Keyword(s):  
Fluid Flow ◽  
Flow Patterns ◽  
Physical Parameters ◽  
Forced Expiration ◽  
Flow Limitation ◽  
Conducting System ◽  
Dimensional Model ◽  
One Dimensional

A simple, continuous, one-dimensional model for the geometry and structure of the bronchial airways is used for the analysis of fluid flow patterns which have been observed in forced expiration maneuvers. Various phenomena within the conducting system associated with flow limitation are investigated: (a) the conditions in which a “choke” (flow limitation) can occur in a compliant system; (b) theoretical flows that are physically impossible; (c) the possibility of having elastic jumps downstream of the choke point; (d) perturbations in the physical parameters of the conducting system.

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