Numerical modeling of local effects on the petroleum reservoir using fixed streamtubes for typical waterflooding schemes

The difficulty of numerical modeling of areal methods of flows redistribution in the oil reservoir is the need for detailed resolution of local hydrodynamic effects and the fine geological structure of the reservoir, which are centimeter-wide, at inter-well distances of the order of several hundred meters. The dimension of computational grids of traditional 3D models of such resolution, even for impact areas containing a small number of injection and production wells, turns out to be excessively large for design calculations. To overcome these limitations, it is proposed to perform a detailed simulation of the flow in two-dimensional cross sections of the reservoir along fixed streamtubes of variable width between each pair of interacting injector and producer wells. Reducing the dimension of the problem allows the use of high-resolution grids to simulate short-term local effects. In this paper, we present an algorithm for constructing a single fixed streamtube between injector and producer, which provides a minimum error in calculating of flow rate and water cut using a two-phase flow problem of reduced dimension along the streamtube. The algorithm is demonstrated by the example of the two-dimensional two-phase flow problem neglecting capillary and gravitational forces in a homogeneous reservoir of constant thickness for three waterflooding elements corresponding to seven vertical well flooding patterns – standard and inverted four-spot, five-spot and seven-spot, as well as staggered line drive. For these waterflooding elements, efficient streamtubes have been constructed, the relative width of which is approximated by piecewise linear functions. On the example of a staggered line drive or five-spot well patterns, the width of the effective streamtube was parameterized for an arbitrary ratio of the sides of the waterflood element. Presented streamtubes can be used as ready templates for subsequent modeling of geological and technical treatments in the relevant elements of the water flooding of the oil reservoir.

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On the Characteristics of a Two-Dimensional Two-Fluid Model

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels ◽

10.1115/icnmm2008-62166 ◽

2008 ◽

Author(s):

Moon-Sun Chung ◽

Sung-Jae Lee ◽

Jong-Won Kim

Keyword(s):

Two Phase Flow ◽

Flow Problem ◽

Fluid Model ◽

Phase Flow ◽

Two Dimensional ◽

Two Phase ◽

One Dimensional ◽

Pipe System ◽

Two Fluid Model ◽

Two Fluid

In this study, we will suggest a two-dimensional two-fluid model considering the effect of mass and momentum interactions to simulate more realistic two-phase flow than the conventional model did. A hyperbolic two-fluid model had been developed for one-dimensional two-phase flow by Chung et al. [1] and it has been improved and applied to analyze one-dimensional two-phase flow problem including surface tension effect for either ordinary pipe system or minichannels. However, in order to simulate the two-dimensional two-phase flow problem efficiently in the future, the above one-dimensional model has need to be extended to two-dimensional equations and adopted to an upwind numerical method.

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Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

Journal of Fluids Engineering ◽

10.1115/1.1400747 ◽

2001 ◽

Vol 123 (4) ◽

pp. 811-818 ◽

Cited By ~ 6

Author(s):

Jun Ishimoto ◽

Mamoru Oike ◽

Kenjiro Kamijo

Keyword(s):

Phase Transition ◽

Gas Phase ◽

Liquid Helium ◽

Two Phase Flow ◽

Fluid Model ◽

Numerical Results ◽

Phase Flow ◽

Two Dimensional ◽

Two Phase ◽

Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

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Experiment and Numerical Simulation of Bubble Behaviors in Argon Gas Injection Into Lead-Bismuth Pool

Volume 2: Thermal Hydraulics ◽

10.1115/icone14-89431 ◽

2006 ◽

Author(s):

Yumi Yamada ◽

Toyou Akashi ◽

Minoru Takahashi

Keyword(s):

Direct Contact ◽

Two Phase Flow ◽

Experimental Result ◽

Feed Water ◽

Force Model ◽

Phase Flow ◽

Two Dimensional ◽

Two Phase ◽

Argon Gas ◽

Bubble Rising

In a lead-bismuth alloy (45%Pb-55%Bi) cooled direct contact boiling water fast reactor (PBWFR), steam can be produced by direct contact of feed water with primary Pb-Bi coolant in the upper core plenum, and Pb-Bi coolant can be circulated by buoyancy forces of steam bubbles. As a basic study to investigate the two-phase flow characteristics in the chimneys of PBWFR, a two-dimensional two-phase flow was simulated by injecting argon gas into Pb-Bi pool in a rectangular vessel (400mm in length, 1500mm in height, 50mm in width), and bubble behaviors were investigated experimentally. Bubble sizes, bubble rising velocities and void fractions were measured using void probes. Argon gas was injected through five nozzles of 4mm in diameter into Pb-Bi at two locations. The experimental conditions are the pressure of atmospheric pressure, Pb-Bi temperatures of 443K, and the flow rate of injection Ar gas is 10, 20, and 30 NL/min. The measured bubble rising velocities were distributed in the range from 1 to 3 m/s. The average velocity was about 0.6 m/s. The measured bubble chord lengths were distributed from 1mm up to 30mm. The average chord length was about 7mm. An analysis was performed by two-dimensional and two-fluid model. The experimental results were compared with the analytical results to evaluate the validity of the analytical model. Although large diameter bubbles were observed in the experiment, the drag force model for spherical bubbles performed better for simulation of the experimental result because of high surface tension force of Pb-Bi.

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