Numerical Simulation of Water Imbibition in Fractured Cores

1979 ◽  
Vol 19 (03) ◽  
pp. 175-182 ◽  
Author(s):  
Hossein Kazemi ◽  
L.S. Merrill
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Oil Recovery ◽  
Matrix System ◽  
Two Dimensional ◽  
Two Phase ◽  
Flow Equations ◽  
Water Imbibition ◽  
The Matrix ◽  
Numerical Simulator

Original manuscript received in Society f Petroleum Engineers office Sept. 15, 1977. Paper accepted for publication June 9, 1978. Revised manuscript received Feb. 19, 1979. Paper (SPE 6890) first presented at the SPE-AIME 52nd Annual Fall Technical Conference and Exhibition, held in Denver, Oct. 9-12, 1977. Abstract A two-dimensional, two-phase, semi-implicit, numerical simulator was used to simulate water imbibition and oil recovery in artificially fractured and unfractured cores. Experimental results were matched satisfactorily by the numerical simulator. These results provide evidence of the reliability of the concepts underlying an earlier numerical simulator, which was tailored specifically for field applications. We show that the flow equations used to match the laboratory data reduce to the equations used in the field simulator. In addition, the experiments themselves were conducted quite differently from those commonly used in imbibition experiments and provide added insight into oil recovery from fractured reservoirs. Introduction Previously, we reported on the development of a Previously, we reported on the development of a numerical reservoir simulator for use in field applications. In this paper, we examine the reliability of the concepts underlying the numerical simulation by matching experimental results of fractured and unfractured cores with a simulator that accounts for the fracture and the matrix components. The simulator is a conventional two-dimensional, two-phase, semi-implicit simulator, but we show that it reduces to the formulation used in the field simulator. Several studies have reported on water imbibition in fractured media. These studies were concerned primarily with the imbibition aspects of the flow primarily with the imbibition aspects of the flow mechanism in the matrix rather than the total flow problem in the fracture-matrix system. Mattax and problem in the fracture-matrix system. Mattax and Kyte developed equations for scaling up imbibition effects. Parsons and Chaney used these equations to study imbibition effects in carbonate rocks. Iffly et al., in addition to experimental work, used a one-dimensional, two-phase, semi-implicit mathematical model to match oil recoveries from the matrix. A similar mathematical model in two dimensions was used by Kleppe and Morse to match the results of their imbibition experiments. While the last two papers show that imbibition oil recovery can be simulated numerically, the total concept of fluid flow in fracture-matrix systems has not been investigated adequately either numerically or experimentally. Mathematical Model The porous media used here were cylindrical cores or rectangular blocks cut along the long axis. The flow experiments were conducted so that the fracture plane and the entire core were horizontal. Therefore, the fractured cores were simulated by a layered two-dimensional simulator. The core halves were simulated as two matrix layers having the properties of the original core. The fracture was simulated as a very thin, high-permeability, and high-flow-capacity layer, where capillary pressure was essentially zero. The basic flow equations, assuming imcompressible flow, are w w----- wx ------ + ----- wz --------x x x zax az Sw+ qw Bw (X - Xo) = -------................(1)at t o o------ ox------ + ------ oz -------qoBo (X-Xo)x x z z So= ---------..................................(2)t Sw + So = 1.....................................(3) Pc(Sw) = po - pw....................................(4) kxkrwwx = 0.006328 -----------,......................(5)w SPEJ P. 175

A Ternary, Two-Phase, Mathematical Model of Oil Recovery With Surfactant Systems

1984 ◽  
Vol 24 (06) ◽  
pp. 606-616 ◽  
Author(s):  
Charles P. Thomas ◽  
Paul D. Fleming ◽  
William K. Winter
Keyword(s):  
Mathematical Model ◽  
Oil Recovery ◽  
Arbitrary Number ◽  
The Other ◽  
Phase System ◽  
Chemical Flooding ◽  
Two Phase ◽  
Oil Displacement ◽  
Surfactant Systems ◽  
And Diffusion

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.

Numerical Simulation of Subsea Cluster Manifold Installation by the Sheave Method

2018 ◽  
Author(s):  
Yu Zhao ◽  
Yingying Wang ◽  
Liwei Li ◽  
Chao Yang ◽  
Yang Du ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
South China Sea ◽  
Deep Sea ◽  
High Reliability ◽  
Two Dimensional ◽  
Complex Environment ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
The Mathematical Model

The sheave installation method (SIM) is an effective and non-conventional method to solve the installation of subsea equipment in deep water (>1000m), which has been developed to deploy the 175t Roncador Manifold I into 1,885 meters water depth in 2002. With the weight increment of subsea cluster manifold, how to solve its installation with the high reliability in the deep sea is still a great challenge. In this paper, the installation of the 300t subsea cluster manifold using the SIM is studied in the two-dimensional coordinate system. The mathematical model is established and the lumped mass method is used to calculate the hydrodynamic forces of the wireropes. Taking into account the complex environment loads, the numerical simulation of the lowering process is carried out by OrcaFlex. The displacement and vibration of the subsea cluster manifold in the z-axis direction and the effective tension at the top of the wireropes can be gotten, which can provide guidance for the installation of the cluster manifold in the South China Sea.

scholarly journals Magma ascent mechanisms in the transition regime from solitary porosity waves to diapirism

Solid Earth ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 1549-1561
Author(s):  
Janik Dohmen ◽  
Harro Schmeling
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Two Phase Flow ◽  
Magma Ascent ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Equations ◽  
Time To Build ◽  
Wide Range ◽  
The Matrix

Abstract. In partially molten regions inside the Earth, melt buoyancy may trigger upwelling of both solid and fluid phases, i.e., diapirism. If the melt is allowed to move separately with respect to the matrix, melt perturbations may evolve into solitary porosity waves. While diapirs may form on a wide range of scales, porosity waves are restricted to sizes of a few times the compaction length. Thus, the size of a partially molten perturbation in terms of compaction length controls whether material is dominantly transported by porosity waves or by diapirism. We study the transition from diapiric rise to solitary porosity waves by solving the two-phase flow equations of conservation of mass and momentum in 2D with porosity-dependent matrix viscosity. We systematically vary the initial size of a porosity perturbation from 1.8 to 120 times the compaction length. If the perturbation is of the order of a few compaction lengths, a single solitary wave will emerge, either with a positive or negative vertical matrix flux. If melt is not allowed to move separately to the matrix a diapir will emerge. In between these end members we observe a regime where the partially molten perturbation will split up into numerous solitary waves, whose phase velocity is so low compared to the Stokes velocity that the whole swarm of waves will ascend jointly as a diapir, just slowly elongating due to a higher amplitude main solitary wave. Only if the melt is not allowed to move separately to the matrix will no solitary waves build up, but as soon as two-phase flow is enabled solitary waves will eventually emerge. The required time to build them up increases nonlinearly with the perturbation radius in terms of compaction length and might be too long to allow for them in nature in many cases.

scholarly journals A New Method for Artificial Core Reconstruction of a Fracture-Control Matrix Unit

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qiang Liu ◽  
Jianjun Liu ◽  
Guihong Pei ◽  
Zhengwen Zhu ◽  
Yun Lei
Keyword(s):  
Numerical Simulation ◽  
Fractured Reservoirs ◽  
Low Permeability ◽  
Fracture System ◽  
Matrix System ◽  
The Core ◽  
Matrix Unit ◽  
The Matrix ◽  
Control Matrix ◽  
Fracture Control

The fracture-control matrix unit (F-CMU) is a special body present in low-permeability fractured reservoirs that can be distinguished by a fracture system and a matrix system. The imbibition phenomenon of the F-CMU provides the possibility for secondary development of low-permeability fractured reservoirs because of the driving force including capillary force and gravity. However, the F-CMU is difficult to obtain during the field core drilling, which has limited the development for laboratory dynamic imbibition tests. Therefore, a new F-CMU reconstruction method is proposed in this study. According to the geometry and parameters, combining laser engraving technology, the fracture system is designed and engraved. Then, the F-CMU is established using a three-dimensional (3D) printed material called polyvinyl alcohol (PVA) as fracture support material which has a faster dissolution rate and causes less damage to the core due to water being the solvent. Finally, the porosity, permeability, and wettability of the matrix system and the T2 spectra from nuclear magnetic resonance (NMR) before and after reconstruction are measured. In addition, numerical simulation calculation of F-CMU permeability is performed. The results show that the characteristic parameters of the matrix system hardly change, indicating low damage to the core. The reconstructed fracture system is found on the T2 spectra, and the fracture permeability is consistent by comparing with the experimental and numerical simulation results. The permeability of the fracture system is about 104 orders of magnitude of the matrix system, which is closer to real core and meets the requirements needed for dynamic permeability experiments.

scholarly journals Simulation of the absorption of gaseous SO2 by fog droplets using a refined interpolation-sectional droplet model

2020 ◽  
pp. 19-32
Author(s):  
Vladimir Viktorovich Pekunov
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Sulfur Dioxide ◽  
Road Transport ◽  
Two Phase ◽  
Phase Dynamics ◽  
Lagrangian Modeling ◽  
Gaseous Sulfur ◽  
Kinetics Of ◽  
Droplet Phase

This article examines the problem of numerical simulation of interaction between the gaseous sulfur dioxide emitted by road transport and fog in the conditions of high humidity. For this purpose, the author applies a multi-factor two-phase mathematical model, which takes into account the dynamics of turbulent main phase, dynamics and kinetics of the multi-sectional droplet phase, presence of thermal inconsistencies formed as a result of direct and diffused solar radiation in various ranges, diffusion of sulfur dioxide, and its absorption by the fog droplets. The article carries out a numerical calculation of the corresponding task within the modeling system of environmental processes AirEcology-P, which allows generating the optimal calculation code for a particular mathematical model. The proposed complex mathematical model that descries interaction between the emitted sulfur dioxide gas and the fog droplets is new; it specifies the calculation of the kinetics of droplet phase based on consideration of the additional factor of droplet fusion characteristic to fog. The submodel of the droplet phase was tested in the numerical simulation (the results were compared with the data of direct Lagrangian modeling of the composite of 1,000 droplets), indicating decent accuracy results. The article obtains the results of numerical simulation of interaction between the emitted SO2 and the droplets. The author demonstrates the self-cleaning ability of the atmosphere, the degree of which correlates with the initial concentration of the smallest droplets and the height from the surface.

Numerical Simulation of Heat Transfer in Shear Flow of Liquid-Solid Two-Phase Media by Immersed Solid Approach

2015 ◽  
Author(s):  
Takeo Kajishima ◽  
Katsuya Kondo ◽  
Shintaro Takeuchi
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Thermal Convection ◽  
Heat Conductivity ◽  
Three Dimensional ◽  
Effect Of Temperature ◽  
Two Dimensional ◽  
Two Phase ◽  
Dimensional Simulation ◽  
Conductive Particles

We developed a direct numerical simulation (DNS) method of solid-fluid two-phase flows to study the effects of heat conductivity within a solid particle and the particle motion on the heat transfer. Heat transfer and particle behaviors were studied for different ratios of heat conductivity (solid to liquid) and solid volume fractions. The simulation results emphasize the effect of temperature distributions within the particles, and the heat transfer through each particle plays an important role for the motion of the particulate flow. The particle-laden flow in a two-dimensional channel of instable thermal stratification, namely hot wall at the bottom and cold wall at the top, is simulated. In the two-dimensional computation, the heat transfer attenuates by increasing the neutral conductive particles because of the resistance to the thermal convection. In case of highly conductive particles, the thermal convection and conductions are enhanced to some extent of addition but the overload of particles suddenly reduces the intensity of convection, resulting in the lower heat transfer. The inverse gradient of mean temperature is observed particularly in case of moderate loading of neutral conductive particles. It is due to the modulation of the profile of convection cells. Most of the above-mentioned findings are reproduced by the fully three-dimensional simulation.

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