Analysis of unsteady pipe flow using the modified finite element method

Szymkiewicz, Romuald; Mitosek, M.

doi:10.1002/cnm.741

Cited by 26 publications

(14 citation statements)

References 16 publications

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“…In addition, interpolations may be necessary when the pipe's diameter varies which leads to variation of wave velocity. In such a case, it is difficult to keep the Courant number close to 1, and consequently this method will always produce numerical diffusion (Szymkiewicz and Mitosek, 2005) .…”

Section: Methods Of Solutionmentioning

confidence: 99%

Fracture Dissolution of Carbonate Rock: An Innovative Process for Gas Storage

Castle¹,

Falta²,

Bruce³

et al. 2006

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The goal of the project is to develop and assess the feasibility and economic viability of an innovative concept that may lead to commercialization of new gas-storage capacity near major markets. The investigation involves a new approach to developing underground gas storage in carbonate rock, which is present near major markets in many areas of the United States. Because of the lack of conventional gas storage and the projected growth in demand for storage capacity, many of these areas are likely to experience shortfalls in gas deliverability. Since depleted gas reservoirs and salt formations are nearly non-existent in many areas, alternatives to conventional methods of gas storage are required. The need for improved methods of gas storage, particularly for ways to meet peak demand, is increasing. Gas-market conditions are driving the need for higher deliverability and more flexibility in injection/withdrawal cycling. In order to meet these needs, the project involves an innovative approach to developing underground storage capacity by creating caverns in carbonate rock formations by acid dissolution. The basic concept of the aciddissolution method is to drill to depth, fracture the carbonate rock layer as needed, and then create a cavern using an aqueous acid to dissolve the carbonate rock.Assessing feasibility of the acid-dissolution method included a regional geologic investigation. Data were compiled and analyzed from carbonate formations in six states: Indiana, Ohio, Kentucky, West Virginia, Pennsylvania, and New York. To analyze the requirements for creating storage volume, the following aspects of the dissolution process were examined: weight and volume of rock to be dissolved; gas storage pressure, temperature, and volume at depth; rock solubility; and acid costs. Hydrochloric acid was determined to be the best acid to use because of low cost, high acid solubility, fast reaction rates with carbonate rock, and highly soluble products (calcium chloride) that allow for the easy removal of calcium waste from the well. Physical and chemical analysis of core samples taken from prospective geologic formations for the acid dissolution process confirmed that many of the limestone samples readily dissolved in concentrated hydrochloric acid. Further, some samples contained oily residues that may help to seal the walls of the final cavern structure. These results suggest that there exist carbonate rock formations well suited for the dissolution technology and that the presence of inert impurities had no noticeable effect on the dissolution rate for the carbonate rock.A sensitivity analysis was performed for characteristics of hydraulic fractures induced in carbonate formations to enhance the dissolution process. Multiple fracture simulations were conducted using modeling software that has a fully 3-D fracture geometry package. The simulations, which predict the distribution of fracture geometry and fracture conductivity, show that the stress difference between adjacent beds is the physical property of the f...

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Section: Methods Of Solutionmentioning

confidence: 99%

Fracture Dissolution of Carbonate Rock: An Innovative Process for Gas Storage

Castle¹,

Falta²,

Bruce³

et al. 2006

View full text Add to dashboard Cite

show abstract

“…This hyperbolic system of partial differential equations consists of the momentum equationEquation (1), and the continuity equation-Equation (2). For given initial and boundary conditions, these equations are solved numerically in x and t plan.…”

Section: R Szymkiewicz and M Mitosekmentioning

confidence: 99%

“…where is the density of the liquid, K the bulk modulus of elasticity of the liquid, E the modulus of elasticity of pipe-wall material, and b the thickness of pipe wall. This hyperbolic system of partial differential equations consists of the momentum equation-Equation (1), and the continuity equation-Equation (2). For given initial and boundary conditions, these equations are solved numerically in x and t plan.…”

Section: Introductionmentioning

confidence: 99%

Numerical aspects of improvement of the unsteady pipe flow equations

Szymkiewicz

Mitosek

2007

Numerical Methods in Fluids

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SUMMARYThe paper presents an analysis of some recently proposed improvements of the water hammer equations, which concern the friction term in the momentum equation. A comparison of the experimental data and numerical results shows that the required damping and smoothing of the pressure wave cannot be obtained by modification of the friction factor only.In order to evaluate the significance of the introduced improvements into the momentum equation, the accuracy of the numerical solution has been analysed using the modified equation approach. The analysis shows why the physical dissipation process observed in the water hammer phenomenon cannot be reproduced with the commonly used source term in Darcy-Weisbach form, representing friction force in the momentum equation. Therefore, regardless of the proposed form of the friction factor for unsteady flow, the model of water hammer improved in such a way keeps its hyperbolic character. Consequently, it cannot ensure the expected effects of damping and smoothing of the calculation head oscillations.

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“…Many numerical tests have indeed confirmed the inappropriate nature of these models; for recent work see, e.g., Refs. [5,6]. Even axisymmetric and unidirectional flow model does not work, because steady or unsteady unidirectional shear flow does not permit variable axial pressure gradient [7].…”

Section: Introductionmentioning

confidence: 95%

Water hammer prediction and control: the Green’s function method

2012

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By Green's function method we show that the water hammer (WH) can be analytically predicted for both laminar and turbulent flows (for the latter, with an eddy viscosity depending solely on the space coordinates), and thus its hazardous effect can be rationally controlled and minimized. To this end, we generalize a laminar water hammer equation of Wang et al. (J. Hydrodynamics, B2, 51, 1995) to include arbitrary initial condition and variable viscosity, and obtain its solution by Green's function method. The predicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and, by adjusting the eddy viscosity coefficient, experimentally measured turbulent flow data. Optimal WH control principle is thereby constructed and demonstrated.

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Analysis of unsteady pipe flow using the modified finite element method

Cited by 26 publications

References 16 publications

Fracture Dissolution of Carbonate Rock: An Innovative Process for Gas Storage

Fracture Dissolution of Carbonate Rock: An Innovative Process for Gas Storage

Numerical aspects of improvement of the unsteady pipe flow equations

Water hammer prediction and control: the Green’s function method

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