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Summary Korf Hydraulics is a powerful, graphical program for calculating flow rates and pressure profiles in pipes and piping networs. Korf Hydraulics differs from other similar programs in that the user is free to specify any valid combination of flows and pressures, and allow Korf to determine the unnown quantities. The only requirement is that a unique solution must be theoretically possible. Korf can solve fluid flow problems ranging from a single pipe, to a complex, twophase networ of pipes, pumps, valves and other fittings.

Principle of Operation Several methods are available in the literature for solving piping networs, including the Hardy-Cross, Newton- Raphson and Linear Theory method [1]. Although Korf was developed independently, it does share certain characteristics with the Linear Theory method. Korf s method is fast and almost always converges with valid specifications.

One notable exception is a circuit consisting of a pump or compressor with an unnown flow rate and head specified by a pump curve or compressor curve.

In this case only, Korf uses an Aiten-Steffensen iteration method to aid convergence. Korf regards all flow rates and all equipment inlet and outlet pressures as variables or unnowns. To determine these unnowns, Korf performs a mass balance around every piece of equipment and a pressure drop calculation over every pipe.

These are called internal specifications. Even with these internal specifications, a unique solution to the problem is not possible without the user specifying an additional number of flows, pressures, pressure drops, beta ratio s, valve Cv s, etc.

A unique solution is possible when the number of independent specifications including the internal specifications equals the number of variables as defined above. Keeping trac of these specifications is not a trivial tas for the user, but Korf has four features that greatly simplifies this process.

Firstly, Korf continuously counts and displays the number of specifications and variables. Secondly, when a new circuit is drawn, Korf assumes certain defaults that result in the number of specifications always equaling the number of variables.

If the user subsequently deletes one, a new one must be added somewhere else. Fourthly, when the problem is run, Korf first evaluates the specifications to determine if they are independent.

Discussion and Examples The top circuit in Figure 1, which is a screenshot from Korf, represents a single pipe. Korf will analyze this circuit to have three variables, viz. It will find only one internal specification, viz.

The user can thus specify any two of the variables listed above to ensure a unique solution. That is, pressure in and out, or pressure in and flow, or pressure out and flow. The bottom circuit in Figure 1 represents a series circuit with three pipes, a pump and a control valve.

Korf will analyze this circuit to have nine variables, viz. Korf will find five internal specifications, viz. The user can thus specify any four of the variables listed above, as long as they are independent. Being independent implies that the user cannot specify two mass flow rates which is obviously the same in pipes in series , as that is equivalent to the mass balance Korf performs internally.

It also implies that at least one specification must be a pressure, as Korf needs at least one pressure somewhere in the circuit to base the other pressures on. In addition to the variables listed above, the user may also choose to specify the pump head directly or indirectly via a pump curve. Similarly for the control valve, where the user may also specify a pressure drop directly or indirectly via a valve Cv.

Furthermore, any or all of the pipe diameters may be unnown if the user wants Korf to size it based on any of five selectable sizing criteria. The principles in these examples can be extended to circuits with almost any combination of pipes in series and parallel. The two circuits shown in Figure 1 can also be in the same problem, as Korf will still be able to determine if each has a unique solution.

Graphical Interface The graphical interface for Korf allows the user to create equipment by dragging them from a template onto the form. Equipment is then connected by pipes using the mouse. Pipes can have up to ten bends. After creating the circuit, the user can move, delete, reroute and edit the equipment and pipes.

A vessel can be represented by a mixer, splitter or miscellaneous equipment. Fittings, such as elbows, are considered part of the pipe and are entered as part of the pipe input data.

The name, number and resistance of these fittings are editable. The user can copy pipe and fluid physical properties from one pipe to another to limit the amount of typing. Selected results and all user specifications can be viewed on the drawing below the equipment. A result file is also generated every time the simulation is run. This is a text file that can be viewed, saved and opened in any word processor. Korf reads the standard pipe sizes and other pipe information from an external file which can be edited from inside Korf.

For gas flow, the user can use the Darcy equation incompressible model or the isothermal compressible model. For two-phase pressure drop calculations, Korf supports several methods, including the Duler constant slip method [3], Lochart- Martinelli method [4] and Chenoweth-Martin method [5]. The current version does not include acceleration effects.

Korf can also display a graphical representation of the current flow regime for the selected pipe. Korf does not do any flash calculations.

For every pipe it uses the liquid mass fraction and physical properties for each phase supplied by the user. If none is supplied by the user, Korf defaults to the physical properties for water. The change in static pressure due to changes in velocity is accounted for in reducers and expanders, but not currently in mixers or splitters or any other equipment.

The user can however specify a pressure increase or decrease over the mixer or splitter, but that pressure drop will be applied to all pipes leaving the splitter or entering the mixer.

Control valve calculations are done according to the equations presented in the Masoneilan bulletin [6], except for two phase flow. For two phase flow Korf assumes the Cv to be the sum of the Cv s calculated for the liquid and vapor phases at the outlet vapor fraction. Orifice calculations are performed by the equations presented in Spin. For two phase flow Korf assumes the orifice area is the sum of the areas calculated for the liquid and vapor phases at the outlet vapor fraction.

At high gas phase pressure drops, the method of Cunningham [7] is used. Although there is no programming limit on the number of pipes and equipment, there is a limit to the number of pipes and equipment that can be drawn and displayed on the screen without overlapping.

The largest drawing size is A3 or 11x Contacts Korf Version 1. For any other technical or commercial information, please the author at 7. References 1. Wood D.

An Approach through Similarity Analysis, A. Journal, 10 1 , , Lochart R. Symbols P - Pressure Pi - Pressure at inlet Po - Pressure at outlet Wl - Liquid weight flow rate D - Pipe nominal diameter Korf toolbar from left ro right in Figure 1 : Open file, Save file, Print drawing, Run hydraulics, Resume run initialize from previous results , Show current specifications on drawing, Show selected results on drawing, Enable or disable drawing, Zoom drawing in or out.

Figure 1. Rosen, EMR Technology Group Partial differential equations arise in a wide variety of chemical engineering problems 1.

If the spatial dimension is represented using a finite difference relationship and the time derivative is considered an ordinary differential equation, the procedure is nown as the numerical method of lines 2. The number of ordinary differential equations that must be solved simultaneously is determined by the number of sections into which the plate is divided in the x direction. Any ordinary differential equation integration method may be used for the integration.

The numerical method of lines can be implemented within Excel 7. The method has a detailed description 4. An alternate approach to the solution of Eq. Both the spatial and the time dimensions are represented by finite difference schemes. The Cran-Nicolson method 5 provides an implicit scheme that is second order accurate in both space and time.

To provide this accuracy, difference approximations are developed at the midpoint of the time increment. Although Eq. The values of the parameters are shown in Fig.

Page 4 Spring The analytical solution is o C. Conclusions Partial differential equations which arise in chemical engineering applications may often be suitable candidates for solution by Excel 7. The accuracy of the of the solution appears adequate for engineering purposes.

Nelson, H. Chapra, S. Canale, Numerical Methods for Engineers, 2 nd Ed. Abstract The ability to quantify hazards is extremely important in the chemical process industries. Quantification maes it possible to assess the physical effects of accidental releases of hazardous materials. With the increased availability of powerful personal computers, the ability exists to apply rigorous numerical methods for the application of analytical models and physical correlations.

Releases of process materials during loss of containment events have different characteristics depending on the prevailing thermodynamic conditions upstream of the rupture. A wide spectrum of flow regimes from all-flashing to totally non-flashing discharges may be encountered.

This report briefly reviews the mathematical correlations used to calculate release rates of fluids liquid, gas or two-phase from chemical process operations following loss of containment accidents. Time varying unsteady state release rates are solved iteratively using stepwise finite element calculations performed using Dyadem ReleaseRate TM software, an integrated finite-element Windows - based computer program used for transient flow modeling. The software has the ability to model both hole-type discharges and pipeline releases of liquids and gases.

Introduction Ris analysis studies often address the releases of hazardous materials from accidental punctures or leas in process vessels or storage tans. Scenarios often deal with calculating the time-varying discharge rates following loss of containment events in order to quantify release amounts and times.

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