“Cassandra” Mathematical Model
Cassandra is software for modeling hydrodynamic processes in complex branched pipeline systems.
Factors taken into account in modeling:
- Distribution of flow parameters along the pipeline;
- Elevation profile of the pipeline;
- Gravity flows and cavities;
- Nonlinear dependence between head loss and flow velocity (Darcy – Weisbach equation with different methods of Darcy friction factor calculation is used);
- PID algorithm for control valve;
- User-defined head-flow characteristic of pumps;
- Pigs calculation;
- User-defined properties of fluid along the pipeline;
Cassandra`s interface allows to assemble pipeline schemes in “Construction” mode.
User can create modeling scheme of any pipeline using a default set of elements (pipe, Y-intersection, gate valve, pump, check valve, tank, control valve, safety valve, PID controller etc.) New elements can be added to a default set of modeling elements. In addition to the hydraulic elements of scheme, there are display facilities of model calculation (sensors).
After assembling pipeline scheme, user can switch to “Tuning” mode, where geometrical and constructive characteristics of elements, parameters of control valves, pumps and sensors can be defined. Sensors can be attached to any parameter of the flow, such as pressure, flow rate, density, viscosity, etc. at any pipe section, pressure difference on pump or valve, position of any valve.
Modeling results can be displayed as graphs and saved in files.
User can calculate both steady-state flow and transient state in pipeline system, analyze the influence of one characteristic of selected element on the characteristics of system generally.
Cassandra can make reports in case if pressures during transient processes excesses maximal allowed values (these values are determined by the pipeline’s bearing capacity).
Cassandra has an integrated OPC-server for communication with other systems during model calculation.
Fig. 1. Cassandra program interface (pumping station, computational mode).
Fig. 2. Defining head-flow pump characteristic.
Fig. 3. Defining an elevation profile of pipeline.
Fig. 4. Graphs in Cassandra.
Red line – hydraulic head (pressure head + elevation head), green line – flow rate, grey line – elevation profile, blue line – pipeline bearing capacity