Calculation of power production for EcCM

In this page, you can find an applet which calculates the power production with an "externally charged capacitive mixing" device.

Description of the model and parameters

In this calculation, we consider the following electrical model:

The model is characterized by the capacitors C1 and C2, the internal resistance Rint (equivalent series resistance) and transfer resistance RT. The ΔI current is the leakage current, and is proportional to the square of the base (average) voltage: ΔI = k V02.

Electrode properties panel

The panel contains the parameters described above, namely the capacitances C1 and C2, the transfer and internal resistance RT and Rint, and the characteristic time τ for the salinity change phase. All those parameters are provided for low salinity and high salinity (20 mM and 500 mM).
Moreover, the parameters include the constant k for the leakage, the voltage increase δV which takes place after the flux of fresh water, and the leakage charge q per salinity change cycle.

Electrode dimensions panel

The panel contains the dimensions of the rectengular electrodes, W and L and the gap thickness H. Those parameters are used for extrapolating the power production per square meter, but also for evaluating the pumping power. The flow is perpendicular to the side W, and takes place for the length L, through the gap. The thickness of the film is used to evaluate the volume of solution inside the film. The factor N defines the volume which must flow through the cell: it is N times the volume of solution inside the films.

Cycle parameters

The panel contains the parameters of the cycle: duration of phase A and C (charge and discharge), external resistance in salt and fresh water, and base voltage. The duration of phases B and D are taken equal to the salinity change characteristic time.
Selecting one of the radio-buttons allows to scan one of the above mentioned parameters.

Calculation

Pressing the "Calculate" button starts the calculation. The resulting graph is shown within a few seconds.

The graph represents the total (gross) produced power (when negative, the energy is consumed instead of produced). The vertical scale is in mW. Only the yellow part is actually extracted, while the other colors represent the power losses.
Red: power loss due to leakage current
Green: power loss due to transfer resistance
Blue: power loss due to internal resistance (equivalent series resistance)
Magenta: power loss due to pumping
Yellow: (net) extracted power

The horizontal axis represents the external resistance (in Ω) or the charge/discharge phase duration (in seconds), depending on the selection.