Chemistry: electrical and wave energy – Processes and products – Electrophoresis or electro-osmosis processes and electrolyte...
Reexamination Certificate
2000-10-18
2001-12-04
Phasge, Arun S. (Department: 1741)
Chemistry: electrical and wave energy
Processes and products
Electrophoresis or electro-osmosis processes and electrolyte...
C204S554000, C204S555000, C204S600000, C204S660000, C204S661000
Reexamination Certificate
active
06325907
ABSTRACT:
BACKGROUND OF THE INVENTION
Flow-through capacitors have proven commercially useful for water purification and are well represented in the patent literature. For example, U.S. Pat. No. 3,658,674, issued Apr. 25, 1972; U.S. Pat. No. 5,192,432, issued Mar. 9, 1993; U.S. Pat. No. 5,196,115, issued Mar. 23, 1993; U.S. Pat. No. 5,200,068, issued Apr. 6, 1993; U.S. Pat. No. 5,360,540, issued Nov. 1, 1994; U.S. Pat. No. 5,415,768, issued May 16, 1995; U.S. Pat. No. 5,425,858, issued Jun. 20, 1995; U.S. Pat. No. 5,538,611, issued Jul. 23, 1996; U.S. Pat. No. 5,547,581, issued Aug. 20, 1996; U.S. Pat. No. 5,620,597, Apr. 15, 1997; U.S. Pat. No. 5,748,437, issued May 5, 1998; and U.S. Pat. No. 5,779,891, issued Jul. 14, 1998. The flow-through capacitors of the prior art become less energy efficient with increased solution concentration, and lose energy with concentrated solutions, including seawater. Therefore, the need exists for an improved flow-through capacitor with increased energy and weight efficiency, useful for purification concentrated solutions over 2000 ppm, including desalination of seawater, as well as more dilute solutions with increased energy efficiency.
SUMMARY OF THE INVENTION
The invention relates to a flow-through capacitor, system and method, particularly for energy efficient seawater desalination. Flow-through capacitors have a basic advantage over energy storage capacitors. The flow-through capacitor seeks to store charge, not energy. In order to store the most charge per unit time, the flow-through capacitor should be optimized for power characteristics, not energy storage. Power happens to be what capacitors are known to excel at, not energy storage. For most efficient power, the flow-through apacitor should have a series resistance of 1 ohm or less.
In order to achieve low energy purification, it is necessary to take advantage of the fact that a capacitor is not a constant voltage device. The flow-through capacitor may be utilized at the low voltage part of its charging curve in order to achieve low energy purification. Optimal voltage during the charge cycle should not exceed 1 volt.
Kinetics
FIG. 1
shows a semilog graph of classic first order kinetics.
Z/Z
o
=e
−kt
(1)
and
Ln Z/Z
o
=−kt (2)
Where k is constant, Z equals solution concentration at time t, and Z
o
equals starting concentration. By equation (2), the semilog graph of FIG. (
2
) gives slope of constant −k and y intercept Ln Z/Z
o
. First order kinetics have favorable scale up properties. Purification to a given percentage is only a function of starting concentration and time. This means that the same size equipment can be used across a broad range of concentrations. Equation (1) observed empirically, is of the exact same form as (3), below the equation for transient charging current of a capacitor. Equation (3) is true for a flow-through capacitor or any other kind of capacitor.
|/|
o
=e
−t/RC
(3)
where | equals current at any time, t and |
o
is the initial charging current, R is the series resistance, and C is capacitance. The initial current |
o
is simply ohm's law:
|=V/R (4)
where R is the resistance of the capacitor materials and leads. This is the maximum amount of current that you can put into the capacitor. You can also calculate the starting current based upon the capacitor size, resistance, and total charge on the capacitor (see (6) and (12) below).
In order to relate purification with amp and power requirements, it is required to relate equations (1) and (3).
Q=|t (5)
Where Q=charge, and F is Faradays constant, 9.648×10
4
coulombs/mole. Combining (4) ohms law with (5) we get Q/t=V/R at t=0. This means the charge rate at t=0 is inversely proportional to the resistance. Current, and therefore charge per unit time, according to (3) and (5), tapers off exponentially with time as the capacitor is charged.
It is desirable to purify a given amount of charge Q.
Q=CV=FZL (6)
where C equals capacitance, V equals final voltage that the capacitor is charged up to, | equals current, and t is in seconds, F is Faraday constant of 9.648×10
4
coulombs/mole, Z is moles/liter, and L=liters. Combining (6) with (5) shows that equations (1) and (3) are the same, and −k in (1) is therefore equal to −1/RC. This is an advantageous result because (1) was arrived at empirically for a flow-through capacitor. There is an implicit assumption in (6) that there is parity between electronic charge and ionic charge, which is discussed in the experimental section.
Energy Efficient Purification by Rapid Charge Cycling; the 1
Charge Scheme.
Equation (6) shows that for small C, you cannot adsorb enough charge Q to desalt much seawater. However, if the capacitor is fast enough, i.e., has a high enough power rating, one can repeatedly charge/discharge a small weight efficient capacitor many times in order to get the same additive amount of Q.
In addition to weight efficiency, energy efficiency in watt hours/gallon is important for both dilute and concentrated ion, as well as seawater purification, so that small, including portable, power sources may be used. The energy to charge a capacitor is:
Energy=½CV
2
=½(1/C)Q
2
(Joules) (7)
Equation (7) shows that it costs more energy per coulomb of charge to put that charge into a capacitor as voltage increases. It also shows it costs more and more energy as each additional unit of charge is put into the capacitor. Happily, with the flow-through capacitor, we do not want to store energy. It is desired to adsorb charge Q, for the least amount of energy, or joules per coulomb. To ascertain how much power it takes to absorb a given amount of charge, divide (7) by (6):
Joules/coulomb=½CV
2
/CV=½V (8)
The units are in volts, which makes sense because the definition of a volt is joules/coulomb. Here we are referring to an “ionic volt”, as opposed to an electronic one. Equation (8) shows that the less voltage the capacitor is charged to, the less joules are required to store a given coulomb of charge, by a factor of ½.
A same amount of charge Q can be adsorbed by charging a capacitor n times at 1
'th voltage, as can be adsorbed by charging the capacitor once to the fully charged voltage. This will require n times less energy. A smaller capacitor can also be used to store the same amount of charge at the same energy by charging a 1
'th sized capacitor n more times. These cases are calculated as follows, for repeatedly charging and discharging a capacitor n times:
Q
=
CV
=
∑
i
=
1
i
=
n
∑
j
=
1
j
=
n
C
i
V
j
(
9
)
Energy
=
1
2
∑
i
=
1
i
=
n
∑
j
=
1
j
=
n
C
i
(
V
j
)
2
(
Joules
)
(
10
)
For our design Vi=V
fraction of full voltage V. In a case where C
i
is just a full sized capacitor C (10) becomes:
Energy=(1/2n)CV
2
(Joules) (11)
Dividing (11) by (6) above gives 1
for the energy needed to adsorb a given amount of charge using the multiple charge strategy compared to charging all at once up to the full voltage. This only works as long as the time to adsorb an amount of charge (from the water) is less than the RC time constant to charge the capacitor, which is taken into account in the analysis below.
Transient Effects
All above discussion is for an ideal capacitor with no resistance. Real capacitors have series resistance.
Current at any time t is calculated from the resistance and capacitance.
|=|
o
e
−t/RC
(3)
The charge at any time t is the integral of (3)
Q
=
∫
t
=
o
t
I
o
ⅇ
-
t
/
RC
=
I
o
RC
|
(
ⅇ
-
t
/
RC
-
1
t
=
o
t
)
(
12
)
for large RC, such as we are dealing with here, using ohms law (4), this reduces back to (6)
Q=|
o
RC (6)
The energ
IP Legal Strategies Group P.C.
Meyer-Leon Esq. Leslie
Phasge Arun S,.
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