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Apparatus and method for in situ controlled heat processing of hydrocarbonaceous formations
Assignee: IIT Research Institute
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Filing: 1982-01-29
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Granted: 1984-05-22
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Expires: 2002-01-29
Abstract
Abstract A system and method for the controlled in situ heat processing of hydrocarbonaceous earth formations involves the application of electromagnetic energy at a selected frequency or at selected frequencies to a waveguide structure formed by electrodes bounding a particular volume of hydrocarbonaceous material. Terminating one end of the structure with different impedances at different times produces electric field standing waves of different respective phase at that end at a selected frequency. Two standing waves substantially 90° out of phase in formations having relatively uniform dielectric properties result in substantially uniform application of heating power if the product of the amplitude-squared of the electric field standing wave and dwell time is substantially the same in each of the two modes. Feeding the line at both ends provides partial offset for attenuation. Various desired controlled heating patterns other than uniform may be effected by utilizing different dwell times or applied fields. Different frequencies provide further flexibility, particularly where the line is terminated differently at the respective frequencies. Energy at the different frequencies may be applied simultaneously.
Inventors
- 👤 Jack E. Bridges
- 👤 Allen Taflove
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-23 18:18
CPC Classifications
E; E21; E21B; E21B43/00; E21B43/16; E21B43/24; E21B43/2401; E21B36/00; E21B36/04; E21B43/30; E21B43/305
Claims Analysis
Total Claims: 69
Claim 1
Independent Claim
152 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propogation therein is approximately parallel to an elongate axis of said electrodes, said structure having first and second axially displaced ends; supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with different effective termination impedances at different times to produce electric field standing waves of different respective phase at said one end at the selected frequency.
Claim 2
Independent Claim
152 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propogation therein is approximately parallel to an elongate axis of said electrodes, said structure having first and second axially displaced ends; supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with different effective termination impedances at different times to produce electric field standing waves of different respective phase at said one end at the selected frequency.
Claim 3
Dependent Claim
17 words
A method according to claim 1 wherein said energy is supplied at the other of said ends.
Claim 4
Dependent Claim
22 words
A method according to claim 1 wherein electromagnetic energy is supplied to said waveguide structure at a plurality of axially displaced points.
Claim 5
Dependent Claim
16 words
A method according to claim 3 wherein said points are at said first and second ends.
Claim 6
Dependent Claim
20 words
A method according to claim 4 wherein energy is supplied at said first and second ends at the same time.
Claim 7
Dependent Claim
20 words
A method according to claim 4 wherein energy is supplied at said first and second ends at the different times.
Claim 8
Dependent Claim
28 words
A method according to claim 4 wherein said one of said ends is an end opposite to an end to which such energy is supplied at the time.
Claim 9
Dependent Claim
15 words
A method according to claim 1 wherein said energy is supplied at different such frequencies.
Claim 10
Dependent Claim
16 words
A method according to claim 8 wherein said energy is supplied at said different frequencies simultaneously.
Claim 11
Dependent Claim
13 words
A method according to claim 9 wherein said different frequencies are harmonically related.
Claim 12
Dependent Claim
51 words
A method according to claim 8 wherein the selected frequencies, magnitude of power supplied at the respective frequencies, the duration of application thereof, and the phases of the standing waves produce a combined application of energy differing in a controlled predetermined manner to respective axially displaced portions of the earth formations.
Claim 13
Dependent Claim
34 words
A method according to claim 1 wherein the duration of application of power at said respective different times is controlled to provide a controlled axial distribution of average power applied to the earth formations.
Claim 14
Independent Claim
34 words
A method according to any one of claims 1 to 12 wherein said one end is terminated by a substantially effectively open circuit and a substantially effectively short circuit at said respective different times.
Claim 15
Independent Claim
33 words
A method according to any one of claims 1 to 12 wherein said one end is terminated by a substantially effectively impedance and a substantially effectively inductive impedance at said respective different times.
Claim 16
Independent Claim
25 words
A method according to any one of claims 1 to 12 wherein said respective phases of the electric field standing waves are substantially 90° apart.
Claim 17
Dependent Claim
14 words
A method according to claim 15 wherein said respective different times are substantially equal.
Claim 18
Dependent Claim
59 words
A method according to claim 15 wherein the product of dwell time and the amplitude-squared of the electric field standing wave when said structure is terminated with one of said impedances is substantially equal to the product of dwell time and the amplitude-squared of the electric field standing wave when said structure is terminated with another of said impedances.
Claim 19
Dependent Claim
59 words
A method according to claim 1 wherein the product of dwell time and the amplitude-squared of the electric field standing wave when said structure is terminated with one of said impedances is substantially equal to the product of dwell time and the amplitude-squared of the electric field standing wave when said structure is terminated with another of said impedances.
Claim 20
Independent Claim
159 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode, said structure having first and second axially displaced ends; supplying electromagnetic energy to said waveguide structure simultaneously at a plurality of respective frequencies selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with different effective impedances at the respective frequencies at the same time to produce standing waves of different respective phase at said one end at the respective selected frequencies.
Claim 21
Independent Claim
159 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode, said structure having first and second axially displaced ends; supplying electromagnetic energy to said waveguide structure simultaneously at a plurality of respective frequencies selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with different effective impedances at the respective frequencies at the same time to produce standing waves of different respective phase at said one end at the respective selected frequencies.
Claim 22
Dependent Claim
13 words
A method according to claim 19 wherein said different frequencies are harmonically related.
Claim 23
Dependent Claim
50 words
A method according to claim 19 wherein the selected frequencies, magnitudes of power supplied at the respective frequencies, the duration of application thereof, and the phases of the standing waves produce a combined application of energy differing in a controlled predetermined manner to respective axially displaced portions of earth formations.
Claim 24
Independent Claim
148 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode; supplying electromagnetic energy to said waveguide structure simultaneously at a plurality of respective frequencies selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with an effective termination impedance producing an electric field standing wave at each selected frequency, the respective standing waves producing heating minima axially displaced from one another.
Claim 25
Independent Claim
148 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode; supplying electromagnetic energy to said waveguide structure simultaneously at a plurality of respective frequencies selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with an effective termination impedance producing an electric field standing wave at each selected frequency, the respective standing waves producing heating minima axially displaced from one another.
Claim 26
Dependent Claim
17 words
A method according to claim 22 wherein said termination impedance is substantially the same at all frequencies.
Claim 27
Dependent Claim
21 words
A method according to claim 23 wherein said one end of said structure is terminated in a substantially effectively open circuit.
Claim 28
Independent Claim
126 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode, said structure having first and second axially displaced ends; and supplying electromagnetic energy to said waveguide structure at each of said ends thereof at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations.
Claim 29
Independent Claim
126 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode, said structure having first and second axially displaced ends; and supplying electromagnetic energy to said waveguide structure at each of said ends thereof at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations.
Claim 30
Dependent Claim
35 words
A method according to claim 25 including terminating the respective end of said structure opposite an end to which such energy is supplied at the time in a manner producing an electric field standing wave.
Claim 31
Dependent Claim
40 words
A method according to claim 25 including terminating the respective end opposite an end to which such energy is supplied at the time in an effectively resistive termination providing suppression of reflection of the applied energy at said terminated end.
Claim 32
Independent Claim
143 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propogation therein is approximately parallel to an elongate axis of said electrodes, said structure having first and second axially displaced ends; supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with an effectively resistive termination impedance to suppress reflection of the applied energy at said one end.
Claim 33
Independent Claim
143 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propogation therein is approximately parallel to an elongate axis of said electrodes, said structure having first and second axially displaced ends; supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and terminating one end of said structure with an effectively resistive termination impedance to suppress reflection of the applied energy at said one end.
Claim 34
Independent Claim
161 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure including a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; means for supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and termination means for providing a selectable one of a plurality of different effective termination impedances at one of said ends of said structure, each impedance providing an electric field standing wave of respective phase at said one end at the selected frequency, said termination means including means for selecting respective ones of said termination impedances.
Claim 35
Independent Claim
161 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure including a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; means for supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and termination means for providing a selectable one of a plurality of different effective termination impedances at one of said ends of said structure, each impedance providing an electric field standing wave of respective phase at said one end at the selected frequency, said termination means including means for selecting respective ones of said termination impedances.
Claim 36
Dependent Claim
24 words
A system according to claim 29 wherein said means for supplying energy includes means for supplying such energy at the other of said ends.
Claim 37
Dependent Claim
30 words
A system according to claim 29 wherein said means for supplying electromagnetic energy includes means for supplying such energy to said waveguide structure at a plurality of axially displaced points.
Claim 38
Dependent Claim
30 words
A system according to claim 31 wherein said means for supplying such energy at a plurality of points includes means for supplying such energy at said first and second ends.
Claim 39
Dependent Claim
29 words
A system according to claim 32 wherein said means for supplying such energy includes means for supplying such energy at said first and second ends at the same time.
Claim 40
Dependent Claim
28 words
A system according to claim 32 wherein said means for supplying such energy includes means for supplying such energy at said first and second ends at different times.
Claim 41
Dependent Claim
28 words
A system according to claim 32 wherein said one of said ends is an end opposite to an end to which such energy is supplied at the time.
Claim 42
Dependent Claim
22 words
A system according to claim 29 wherein said means for supplying energy includes means for supplying such energy at different such frequencies.
Claim 43
Dependent Claim
23 words
A system according to claim 36 wherein said means for supplying energy includes means for supplying such energy at said different frequencies simultaneously.
Claim 44
Dependent Claim
23 words
A system according to claim 37 wherein said termination means includes means for providing different impedances at respective frequencies at the same time.
Claim 45
Dependent Claim
19 words
A system according to claim 37 wherein said different frequencies are harmonically related and derived from a single source.
Claim 46
Dependent Claim
49 words
A system according to claim 36 wherein the selected frequencies, the magnitudes of the power supplied at the respective frequencies and the phases provided by the respective impedances produce a combined application of energy differing in a controlled predetermined manner to respective axially displaced portions of the earth formations.
Claim 47
Independent Claim
35 words
A system according to any one of claims 29 to 40 wherein said termination impedances consist of two impedances providing respective phases of the electric field standing waves at said one end substantially 90° apart.
Claim 48
Independent Claim
23 words
A system according to any one of claims 29 to 40 wherein said termination impedances are respective substantially effectively open and short circuits.
Claim 49
Independent Claim
23 words
A system according to any one of claims 29 to 40 wherein said termination impedances are respective substantially effectively capacitive and inductive loads.
Claim 50
Independent Claim
27 words
A system according to any one of claims 29 to 40 wherein said waveguide structure is formed by a plurality of serially connected parallel laterally offset sections.
Claim 51
Dependent Claim
15 words
A system according to claim 44 wherein said waveguide structure comprises a folded triplate line.
Claim 52
Dependent Claim
17 words
A system according to claim 45 wherein first and second ends are at substantially the same elevation.
Claim 53
Dependent Claim
19 words
A system according to claim 46 including means for exchanging the connections at the respective first and second ends.
Claim 54
Independent Claim
145 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure including a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; and means for simultaneously supplying electromagnetic energy to said waveguide structure at a plurality of respective frequencies selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations, said structure terminating at one of said ends in an effective termination impedance providing an electric field standing wave at each selected frequency, the respective standing waves producing heating minima axially displaced from one another.
Claim 55
Independent Claim
145 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure including a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; and means for simultaneously supplying electromagnetic energy to said waveguide structure at a plurality of respective frequencies selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations, said structure terminating at one of said ends in an effective termination impedance providing an electric field standing wave at each selected frequency, the respective standing waves producing heating minima axially displaced from one another.
Claim 56
Dependent Claim
18 words
A system according to claim 48 wherein said termination impedance is substantially the same at all selected frequencies.
Claim 57
Dependent Claim
16 words
A system according to claim 49 wherein said termination impedance is a substantially effectively open circuit.
Claim 58
Independent Claim
112 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure comprising a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; and means for supplying electromagnetic energy to said waveguide structure at each of said ends thereof at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations.
Claim 59
Independent Claim
112 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure comprising a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; and means for supplying electromagnetic energy to said waveguide structure at each of said ends thereof at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations.
Claim 60
Dependent Claim
48 words
A system according to claim 51 including termination means at the respective end of said structure opposite an end to which such energy is supplied at the time for providing a termination impedance at said respective end, said impedance providing an electric field standing wave in said structure.
Claim 61
Dependent Claim
53 words
A system according to claim 51 including termination means at the respective end of said structure opposite an end to which such energy is supplied at the time for providing an effectively resistive termination impedance at said respective end, said impedance providing suppression of reflection of the applied energy at said respective end.
Claim 62
Independent Claim
133 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure including a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; means for supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and termination means for providing an effectively resistive termination impedance at one of said ends of said structure, said impedance providing suppression of reflection of the applied energy.
Claim 63
Independent Claim
133 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure including a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; means for supplying electromagnetic energy to said waveguide structure at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations; and termination means for providing an effectively resistive termination impedance at one of said ends of said structure, said impedance providing suppression of reflection of the applied energy.
Claim 64
Independent Claim
137 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode, said structure having first and second axially displaced ends; and supplying electromagnetic energy to said waveguide structure at each of said ends thereof at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations, said energy being supplied at different times to respective said ends.
Claim 65
Independent Claim
137 words
A method for the controlled in situ heat processing of hydrocarbonaceous earth formations comprising the steps of: placing a plurality of electrodes into a particular volume of hydrocarbonaceous material in a pattern which bounds said volume and defines a waveguide structure having said bounded volume present as a dielectric medium bounded therein, and which is configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrode, said structure having first and second axially displaced ends; and supplying electromagnetic energy to said waveguide structure at each of said ends thereof at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations, said energy being supplied at different times to respective said ends.
Claim 66
Dependent Claim
40 words
A method according to claim 55 including terminating the respective end opposite an end to which such energy is supplied at the time in an effectively resistive termination providing suppression of reflection of the applied energy at said terminated end.
Claim 67
Independent Claim
115 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure comprising a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; and means for supplying electromagnetic energy to said waveguide structure at each of said ends thereof at different times at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations.
Claim 68
Independent Claim
115 words
A system for the controlled in situ heat processing of hydrocarbonaceous earth formations, comprising a waveguide structure comprising a plurality of elongate electrodes and configured such that the direction of propagation of aggregate modes of wave propagation therein is approximately parallel to an elongate axis of said electrodes and bounding a particular volume of earth formations as a dielectric medium bounded therein, said structure having respective first and second axially separated ends; and means for supplying electromagnetic energy to said waveguide structure at each of said ends thereof at different times at a frequency selected to confine said electromagnetic energy substantially in said structure and to dissipate said electromagnetic energy substantially to the earth formations.
Claim 69
Dependent Claim
53 words
A system according to claim 57 including termination means at the respective end of said structure opposite an end to which such energy is supplied at the time for providing an effectively resistive termination impedance at said respective end, said impedance providing suppression of reflection of the applied energy at said respective end.
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USPTO Annuity & Maintenance Windows
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| 3.5 Years (Year 4) | 1987-05-22 | 1987-11-21 | 1988-05-22 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1991-05-22 | 1991-11-21 | 1992-05-22 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1995-05-22 | 1995-11-21 | 1996-05-22 | $7700.00 | Window Closed / Lapsed |