Non-equidistant open transmission lines for electromagnetic heating and method of use

An apparatus for electromagnetic heating of an underground hydrocarbon formation, the apparatus comprising:

• (a) an electrical power source;
• (b) at least one electromagnetic wave generator for generating alternating current, the at least one electromagnetic wave generator being powered by the electrical power source;
• (c) at least two transmission line conductors positioned in the hydrocarbon formation, the at least two transmission line conductors having a proximal end and a distal end, the proximal end of the at least two transmission line conductors being coupled to the at least one electromagnetic wave generator, the at least two transmission line conductors being excitable by the alternating current to propagate a travelling wave within the hydrocarbon formation from the proximal end of the at least two transmission line conductors to the distal end of the at least two transmission line conductors, the at least two transmission line conductors comprising a first transmission line conductor and a second transmission line conductor;
• (d) at least one waveguide for carrying the alternating current from the at least one electromagnetic wave generator to the at least two transmission line conductors, each of the at least one waveguide having a proximal end and a distal end, the proximal end of the at least one waveguide being connected to the at least one electromagnetic wave generator, the distal end of the at least one waveguide being connected to at least one of the at least two transmission line conductors;
• and
• (e) a producer well positioned between the at least two transmission line conductors and at a greater depth than at least one of the at least two transmission line conductors to receive heated hydrocarbons via gravity;
• wherein:
• the producer well defines a longitudinal axis, each of the at least two transmission line conductors extend along the longitudinal axis, a proximal end of the longitudinal axis corresponds to the proximal end of the at least two transmission line conductors;
• at a reference location along the length of the longitudinal axis and proximal to a ground surface, the first transmission line conductor is laterally spaced from the producer well by a first reference distance and the second transmission line conductor is laterally spaced from the producer well by a second reference distance to generate an electromagnetic field having a reference shape and a reference position with respect to the longitudinal axis;
• at the distal end of the transmission line conductors, the first transmission line conductor is laterally spaced from the producer well by a third distance and the second transmission line conductor is laterally spaced from the producer well by a fourth distance, at least one of (i) the third distance being greater than the first reference distance, and (ii) the fourth distance being greater than the second reference distance, to generate an electromagnetic field having a shape that is more elongated than the reference shape;
• and
• a shape of the first transmission line conductor along the longitudinal axis comprises at least a first crest and a second crest, the first crest defining a first plane having a first roll angle with respect to the producer well, the second crest defining a second plane having a second roll angle with respect to the producer well, a magnitude of the first roll angle being unequal to a magnitude of the second roll angle.