Multilateral open transmission lines for electromagnetic heating and method of use

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

• (a) at least one electromagnetic power source for generating a time-varying current or a time-varying voltage;
• (b) at least two transmission line conductors positioned in the hydrocarbon formation, the transmission line conductors electrically connected at a proximal end to the at least one electromagnetic power source, the transmission line conductors being excitable by the time-varying current or the time-varying voltage to propagate an electromagnetic wave within the hydrocarbon formation, at least one of the transmission line conductors comprise a primary arm and at least one secondary arm branching from the primary arm, the at least one secondary arm comprising at least one electrically isolatable connection for electrically isolating at least a portion of the at least one secondary arm;
• (c) at least one waveguide for carrying the time-varying current or the time-varying voltage from the at least one electromagnetic power source to the 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 power source, the distal end of the at least one waveguide being connected to at least one of the transmission line conductors;
• and
• (d) a producer well having a length that defines a longitudinal axis, at least a portion of each of the transmission line conductors extend along the longitudinal axis, at least a portion of the producer well being positioned laterally between the transmission line conductors and at a greater depth underground than at least one of the transmission line conductors to receive heated hydrocarbons from the hydrocarbon formation via gravity.