Wellbore cementing using a burst disc sub and reverse circulation

A method for cementing casing using reverse circulation for cementing with a burst disc as an internal barrier, the method comprising:

• injecting a casing fluid under pressure from a surface into a cavity of a casing string disposed in a wellbore using a pump and without a rig in place above an opening of the wellbore, wherein the casing string comprises a plurality of casing pipes and a burst disc sub that is coupled to and disposed between two of the plurality of casing pipes toward a distal end of the casing string, wherein the burst disc sub comprises a burst disc that is disposed within a cavity formed by the casing string, wherein the burst disc provides a physical barrier in the cavity dividing the cavity into an upper portion and a lower portion when the burst disc is in a default state, and wherein the burst disc breaks apart after the casing fluid under pressure contacts the burst disc to allow flow of the casing fluid from the upper portion to the lower portion of the cavity through the burst disc sub;
• and
• injecting, after the casing fluid flows out of an annulus formed between the casing string and a formation wall of the wellbore at the surface, using the pump, and without the rig in place above the opening of the wellbore, a cement slurry into the annulus at the surface until the cement slurry flows into the cavity at the distal end of the casing string.

A burst disc sub of a casing string, the burst disc sub comprising:

• a body having a wall that forms a cavity, wherein a first end of the body is configured to couple to a first casing pipe in the casing string, and wherein a second end of the body is configured to couple to a second casing pipe in the casing string;
• and
• a burst disc coupled to an inner surface of the wall, wherein the burst disc provides a physical barrier in the cavity dividing the cavity into an upper portion and a lower portion when the burst disc is in a default state, wherein the burst disc, when exposed to a force from above in the cavity exceeding a threshold value, is configured to break apart, wherein the force is configured to be applied using a pump and without a rig in place above an opening of a wellbore, and wherein the body is configured to allow for reverse flow of casing fluid therethrough when a cement slurry is injected down an annulus formed between the casing string and a formation wall of the wellbore using the pump and without the rig in place above the opening of the wellbore.