Abstract: The present invention addresses to a system consisting of one or more pipes of low flexural rigidity (upper and intermediate extension pipes), connected to a thicker pipe section (lower extension pipe) by means of a varied cross-section pipe (conical profile) and further an adapter shaped like a helmet of a bend stiffener of a flexible riser, to enable, without operational losses, the use of rigid risers in Stationary Production Units (SPUs) initially designed to receive only flexible risers, therefore not having specific supports for rigid risers. The low flexural rigidity of the pipe is achieved through the correct selection of specific materials, preferably by using a titanium alloy that has a low modulus of elasticity and a high yield strength compared to steel.