Methods and apparatuses for deriving wellbore fluid sag from thermal conductivity measurements

A method comprising:

• measuring a thermal conductivity of a drilling fluid as a function of time at two or more locations along a height of a first vessel containing the drilling fluid that comprises particles dispersed in the drilling fluid;
• measuring a thermal conductivity of the drilling fluid as a function of time at two or more locations along a height of a second vessel containing the drilling fluid, wherein a condition of the drilling fluid contained in the first and second vessels, a geometry of the first and second vessels, or both are different;
• calculating a sag rate of the drilling fluid based on the thermal conductivity as a function of time at the two or more locations in the first vessel and the second vessel;
• and
• adjusting an operational parameter of a wellbore operation using the wellbore fluid based on the sag rate of the drilling fluid.

A system comprising:

• a drilling platform operably coupled to a drill string extending into a wellbore;
• a drill bit attached to the distal end of the drill string;
• a pump operably connected to the drill string for circulating a drilling fluid through the drill string to an annulus defined by the drill string and the wellbore to a fluid processing unit and to a retention pit;
• and
• one or more thermal conductivity measurement apparatuses in fluid communication with the retention pit, the one or more thermal conductivity measurement apparatuses comprising:
• a first vessel with two or more thermal conductivity sensors disposed therein and located within the first vessel at two or more locations along a height of the first vessel, and a second vessel with two or more thermal conductivity sensors disposed therein and located within the second vessel at two or more locations along a height of the second vessel, wherein a condition of the drilling fluid contained in the first and second vessels, a geometry of the first and second vessels, or both are different.