Methods and apparatus for measuring the erodability of drilling fluid deposits

A method of measuring the erodability of drilling fluid deposits formed on the walls of a well bore containing a drilling fluid and penetrating one or more permeable formations comprising the steps of:

• (a) circulating said drilling fluid through a test apparatus which simulates a permeable section of a well bore at a selected flow rate and for a time period whereby a pressure drop of said drilling fluid through said permeable section stabilizes;
• (b) terminating the circulation of said drilling fluid and maintaining said drilling fluid in a static state in said permeable section at a pressure and for a time period such that drilling fluid deposits comprised of filter cake and gelled drilling fluid are formed therein;
• (c) circulating said drilling fluid through said permeable section at three or more progressively increasing flow rates and maintaining each of said flow rates for a time period whereby the pressure drop of said drilling fluid through said permeable section stabilizes while measuring said flow rate, said pressure drop, the viscosity, the temperature and the density of said drilling fluid;
• (d) determining the stabilized pressure drop measured in step (c) below which no significant erosion of said deposits takes place by calculating the well bore size equivalents to said stabilized pressure drops measured in step (c) based on the relationship:
• ##EQU12## wherein:
• D.sub.e is the equivalent diameter through which the drilling fluid is flowing,
• f is the friction factor of the drilling fluid based on the drilling fluid viscosity and temperature,
• L is the length of the flowing area,
• V is the velocity of the drilling fluid,
• .rho. is the drilling fluid density,
• g.sub.c is the gravitational constant,
• .DELTA.p is the stabilized pressure drop across the length of the flowing area (L),
• where the above variables are in consistent units, and
• comparing said well bore size equivalents to determine the pressure drop below which no significant erosion takes place;
• (e) determining the minimum shear stress required to erode said drilling fluid deposits corresponding to the pressure drop below which no significant erosion takes place determined in step (d) based on the relationship:
• ##EQU13## wherein:
• .tau..sub.w is the minimum shear stress at the wall required to erode said drilling fluid deposits,
• D.sub.e is the equivalent diameter through which the drilling fluid is flowing,
• .DELTA.p.sub.bne is the pressure drop across the length of the flowing area (L) below which no significant erosion takes place, and
• L is the length of the flowing area,
• where the above variables are in consistent units, and
• (f) calculating the erodability of the drilling fluid deposits formed by said drilling fluid based on the relationship:
• ##EQU14## wherein:
• E.sub.df is the erodability of the drilling fluid deposits,
• .tau..sub.w is the minimum shear stress at the wall required to erode said drilling fluid deposits,
• A is 3.times.10.sup.-20 joules,
• a is the average radius of particles in the drilling fluid deposits, and
• h is the separation distance between particle surfaces,
• where the above variables are in consistent units.

Apparatus for measuring the minimum shear stress required for eroding drilling fluid deposits formed on the walls of a well bore containing a drilling fluid and penetrating one or more permeable formations comprising:

• means for simulating a permeable subterranean formation disposed within a container;
• a first pipe simulating a well bore positioned within said container and within said means simulating a permeable formation having a closed lower end, a plurality of openings in the sides thereof and an upper end;
• a second pipe positioned concentrically within said first pipe simulating a conduit to be cemented within a well bore, said second pipe having an open lower end and an upper end;
• means for circulating a drilling fluid at a selected flow rate downwardly through the interior of said second pipe and upwardly through the annulus between said first and second pipes connected to the upper ends of said first and second pipes;
• means for measuring the flow rate of drilling fluid circulating through said first and second pipes connected to said means for circulating said drilling fluid;
• means for measuring the pressure drop of said drilling fluid through the annulus between said first and second pipes connected thereto;
• means for measuring the temperature of said drilling fluid flowing through said first and second pipes connected to said pipes;
• means for selectively withdrawing samples of circulating drilling fluid for measuring the viscosity and density thereof connected to said drilling fluid circulating means;
• and
• means for selectively applying pressure to said drilling fluid contained within said first and second pipes when said drilling fluid is not being circulated connected to said first and second pipes.