One function of cement is to support casing string and the shear strength of cement holds casing string once cement is set. You may think about other load supporting casing as compressive loading at coupling areas or thermal movement. They are the part of the supporting force as well but the most support is from the cement shear strength.
(Diagram above shows how shear strength of cement supports casing string)
We don’t normally measure shear strength of cement but we can apply knowledge from Civil engineer to estimate the shear strength from the compressive strength. Generally, cement has the shear strength approximately 1/12 of compressive strength. For instant, if the cement 1000 psi compressive strength, its shear strength is 83.3 (1000 x 1/12) psi.
Let’s take a look into the detailed calculation for more understanding.
The information given is listed below
Casing 9-5/8”, 40 ppf (pound per foot), ID of casing = 8.835”
Casing is set at 3,200’MD/3,000’TVD
Top of cement at 600’MD/550’TVD
Previous casing shoe (13-3/8”) = 1000’MD/900TVD
(The diagram shows all figures as per the data)
We will use the pressure and force concept (Force = Pressure x Area).
1. The outer surface area of casing covered with cement is equal to circumference of casing multiplied by length of cement covering casing.
Area = Π x D x L
Area in square inch.
Π (called pi) =22/7
D is diameter in inch.
L is length of cement in inch
Area = Π x 9.625 x (2600 x 12)
Area = 943,420 square inch.
2. Casing weight = weight in ppf x total length of casing
Casing weight = 40 x 3200 = 128,000 lb
3. Shear force is required to support whole weight of casing
Shear strength (lb/square inch) = Casing weight ÷ Area of casing covered by cement
Shear strength (psi) = 128,000 ÷ 943,420 = 0.136 psi
We can estimate the compressive strength of cement based on 1/12 figure.
Shear Strength ÷ Compressive Strength =1/12
Compressive strength = 12 x 0.136 = 1.63 psi
The figure tells us that you need only 1.63 psi compressive strength to support whole casing string.
Ps, This is rough estimation without any consideration regarding complex load, thermal movement, etc.
Ref books: Cementing Technology Books