as diameter of bit increses for same depth torque increases. but readable torque would only be observed in PDC bit. with increase in RPM torque increases. ROP is a matter of formation. but in general with PDC bit ROP increases torque decreases. for thrust, RPM has no role, but if ROP and bit diameter increases due to more cutting generation thrust(Stand pipe pressure) increases. this concept applies to normal drilling as well as core drilling operation. i think it would be helpful.

If you take the MSE approach as a starting point I would advise referencing:

Teale, The Concept of Specific Energy in Rock Drilling, Int._J._Rock_Mech._Mining_Sci (1965) pages 57-73

Pessier, Fear, Quantifying Common Drilling Problems With Mechanical Specific Energy and Bit-Specific Coefficient of Sliding Friction, SPE-24584, Presented at the 67th SPE ATCE, 4-7 Oct 1992

From this, simply speaking, torque will depend on the weight on bit and relative aggression of the bit in use (Bit-Specific Coefficient of Sliding Friction, μ), such that:

T = (μ * Db * WOB) / 36

Where: T = Torque (ft.lbf)

μ = Bit specific coefficent of sliding friction

Db = Bit Diameter (in.)

WOB = Weight on Bit (lb)

But this relationship was defined for conventional rock & PDC bits not necessarily core heads.

Similarly for a drilling system without dysfunction the Thrust can be derived from:

ROP = (13.33μN)/(Db((MSE/WOB*EFFm)-(1/Ab))

Where:

N = rpm

MSE = Mechanical Specific Energy required to drill rock - an analogy for drilling strength of the formation

EFFm = MSE mechanical bit efficiency (~0.25-0.40)

Ab = Bit Area

Both of these equations can be used to identify the bit specific parameter relationships, but in the real world consideration will also have to be given to the drilling system as a whole. Considerations need to include the bottom hole assembly, drilling depth, available weight, etc. With a diamond impreg corehead where very little torque is generated by cutting the main component of torque may well be the drilling string and BHA itself as a result of the sideforces encountered by the string.

Kaushal said it best . However if the increased penetration is due to a change in rock type during drilling and not in the parameters controlled by the driller, the torque should decrease.