In a drilling process speed, bit thrust and penetration are monitored. Data stored in a data base relating rotational speed and thrust as adjustable variables is correlated with data on the penetration rate as controlled parameter to produce a matrix to enable prediction of penetration rate to be expected at known thrust and rotational rates. Likewise a similar matrix may be constructed for relating wear rate to adjustable variables for example speed and thrust. The parameters predicted from these variables at various values for the speed and thrust are used to construct a further matrix relating bit penetration and bit wear rates with cost per unit distance drilled and this third matrix searched for minimum cost. From the first two matrices rotation rate of the drill bit and thrust applied to the drill bit are adjusted to give a predicted penetration rate for minimum cost and the drill bit is operated at these conditions. All conditions are monitored and the information used to recalculate the various matrices to define the process.
