Kindly note that sometimes insulation is provided for process and quality control reasons, as well as for personel protection (45 deg C for metals, and 60 deg C for canvas), and not only as a heat-saving approach.
I agree with Art Montemayor in that there are various economic models to estimate the optimum economic thickness of insulation based on heat lost or saved. The estimated thicknesses using these methods are totally dependent on the input data with their inherent variability and uncertainty.
Companies I knew, doing their own (not contracted for) insulation used approaches based on cash flow present worth estimates, or payback periods. Then made tables for designers to use according to the type of insulation, the pipe diameter and the fluid temperature, considering that commercial insulation was sold in 1/2-in. increments.
Many plant owners treat insulation as another investment in equipment. But this is not entirely true, or even reasonable, since savings from insulation are quite predictable and risk-free, whereas return on investment in plant or added production is surely not so predictable.
Then there is the "engineering" -in contrast to the "accountancy"- approach based on an
acceptable heat loss thickness, as asked by skvishwa. This is based on the heat losses estimated using added insulation thicknesses compared with the bare pipe, expressed as %.
It is noted that incremental thicknesses of insulation show diminishing returns below a 3% heat-loss rate. Until the end of the 20th century the
reasonable heat-loss rate was 3% to 5%.
So, nowadays what would the optimum be, 2%, 1.5%? I couldn't tell in view of the high energy costs of these days. Probably the model using the minimum amount resulting from adding the cost of heat lost plus the cost of insulation (installation and maintenance), both per linear foot of pipe, with a reasonably (probably shorter than the envisaged plant life) amortization period, would be a safer approach.
I know this is a debatable item, and I'appreciate any comments that colleagues may have.