Analytic formula of steady-state temperature field for the oil pipeline and refined oil product pipeline laid in one ditch

For the pipelines served as crude oil and refined oil product laid in one ditch, soil temperature field of hot crude oil pipeline is influenced by the cool refined oil product pipeline. Analytic formula of steady-state soil temperature field is deduced by conformal mapping. As an illustration, the static temperature field of the pipelines laid in one ditch in China is respectively calculated by analytic formula and numerical simulation. The result obtained by the numerical simulation is higher than the result calculated by the analytic formula within 2.5 meters of the pipe. Outside of that range, the result computed by the analytic formula is higher than the result obtained by numerical simulation. The relative error by using these two methods is less than 5%. So the analytic formula is validated. The error is caused by the two reasons as follows: in the analytic method, the first reason is that the computed domain for different methods is different, the natural soil temperature is regarded as not influenced by the heated pipeline, i.e., the computed domain is not bounded; While in the numerical simulation, the computed domain is bounded. The second reason is that some parameters are simplify chosen as their mean value during the formula derivation process.