| Summary: | In this work, we apply a computational diffusion model based on Fick’s laws to study the generation and transport of methane (CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula>) during the production of a cross-linked polyethylene (XLPE) insulated cable. The model takes into account the heating process in a curing tube where most of the cross-linking reaction occurs and the subsequent two-stage cooling process, with water and air as the cooling media. For the calculation of CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> generation, the model considers the effect of temperature on the cross-linking reaction selectivity. The cross-linking reaction selectivity is a measure of the preference of cumyloxy to proceed either with a hydrogen abstraction reaction, which produces cumyl alcohol, or with a <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-scission reaction, which produces acetophenone and CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula>. The simulation results show that, during cable production, a significant amount of CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> is generated in the XLPE layer, which diffuses out of the cable and into the conductor part of the cable. Therefore, the diffusion pattern becomes a non-uniform radial distribution of CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> at the cable take-up point, which corresponds well with existing experimental data. Using the model, we perform a series of parametric studies to determine the effect of the cable production conditions, such as the curing temperature, line speed, and cooling water flow rate, on CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> generation and transport during cable production. The results show that the curing temperature has the largest impact on the amount of CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> generated and its distribution within the cable. We found that under similar curing and cooling conditions, varying the line speed induces a notable effect on the CH<inline-formula> <math display="inline"> <semantics> <msub> <mrow></mrow> <mn>4</mn> </msub> </semantics> </math> </inline-formula> transport within the cable, while the cooling water flow rate had no significant impact.
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