The urgency of taking actions against climate crisis is unprecedented. The human-produced CO2 is the largest contributor to global warming, which drives the climate change. Many countries around the world have committed to net-zero greenhouse gas emissions in the next coming decades. Power-to-X (PtX) technologies in combination with carbon capture technologies might contribute to a carbon-neutral future, since they can convert electricity and captured carbon to synthetic gases (e.g. hydrogen, methane), chemicals (e.g. propylene, ethylene) and liquids (e.g. methanol). This thesis aims to research the techno-economic potential of a system that is able to produce methanol at industrial scale via a PtX scheme, which is coupled with carbon capture technologies. The system of this thesis consists mainly of PV panels, an alkaline water electrolyzer, a polymer electrolyte membrane (PEM) CO2 electrolyzer and a single-stage Lurgi quasi-isothermal methanol reactor. The feedstocks for this system are water and carbon dioxide (captured from the flue gases of a cement plant). The whole production process of this system has been designed and modelled in such a way, that both electrolyzers can follow the intermittent power supply from the PV panels. The electrolyzer's dynamic operation is controlled by a deterministic control logic, which takes into account the variable energy efficiencies of the electrolyzers and the intermittent power output of the PVs. Moreover, it has been decided that the methanol synthesis is based on the CO2 hydrogenation process, which converts syngas (i.e. a mixture of CO, CO2 and H2) into methanol with the use of the methanol reactor. Hydrogen is produced by the water electrolyzer and the captured CO2 is reduced to CO by the CO2 electrolyzer. As far as the sizing and production results are concerned, the system is able to produce 3.999 kT of methanol per year, consuming 2,147 tons of CO2 per year and requiring an energy input of 30.3 GWh/year. The installed peak PV power is equal to 18 MWp and 99.60% of their energy yield is exploited by the system (the rest is dumped). Due to the implemented control logic, the operating energy efficiency range for the CO2 electrolyzer is 45.07-55.32% and for the H2O electrolyzer is 75.83-81.71%. In terms of economic analysis, the proposed system requires a total capital investment (TCI) of 195.7 M€ and its operational expenditures are equal to almost 2 M€ per year. The performed cash flow analysis showed that the system has an annual gross profit of € 855,535 per year. Despite the yearly profit, it was found that the system's net present value (NPV) is negative and equal to -179.5 M€ at the end of its lifetime (i.e. 20 years). Also, the levelized cost of methanol (LCOM) was found to be equal to 4.44 €/kg, which is almost 10 times higher than the current market price of methanol. Therefore, such an investment would be economically unfeasible, despite its environmental benefit, because it would result in a net loss of capital.