The electrolysis of black liquor (BL) has emerged as a new form to valorize this byproduct from the pulp and paper industry. BL electrolysis produces a green fuel, hydrogen, and lignin, a high added-value compound. In opposition to water electrolysis, a symmetric process with two different gases produced at the electrodes, hydrogen and oxygen, BL electrolysis is seen as an asymmetric process, as hydrogen is the only gas generated (at the cathode), while solid lignin is electrodeposited at the anode. The present work intended to develop a model in Aspen Plus® to simulate BL electrolysis and consequently evaluate the performance of the BL electrolyzer. Aspen Plus® does not include a package for electrolyzers, so it was necessary to use the Aspen Custom Modeler (ACM) tool. The model developed in ACM is valid for the following conditions: nickel electrodes with 2 cm interelectrode distance, cell voltage between 1.5 V and 2.0 V, and temperatures between 25 and 35 °C for batch operation and 25 and 65 °C for continuous operation. Sensitivity analysis demonstrated that the optimum working temperature for batch operation is 35 °C, whereas it is 45 °C for continuous operation. An economic analysis was carried out, calculating the real gross profit (RGP) for the process and the electricity cost. A 2 kW electrolyzer with 80 cells and an active area of 0.3 m2 was simulated. For the electrolyzer in batch operation, RGP values of 1056 €/year and 1867 €/year for the worst and the best scenario were obtained, respectively, and the electricity cost was 1431 €/year. For continuous operation, the RGP values were 2064 €/year and 3648 €/year for the worst and best scenario, respectively, and 2967 €/year for the electricity costs.