Biorreactor de fermentación con tasa estocástica de consumo

Fermentation bioreactor with stochastic consumption rate

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DOI:

https://doi.org/10.56754/0719-0646.2702.267

Abstract

We present a mathematical model to describe the operation of a bioreactor designed to reduce the substrate concentration in an aqueous solution via microbial activity. The system works in cycles: once the substrate concentration reaches a pre-established minimum level, the bioreactor empties and is reloaded with a new solution that restores the initial concentration. The study evaluates the system's operational viability, analyzing the length of the intervals between consecutive filling and emptying cycles. To achieve this, we establish mathematical bounds —defined by the model's parameters— guaranteeing the finiteness of these waiting times. In addition, we propose minimal conditions for the microbial consumption rate of the substrate, including stochastic perturbations to the metabolic process.

Resumen

Se presenta un modelo matemático para describir el funcionamiento de un biorreactor diseñado para reducir la concentración de sustrato en una solución acuosa mediante actividad microbiana. El sistema opera en ciclos: una vez que la concentración de sustrato alcanza un nivel mínimo preestablecido, el biorreactor se vacía y se recarga con una nueva solución que restaura la concentración inicial. El estudio se centra en evaluar la viabilidad operativa del sistema, analizando la duración de los intervalos entre ciclos consecutivos de vaciado y llenado. Para ello, se establecen cotas matemáticas —definidas por los parámetros del modelo— que garantizan la finitud de estos tiempos de espera. Además, se proponen condiciones mínimas para la tasa de consumo microbiano del sustrato, incorporando perturbaciones estocásticas en dicho proceso metabólico.

Keywords

Climate biomathematics , stochastic differential equation , bioreactor

Mathematics Subject Classification:

92B05 , 60H10
  • Pages: 267–283
  • Date Published: 2025-08-20
  • In Press

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Published

2025-08-20

How to Cite

[1]
R. Castro Santis, F. Córdova-Lepe, and A. B. Venegas, “Biorreactor de fermentación con tasa estocástica de consumo: Fermentation bioreactor with stochastic consumption rate”, CUBO, pp. 267–283, Aug. 2025.

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