Circuital modeling from electronic devices to oil production

In this paper we discuss the general topic of deriving equivalent circuits from the differential equations that determine the response of a given system. This is the procedure which is normally followed in modeling solid state devices, where the distributed parameters of the equivalent circuits are derived from the solutions to Laplace or Poisson equations. We apply the procedure to the case of the thermal excitation-through electrical heaters-of heavy oil reservoirs. The circuital visualization of this process provides insights which are extremely helpful in understanding the system response.