Dynamic simulation of flash drums using rigorous physical property calculations

Abstract

-The dynamics of flash drums is simulated using a formulation adequate for phase modeling with equations of state (EOS). The energy and mass balances are written as differential equations for the internal energy and the number of moles of each species. The algebraic equations of the model, solved at each time step, are those of a flash with specified internal energy, volume and mole numbers (UVN flash). A new aspect of our dynamic simulations is the use of direct iterations in phase volumes (instead of pressure) for solving the algebraic equations. It was also found that an iterative procedure previously suggested in the literature for UVN flashes becomes unreliable close to phase boundaries and a new alternative is proposed. Another unusual aspect of this work is that the model expressions, including the physical properties and their analytical derivatives, were quickly implemented using computer algebra.

Differential-Algebraic Approach to Dynamic Simulations of Flash Drums with Rigorous Evaluation of Physical Properties

“…A significant decrease on computational cost has been verified using this procedure in comparison with previous work [6], in which all the algebraic equations were solved separately in every step. Using PSIDE, the algebraic constraints were solved together with the discretized form of the differential equations by a very efficient Newton process.…”

“…Differentiation of function Q F with respect to the independent variables in a system with p phases gives [6]:…”

“…This example deals with a mixture of ethane(1), propene(2), propane(3), n-butane(4), isobutane(5) and n-pentane(6) whose composition is in the range of liquefied petroleum gases (LPG) [6]. Table 2 presents the initial conditions, in which a liquid and a vapor phase are in equilibrium inside the drum.…”

“…The direct use of temperature, phase volumes, and mole number of each component in each phase as iteration variables has been suggested [4]. This approach was adopted [6] in the development of a procedure to simulate flash drum dynamics, in which a conventional integrator for ordinary differential equations was used and the algebraic equations of the model were solved separately in every step. Attempts to solve the system directly using a procedure available in MATLAB for DAE (ode15s solver) were unsuccessful [6].…”

“…This approach was adopted [6] in the development of a procedure to simulate flash drum dynamics, in which a conventional integrator for ordinary differential equations was used and the algebraic equations of the model were solved separately in every step. Attempts to solve the system directly using a procedure available in MATLAB for DAE (ode15s solver) were unsuccessful [6]. The most likely reason is that the ode15s integrator can only solve linearly implicit ODE systems of general form: M(t) · y' = f(t, y) with a mass matrix M(t) that is non-singular, (usually) sparse and exclusively time dependent [7].…”