A risk based heat exchanger analysis subject to fouling: Part II: Economics of heat exchangers cleaning

Fouling is one of the major uncertainties associated with the operation and maintenance of heat exchangers in the power and process industries. The decision regarding periodic maintenance (cleaning) to meet the target performance level is generally based on both thermal and economic behavior of the process. In this paper, we present a cost model, which includes the risk level and the scatter parameter of random fouling growth models. Four models, namely linear, power law, falling rate and asymptotic fouling growth are integrated in the model. The non-dimensional cost function Γ as a function of reduced time t/M is examined by considering the dimensionless cost parameters γ₁, γ₂ and γ₃, representing additional fuel cost, antifoulant cost and miscellaneous costs, respectively. These dimensionless cost elements are examined for a heat exchanger that is used in a crude oil preheat train. The results are presented in terms of risk level p and scatter parameter α for the underlying fouling models. Furthermore, a simplified closed-form solution is also obtained to study the optimal cycle time, representing minimum cost of operation and maintenance of heat exchangers.A =External heat exchanger surface (m²)C_A =Cost of additional fuel consumption ($)C_A′ =Cost of additional fuel consumption per day ($.day^-1)C_H =Cost of fuel consumption ($)C_S =Cost of steam consumption ($)C_AF =Cost of antifoulant ($)C_AF′ =Cost of antifoulant per day ($ day^-1)C_C =Cost of heat exchanger cleaning ($)C_C′ =Cost of heat exchanger cleaning per day ($ day^-1)C_M =Miscellaneous cost ($)C_T =Total cost ($)ΔH =Change in enthalpy (kJ kg^-1)k_H =Cost of additional fuel consumed ($ W^-1 day^-1)k_S =Cost of additional steam used ($ .W^-1 day^-1)ṁ =Mass flow rate (kg h^-1)NTU =Number of transfer unitsp =Risk level, p=P(R_f(t)≤R_f,c)Q̇ =Heat transfer rate (W or MW)R_f =Fouling resistance (m² K W^-1)R^*_f =Asymptotic fouling resistance (m² K W^-1)t =Time (days)t_down =Down time (days)T =Temperature (K)T₀ =Cycle time (days)T^*₀ =Optimum cycle time (days)U =Overall heat-transfer coefficient (W m^-2 K^-1)α =Scatter parameter for the fouling modelγ₁ =Dimensionless fuel costγ₂ =Dimensionless antifoulant costγ₃ =Dimensionless miscellaneous costΓ =Dimensionless total costε =Heat exchanger effectivenessε(0) =Effectiveness of the heat exchanger at time t=0Φ( ) =Standard normal cumulative distribution function