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Multi-stage artificial neural network structure-based optimization of geothermal energy powered Kalina cycle

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Abstract

In this study, the geothermal energy powered Kalina cycle (GEP-KC) was optimized by using a multi-stage artificial neural network (ANN) analysis. The ANN model was basically composed of two stages. The first stage has one network, and the second stage consists of three networks in this ANN model. The 365 GEP-KCs were designed for four variable parameters. These designs were analytically analyzed by means of thermodynamic and economic analysis. The obtained data were used for modeling of multi-stage ANN structure. This multi-stage ANN model was designed with the aim of maximizing net present value (NPV). Turbine inlet pressure, geothermal water outlet temperature at evaporator, condenser pressure and ammonia mass fraction were input parameters of the multi-stage ANN model. Energy efficiency and exergy efficiency of the GEP-KC were outputs of the first stage, and the NPV of the GEP-KC was the output of the third network of the second stage. The most suitable network structure for the optimization of GEP-KC was performed by using the Levenberg–Marquardt variant of back-propagation learning algorithm for multi-stage ANN. The cov, MPE, RMSE and R2 values of multi-stage ANN were calculated as 2.558308, 1.077997189, 1.777658128 and 0.994693, respectively, for NPV. The calculated masses and biases of this structure were used to determine the optimum operating parameters of GEP-KC. The analytical findings of the NPV, energy and exergy efficiencies of the optimum GEP-KC model were, respectively, determined as 113.0732 M$, 6.7285% and 46.8701% in a high accuracy with the ANN results.

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Abbreviations

ANN:

Artificial neural network

b :

Bias

C :

Cost ($)

c :

Specific heat (kJ kg−1 K−1)

cov:

Coefficient of variation

CEPCI:

Chemical Engineering Plant Cost Index

\(\dot{E}x\) :

Exergy rate (kW)

GEP-KC:

Geothermal energy powered Kalina cycle

h :

Specific enthalpy (kJ kg−1)

\(\dot{m}\) :

Mass flow (kg s−1)

MPE:

Mean percentage error

NPV:

Net present value

\(\dot{Q}\) :

Heat power (W)

R 2 :

Percentage of absolute change

RMSE:

Error of the square root

T :

Temperature (K)

\(\dot{W}\) :

Power (W)

ε :

Exergy efficiency (%)

α :

Ammonia mass fraction (%)

ψ :

Specific exergy (kJ kg−1)

η :

Energy efficiency (%)

b:

Benefit

con:

Condenser

ch:

Chemical

cw:

Cooling water

elec:

Electricity

eva:

Evaporator

g:

Generator

gf:

Geothermal fluid

i:

Interest rate

ic:

Investment cost

j:

Discount rate

l:

Liquid

m,i:

Inlet mass flow

m,o:

Outlet mass flow

mo:

Maintenance and operating

ol:

Life time of system

ncf:

Net cash flow

p:

Pump

ph:

Physical

r:

Recuperator

sc:

Salvage cost

sys:

System

t:

Time (year)

tr:

Turbine

0:

Dead state

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  1. Mechanical Engineering Department, Engineering Faculty, Bilecik Seyh Edebali University, Bilecik, Turkey

    Merve Senturk Acar

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Senturk Acar, M. Multi-stage artificial neural network structure-based optimization of geothermal energy powered Kalina cycle. J Therm Anal Calorim 145, 829–849 (2021). https://doi.org/10.1007/s10973-020-10125-y

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