(664h) Monte Carlo method to calculate the lifetime efficiency of a solar reactor for reduction of zinc oxyde

Monte Carlo method to calculate

the lifetime efficiency of a solar
reactor for reduction
of zinc oxyde

O. Farges, J.J.   B´ezian,
and M. El Hafi

Universit´e F´ed´erale de Toulouse Midi-Pyr´en´ees, Mines Albi, UMR CNRS 5302, Centre Rapsodee, Campus Jarlard,

f-81013 Albi ct cedex 09, France

Concentrated solar plant are ommonly
 used
to produce electricity through
ther- modynamic  cycles (Gemasolar Power Plant, Ivanpah Solar
Power Plant, ...) and can
also be seen as an alternative to fossil fuel-based methods for H2   generation
[5]. High temperature solar
thermochemical processes make  use of concentrated solar energy to realize metal oxydes reduction.
These processes can be considered as a solar energy
storage :  products may be stored and transported (H2  
 in this case). Among all metal oxydes
reduction, the zinc oxyde to zinc (ZnO/Zn) redox reactions are particularly attractive as the first part of a two step water splitting cycle (eqs. (1a) and (1b)).

As presented on fig. 1, a thermochemical reactor R, placed
at the top of a solar
tower receives concentrated solar
energy emited from the sun S and
reflected by heliostats H. Thus, the reactor, feeded
with zinc oxyde, reaches high temperature, ie above 1400 K, to achieve reduction of zinc oxyde and to procude zinc Zn.

In
order to evaluate the performance of a thermochemical solar plant and to allow an optimally design
of both the reactor
and the whole facility  (heliostat field,

Figure 1: H2   solar production process

tower), numerical modelling of this process is required.
We
present here a Monte
Carlo algorithm that allows the estimation of the solar plant annual productivity
which is a non-linear problem. This non-linearity is
due to the coupling between
photon transport and the metal oxyde reduction reaction. The widespread opinion is
currently that “Monte Carlo methods are not generally effective for nonlinear
problems mainly because expectations
 are linear in character”[3]. This difficulty has been overcome by Dauchet who proposed a methodology in his Phd thesis [1].

To evaluate the quantity of interest,
ie the annual solar-to-chemical conversion
rate (ηr ), this Monte Carlo algorithm
firstly computes the instantaneous
power re- ceived at the entrance of the reactor
at an instant i, (Pth(X |i)). A Monte Carlo algorithm previously presented in [2] is used as a first step
of the proposed algo- rithm to evaluate this quantity.
 The random variable
Pth(X |i) is the contribution of optical paths X
|i to the thermal power collected at instant i. Then,
(Pth(X |i)), the expectation of this random
variable, is the instantaneous thermal
power col- lected at moment i. A part of the power received by the reactor, the instantaneous useful power Pu  = f (Pth(X |i)),  represents the efficient  energy used to achieve redox reactions
with  an instanteneaous reaction rate described by a zero-order
Arrhenius-type  law, strongly non-linear.  Integration over time of the instanta- neous conversion  rate leads to the lifetime
conversion rate (ηr ((Pth(X |i))))i 
 as presented eq. (2).

To treat this non-linearity, the Monte Carlo algorithm
is based on a Taylor expansion of (ηr ) around Pth0  > Pth (X ).  Independent  and equally distributed
optical-path random variables
Xj |I
are introduced  and the infinite power series
is statistically formulated thanks to the discrete
random variable J whose realization

j is the order of Taylor expansion. The Taylor expansion is stopped through
a Bernoulli process in order to decide whether
the algorithm stops
or continues without introducing a statistical bias.

Simulations are performed for the 1 MW reactor
presented in [4]. A simplified
model
of thermal losses is applied
and a comparison of the nominal performance
between results obtained with the Monte Carlo
algorithm and experimental results
presented in [4] are presented in table 1.
 The
difference between the measured and calculated results are due to the simplified thermal losses model as well as
uncertainties of the measurements.

We have shown in this work that we are able to calculate the efficiency by a Monte Carlo Method, of a solar chemical reactor
involving non-linearities between the
heat source and the products of the reaction.  A futur  work could be the
improvement of the heat loss model.

References

[1] J. Dauchet. Analyse radiative
des photobioracteurs.   PhD thesis, 2012.

[2] O. Farges, J. B´ezian, H. Bru, M. E. Hafi, R. Fournier, and C. Spiesser.
 Life- time integration using monte carlo methods when optimizing the design of concentrated solar power plants. Solar Energy, 113(0):57 – 62, 2015.

[3] M. H. Kalos and P. A. Whitlock.
 Monte Carlo Methods.
John Wiley &
Sons,

2008.

[4] L. Schunk,
 W.
Lipin´ski,  and A. Steinfeld.  Heat transfer model of a solar receiver-reactor for the thermal
dissociation of zno-experimental validation at

10 kw and scale-up
to 1 mw. Chemical Engineering Journal, 150(23):502 – 508,

2009.

[5]   A. Steinfeld. 
 Solar  thermochemical production of hydrogen--a review.  Solar

Energy, 78(5):603-615, 2005.