Idealized adsorption process

EXERGY ANALYSIS OF ADSORPTION-BASED CARBON CAPTURE SYSTEMS

A. S. Calbry-Muzyka, S. Sweeney Smith, A. Brandt, and C. F. Edwards ∙ ∙ GCEP Symposium 2013

MOTIVATION • With the world continuing to rely on a significant use of fossil

fuels for electricity generation and other large-scale industrial processes, the capture and subsequent storage of atmospheric CO2 emissions will likely be a necessary part of future climate change abatement strategies.

• Many technologies have been and are being proposed to effectively separate and capture CO2 emitted from these processes. This leads to two key questions: How do these varied technologies compare against each other? How does each compare to its thermodynamic limits of operation (how well is it performing)?

• Performing an exergy analysis is a way to analyze systems while (1) tracking energy flows and transformations; (2) tracking entropy generation, which leads to system inefficiencies; and (3) acknowledging that the system’s outputs must be returned to the environment. It directly establishes how the system is performing relative to its own absolute thermodynamic limits, while interacting with a known environmental state.

• Because exergy is a thermodynamic quantity (like internal energy or entropy) that can be defined for any substance, it provides a cross-comparable metric even for wildly different systems. For example, we could directly compare the operation of an amine-based CO2 scrubber on a coal plant to a mineral carbonation process on a cement plant.

PROBLEM STATEMENT

• In order to perform an exergy analysis, we need to be able to account for the accumulation of exergy in system devices or process steps.

• In batch-cycle adsorption processes in particular, accounting for accumulation of an adsorbed phase in the column is critical.

METHOD DEVELOPMENT: EXERGY OF THE ADSORBED PHASE

METHOD APPLICATION: EXERGY OF CO2 ADSORBED ON ZEOLITE-13X We can demonstrate our derived expression for the exergy of the adsorbed phase by applying it to any

CONCLUSIONS • We have developed a general expression for the exergy of the adsorbed

phase, based on known thermodynamic properties.

• This expression is the basis for performing an exergy analysis of adsorption-based carbon capture systems. Analyzing the exergy destroyed in these processes will tell us how well these systems are performing relative to absolute thermodynamic limits.

• Although it was developed for the analysis of carbon capture systems, the expression for the exergy of the adsorbed phase can be used to perform exergy analyses of any adsorption-based system (air separation, hydrogen purification, gas dehumidification, etc.). This generality could therefore be useful across a wide range of applications.

• As an example, we have applied this general expression to the specific case of CO2 adsorbed on zeolite 13X, using a dual-site Langmuir adsorption isotherm.

NEXT STEPS • Currently, we are using our derived exergy expression to perform the

exergy analysis of a pressure-swing adsorption CO2 capture cycle (thanks to Reza Haghpanah).

• An eventual goal would be to use exergy efficiency as the objective for the optimization of adsorption systems for carbon capture.

BACKGROUND: THERMODYNAMIC PROPERTIES OF ADSORBED PHASES

• The boundaries of the adsorbed phase (as separate from gas or solid) were originally defined by Gibbs. Although in reality the particle number density transitions smoothly between phases, he defined a sharp interface between gas and solid phases, where all properties of the adsorbed phase would exist as a delta function on that interface. This allowed clear definitions with no loss of thermodynamic information. This is still the basis for void fraction measurements.

• Often, the additional free energy that a surface phase has (as a result of having an additional energy storage mode) is referred to in terms of a spreading pressure Π and area A. Myers 2002 argues that for porous sorbents, A is undefined, so this free energy term is better represented by a surface potential, Φ.

From D’Alessandro et al., 2010.

Reality of phase transitions Gibbs’ model Properties of the adsorbed phase from Myers 2002. The tilde

indicates that the property is defined per unit mass of sorbent.

DERIVATION: EXERGY OF ADSORBED PHASES

• We start with a system at Tsys and Psys, that is composed of a mass Ms of sorbent, moles Ng

i,sys of all species i in the gas phase, in equilibrium with moles Na

i,sys of species i adsorbed on the sorbent.

• By allowing transfers of heat (δQ), boundary work (δWb = P0dV), and species i (δNi), the system comes into equilibrium with an environment at T0 and P0, with chemical potentials μi,0 of species i (this is known as the dead state). We extract useful work δW during this process. Exergy is defined to be the maximum possible value of this useful work.

• By combining the balance equations for energy, entropy, and the amount of species i, we can arrive at an expression for the useful work δW : which we can maximize by imposing reversibility, then integrate from the system state to the dead state:

• This is the exergy of the total combined system, with gas, sorbent, and adsorbed phases. We can expand each extensive quantity (where Z represents any extensive quantity):

• We can also substitute the Euler equation for each of the gas and the adsorbed phases at the dead state:

• After assuming an incompressible, non-reactive solid (same assumptions as Myers), we arrive at a general form for the total system exergy:

geni

NS

i

i

ttt STNddSTdVPdUW 00,00

t

0,

t

0,

t

0

t

0

t

0

t

0

t

0

t

max exergy ii

i

i

tt NNSSTVVPUUXW

asgt ZZZZ

• But we wanted the exergy of the adsorbed phase alone, so we need to subtract the exergy of the gas and of the solid sorbent, defined as:

• Subtracting these from the total system exergy, we arrive at a general expression for the exergy of an adsorbed phase on a sorbent mass Ms:

• Up to this point, we have assumed that the species i are only species present in the fully equilibrated environment. We can extend the exergy expression to include chemical species j that are not present in the environment, but would react to form environmental species (derivation not shown here): where ν’s are stoichiometric coefficients for the chemical reaction which is the generalized form of a chemical reaction that forms environmental species i from non-environmental species j, e.g.:

. 0,,0,00

00

sa

sysi

g

sysi

i

i

sa

sys

s

sys

g

sys

g

sys

sa

sys

s

sys

g

sys

t

MNNSSSST

VPUUUUX

0 :phase Gas 0,0,00000 i

g

ii

ggg NVPSTU

00,0,000 :2002) Myers (from phase Adsorbed s

i

a

ii

aa MNSTU

g

sysi

i

i

g

sys

g

sys

g

sys

g NSTVPUX ,0,00exergy phase Gas

ss

sys

ss

sys

s SSTUUX 000exergy reactive)-non (incompr.,Sorbent

. 0,0,0

sa

sysi

i

i

a

sys

a

sys

a MΦNSTUX

.0,0,,0,0 MΦNNSTUX sa

sysj

ji

i

a

sysi

i

i

a

sys

a

sys

a

j

ij

i

iijjj AA

not). isA l;envt' are D C, B, (where dDcCbBaA

i ii

iisati

i ii

iisati

i

PeRT

PeN

PeRT

PeNN

RTiU

RTiU

RTiU

RTiU

0,

0,,

0,

0,,

~~~

known adsorbed phase loading form. The plots below are made using data from Krishnamurthy et al. 2012, assuming a dual-site Langmuir form:

A substance that adsorbs strongly onto a solid accumulates on that solid’s surface at a high particle density relative to the gas phase of that substance. Some substances adsorb more strongly than others; this is what drives separation processes.

• The only previous direct definition of the exergy of an adsorbed substance in terms of known thermodynamic properties (Kearns & Webley 2003) did not account for a chemical component to exergy, and assumed a linear form of an adsorption isotherm, both valid assumptions but only under very specific circumstances.

• To complete an exergy analysis of adsorption-based CO2 capture systems, there is a need for a completely general, rigorously derived expression for the exergy of an adsorbed phase.