Neutron imaging and molecular simulation of systems from methane and p-xylene

Abstract

Bulk properties of two-phase systems comprising methane and liquid p-xylene were derived experimentally using neutron imaging and theoretically predicted using molecular dynamics (MD). The measured and predicted methane diffusivity in the liquid, Henry’s law constant, apparent molar volume, and surface tension compared well within the experimentally studied conditions (273.15 to 303.15 K, ≤ 100 bar). Since MD is a physical model, extrapolations of the two-phase systems properties were performed for a broader temperature range (260 to 400 K, ≤ 100 bar). Moreover, the species diffusivities in single phases formed by infinitely diluted p-xylene in methane were predicted under conditions relevant to the methane liquefaction (90 to 290 K, 50 bar). The predicted p-xylene diffusivity in the supercritical methane was one order of magnitude higher than that calculated using Wilke–Chang and He–Yu correlations. This study provides novel experimental and MD-simulated characteristics for this industrially relevant system, for which intensive freeze-out formation from the supercritical methane is predicted.

Full text

Neutron imaging and molecular
simulation of systems from
methane and p-xylene
MartinMelčák1,4,Tereza-MarkétaDurďáková1,4,ŠtěpánTvrdý1,JonatanŠercl1,
JongMinLee2,PierreBoillat2,3,JanHeyda1,PavelTrtik2&OndřejVopička1
Bulkpropertiesoftwo-phasesystemscomprisingmethaneandliquidp-xylenewerederived
experimentallyusingneutronimagingandtheoreticallypredictedusingmoleculardynamics(MD).
Themeasuredandpredictedmethanediusivityintheliquid,Henry’slawconstant,apparentmolar
volume,andsurfacetensioncomparedwellwithintheexperimentallystudiedconditions(273.15
to303.15K,≤100bar).SinceMDisaphysicalmodel,extrapolationsofthetwo-phasesystems
propertieswereperformedforabroadertemperaturerange(260to400K,≤100bar).Moreover,the
speciesdiusivitiesinsinglephasesformedbyinnitelydilutedp-xyleneinmethanewerepredicted
underconditionsrelevanttothemethaneliquefaction(90to290K,50bar).Thepredictedp-xylene
diusivityinthesupercriticalmethanewasoneorderofmagnitudehigherthanthatcalculatedusing
Wilke–ChangandHe–Yucorrelations.ThisstudyprovidesnovelexperimentalandMD-simulated
characteristicsforthisindustriallyrelevantsystem,forwhichintensivefreeze-outformationfromthe
supercriticalmethaneispredicted.
Benzene, toluene, ethylbenzene, xylenes (BTEX) and water are impurities of natural gas relevant to the formation of
solids deposits (freeze-out) which can block devices in the processing and transportation1–5. Water and p-xylene are
the most severe volatile contaminants due to the high temperature of normal melting and hydrate formation. Solid
deposits are formed, for instance, at 172bar and 276K (methane hydrate6), or at 163bar and 278K (solid p-xylene)4.
In this work, the focus is on the p-xylene – methane system. In recent studies, equilibrium conditions for the solid p-
xylene formation have been determined experimentally and modelled using equations of states1,4. e intensity of the
p-xylene freeze-out formation on the cold spots is presumably controlled by its diusivity in the uid. Understanding
of not only the equilibrium condition but also freeze-out formation intensity can clearly contribute to the engineering
of the natural gas purication and liquefaction devices5.
As we have previously demonstrated, multiple system characteristics can be derived based on the recent one-
pot neutron imaging method7,8of observing pressurized gas absorption into liquids, namely methane diusivity,
solubility, apparent volume, and interfacial energy. Molecular dynamics (MD) simulation is a physical
model that enables the prediction of related system characteristics, such as diusivity9–11, surface excess and
interfacial energy12, partial molar volume13, and viscosity11,14,15. Clearly, the two independent methods (one
experimental and one simulation-based), each of which necessitates single-component data only in this work,
can be critically compared and complement each other. Besides that, MD can be used to study systems at wider
ranges of conditions, and to provide experimentally hardly accessible quantities, such as partial molar volume or
diusivity of the major component.
In this work, we provide new experimental data for the two-phase system of p-xylene with methane using
neutron imaging with focus on the region of supercooled liquid4. Based on the high dierence of neutron
cross-section between protium and deuterium16, neutron imaging enabled us to derive methane diusivity
in the liquid, apparent molar volume in the liquid, apparent Henry’s law constant, and surface tension from
each experiment – multiple parameters are determined in one pot. is method represents an alternative to
known chiey single-purpose methods, such as the pendant drop method17, capillarity measurements18,
methods based on sensing capillary waves19,20, and methods for the measurement of solubility, diusivity, and
density21–24. anks to low opacity of several engineering materials to neutrons, the neutron imaging is suited
for investigations of pressurized systems. As a complement, the MD simulation model can be extrapolated to
temperatures below and above the equilibrium condition of the solid p-xylene formation4, and was used for the
1Department of Physical Chemistry, University of Chemistry and Technology, Prague, Technická 5, 166 28 Prague
6, Czech Republic. 2Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen PSI,
Switzerland. 3Electrochemistry Laboratory, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland. 4Martin Melčák
and Tereza-Markéta Durďáková have contributed equally. email: pavel.trtik@psi.ch; ondrej.vopicka@vscht.cz
OPEN
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prediction of p-xylene and methane diusivity in supercritical and liquid methane at50bar and innite p-xylene
dilution. us, molecular-level models are used to predict the properties of highly supercooled liquids and uids
at industrially relevant conditions. Common predictive models for the diusivity in diluted liquids25,26and
supercritical uids26,27 are used for comparison.
Methods
Onepotneutronimaging
e neutron imaging experiments were conducted using a previously reported setup7,8 at the NEUTRA
beamline28 at Paul Scherrer Institut at the measuring position No.2 (L/D = 365). e setup contained a pair of
equivalent axially symmetric titanium measuring cells placed in a duralumin block maintained at a constant
temperature to within ± 0.1 °C using a Julabo F12-MA water circulator and sensed to within ± 0.1K using
a thermometer (Pt100, Greissinger GMH 3710), pressure was sensed using a transducer (Omega PXM409-
100BAV). e cells were rinsed with acetone, vacuumed (< 0.01Pa,Leybold D4B), and twice washed with fresh
sample liquid prior to the lling. e cells were lled with the same liquid (p-C8D10, Table1) thus providing two
repeats for the measurement at each conditions. MIDI-box detector system using a30µm-thick Gd2O2S:Tb
scintillator screen(RC-Tritec AG, Teufen, Switzerland) and a sCMOS camera (Andor Neo) tted with a100-
mm objective (Zeiss Makro-Planar) were used, images of 2560(W) × 2160 (H) pixels in size were collected with
an isotropic pixel pitch of 21.59µm, the spatial resolution is therefore estimated to be better than 80µm. e
acquisition scheme of the neutron radiographies consisted of several (usually seven) series of 50 images each of
the 10s acquisition time for each investigated system. For the evaluation of the data from the rst two respective
series, 10 data points were provided as an average of 10 images having the respective time stamp of the average
time of the respective 10 images; for the latter series, the entire 50 images were averaged into a single data point
having the time stamp of the average of the 50 images.
Neutron radiographies of two perpendicular axially-symmetric test tubes (inner radius R = 4.5mm) were
acquired, each containing p-xylene equilibrated with methane at 1bar. ese tubes were subject to the methane
pressure step, the diusion of methane into the liquid was imaged. Aer applying lters and corrections29,30,
the radiographs were reconstructed at the central plane of the sample via the onion-peeling algorithm31. e
resulting tomographic reconstructions at the central plane of the sample (Fig.1) are matrices of the overall linear
attenuation coecient (Σ) for the individual pixels.
Theory
e overall attenuation by the binary mixture is contributed by the constituents, A(CH4) and B (p-C8D10). e
contribution of B is negligible for the gaseous (supercritical) phase at the studied conditions21,24. For the liquid,
concentration can thus be derived using the Beer-Lambert law
ln
I
0
I
=σAN0cAd+σBN0cBd=Σ
Ad+Σ
B
d
(1)
e diusion of A into the initially pure B causes liquid swelling. In turn, both molar concentrations cA = nA/V
and cB depend on time and the spatial coordinates (level coordinate z, distance from axis r), while the path
length (d), Avogadro number (N0), and cross-sectional areas (σ) are constants; the latter were adjusted based on
the observation of the pure components at the conditions of the experiment, yielding
Σ0
A
and
Σ0
B
. e phase
interface was detected by searching extrema of Σ, thus providing the interface shape and volume of the (liquid)
body of revolution. Clearly, the linear attenuation coecient of the dissolved methane can be estimated by the
use of Eq.(1) assuming constant concentration of B in the liquid body corresponding to
Σ0
B
. Its integral mean
with respect to the liquid height
z∈⟨0,Z⟩
was used as an accessible variable determining the liquid swelling.
Σ
A(r)=
1
Z
Z
∫
0
Σ(r, z)
−
Σ0
Bdz=
1
Z
Z
∫
0
Σapprox
A(r, z)d
z
(2)
e interface shape changed rapidly upon the pressure step and then remained constant to within the experimental
sensitivity, while the interface position changed over time (see below). e convenient measure of swelling is:
Z
Z
0(r)=1+k
·
ΣA(r
)
(3)
Chemical Supplier, initial purity
Methane (CH4) Linde, 5.5, CAS 74–82-8
Nitrogen (N2) PanGas, 5.0, CAS 7727–37-9 (purge gas – outer apparatus box)
p-xylene (p-C8D10) Armar, 99.59 atom-% D, > 99.9wt.%#, CAS 41051–88-1
Acetone Penta, > 99.9 wt.%(rinsing agent)
Table1. Used gases and chemicals, initial purity as in the certicate of analysis by the supplier unless indicated
otherwise. #Chemical purity was not declared by the supplier and was determined using a GC–MS(Clarus
500, Perkin Elmer) with a capillary column containing Elite WAX ETR stationary phase (Perkin Elmer), value
represents purity with respect to other C8 aromatic hydrocarbons.
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in which kis radius-independent adjustable parameter and
Z0
is the liquid level short aer the pressurization.
e estimate of the distributed linear attenuation coecient of B is then:
Σ
B(r, z)∼
=
Σ0
B
1+k·Σ
approx
A(r, z)
(4)
e true linear attenuation coecient of methane (ΣA) was then calculated from the overall according to Eq.(1).
e use of Eq.(1) to Eq.(4) allowed for the calculation of the concentrations cA and cB in the liquid phase for
the tomographic reconstructions, and the transformation of the physical depth coordinate (z) to the B-xed
coordinate
ξ∈⟨0
,Z
0⟩
, for which the diusivity of B holds
DB
B=0
. In the B-xed reference frame, the height
of the physical pixel, Δz, scales to:
∆
ξ∼
=
∆z
1+
k
·Σ
approx
A(
r, z
)
(5)
is choice of reference frame is useful for modeling diusion in swelling bodies32. e Fick’s second law for
axially-symmetric body in the cylindrical B-xed coordinates then has the form33,34:
∂C
∂τ
=DB
A
∂
2
C
∂ξ
2+DB
A
1
r
∂
∂r (
r∂C
∂r )
(6)
e above equation is a model of the concentration distribution at the central plane of the probe liquid body in
the B-xed reference frame,
DB
A
is methane (A) diusivity in the B-xed reference frame, and C =
cA
/
cB
=
xA
/
xB
. We remind that
DB
A
simplies, for instance, to the diusivity of A in the cell reference frame (DA) if swelling
and the diusivity of B are negligible, such as for diusion of diluted A in solid B. In this work, concentration
independence of
DB
A
was assumed, and Eq.(6) was solved at the Dirichlet boundary condition (concentration
at the interface set to CIFthat was determined by extrapolation of concentration proles to the phase interface)
and Neumann boundary conditions (impermeable walls of the cell) using an explicit dierentiation scheme33,35.
e optimum value and uncertainty due to random errors (ur, cover factor 2) of
DB
A
and CIFwere calculated
using Gauss–Newton and Bonferroni methods35,36. e so calculated
DB
A
is then the integral mean for the
concentration-dependent diusivity32. Importantly, molecular simulations enable the prediction of volume
fraction of the species (ϕi) and diusivity in the cell reference frame (
Di
). e relation among the integral mean
DB
A
and
Di
32,37 allowing for the comparison of experimental and simulated data is:
D
B
A=
1
CIF
C
IF
∫
0
ϕ2
B[ϕA(DB−DA)+DA]dC (7)
Concentration at the phase interface was expressed using the apparent Henry’s law constant (H) relating methane
pressure (pA) in the gas (or supercritical uid) and its molar fraction (xA) in the liquid:
Fig. 1. Central-plane tomographic reconstruction for cell with supercooled liquid p-C8D10 at 0.0°C, methane
pressure was increased at zero time. Gray value corresponds to the linear attenuation coecient, inner
diameter of the cell was 9.0mm. Regression with solution of Eq.(10) is shown as purple curve, green curve is a
reference line for the interface position.
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H
=p
gas/fluid
A
xliq
A
(8)
We remind that true Henry’s law constant is dened for the innite dilution of A, and denoted below as
H∞
.
Besides that, methane fugacity rather than pressure and the Poynting correction are generally to be used at high
pressures26. e above simplied form of Henry’s law, Eq.(8), is practical, as it contains quantities accessible both
experimentally and using molecular simulation (see below) without further conversions.
Density of the liquid at the phase interface was calculated based on the methane concentration at the interface
and its partial molar volume. e latter was calculated as follows. e total amount of B in the liquid body of
revolution (nB,t) was set equal to that of the initial pure B due to its small volatility21,24. e total amount of A in
the liquid body of revolution (nA,t) was calculated based on the central-plane reconstruction using Eq.(1), while
the total liquid volume takes the form according to the Euler’s rst theorem for homogenous functions:
V=VAnA,t+VBnB,t
(9)
Apparent molar volume of methane in the liquid (
Vapp
A
) was calculated by setting
VB
equal to the molar volume
of the pure B at the system pressure38. is quantity equals partial molar volume of A at innite dilution of A,
see Eq.(16).
e shape of the phase interface in the test tube in gravity possesses axial symmetry and its shape at the
central plane is described by the solution of the Young–Laplace equation39,40:
z
=γ
∆ρg
(
z
′′
(1 + z′
2
)
3/2+z
′
r(1 + z′
2
)
1/2
)
(10)
Equation(10) can be numerically solved for z'(r = 0) = 0 and z'(r = R) = cot(θ), the distance form axis ranges from
zero to the tube inner radius, r
∈
(0,R). Parameters have the usual meaning: density dierence at the interface
(Δρ), interfacial energy (γ), contact angle (θ). Density of the gas phase (methane) was calculated using the
Setzmann–Wagner equation of state41. Density of the liquid at the interface was calculated from the respective
concentrations and molar volumes at the interface as described above.
Molecular dynamics
MD simulations were used to model the macroscopic behavior of experimentally investigated 2-phase systems
from methane (A) + p-xylene (B), exceed the range of experimentally achieved conditions in this work, and
gain microscopic insight into the structure of bulk phases and of the interface. MD simulations were performed
with united-atom Trappe force-eld42, which is an ecient simulation model due to its simplicity (united atom,
no partial charges), transferability, and very good accuracy owing to benchmarking to gas–liquid equilibrium
experimental data. Lennard–Jones (LJ) cut-o was set to 2.99nm, which was shown to quantitatively reproduce
the phase behavior and also surface tension (Fig. S1 in Supplementary Information, SI) of neat p-xylene. All
MD simulations were performed in the GROMACS simulation package43 with a timestep of 2fs. e simulated
systems were divided into two main groups by the number of phases in the system.
First, we have simulated systems containing 2coexisting phases with an explicit presence of the interface, i.e.
the slab simulation setup (Fig.2a). is setup enabled the evaluation of surface tensions, equilibrium density
proles across the interface (Fig. S2 and Fig.S3 in SI), and the direct measurement of the apparent Henry’s law
constants. e system for the slab simulations was a rectangular cuboid with side lengths of 6.0nm, 6.0nm and
50nm. System consisted of 1000 p-xylene molecules and 400–5000 methane molecules, which were distributed
in the p-xylene-rich liquid phase (xAliq= 0 to 0.25) and in the methane gas phase (according to experiment
Fig. 2. Simulation setups used in this work to determine target macroscopic properties, and to get insight in
the structure of the solution and of the interface. a slab simulation setup, b homogeneous phase of p-xylene
with dissolved methane, c pure p-xylene phase. Methane is in green spheres, p-xylene in red licorice.
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and Henry’s law) utilizing the PACKMOL package44. e slab was equilibrated for 10ns in semi-isobaric NpT
ensemble (compressible in z-direction only) in order to obtain targeted pressure. e production was carried out
in NVT ensemble with the total simulation time 40ns from which the rst 20ns were used as equilibration to
ensure that equilibrium of methane between gas and p-xylene liquid phase is reached (via convergence of density
proles). All 2-phase simulations were performed with two separate V-rescale thermostats45 (τT = 0.1ps) used
for temperature coupling of methane and p-xylene.
Second, we have carried out bulk simulations (Fig.2b, c), which present an ecient and reliable route for the
determination of bulk properties, such as molar volume, diusion, viscosity, density, true Henry’s law constant,
chemical potentials or local solution structure (Fig. S4 in SI). ese simulations were performed in isobaric-
isothermal (NpT) ensemble with C-rescale barostat (τp = 2ps) and V-rescale thermostat (τT = 0.1ps). Simulation
time was 40ns with the rst 20ns used for equilibration and not used for analysis. e system consisted of 1000
particles, the numbers of methane and p-xylene particles were varied.
Theory
Surface tension was calculated from the pressure tensor, which was measured during the slab simulations
(Fig.2a) using the following equation:
γ
(t)= Lz
2
(
Pzz (t)−Pxx
(
t
)+
Pyy
(
t
)
2
)
(11)
where Lz is the length of the simulation box along the z-axis, Pzz is the perpendicular component (and the
macroscopic pressure in the system), while Pxx, Pyy are the lateral components.
e diusion coecient of methane in the p-xylene solution was calculated from the mean square displacement
according to Einstein’s formula (DPBC, Eq.(12), literature46). In order to account for long range hydrodynamic
eects due to PBC in nite systems, nite size correction was applied and system size independent (true) D0
evaluated via Eq.(13) as recommended in the literature11. In Eq.(13), kB and T are the Boltzmann constant and
thermodynamic temperature, constant ξ= 2.83729746, ηMD is p-xylene viscosity, and L is the side of the cubic
simulation box.
As diusivity is inversely proportional to the viscosity of the solvent medium, another correction [ηMD/ηexp
in Eq.(14)] is routinely applied in the literature, accounting for the dierence between pure solvent (p-xylene)
viscosity in the simulation (ηMD) and in the experiment (ηexp). is factor was determined based on experimental
and MD viscosity data at 293K47. is uniform scaling proved quantitative for solutions, the viscosity of which
does not signicantly vary with composition (e.g. pure liquids, diluted solutions). However, in the case of
complex solutions mixtures of signicantly varying density (10–20mol.% of supercritical methane in liquid
p-xylene) for which experimental viscosity data are not available, the scaling based on pure liquid viscosities
cannot be expected to be quantitative. To practically overcome these various limitations and uncertainties, we
have introduced a universal eective scaling parameter [kη in Eq.(14)] by calibrating diusion coecients from
MD simulations to our experimental data. We note that scaling performed in Eq.(14) does not bias temperature
or composition dependences of diusion coecients (A, B). Moreover, kη is not expected to signicantly deviate
from unity, and kη = 1 in pure liquids (and at innite dilution of solute).
D
PBC =
1
6
lim
t→∞
∂
∂t
MSD (t
)
(12)
D
0=DPBC +
k
B
Tξ
6πηMDL
(13)
D=
D0
ηMD
ηexp
kη (14)
Solution viscosity is another important property, which steps in the continuous modeling and interpretation
of time-resolved data of neutron imaging. In this theoretical study, we have calculated viscosity via Einstein’s
approach (-evisco option in gmx energy routine of GROMACS package). To improve convergence, the averaging
was performed over 100 independent simulations, each of a length of 2ns, following the recommendation from
the literature48.
e volumetric properties, namely partial molar volumes (
Vi
) and volume fractions (
ϕi
), present an
important input to continuous modeling. eir evaluation from MD simulations starts by a direct calculation
of apparent molar volume of methane (
Vapp
A
) according to Eq.(15), which requires only system volumes for a
series of compositions, i.e., numbers of molecules [
V(NA,N
B)
] and that of pure p-xylene liquid(
V•
B
)13.
V
app
A=
N0
NA
(V(NB,N
A)
−
V•
BNB
)
(15)
Following the formula from the literature49, partial molar volume of methane (
VA
) is determined according to
Eq.(16)
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V
A=Vapp
A+xAxB
(
∂V
app
A
∂xA
)
(16)
In case that
Vapp
A
is linear in
xA
, i.e.
Vapp
A=V∞
A+bxA
, the partial molar volume of methane takes a simple
form
VA=Vapp
A+bxAxB=V∞
A+bxA(1 + xB)
. e calculation of
VB
is straightforward. e molar
fractions and partial molar volume of p-xylene are determined from known composition (molar concentrations,
ci) according to:
ϕi=ciVi
(17)
Insight into the p-xylene-methane interactions is captured in the excess (residual) chemical potential50. at
of methane in the p-xylene phase was eciently calculated via the Widom insertion method, where ψ is the
interaction energy of an inserted methane particle and the ensemble average
⟨.⟩
is performed over congurations
(20000 frames) of p-xylene phase. 20 000 methane insertions per frame were attempted.
µ
ex
A=
−
kBTln
⟨
e−
ψ
kBT
⟩
(18)
is opens a path for a calculation of the true Henry’s law constant (low methane pressure) for methane into
pure p-xylene liquid of particle density (molar concentration) ρB
H∞=ρBkBTe
µex
A
kBT (19)
thus independently conrming the equilibrium methane concentration in p-xylene, which was determined
directly in the slab simulation. e apparent Henry’s law constant, determined at nite methane pressures, was
calculated from slab simulations according to Eq.(8).
Resultsanddiscussion
Experimental data derived from the neutron imaging of the supercritical methane (CH4, component A) absorption
in liquid perdeuterated p-xylene (p-C8D10, component B), and the results of the MD simulation are compared in this
section, followed by predictive simulations. Figure3a shows the simulated mean diusivity of A in the liquid B in
the experimentally accessible B-xed reference frame (
DB
A
), see Eq.(7), together with the selection of experimental
results. Complete sets of experimental and simulated results are available in the Supplementary Dataset (SD). e
supercooling boundary, that is the equilibrium condition at which solid p-C8D10 occurs4,7, is shown. No inuence
of the supercooling on the master trends was discerned either for the experimental or simulated diusivity. As a
calibration eort, the experimentally derived
DB
A
was predicted quantitatively using MD (Fig.3a), which well captures
trends in temperature and pressure aer adjusting the viscosity scaling parameter. It is noteworthy that diusion
ux of methane through the phase interface causes accumulation at the interface10, which is a possible reason for
the inertia of the boundary condition upon the step pressurization reported in our previous works on the one-pot
imaging7,8. In contrast to the experimental setup, diusion in MD was determined from uctuations in an equilibrium
system with no macroscopic ux. e respective diusivities of methane (A) and p-xylene (B) in the binary liquid
solutions in cell coordinates (Di) calculated using MD (Fig.3b) are presented as regressions (models t to data) with
shown average absolute deviation(AAD).
Measured and simulated apparent molar volume of methane in p-xylene (
Vapp
A
) compared well within the
uncertainties (selection is in Fig.4a, measured and simulated results for all studied conditions are in SD). us,
partial molar volumes of both components (
Vi
) were predicted using MD (Fig.4b), see Eq.(16). Importantly,
MD provided partial molar volume of the major component, B, that is not accessible using the used experimental
setup. e species volume fractions (ϕi) were calculated using Eq.(17).
Simulated (true) Henry’s law constant (
H∞
) for innitely diluted methane in p-xylene rose slightly with
the increasing absolute pressure and with increasing temperature (simulation results are in SD). e following
regression, in which
H∞
and p are in bar, T in K, and R = 8.31451 JK-1mol-141, approximated the results at
AAD = 2bar for T and p ranging 260 to 400K and 10 to 100bar, respectively.
H
∞= 52 exp
(14400
RT −
3
.
12
·
106
RT 2+ 161 ·10−5p
)
(20)
e measured and simulated apparent Henry’s law constant [Eq. (8)] are compared in Fig.5. Simulation
systematically underestimated experimental apparent Henry’s law constants by 100 ± 25bar. is originates in
the exponential dependence of the Henry’s law constant on the excess chemical potential
µex
A
[see Eq.(19)].
Although the force eld approximated the system adequately, the error of 1kJ mol-1 in
µex
A
propagates as
e−
err(
µ
ex
A
)
RT
and results in the error of 30% in
H∞
.
Since the macroscopic observables were quantitatively captured by MD simulations, the molecular insight
into the solution structure of investigated solutions may follow. e structure of a bulk solution of p-xylene with
methane is described by series of radial distribution functions (RDF) for increasing molar fraction of dissolved
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Fig. 4. Apparent volume of methane in p-xylene, average experimental uncertainty is 5cm3mol-1, upper
estimate of uncertainty for simulation is 0.5 cm3mol-1 (at xA = 0.05, decreases with increasing concentration),
AAD for the MD simulated data regression is 0.5cm3mol-1 (a). Simulated partial molar volumes of methane
and p-xylene at the indicated conditions, AAD for partial molar volume regression is 0.6cm3mol-1 and
0.2cm3mol-1 for methane and p-xylene, respectively. Upper estimates of uncertainty for partial molar volume
simulation is 0.5cm3mol-1 and 0.03cm3mol-1 for methane and p-xylene, respectively (b). *indicates data
from7, #indicates datum for methane and n-hexane from54.
Fig. 3. Integral mean diusivity of methane in p-xylene (
DB
A
) for the B-xed reference frame is shown
in (a). Points were observed using neutron imaging, curves are regressions derived from MD simulation
processed using Eq.(7), *indicates data from our previous study7. Regressions of the MD simulated diusivity
for A and B in the cell reference frame derived for ranges of temperature (260 to 400K), concentration
(0.01to0.33mol(A)/mol(B)), absolute pressure (10to100bar) are shown in (b). Simulated data for the
conditions at which solidication occurs4 are shown (dashed curve, supercooling boundary). Average
uncertainty of the experimental
DB
A
equals 0.2 × 10–9 m2s-1. Average uncertainty of simulated DA and DB is
0.3 × 10–9 m2s-1 and 0.1 × 10–9 m2s-1, respectively. kη = 1.284 was used in processing of MD simulation data [see
Eq.(14)] to eectively account for unknown experimental viscosity of complex p-xylene solutions saturated by
methane at elevated pressures.
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methane. For illustration, Fig. S4 (SI) presents mutual distributions of methane and p-xylene molecules and
associated running coordination numbers. Only minor changes in RDFs with methane concentration are found,
suggesting that methane dissolves well in p-xylene and together form nearly regular solution.
e quantitative insight into composition of the interfacial region is captured in z-resolved density proles of
p-xylene and methane. Fig. S2 (SI) illustrates the composition for a series of methane pressures (at298K). It is
conrmed that methane density in the p-xylene phase is lower than in the gas phase, methane is surface active,
and its surface excess relatively decreases with increasing methane pressure. A random simulation snapshot
at298K, 45bar (Fig. S3, SI) presents the side and top view to the structure and arrangement of the intrinsic
interface. Qualitatively, the surface excess of methane and lowering of methane concentration in the p-xylene
phase is visually observed. Importantly, these snapshots conrmed that the methane distribution within any of
the interfacial layers is random, i.e., no methane-rich associates or domains are formed.
Measured surface energy at 1bar (methane, liquid p-xylene) is shown for selected conditions in Fig.6a (all
data are in SD). While simulation eectively resembled the literature data for the pure p-xylene7,51, systematic
error of approx. 2mN m-1 was observed for the experimental data at 1bar, for which the average (random)
uncertainty of the interfacial energy measurement was 2mN m-1. e inuences of the cell alignment with
respect to gravity and the presence of methane at1bar were checked by measuring with tilted apparatus (± 1°)
and upon removal of methane (vacuuming) without observing systematic changes of surface energy and its
uncertainty. Simulated and measured surface energy for the interface of methane and p-xylene showed similar
trends, while the systematic experimental error (2 mN m-1) vanished with increasing pressure (Fig. 6b).
e average uncertainty of the interfacial energy measurement at elevated pressures is 1mN m-1, attributed
to the higher sensitivity of the method at lower surface energies52. MD simulation resembled experimental
interfacial energies within the achieved uncertainties. is fully justies the use of MD for predictions within
the experimentally provided temperature and pressure domain, and supports its use for the parameter domains
outside those calibrated by the provided experiments.
Simulated diusivities of p-xylene and methane at the innite dilution of p-xylene at 50 bar followed
expectable trends(Fig.7) within the studied conditions that correspond to liquid and supercritical methane41.
Diusivity of innitely diluted p-xylene was also predicted using the engineering equations according to Wilke
and Chang25,26, and He and Yu26,27 with parameters from the databases51,53. ese predictions diered, on
average, by just 28% (Wilke and Chang), 17% (He and Yu), and 11% (Wilke and Chang with association factor
adjusted to 1.963, curve not shown in Fig.7) from the simulated p-xylene diusivity in its innitely diluted
solution in liquid methane. On the contrary, substantial dierences (average 65% of the simulated value for both
equations) were observed for the supercritical methane at reduced density down to 0.2. It is noteworthy that the
more recent He and Yu26,27 model was developed mainly based on data for systems of higher reduced densities.
Fig. 5. Apparent Henry’s law constant (H) for methane in p-xylene, see Eq.(8). Points were observed using
neutron imaging, curves represent regression of simulated data (AAD = 5bar), average relative deviation of
simulation from the experiment was approximately 30%, which corresponds to the uncertainty of 1kJ mol-1 in
µex
A
.*indicates data from7, #indicates datum from4.
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Fig. 7. Simulated diusivity of p-xylene (component B) and methane (component A) at the innite dilution of
B at 50bar, curves are engineering predictions according to Wilke and Chang (W–C)25, and He and Yu(H–
Y)27. Fluid properties of pure methane were taken from database53, constants from database51. kη = 1 was used
in processing of MD simulation data [see Eq.(14)] as p-xylene is present at innite dilution.
Fig. 6. Surface energy observed experimentally using neutron imaging and simulated, regression equations are
shown in (b), their plots for 1 bar and 293.2 K are in (a) and (b), respectively. Regression of the MD simulated
interfacial energy was derived for broad ranges of T (260 to 400K) and xA (0to0.3). Regression of the
experimental interfacial energy was derived for ranges of T (273.2 to 303.2K) and xA(0 to 0.26). Comparison
to the literature data7,51 (* and #) is shown in (a).
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As a result, a high diusion ux, and consequently intensive solid p-xylene deposition at cold spots during the
supercritical methane cooling, is predicted. Moreover, MD enabled the prediction of the self-diusivity of the
major component (methane) at the innite dilution of p-xylene, at the same conditions.
Conclusion
is study provides novel experimental and molecular dynamics insights into the properties of the two-phase
methane and liquid p-xylene systems, which is an industrially relevant pair for natural gas processing. rough
the combination of neutron imaging and MD simulations, key properties such as methane diusivity, Henry’s law
constant, apparent molar volume, and surface tension were determined and compared. e results demonstrate
that MD simulations align with experimental data with dierences within acceptable limits, thereby validating
the MD model under the studied conditions. While the experimental study was conducted at temperature and
pressure ranging 0.0 to 20.0°C and 1to100bar, respectively, MD enabled the prediction of the system properties
for a broad range of temperatures (260–400K) at pressures up to 100bar.
MD simulations allowed for predictions of system properties at experimentally inaccessible conditions.
e prominent example is the prediction of p-xylene diusivity in liquid and subsequently in supercritical
methane(both done using innitely diluted p-xylene), with the latter found signicantly higher than that
predicted using common engineering correlations (Wilke–Chang and He–Yu). ese MD simulations thus
predict intensive freeze-out formation, and shed light on the understanding of the behavior of volatile impurities
in natural gas, which is related to operational challenges in natural gas liquefaction.
In conclusion, the integrated experimental and computational approach adopted here enables a deeper
understanding of the methane-p-xylene system, providing valuable data for natural gas industries and
establishing a foundation for further exploration of complex uid systems.Building on these ndings, we will
apply similar experimental and simulation protocols to other industrially relevant systems.
Dataavailability
Experimental data will be made available upon request, additional data are provided in Supplementary Dataset.
Inputs for molecular dynamics simulations and raw simulation data for selected systems are available via Zeno-
do: https://doi. org/ht tps://doi.or g/10.5281/z enodo.14266923.
Received: 26 October 2024; Accepted: 31 December 2024
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Acknowledgements
M.M., T-M.D., J.Š., J.L., J.H., P.T., and O.V. acknowledge the nancial support obtained from Czech Science Foun-
dation (GACR) and Swiss National Science Foundation (SNSF) within the research project 23-04741K. M.M.
and J.Š. acknowledge support from the grant of Specic university research – grant No A1_FCHI_2024_001.
J.H. and M.M. acknowledges the support by the project "e Energy Conversion and Storage", funded as project
No. CZ.02.01.01/00/22_008/0004617 by Programme Johannes Amos Commenius, call Excellent Research. is
ScienticReports | (2025) 15:1284 11
| https://doi.org/10.1038/s41598-024-85093-6
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Content courtesy of Springer Nature, terms of use apply. Rights reserved

work was supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA
CZ (ID:90254). J.H. acknowledges the computational resources (project OPEN-30-6). J.H. and M.M. thank prof.
JiříKolafa for discussions on dispersion corrections to pressure and running test simulations in his MACSIMUS
soware55. is work is based on experiments performed at the NEUTRA thermal neutron imaging beamline,
Swiss spallation neutron source SINQ, Paul Scherrer Institut, Villigen, Switzerland56.
Authorcontributions
O.V., J.H., and P.T. conceived and designed this study, T-M.D., Š.T., J.Š., O.V., P.T. realized the experiments, M.M.,
T-M.D., J.Š., J.L., P.B., J.H., P.T., O.V. analyzed data. All the authors discussed the results and commented on the
manuscript.
Declarations
Competinginterests
e authors declare no competing nancial or non-nancial interests.
Additional information
Supplementary Information e online version contains supplementary material available at h t t p s : / / d o i . o r g / 1
0 . 1 0 3 8 / s 4 1 5 9 8 - 0 2 4 - 8 5 0 9 3 - 6 .
Correspondence and requests for materials should be addressed to P.T. or O.V.
Reprints and permissions information is available at www.nature.com/reprints.
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