Internal Volume Change Research Articles

An Improved Method to Calculate Gas-Lift Valve Set Pressure

Summary This study aims to enhance the accuracy of gas-lift valve (GLV) design set pressure calculations by incorporating the effects of silicone thermal expansion, silicone compression, and dome thermal expansion. The proposed method is compared with experimental measurements and current industry methods. The analysis includes an experimental assessment of the impact of internal dome volume changes on the design set pressure, considering various silicone fill levels, pressures, and temperatures. Experimental conditions cover silicone fills of 25%, 50%, and 75%, initial pressures from 975 psig to 1,250 psig, and temperatures from 60°F to 175°F. These conditions cover the conventional operating range in the industry. The results show that silicone expansion is the most dominant factor among silicone compression and chamber thermal expansion. The proposed method significantly improves GLV design set pressure calculations, especially for high-pressure and high-temperature conditions. The study suggests improvements in injection-pressure-operated (IPO) valve design practices to avoid multipoint injection and unloading failures. To the best of the authors’ knowledge, the impact of silicone expansion on GLV set pressure has not been investigated in the open literature. The enhanced method proposed in this research could significantly impact well unloading and production operations for wells equipped with GLVs. In addition, this work suggests an improvement on the American Petroleum Institute (API) recommended practice, especially when dealing with high-pressure, high-temperature wells and when utilizing refurbished GLVs.

Study of the Corrosion Behavior of Cathode Current Collector in LiFSI Electrolyte.

Cycling aging is the one of the main reasons affecting the lifetime of lithium-ion batteries and the contribution of aluminum current collector corrosion to the ageing is not fully recognized. In general, aluminum is corrosion resistant to electrolyte since a non-permeable surface film of alumina is naturally formed. However, corrosion of aluminum current collector can still occur under certain conditions such as lithium bis(fluorosulfonyl)imide (LiFSI)-based electrolyte or high voltage. Herein, we investigates the corrosion of aluminum current collector in the electrolyte of 1.2 M LiFSI in ethylene carbonate (EC) and ethyl methyl carbonate (EMC) mixed solvents. The electrochemical results shows that the corrosion current of aluminum is enhanced by cycling time and potential, which is correlated with the surface species and morphology. The formation of AlF3, which is induced by deep penetration of F- anions through surface passivation film, leads to internal volume change and the surface crack in the end. Our work will be inspiring for future development of high-energy-density and high-power-density lithium-ion batteries in which the LiFSI salt will be intensively used.

Degradation diagnosis of lithium-ion batteries considering internal gas evolution

Degradation diagnosis is essential for the safety of lithium-ion batteries. However, there lacks a method to provide detailed information about battery degradation mechanisms comprehensively. As an important product of electrolyte decomposition, internal gas evolution is rarely involved in degradation diagnosis. In this paper, internal gas evolution is evaluated based on X-ray computed tomography (CT), and used for degradation diagnosis by combination with internal resistances. Internal resistances are identified based on the equivalent circuit model (ECM) to describe different degradation mechanisms. Region of interest (ROI) volume of the tomogram, which reflects internal gas volume, is extracted to describe electrolyte decomposition using an X-ray CT. The proposed method is verified based on accelerated aging experiments and evaluation experiments of two batteries at different C-rates, whose results show that the tested batteries have different primary degradation mechanisms due to different degradation paths. It is recommended that the replacement of lithium-ion batteries adhere to the criteria of internal resistance and ROI volume change rates. The proposed method considers internal gas evolution and thus improves the effect of the degradation diagnosis in terms of degradation mechanisms.

Enhancement of shape accuracy and die quenchability of ultra-high strength steel hollow products in hot stamping of tubes using eco-friendly fiber-reinforced ice mandrel

A hot stamping process of quenchable steel tubes using a mandrel reinforced with eco-friendly fibers was developed to produce ultra-high strength steel hollow parts having enhanced lightweighting and crashworthiness. High internal pressure was generated to improve the die quenchability and shape accuracy of the formed parts by the fiber reinforcement. Wood sawdust, shredded copy paper, and plant fiber made of recycled toilet paper were chosen as the fibers, and not only the strength was evaluated from a uniaxial compression test but also the melting behavior of the mandrel was examined. The influence of the fiber reinforcement on the shape accuracy and die quenchability of hot-stamped parts was investigated. The generated internal pressure with the fiber-reinforced ice mandrel was higher than that with the pure ice mandrel without the reinforcement, and thus, the shape accuracy and die quenchability of hot-stamped parts were significantly improved even for a comparatively small change in internal volume of tubes.

A novel random finite element model for holistically modeling of the frost effects on soils and cold region pavements

This paper describes the development of a random finite element model (RFEM) that allows holistic simulation of frozen soil behaviors, including the effects of phase transition and the consequent internal stress and volume changes. The performance of the model is firstly validated with laboratory experiments. The model is implemented to simulate the effects of frost action on pavement. The coupled thermal-mechanical actions including the mechanical responses of subgrade soils subjected to freezing temperature and its effects on the pavement structure are analyzed. The results show that the frost action and expansion of ice lenses change the interaction modes between pavement layers. This leads to increase of stress and deformation in the pavement layer. Methods to mitigate the effects of frost heave are analyzed with this model. The simulation results indicate that the detrimental effects of frost heave on the pavement structure can be mitigated by increasing the thickness of base layer, use of thermal insulation layer or improve drainage in the subgrade layer. The RFEM combines the advantages of discrete element model (DEM) in holistically describing the microstructure effects and in the finite element model (FEM) in terms of computational efficiency. This allows to focus research on understanding the behaviors of individual soils phase and their interfacial interactions.

Predicting Chemical Shrinkage in Hydrating Cements

This paper presents a prediction of chemical shrinkage volume created during the hydration of two cements over time using a thermodynamic model. Chemical shrinkage in hydrating cements is a result of internal volume change over time within sealed conditions due to exothermic reactions during hydration and the resulting precipitation of solid hydrates. Each precipitated phase will contribute to chemical shrinkage due to their individual reactions and stoichiometric properties. As these factors (including early age, drying and autogenous nature) contribute to the overall shrinkage of concrete which may cause long-term performance problems, they are important properties to understand. The current paper presents a thermodynamic model that quantifies the chemical shrinkage volume created during the first 1000 days of hydration using the cemdata18 database and a series of discrete solid phases (DSPs) to represent C-S-H, which has not been quantified in the literature to date. DSPs account for the amorphous and poorly crystalline nature of C-S-H in cement, and its incongruent dissolution behavior of C-S-H as calcium is released in solution more so than silicon. A description of chemical shrinkage in hydrating cements is provided, along with a review of past methods used to quantify its development over time. The paper also shows the linear relationship between chemical shrinkage and the overall degree of hydration.

Large-scale sodiophilic/buffered alloy architecture enables deeply cyclable Na metal anodes

The application of Na metal anodes is hindered by the formation of dendrites, which evolves from the initial heterogeneous nucleation. The construction of sodiophilic pure metal layers on substrates can partly improve Na deposition behavior, but huge volume change during the repetitive alloy/dealloy process renders their rapid failure, especially under the high depth of discharge. Inspired by the assets of alloy anodes compared with monometallic anodes in Li/Na ion batteries, a Cu6Sn5 alloy layer is constructed on commercial Cu foils with a huge size of 850 mm × 650 mm via a facile electroless Sn plating approach. The sodiophilic Sn phase can alloy with Na and contribute to an ultralow nucleation overpotential as well as dendrite-free morphology. Meanwhile, the inactive Cu phase acts as buffer media to mitigate the internal stress and volume change induced by the alloy reaction, which prevents the alloy layer from peeling. Based on these synergetic effects, the Cu6Sn5 alloy coated Cu current collector gives rise to a highly prolonged Coulombic efficiency (99.84%) for 2000 cycles and 600 h lifetime under an ultrahigh depth of discharge (80%), which is superior to those of single Sn metal-coated Cu current collector. Furthermore, the full cells coupled with FeS2 cathode can stably operate for 1500 cycles with a decent capacity retention of ∼ 95%.

Sex-dependent jugular vein optical attenuation and distension during head-down tilt and lower body negative pressure.

Non‐contact coded hemodynamic imaging (CHI) is a novel wide‐field near‐infrared spectroscopy system which monitors blood volume by quantifying attenuation of light passing through the underlying vessels. This study tested the hypothesis that CHI‐based jugular venous attenuation (JVA) would be larger in men, and change in JVA would be greater in men compared to women during two fluid shift challenges. The association of JVA with ultrasound‐based cross‐sectional area (CSA) was also tested. Ten men and 10 women completed three levels of head‐down tilt (HDT) and four levels of lower body negative pressure (LBNP). Both JVA and CSA were increased by HDT and reduced by LBNP (all p < 0.001). Main effects of sex indicated that JVA was higher in men than women during both HDT (p = 0.003) and LBNP (p = 0.011). Interaction effects of sex and condition were observed for JVA during HDT (p = 0.005) and LBNP (p < 0.001). We observed moderate repeated‐measures correlations (r rm) between JVA and CSA in women during HDT (r rm = 0.57, p = 0.011) and in both men (rr m = 0.74, p < 0.001) and women (r rm = 0.66, p < 0.001) during LBNP. While median within‐person correlation coefficients indicated an even stronger association between JVA and CSA, this association became unreliable for small changes in CSA. As hypothesized, JVA was greater and changed more in men compared to women during both HDT and LBNP. CHI provides a non‐contact method of tracking large changes in internal jugular vein blood volume that occur with acute fluid shifts, but data should be interpreted in a sex‐dependent manner.

Unraveling improved electrochemical kinetics of In2Te3-based anodes embedded in hybrid matrix for Li-ion batteries

Although the introduction of hybrid matrices (e.g., metal oxide–carbon (e.g., TiO2–C) and metal carbide–carbon (e.g., TiC–C)) has shown to be effective for enhancing the electrochemical performance of alloy-based active materials, reliable evidence that verifies these favorable effects remain ambiguous. Herein, we propose a simple and effective strategy that can effectively resolve these issues and significantly extend the battery lifespan. To elucidate this phenomenon more clearly, In2Te3-based active materials with/without a TiO2–C matrix were prepared via simple two-step high-energy ball milling. To precisely elucidate the dynamics of Li-ion diffusion, various electrochemical techniques, including electrochemical impedance spectroscopy, cyclic voltammetry, and the galvanostatic intermittent titration technique, were used. The results indicate the synergetic roles of TiO2 and C; whereas the TiO2 phase improves the Li-ion diffusion dynamics, amorphous carbon reduces the internal resistance and volume change of the active In2Te3 material. Consequently, the In2Te3 embedded in the TiO2–C matrix (In2Te3–TiO2–C) exhibits good electrochemical performance for Li-ion storage, i.e., high specific capacity (∼846 mAh g−1 at 100 mA g−1 after 200 cycles and ∼704 mAh g−1 at 200 mA g−1 after 300 cycles), high rate capability (∼450 mAh g−1 at 10A g−1 and ∼99% capacity recovery after a series of different current densities), and good long-term cycling performance (∼435 mAh g−1 of specific capacity after 500 cycles at a high current density of 500 mA g−1), compared with three control counterpart electrodes. Therefore, the In2Te3–TiO2–C composite developed in this study is a promising anode material for next-generation LIBs.

Hollow multi-nanochannel carbon nanofiber/MoS2 nanoflower composites as binder-free lithium-ion battery anodes with high capacity and ultralong-cycle life at large current density

The electrode materials with high pseudocapacitance can enhance the rate capability and cycling stability of lithium-ion storage devices. Herein, we fabricated MoS2 nanoflowers with ultra-large interlayer spacing on N-doped hollow multi- nanochannel carbon nanofibers (F2-MoS2/NHMCFs) as freestanding binder-free anodes for lithium-ion batteries (LIBs). The ultra-large interlayer spacing (0.78∼1.11 nm) of MoS2 nanoflowers can not only reduce the internal resistance, but also increase accessible active surface area, which ensures the fast Li+ intercalation and deintercalation. The NHMCFs with hollow and multi-nanochannel structure can accommodate the large internal strain and volume change during lithiation/delithiation process, it is beneficial to improving the cycling stability of LIBs. Benefiting from the above combined structure merits, the F2-MoS2/NHMCFs electrodes deliver a high rate capability 832 mA h g−1 at 10 A g−1 and ultralong cycling stability with 99.29 and 91.60 % capacity retention at 10 A g−1 after 1000 and 2000 cycles, respectively. It is one of the largest capacities and best cycling stability at 10 A g−1 ever reported to date, indicating the freestanding F2-MoS2/NHMCFs electrodes have potential applications in high power density LIBs.

Microstructure-Based Random Finite Element Method Model for Freezing Effects in Soils and Cold Region Retaining Walls

This paper describes the development of a random finite element model that allows holistic simulation of the phase transition and consequent development of internal stress and volume changes in frozen soils. The simulation capabilities of the model are first validated with laboratory scale experiments. The validated model is then implemented to study the soil lateral stress on the retaining wall subjected to frost action. The results show that the frost action leads to an increase of lateral stresses along the retaining wall. Strategies to mitigate the frost loads on the retaining wall are analyzed with this model; drainage of water in the backfill and use of thermal insulation layer both help to mitigate the lateral frost loads. Overall, by accounting for the spatial nonhomogeneity and coupled thermo-mechanical responses in frozen soils, the model provides holistic simulation of the responses of retaining walls subjected to freezing conditions.

Fracture mechanics approach to the problem of subsidence induced by resource extraction

A new area of application of Fracture Mechanics methods is proposed: the determination of surface deformation induced by internal volume change (e.g. due to underground hydrocarbon extraction). The finite layer-like zone of volume alteration is modelled as a crack, that is as a continuous distribution of dislocation loops. This approach allows the determination of surface deformation and can serve as the basis for monitoring of the volume alteration from surface measurements. In a limiting case of nearly uniform deformation of the reservoir boundaries the model consists of a single dislocation loop (an inserted cylindrical body of a constant height) in half-space and results in simple approximate expressions for the normal and tangential displacement components of the free surface. For the example of subsidence in the Groningen gas field the proposed method produces more realistic results describing reality better than the traditional models based on representing the reservoir as a collection of independent dilation centres. Also, analytical expressions are proposed for the nuclei – the basic Green’s function type expressions that allow representation of a planar horizontal reservoir layer of an arbitrary shape as a distribution of infinitesimal dislocation loops. For the case of a cylindrical reservoir, the nuclei integration recovers the exact distribution of the surface displacements.

Effects of coupled sulphate and temperature on internal strain and strength evolution of cemented paste backfill at early age

Cement hydration is a volume reduction reaction which can result in negative pore water pressure while strengthening the structural stiffness of cemented paste backfill (CPB). Both sulphate and temperature significantly affect the hydration process and thus influence the internal volume change and mechanical properties of CPB. The expansive hydration products produced in sulphated CPB may create an increase in volume which subsequently weakens the CPB. This paper presents an experimental study conducted to evaluate the coupled effects of sulphate and curing temperature on the internal strain evolution of early aged CPB. CPB samples of various initial sulphate concentrations (0, 5000 and 25,000 ppm) were prepared and cured at various temperature (20 °C and 35 °C) at early ages (≤7 days). Mechanical tests were conducted on the samples as internal strain was monitored by Fiber Bragg Grating (FBG) sensors. The results indicate that the FBG sensor is sufficiently sensitive to detect the internal strain development of sulphated CPB mixtures during the hydration process. At sulphate concentration of 25,000 ppm, the expansive strain occurred at curing temperature of 35 °C due to the internal expansive force of the expansive materials. The final internal strain value corresponds closely to the strength of the sulphated CPB. As the internal strain of sulphated CPB decreased, the uniaxial compressive strength and tensile strength showed similar trends throughout the experiment. When expansive strain emerged after the initial thermal strain stage, however, there was a higher ratio of uniaxial compressive strength to tensile strength. This phenomenon merits careful consideration in the stability analysis of exposed CPB in underground mines.

Fluidic origami cellular structure with asymmetric quasi-zero stiffness for low-frequency vibration isolation

This study investigates a unique asymmetric quasi-zero stiffness (QZS) property from the pressurized fluidic origami cellular structure, and examines the feasibility and efficiency of using this nonlinear property for low-frequency vibration isolation. This QZS property of fluidic origami stems from the nonlinear geometric relationships between folding and internal volume change, and it can be programmed by tailoring the constituent Miura-Ori crease design. Different fluidic origami cellular structure designs are introduced and examined to obtain a guideline for achieving QZS property. A proof-of-concept prototype is fabricated to experimentally validate the feasibility of acquiring QZS. Moreover, a comprehensive dynamic analysis is conducted based on numerical simulation and harmonic balance method approximation. The results suggest that the QZS property of fluidic origami can successfully isolate base excitation at low frequencies. In particular, this study carefully examines the effects of an inherent asymmetry in the force–displacement curve of pressurized fluidic origami. It is found that such asymmetry could significantly increase the transmissibility index with certain combinations of excitation amplitude and frequency, and it could also induce a drift response. Outcome of this research can lay the foundation for new origami-inspired multi-functional metamaterials and meta-structures with embedded dynamic functionalities. Moreover, the investigations into the asymmetry in force–displacement relationship provide valuable insights for many other QZS structures with similar properties.

Nonlinear tubular organ modeling and analysis for tracheal angioedema by swelling-morphoelasticity

We study one of the important human tubular organs, the trachea, under deformation caused by the disease angioedema. This pathology can suddenly increase the volume of the trachea and cause serious breathing difficulty. Two popular theories, the swelling theory and morphoelasticity theory, which generalize classical hyperelasticity to study material deformation under internal volume change, are integrated into a single model to study tracheal angioedema. Computational modeling results from various combinations of swelling and morphoelasticity are compared to exhibit the difference and similarity of the two theories in modeling tracheal angioedema. Nonlinear behaviors of the tubular radius changes are also illustrated to show how the trachea luminal size alteration depends on the swelling/growth parameters and their effect on modifying tissue stiffness. The possibility of complete tracheal channel closure is also studied to understand if it is possible for the angioedema to close the airway. This article serves as an exemplary study on nonlinear deformation behaviors of human tubular organs with multiple layers.

Effects of compaction temperature on the volumetric properties and compaction energy efforts of polymer-modified asphalt mixtures

In order to determine a proper compaction temperature that affects the workability and compactibility of the polymer-modified asphalt (PMA), the effect of compaction temperature was examined on the volumetric properties and the compaction energy indices. Change in compaction temperature shows an important influence on the maximum specific gravity of mixture (Gmm) by internal volume change of PMA. The change in Gmm mainly affects the effective volume of the aggregate (VEff). Reduction in VEff from Zero shear viscosity (ZSV) to superpave temperature allows 0.1%-0.15% of the asphalt binder to occupy highly the external voids of aggregates. The volumetric properties for all compaction specimens meet superpave criteria, but the energy efforts were the lowest at ZSV temperature. Lower energy efforts at the ZSV temperature reflect easier compaction than those at excessively high temperature. Clearly, excessive compaction temperature may not be necessary to improve the compactibility and to reduce the compaction efforts.

Effect of Aggregate Mineralogy and Concrete Microstructure on Thermal Expansion and Strength Properties of Concrete

Aggregate type and mineralogy are critical factors that influence the engineering properties of concrete. Temperature variations result in internal volume changes could potentially cause a network of micro-cracks leading to a reduction in the concrete’s compressive strength. The study specifically studied the effect of the type and mineralogy of fine and coarse aggregates in the normal strength concrete properties. As performance measures, the coefficient of thermal expansion (CTE) and compressive strength were tested with concrete specimens containing different types of fine aggregates (manufactured and natural sands) and coarse aggregates (dolomite and granite). Petrographic examinations were then performed to determine the mineralogical characteristics of the aggregate and to examine the aggregate and concrete microstructure. The test results indicate the concrete CTE increases with the silicon (Si) volume content in the aggregate. For the concrete specimens with higher CTE, the micro-crack density in the interfacial transition zone (ITZ) tended to be higher. The width of ITZ in one of the concrete specimens with a high CTE displayed the widest core ITZ (approx. 11 µm) while the concrete specimens with a low CTE showed the narrowest core ITZ (approx. 3.5 µm). This was attributed to early-age thermal cracking. Specimens with higher CTE are more susceptible to thermal stress.

Toward Reversible Conversion Reactions and High Initial Coulombic Efficiency in Lithiated SnO2 Based Anode Materials

Tin dioxide (SnO2) has been considered one of the most promising alternative anode materials for lithium batteries. In the past two decades, extensive studies have been directed to gaining a fundamental understanding of the lithiation/delithiation reactions to improve the performance of SnO2-based electrodes. However, the realization of full capacity of SnO2 anode has been hindered by the large initial irreversible capacity loss characterized by low initial Coulombic efficiency (ICE). This is generally attributed to the inferior reversibility of conversion reactions between Sn0/Li2O mixture and SnO2, and highly correlated to the poor stability of the nanostructure of Sn/Li2O mixture. Here we demonstrated that Li2O can indeed be highly reversible in a SnO2 electrode with controlled nanostructure and achieved an initial Coulombic efficiency of ~95.5%, much higher than that previously believed possible (52.4%). I nsitu spectroscopic and diffraction analyses corroborate the highly reversible electrochemical cycling, suggesting that the interfaces and grain boundaries of nano-sized SnO2 may suppress the coarsening of Sn and enable the conversion between Li2O and Sn to amorphous SnO2 when de-lithiated [1]. Furthermore, we have found that the application of super-elastic films of NiTi alloy could accommodate the internal stress and volume change of lithiated nano-SnO2 layer and thus effectively suppress Sn coarsening, to retain the high reversibility of the SnO2 layer with reversible capacity more than 800mAh/g (based on SnO2) for over 300 cycles, demonstrating stable charge capacities of ~400mAh/g in the potential ranges of 0.01-1.0V and 1.0-2.0V(vs. Li/Li+), respectively[2]. To greatly enhance the stability of the Sn nanostructure and the reversibility of conversion reactions in lithiated SnO2, a series SnO2-M-G (M=Fe, Mn, Co) ternary nanocomposites have been produced by scalable ball milling [3]. The SnO2-M-G nanocomposites demonstrate very high ICEs of up to 88.6%, which is the highest values among those reported so far for SnO2-based powder anodes. The SnO2-Fe-G maintains a capacity of 1338 mAh/g after 400 cycles at a current rate of 0.2 A/g, while the SnO2-Mn-G retains an excellent long-term stable capacity of 700 mAh/g throughout 1300 cycles at 2 A/g. Even in soft-packing full cells constructed with LiMn2O4 cathode, a high capacity retention of 85.1% can be maintained after 100 cycles operating in the range 0.5–3.8 V. All these data indicate the promising potential of SnO2-M-G as an interface material for high-performance anodes in lithium ion batteries.

Inhibiting Sn coarsening to enhance the reversibility of conversion reaction in lithiated SnO2 anodes by application of super-elastic NiTi films

The large capacity loss and low initial Coulombic efficiency (ICE) of a conventional SnO2-based anode for Li ion batteries are originated largely from the limited reversibility of the conversion reaction associated with the anode. Often, the reversibility of the lithiation/delithiation of SnO2 (with a high ICE value of ∼82%) declines with Sn coarsening in the Sn/Li2O mixture during cycling, leading to gradual capacity decay. Here we demonstrate that the application of super-elastic films of NiTi alloy could accommodate the internal stress and volume change of lithiated nano-SnO2 layer in a tri-layer NiTi/SnO2/NiTi sandwich anode, effectively suppressing Sn coarsening. This unique electrode configuration has helped to retain the high reversibility of the SnO2 layer with reversible capacity more than 800 mAh/g (based on SnO2) for over 300 cycles, demonstrating stable charge capacities of ∼400 mAh/g in the potential ranges of 0.01–1.0 V and 1.0–2.0 V(vs. Li/Li+), respectively. Insitu spectroscopic and exsitu diffraction analyses corroborate the highly reversible electrochemical cycling, confirming that the reversibility and cyclability of SnO2 anodes can be dramatically enhanced by preserving the nanostructure of Sn/Li2O mixture, which facilitates the reversible conversion reaction.

Assessment of Lung Tumour Motion and Volume Size Dependencies Using Various Evaluation Measures

The purpose of the study was to assess internal target volume changes through the breathing cycle and associated tumour motion for lung patients and to establish possible correlations between different parameters. Respiration-induced volume changes with breathing cycle and the associated tumour motion were analyzed for 11 patients. Selected phases were the maximum and average intensity projections and the 10 phases of equal duration and separation obtained through the respiratory cycle. Tumour centre of mass (COM) motion planes were generated using least square fitting, and their angles and orientations were then compared between the cases studied. Trajectories that are composed by the points of COM location in different phases were identified, and their interrelation was assessed through different similarity measures. The results were used to determine if there is any correlation between parameters chosen and if the margins conventionally used for the planning target volume creation successfully encompassed lung tumour motion and volume change. The results show that the extent of tumour motion was related to its volume and location. The tumour displacement was predominantly left and inferior. Planar fitting to COM motion data through respiratory phases demonstrated some correlation in best fit motion plane positions between different data sets. In the plane fit comparison, for each patient, the lower root mean square error values showed that a good planar fit can be achieved for the COM motion path. The evaluation of the inhale and exhale trajectories may allow, for certain tumour locations and size, contouring on only inhalation or exhalation phases, knowing that tumour motion will be adequately covered on the other phases. Taking all the data into account and knowing the tumour size and location, a good estimate can be made of the motion plane position in the three-dimensional space and the required dosimetric margins.