US20050191453A1 - System and method for computer analysis of pressure decay data and evaluation of shelf-life of material packaged in plastic containers - Google Patents

Abstract

Computer analysis of experimentally obtained in container pressure decay data to evaluate shelf-life of material packaged in plastic containers such as carbonated beverages packaged in plastic containers.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS
• This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application 60/548,725 filed on Feb. 27, 2004 and expressly incorporated herein by reference in its entirety.
TECHNICAL FIELD
• This invention relates to evaluation of shelf-life of material packaged in plastic containers such as, for example, packaged beverages. In a particular embodiment, this invention relates to evaluation of shelf-life of packaged carbonated beverages.
BACKGROUND OF THE INVENTION
• Products are often stored in plastic packages because plastic packages are relatively inexpensive, light, and convenient. For example, carbonated beverages are often packaged in PET bottles. Plastic packaging has a disadvantage, however, that it is not as impermeable to gases as glass or metal. Therefore plastic packaging emits some amounts of diffusion which affects the shelf-life of the product.
• Shelf-life is a common term which describes the time which the product retains its properties. Permeation of gases into or out of a package play a principle role in shelf-life of products packaged in plastic. It is therefore important to quickly and economically measure the gas permeation of plastic packaging so as to determine the shelf-life of the product in the package. There remains a need for quick and effective, but economical measurement of gas permeation through plastic containers.
SUMMARY OF THE INVENTION
• In summary, this invention encompasses computer analysis of experimentally obtained in-container pressure decay data to evaluate shelf-life of material packaged in plastic containers. A preferred embodiment includes computer analysis of pressure decay data to evaluate shelf-life of carbonated beverages packaged in plastic containers.
• One embodiment of this invention is a computer implemented method of evaluating shelf-life and carbonation loss of a plastic container pressurized at least in part with carbon dioxide comprising collecting in-container pressure decay data based on analysis of a plastic container pressurized at least in part with carbon dioxide, inputting the pressure decay data into a computer, and processing the data with a the computer to calculate the shelf-life and carbon dioxide loss of the plastic container. The computer is programmed with an application for calculating the shelf-life and carbon dioxide loss according to certain mathematical equations explained in more detail below. In still another embodiment, the system of this invention quantively determines the contribution of individual loss components of the container. These individual loss components include container volume expansion, container wall-sorption and container wall permeation. One embodiment includes simultaneous evaluation of these loss components from an experimental pressure decay data curve only without direct measurement of container volume expansion and container wall-sorption. In still another embodiment, the pressure decay data collected for processing to calculate the shelf-life and carbon dioxide loss includes the brimful capacity of the container (V_o), the elastic volume expansion less than one day after pressurization (V₁(t₁)), the final volume expansion of the container (V_F), the loss rate (c), the preexponential factor of permeation decay curve (P_o), and the wall saturation rate (β). The filling pressure (F) and the shelf-life limit in volumes (S) can be chosen as desired.
BRIEF DESCRIPTION OF DRAWINGS
• FIG. 1 a is a graphical representation of a pressure decay curve for an uncoated bottle.
• FIG. 1 b is a graphical representation of a pressure decay curve for a contoured bottle.
• FIG. 1 c is a graphical representation of a pressure decay curve for a contoured bottle.
• FIG. 2 is a flow chart of a method in accordance with an embodiment of this invention.
• FIG. 3 a is a schematic diagram of a graphical interface for test parameters in accordance to an embodiment of this invention.
• FIG. 3 b is a schematic drawings of a graphical interface for calculation of filling pressure in accordance with an embodiment of this invention.
• FIG. 3 c is a schematic drawing of a graphical interface for calculation of pressure loss due to volume expansion in accordance with an embodiment of this invention.
• FIG. 3 d is a schematic illustration of a graphical interface for calculation of nonpermeation of pressure lose and wall sorption in accordance with an embodiment of this invention.
• FIG. 3 e is a schematic illustration of a graphical interface for calculation of total nonpermeation and pressure loss and wall sorption in accordance with an embodiment of this invention.
• FIG. 3 f is a schematic illustration of a graphical interface for a shelf-life calculation in accordance with an embodiment of this invention.
• FIG. 3 g is a schematic illustration of a graphical interface for calculation of CO₂ loss in ccm in accordance with an embodiment of this invention.
• FIG. 4 is a flow chart illustrating a method in accordance with another embodiment of this invention.
• FIG. 5 is a schematic illustration of a graphical interface for the process illustrated in FIG. 4.
• FIG. 6 is a flow chart of shelf-life and carbon dioxide loss calculations in accordance with another embodiment of this invention.
• FIG. 7 is a container evaluation sheet for use in the method illustrated in FIG. 4.
• FIG. 8 is a graph illustrating an absorption profile of carbon dioxide.
DETAILED DESCRIPTION OF EMBODIMENTS
• A more detailed explanation of particular embodiments follows.
• “Shelf-life” is the common term, which describes the time during which a product retains its properties. Permeation of gases, particularly oxygen, into a package, and permeation of volatile product components out of the package play a principal role in shelf-life of products packaged in plastic, because other mechanisms leading to product deterioration are normally slower. For the purposes of the present invention, gas permeation is therefore assumed to be the controlling mechanism for determining shelf-life in plastic packages.
• Shelf-life of carbonated beverages is defined as the time, within which the carbonation of a beverage decreases to a predetermined limit. Four independent mechanisms contribute to this loss:
• CO₂-permeation through the bottle wall
• CO₂-permeation through the closure
• Bottle volume expansion after pressurization
• CO₂-sorption in the container wall
• Bottle design and improvements are directed to minimize these losses. In the following description of embodiments, CO₂-losses through the closure are excluded, since this loss can be separated from the other loss mechanisms by applying impermeable closures and by independent measurements of closure loss-rates with suitable (and available) equipment.
• Mathematical Calculations
• a) Permeation Losses
• In the simplest case, when no volume expansion and wall-sorption occurs, the only loss mechanism is permeation through the wall and the in-bottle pressure decrease vs. time can be described by an exponential “decay”-law of the in-bottle pressure p₁(t):
  p ₁(t)=p _o*exp(−c*t)  (1)
  (p_o=filling pressure, c=loss-rate due to wall permeation, t=elapsed time after filling)
• In this case the shelf-life T_s, i.e. the time in which the pressure in the bottle arrives at the shelf-life CO₂-pressure limit p(T_S) is
  T _S=−[ln(1−p _A /p _o)]/c  (2)
  where p_A=p_o−p(T_S) defines the allowable pressure at the limit-limit. As an example, if p_o=4.0 vol. and p(T_S)=3.3 vol. (17.5% carbonation loss at shelf-life limit) it follows that
  T _S=−[ln 0.825]/c  (3)
• Above shelf-life determination only requires the knowledge (=measurement) of the loss-rate c.
• The reality is much more complex and volume expansion as well as wall-sorption have to be taken into account. Both are transient phenomena lasting typically about 1-3 weeks after pressurization until both effects arrive at a final value (“equilibrium”). If shelf-life is much longer then the times to arrive at equilibrium, the calculations can be simplified. Then it can be assumed, that the total pressure decrease Δp correlated with volume expansion and wall-sorption (“non-permeation losses”) appears instantaneously after filling as a pressure step. In this case we obtain for the shelf-life
  T _s=[ln(1−p _A /p _o)−ln(1−Δp/p _o)]/(−c)  (4)
• Experimentally, for the determination of shelf-life, c as well as Δp/p_o, i.e. the relative initial pressure decrease due to expansion and wall-sorption must be known. However, it is not necessary to know, what fraction of this initial pressure decrease is due to volume expansion and wall-sorption, respectively. However, these fractions are important quantities for the design of bottles.
• B) Non-Permeation Losses
• For a separate evaluation of permeation, volume expansion and saturation losses we start with equation (1). This equation is valid for the ideal case, that the container has a perfect volume-stability and wall-sorption losses are completely negligible. In this case, p_o is the filling pressure and p(t) describes the inside pressure loss due to permeation through the walls solely. In this ideal situation, the permeation with a constant loss rate starts immediately after filling. In a more realistic consideration, however, additional CO₂-loss channels, i.e. volume expansion and wall-sorption leading to a delayed permeation to the outside must be taken into account.
• Wall-Sorption
• To consider wall-sorption (no volume expansion is assumed) we modify equation (1):
  p ₂(t)=p _o[1−A*exp(−β*t)]*exp(−c*t)  (5)
• Equation (5) describes the (fictive) in-bottle pressure decrease vs. time caused by permeation to the outside only. The factor [1−A*exp(−β*t)], with β=“wall-sorption rate”, takes into account the delay of permeation through the wall until wall-sorption has come to equilibrium and equation (1) applies for further permeation. This exponential approximation is justified due to experimental results.
• At t=0 there is no permeation to the outside and, thus, the slope of the curve (=permeation loss rate to outside) defined by (5) is zero at this time. This means, that the first derivative of equation (5) must be zero for t=0. From this condition it follows that
  A=c/(β+c)  (6)
• The driving pressure for permeation through the wall to the outside at t=0 is
  p ₂(t=0)=p _o[1−c/(β+c)]  (7)
• Equation (5)-(7) provide a rule to construct an “intercept”, i.e. to trace back the outside permeation from equilibrium to t=0. This is more accurately than applying a simple linear extrapolation to t=0 (i.e. the Fourier Transform IR (FTIR) method).
• If we now additionally include wall-sorption, we obtain
  p3(t)=p _o[1+(B−A)*exp(−β*t)+]*exp(−c*t),  (8)
• • where B accounts for the additional pressure loss due to wall-sorption.
• Volume Expansion
• The additional effect of volume expansion can be taken into account by a further modification of (8):
  p _F(t)=p _o[1+(B−A)*exp(−β*t)+D(t)]*exp(−c*t)  (9)
• • where the time dependent term D (t) now accounts for volume expansion (“creep”)
• Experimental evaluations of creep vs. time curves show, that volume expansion occurs in two steps (“Maxwellian behavior”):
• A “fast” step with an immediate elastic volume expansion after pressurization (according to Hook's law), and
• A “slow” creep according to the viscose flow of the bottle material.
• To account properly for this behavior, the volume expansion D(t) can be approximated by a sum, where the first term accounts for the fast and the second term for the slow expansion behavior.
  D(t)=D ₁*exp(−γ*t)+D ₂*exp(−α*t)  (10)
• Above empirical exponential approximation of volume expansion is justified by experimental experience and D₁, D₂ as well as the volume expansion rates γ (for elastic expansion) and α (for viscose expansion) can be determined by an evaluation of the volume expansion vs. time behavior. From above definition it is clear, that γ>>α.
• p_F(t) now describes the total pressure decrease vs. time. At t=0 we obtain with exp(0)=1:
  p _F(t=0)=p _o[1+(B−A)+D ₁ +D ₂]  (11)
• For practical considerations, equation (11) is written as:
  p _F =p _P +p _S +P _E  (11a)
  p _np =p _F −p _P  (11b)
• • with
  • p_F=p_F(t=0) (=filling pressure at t=0 before any creep or wall saturation occurs).
  • p_S=p_o*B (=part of in-bottle pressure consumed for wall-sorption)
  • p_E=po*(D₁+D₂) (=part of in-bottle pressure consumed for volume expansion)
  • p_P=p_o (1−A) (=part of in-bottle pressure available for permeation loss, A=c/(β+c))
  • p_np (=total non-permeation pressure loss)
• Above equations quantify the simple fact that the filling pressure is consumed by wall-sorption, volume expansion and permeation (finally to pressure zero). The total non-permeation pressure loss is the sum of wall-sorption and volume expansion losses. All (time dependent) effects are traced back to t=0 and. This procedure enables an easy evaluation of the individual loss channels via the experimentally accessible quantities c, A, D₁ and D₂.
• Determination of Permeation Loss Rate
• There exist several methods to determine permeation losses from containers. Current methods include the measurement of
• • 1. the in-bottle pressure decay vs. time by means of pressure gauges
  • 2. the in-bottle pressure decay by means of IR-absorption using the container as absorption cell (FTIR method)
  • 3. the amount of gas appearing outside the container (EST, GMS)
• In the following, methods based on pressure gauges and the EST will be discussed in more detail.
• Permeation Loss from Pressure Gauge Measurements.
• FIGS. 1A-1C show an example of a recorded pressure decay curve obtained by a pressure gauge measurement. This pressure gauge might be a device mounted onto an impermeable cap or a small device placed inside the container recording pressure as well as temperature vs. time (Steinfurth datalogger). Since the in-bottle pressure depends strongly on the temperature, a storage of the bottle in a stable temperature ambient (<0.1° C.) is essential.
• After filling, the pressure decreases strongly due to non-permeation losses (discussed below). After establishment of equilibrium the pressure loss vs. time follows an exponential decay. The exponential factor of an exponential fit to these data points gives the loss rate in units of the time scale applied (multiplication by 100 gives % per time-unit).
• The FTIR method determines pressure decay curves as well and all statements made here for pressure gauges can be applied for this method too.
• A major shortcoming of these methods is the time needed to evaluate the permeation loss rate, since several weeks measurement time after establishment of equilibrium are necessary to determine the exponential fit with sufficient accuracy.
• Permeation Loss from EST—Measurement
• • a) Fundamentals
• EST is a method for measuring the permeation of gases into and out of plastic containers and is described in U.S. patent application Ser. No. 10/234,634 filed in the US Patent Office on Sep. 4, 2002, the disclosure of which is expressly incorporated herein by reference. The EST offers a much faster way to determine the permeation loss rate. This value is available just after establishment of equilibrium.
• The measurement principle of the EST is based on the infrared (IR) absorption of molecules. The EST accumulates the CO₂ molecules permeating through the container walls outside the container. The number of these CO₂-molecules (=CO₂-pressure) can be determined by the characteristic IR-absorption of molecular CO₂-bands. This situation is demonstrated by the schematic in FIG. 8 wherein:
• • I_o(λ)=wavelength-dependent background intensity (intensity before absorption)
  • I(λ)=wavelength-dependent intensity behind absorption cell (transmission)
  • k (λ)=wavelength-dependent absorption coefficient per absorption length unit (proportional to CO₂-pressure)
  • dλ=spectral bandwidth
  • d=effective length of the absorption cell
• For a wavelength position λ with bandwidth dλ the IR-transmission is (Lambert's law):
  I(λ)dλ=I _o(λ)*exp[−k(λ)*d]dλ  [1]
• The whole absorption is obtained by integration over the absorption profile. With the simplifications I_o=I_o(λ) I=I(λ), k=k(λ) and d(λ)=1 we obtain
  k=log(I _o /I)/0.4343*d  [2]
• This evaluation of the (integrated) spectra is made by the software of the FTIR (Fourier Transform InfraRed) spectrometer. The read-out signal of the spectrometer is proportional to k and, therefore, gives a value of the (relative) CO₂-pressure in the absorption cell. This signal can be calibrated to absolute CO₂-pressure, if a known amount of CO₂ is introduced into the absorption cell.
• Theoretically, the value of k (absorption per length unit) cannot depend on d (the absorption length) as long as the CO₂-pressure within the cell is kept at a constant level. In reality, however, always a dependence of k on d is observed (with the exception of very low absorption), whereby k becomes slightly smaller with increasing absorption length d. A possible reason may be a non-linearity of the IR-detector or scattered light within the spectrometer. These effects lead to systematic errors in the evaluated CO₂-pressures, if spectra with rather different absorption are compared. As a precaution, spectra taken from absorption lengths as low as possible should be evaluated.
• b) CO₂ Permeation Loss Rates
• A loss rate is defined as pressure-reduction −dp(t) within a certain time interval dt related to the actual pressure p(t) at a certain time t after filling. This is expressed by
  −dp(t)/p(t)=c*dt.  [3]
  c=−dp(t)*dt/p(t)  [3a]
• Integration of this differential equation leads to the expression (see equation 1 in chapter 2.),
  p(t)=p _o*exp(−c*t),  [4]
• • where
  • p(t)=pressure at time t (in days or weeks) after filling
  • p_o=permeation driving “filling pressure” at t=0.
  • c=loss rate (per time unit)
  • (100*c=loss rate in %/time unit)
• The pre-exponential factor p_o only represents the filling pressure in this ideal approximation without non-permeation losses. [3a] represents the slope of equation [4]
• Equation [4] may also be written as “carbonation loss” L:
  L=[p _o −p(t)]/p _o=1−exp(−c*t)  [5]
• (Remark: Carbonation loss in % is obtained by multiplication with 100).
• For conditions c*t<<1, equation [5] can be approximated by
  L=c*t  [5a]
• In this linear approximation the carbonation loss is proportional to the time t.
• During an EST measurement, the CO₂-loss −dp(t) from a container due to permeation is collected over a certain time interval dt (typically several hours) in an IR-absorption cell and dp(t) is determined by a FTIR-measurement. With the known absorption-length d the absorption coefficient k can be determined according to equation [2] in relative units (called “I_N” in the EssenU-measurements). This quantity is proportional to the container's permeation pressure loss −dp(t) within the time interval dt. c can be determined applying equation [3a].
• However, since the actual permeation driving pressure p(t) in the moment of measurement is not known (but only the filling pressure p_o), p(t) in equation [3a] must be replaced by equation [4]. This leads to the (implicit) expression
  c=[−dp(t)/p _o]*exp(c*t),  [6]
• • from which c can be determined, if filling pressure p_o and elapsed time t since bottle filling are known.
• For relative measurements, e.g., to determine a BIF (barrier improvement factor) c′/c for coated bottles (′ relates to the corresponding quantity of an uncoated reference bottle), equation [6] leads to the relation.
  BIF=c′/c=[dp(t)′/dp(t)]*exp[(c′−c)*t].  [7]
• This means, that the measured BIF is time-dependent and the time t since filling (same filling date for coated bottles and references!) has to be taken into account.
• For typical loss rates <3%/week, the exponential factors in equation [6] and [7] are close to unity, if the measurements are carried out within 15 days after filling. Then the approximation
  dp(t)*/dp(t)=c*/c  [7a]
• • gives the BIF within reasonable error limits of a few percent.
• Before starting the IR-measurements, equilibrium of diffusion conditions, i.e. saturation of bottle walls with CO₂ must be established and volume expansion must have come to a final value. This “saturation time” has to be determined experimentally and is, e.g., about 6 days for a 28 g, 500 ml PET-bottle stored at 38° C. and 14 days for the same bottle stored at 22° C.
• Evaluation of Individual CO₂ Loss Channels and Shelf-Life
• The permeation loss rate through the wall (and closure) is one loss mechanism for carbonation. As stated above, other loss mechanisms affecting the shelf-life are volume expansion and wall-sorption. According to the foregoing mathematical description, shelf-life as well as the losses into the individual loss channels can be determined by a suitable evaluation procedure of pressure decay curves. FIG. 1 provides the justification of this procedure, it shows a comparison of an experimental to a calculated pressure decay curve. As can be seen, a perfect agreement can be obtained by a suitable choice of parameters. This fact can be applied to evaluate these parameters from a fit of the theoretical to the experimental decay curve.
• Establishment of equilibrium is indicated by a pure exponential decay. After onset of equilibrium, the only loss mechanism is permeation and the decay curve is determined by the permeation loss rate (see FIG. 1). To save time, the loss rate can be determined by the EST. Just after establishment of equilibrium, this constant loss rate determines the further slope of the decay curve and, thus, allows to construct the further decay curve.
• From the filling point until establishment of equilibrium the decay curve is determined by several time dependent loss mechanisms
• permeation to the outside,
• wall-sorption,
• volume expansion,
• each mechanism running at its individual time scale. From a measured pressure decay curve these effects can be these traced back to the filling time (t=0). Then the determination of above losses is based on the fractions of the filling pressure distributed into the different loss channels.
• The determination of above quantities requires additional measurements besides the determination of the loss rate. In the following a procedure is described, how to obtain these additional quantities and finally how the distribution into the different loss channels and the shelf-life based thereon can be evaluated.
• Volume Expansion.
• The brimful capacity V_o of the unpressurized bottle is measured (e.g. by the weight of the brimful water content) and then the bottle is pressurized. Before and after pressurization the bottle volume vs. time is measured by a water displacement method. Shortly after pressurization (at time t₁21 1 day) the expanded volume V₁(t₁) is determined. V₁(t₁)−V_o is the elastic volume expansion according to Hook's law. Measurements are continued until the volume expansion has come to a final value V_F (=total final bottle volume). The total volume change is V_F−V_o.
• Filling Pressure
• The (fictive) filling pressure of the non-expanded bottles (brimful capacity V_o) is the reference pressure of the filled bottles, to which all losses are related. Its knowledge is essential for this evaluation.
• To determine p_F the volume V₁(t₁) and the corresponding in-bottle pressure p₁(t₁) of the pressurized bottle at a time t₁ shortly after pressurization (<1 day) must be taken from above volume vs. time dependence. A short time t₁ after pressurization is necessary to keep the additional wall saturation at a negligible level. Then p_F can be determined by means of “Boyle's law”:
  p _F =p(t ₁)*V ₁(t ₁)/V _o  [1]
• Pressure Loss p_E Due to Volume Expansion
• Note: The volume expansion rates γ and α must not be known
  p _E =p _F(1−V _o /V _F)  [2]
• Evaluation of p_o and c
• In case of pressure gauge measurements, these values are determined from an exponential fit to equilibrium part of the pressure decay curve. p_o is the pre-exponential factor and c (=loss rate) the exponential factor. The knowledge of the “academical” quantity p_o is necessary, since the mathematical theory explained above relates all losses to p_o.
• In case of an EST measurement, c is determined as described above. To obtain p_o the exponential curve with a slope c has to be “stitched” to the pressure decay curve at or after equilibrium. If p(t_E) is the (absolute) pressure at the “stitching time” t_E, we get for the pure permeation case after equilibrium:
  p(t _E)=p _o*exp(−c*t _E)  [3]
  p _o =p(t _E)*exp(c*t _E)  [3a]
• Since p(t_E) and t_E are known, p_o can be determined by means of equation [3a]
• Total Non-Permeation Pressure Loss p_np
• Note: β must be determined from wall-sorption vs. time curves. The influence of this quantity on the final results is very weak and it is sufficient to take β=0.4 for 38° C. and β=0.3 for 22° C. measurements. For further explanations, see equations [6] and [7] in the discussion of wall-sorption above. FIG. 1C shows how the permeation to the container outside is traced back to t=0.
  p _np =p _F −p _o[1−c/(c+β)]  [3]
• Wall-Sorption Pressure Loss p_s
  p _S =p _F −p _np −p _E  [4]
• Losses into individual loss channel can be calculated according to the following table:

  Total	Volume	Wall-
  allowable loss	expansion	sorption	Permeation
  (ccm)	(ccm)	(ccm)	(ccm)
  LA =	LV =	LW =	LP =
  Vo*(F − S)	LA *pE/	LA *pS/	LA − LV − LW
  	[ pF · (F − S)/F]	[ pF · (F − S)/F]

• • with
  • L_A=Total allowable loss
  • F=Filling pressure (vols)
  • S=Shelf-life limit (vols)
  • L_V=Loss into volume expansion
  • L_W=Loss into wall-sorption
  • L_P=Loss into permeation (wall and closure)
• The Shelf-life calculation is made according to equation [4], whereby the initial pressure loss is Δp=(p_F−p_o) and p_o must be replaced by the real filling pressure p_F.
• Software for Shelf-Life and Loss Channel Evaluation
• A first computer program according to one embodiment of this invention enables the easy evaluation of shelf-life and losses into the individual loss channels. From above it follows, that for their evaluation the following data must be known:
• Vo=brimful capacity of “virgin” bottle
• V₁(t₁)=elastic volume expansion<1 day after pressurization
• V_F=final volume expansion
• c=loss rate
• p_o=pre-exponential factor of permeation decay curve
• β=wall saturation rate (roughly)
• F=filling pressure and S=shelf-life limit (in vols) can be chosen as desired.
• A flow chart of the process steps performed by this first computer program is shown in FIG. 2 and graphical user interfaces for this first program are illustrated in FIGS. 3A-3G. These graphical interfaces appear subsequently. In the interfaces, the current interface is identified by bold letters in the titles and all titles can be selected by click to the respective field. Numbers for the container to be tested are inserted to preform the program.
• The shelf-life evaluation program illustrated in FIG. 2. The program begins at 10 and test parameters are entered at 12 via the graphical interface titled “Test Parameters” as illustrated in FIG. 3A. The date, bottle number, remarks, bottle type, filling material, filling date, closure type, and the storage temperature are entered in the first graphical interface. Filling pressure data is entered at 14 into the second graphical interface illustrated in FIG. 3B and titled “Calculation of Filling Pressure” (T=0) for unpressurized bottle. The brimful capacity of the container (V_o) and the elastic volume expansion less than one day after pressurization (V₁(t₁)) are entered and the filling pressure is calculated for the unpressurized bottle at 16. The pressure loss data is entered at 18 through graphical interface titled “Calculation of Pressure Loss Due to Volume Expansion” and illustrated in FIG. 3C. The final volume expansion V_f is entered and the pressure loss due to volume expansion is calculated at 20. The total non permeation pressure loss data such as the pre-exponential factor of permeation decay curve p_o is entered at 22 via the graphical interface illustrated in FIG. 3D and titled “Calculation of Non-permeation of Pressure Loss and Wall-Sorption (I).” The wall saturation rate (β) is also entered and the total non-permeation pressure loss and wall-sorption are calculated at 24. This calculation continues at 26 and the data is displayed at the graphical interface titled “Calculation of Total Non-Permeation Pressure Loss and Wall-Sorption (II)” illustration in FIG. 3E. Shelf-life data is entered at 28 automatically as illustrated in the graphical interface titled “Shelf-life Calculation” shown in FIG. 3F and the shelf-life is calculated at 30. Lastly, the carbon dioxide loss is calculated at 32 and the results are shown in graphical interface titled “Calculation Of CO₂ Loss In CCM” illustrated in FIG. 3G.
• According to another embodiment of this invention, a second computer program enables the evaluation of nearly all parameters from just one pressure decay curve. The only prerequisite is the independent determination of the (fictive) filling pressure p_F from V_o and V₁(t₁). This program is based on an “evolution principle” and makes a best fit of the theoretical decay curve equation [9] and [10] described above to an experimental pressure decay curve. This experimental decay curve may be determined by pressure gauge, FTIR, or the stitching method. From this fit all parameters with exception of p_F can be obtained. It is necessary to reduce the value-range of the parameters within certain (reasonable) limits, in order to limit the calculation time. The advantage of this procedure is that this evaluation method delivers all relevant parameters by reducing additional measurements to a minimum.
• The process steps of this second computer program are illustrated in the flow chart shown in FIG. 4. This second program begins at 40 and the test data described above is loaded at 42 and 44. The variable p_o is calculated at 46 and the variable x is calculated at 48. The variable x corresponds to p_s as shown in equation (4) above. Calculation then continues through the steps 50-60 and the results are shown at 32. The graphical interface for this process is illustrated in FIG. 5.
• The shelf-life and carbon dioxide losses are then calculated in accordance with the method steps shown in FIG. 6. The program begins at 70 and test parameters are entered at 72. The non-permeation pressure loss is calculated at 74, the shelf-life values are entered at 76, the shelf-life is calculated at 78 and the individual carbon dioxide losses are calculated at 80. A container evaluation sheet is then displayed as illustrated in FIG. 7. This display shows the parameters and results of the calculations.
• It should be understood that the foregoing relates to particular embodiments of the present invention and that numerous changes may be made therein without departing from the scope of the invention as defined by the following claims.

Claims (1)

1. A method for evaluating shelf-life and carbonation loss of a plastic container pressured at least in part with carbon dioxide comprising:

collecting in container pressure decay data based on analysis of plastic container pressurized at least in part with carbon dioxide;

inputting the pressure decay data into a computer; and

processing the data with the computer to calculate the shelf-life and carbon dioxide loss o the plastic container.

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