Extruder simulation method and simulation program

Abstract

To provide a method of simulating an extruder that can accurately predict the viscosity and temperature of a resin after being processed by high-speed rotation and of the resin inside the device, when the viscosity of the resin is reduced by a screw that rotates at high speed.SOLUTION: A extruder simulation method of the invention comprises: a Nusselt number calculation step S10 of calculating the Nusselt number for each combination of the screw rotation number and barrel temperature of the extruder; an estimation value setting step S11 of setting estimated values of the pressure, temperature and viscosity of the resin using the extruder outlet as the target site; a temperature and viscosity gradient calculation step S15 of calculating the temperature and viscosity gradients at the target site using the Nusselt number, the flow velocity and the pressure gradient; and a pressure / temperature / viscosity calculation step S16 of calculating the pressure, temperature and viscosity of the adjacent site, wherein if the calculated value and the measured value match, the pressure, temperature and viscosity of the resin set as estimated values in step S11 of setting estimated values are used as predicted values.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a simulation method and a simulation program for an extruder, which predict the pressure, residence time, resin filling rate, resin viscosity, temperature, etc. in the extruder and after pyrolysis when the screw of the extruder is rotated at a high speed to pyrolyze the resin.

Background Art

[0002] Melt-blown nonwoven fabrics used for filtration media, medical fabrics, sound-absorbing materials, cushioning materials, etc. are manufactured by passing molten resin through nozzles having small holes of about 0.1 mm. Since the nozzle is damaged when a high pressure is applied to the nozzle, a low-viscosity grade resin having an extremely high melt flow rate (hereinafter, appropriately referred to as MFR) is used as a raw material for manufacturing the melt-blown nonwoven fabric. However, resins such as low-viscosity polypropylene (hereinafter, appropriately referred to as PP) having an MFR value of about 1000 g / 10 minutes are special grades that are not widely available on the market, and thus are several times more expensive than ordinary grades. Therefore, it is useful and economical if a low-viscosity resin can be produced by reducing the molecular weight of a readily available and inexpensive general-purpose resin.

[0003] Conventionally, as one of the known methods for reducing the molecular weight of resins, there is a method using an organic peroxide. In this method, a resin (polymer) and an organic peroxide are mixed using a twin-screw extruder to chemically decompose the resin. However, since the organic peroxide has high reactivity, it is difficult to control the decomposition of the resin. In addition, since decomposition residues of the peroxide are generated by the decomposition of the resin, the resin having a reduced molecular weight by this method is not suitable for medical and sanitary products. In addition, since the organic peroxide is classified as a dangerous substance, there is a problem that care must be taken in handling and storage.

[0004] We have proposed a manufacturing method for reducing the molecular weight of a resin without using an organic peroxide by applying a high shear force to the molten resin to reduce its molecular weight (Patent Document 1). This manufacturing method induces shear heat generation by shear stress to reduce the molecular weight of the resin, and is excellent in that the reduction of the molecular weight can be controlled by the rotational speed of the screw, and resins with different grades (molecular weights) can be manufactured quickly and easily.

[0005] In addition, a simulation method based on the configuration and operating conditions of an extruder for the treatment of a resin using an extruder has also been proposed. For example, Non-Patent Document 1 describes a simulation method for a twin-screw extruder.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Non-Patent Documents

[0007]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] However, the simulation method of Non-Patent Document 1 targets rotational speeds up to 1000 RPM (revolutions per minute) and does not consider the reduction of the molecular weight of the resin by the extrusion process. Therefore, it has been difficult to accurately simulate the case where the viscosity of the resin is rapidly reduced by processing at a high rotational speed of about 2000 to 4000 RPM as in the manufacturing method described in Patent Document 1. An object of the present invention is to provide a simulation method and a simulation program for an extruder that can accurately predict the pressure, residence time, resin filling rate, resin viscosity, temperature, etc. inside and after the extruder when reducing the viscosity of the resin by a screw rotating at high speed.

Means for Solving the Problems

[0009] The simulation method of the extruder of the present invention includes a Nusselt number calculation step of calculating the Nusselt number of the screw for each combination of the screw rotation speed and the barrel temperature of the extruder, an estimated value setting step of setting estimated values of the pressure, temperature, and viscosity of the resin with the outlet of the extruder as the target site, a flow velocity-pressure gradient calculation step of calculating the flow velocity and pressure gradient of the resin at the target site using the physical properties of the resin, the configuration of the extruder, and the operating conditions, a temperature gradient-viscosity gradient calculation step of calculating the temperature gradient and viscosity gradient at the target site using the Nusselt number, the flow velocity, and the pressure gradient, a pressure-temperature-viscosity calculation step of calculating the pressure, temperature, and viscosity of an adjacent site located a predetermined distance away from the target site toward the inlet side of the extruder using the pressure gradient, the temperature gradient, and the viscosity gradient, and a site determination step of determining whether the adjacent site is the inlet of the extruder. In the site determination step, when it is determined that the adjacent site is not the inlet of the extruder, the adjacent site is set as a new target site, and the flow velocity-pressure gradient calculation step, the temperature gradient-viscosity gradient calculation step, the pressure-temperature-viscosity calculation step, and the site determination step are performed using the calculated values calculated by the pressure-temperature-viscosity calculation step. In the site determination step, when it is determined that the adjacent site is the inlet of the extruder, a comparison step of comparing the calculated values calculated by the pressure-temperature-viscosity calculation step with the measured values at the inlet is performed. In the comparison step, when the calculated values and the measured values do not match, the process returns to the estimated value setting step, and another estimated value is set using a root-finding algorithm so that the residuals of the pressure, temperature, and viscosity of the resin are reduced, and the above steps are repeated until the calculated values and the measured values match. In the comparison step, when the calculated values and the measured values match, the pressure, temperature, and viscosity of the resin set as the estimated values in the estimated value setting step are used as the predicted values.

Advantages of the Invention

[0010] The simulation method of the present invention can accurately reflect the screw rotation speed and barrel temperature dependence of heat transfer from the barrel by calculating the Nusselt number of the screw for each combination of the screw rotation speed and barrel temperature of the extruder. Therefore, by using this Nusselt number to calculate the temperature gradient and viscosity gradient at the target site, even when the viscosity of the resin is rapidly decreased by the high-speed rotation of the screw, the viscosity and temperature of the resin after processing and inside the apparatus can be accurately predicted.

Brief Description of Drawings

[0011]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Modes for Carrying Out the Invention

[0012] Hereinafter, embodiments of the present invention will be described with reference to the drawings as appropriate. <Flow of Resin in Extruder> A one-dimensional model of resin flow inside an extruder in the case of a non-Newtonian fluid will be described below. In the simulation of the present invention, the flow of resin in the extruder is assumed to be a fully developed flow in a steady state. Since the ratio of the inner diameter to the outer diameter of the screw is close to 1, the curvature of the screw groove is assumed to be negligible.

[0013] <Screw> Figure 2 is a schematic diagram showing the screw shape of a single-screw extruder. The screw was modeled as a rectangular groove (channel) with a height H and a width W in cross section. The barrel was modeled as a moving plate covering the groove of the screw. In this case, the moving speed V of the plate is represented by V = πDN (where D is the inner diameter of the barrel and N is the rotational speed of the screw).

[0014] In the rectangular groove, the length direction of the groove was taken as z. In a shallow and wide groove, the resin flow velocity v in the z direction z can be treated as a function of the groove depth direction y. The equation of motion of the resin is shown below. In each of the equations described below, each symbol represents the same content.

Equation

[0015] The boundary conditions are shown below.

Number

[0016]

Number

[0017] When the target part in the screw is in a non - filled state partially filled with resin, the pressure gradient α is zero. Therefore, the flow of the resin in the non - filled region is represented by the following simple equation (4) based on Equation (1).

Number

[0018] The filling ratio f at the target part that is the object of the calculation evaluation is defined by the following equation.

Number

[0019] The viscosity of the molten resin is generally a function of the shear rate shown by the following equation.

Number

[0020] In the following simulation method, the Cross model is adopted as the viscosity model of non-Newtonian fluid. However, the viscosity model of non-Newtonian fluid is not limited to the Cross model, and other models may be adopted.

Number

[0021] η 0 is assumed to follow the Arrhenius law.

Number

[0022] The equation of motion of the resin is shown below.

Number

Number

[0023] The initial conditions are shown below.

Number

[0024] The boundary conditions are shown below.

Number

[0025] Performing partial integration of Equation (8) with respect to y and using Equation (1), the following equation is obtained.

Number

Number

[0026] The second term and the last term on the right side of Equation (13) are caused by shear heating. The first term on the right side of Equation (13) represents heat conduction from the fluid to the barrel and can be modeled as follows in the case of a one-dimensional problem.

Number

[0027] When operating conditions of an extruder are selected from a wide numerical range with respect to the screw rotation speed and the barrel temperature, it is not appropriate to set the Nusselt number as a constant under all operating conditions. Therefore, for each condition of the screw rotation speed and the barrel temperature, assuming a uniform temperature distribution at the extruder inlet and assuming the case of simple shear flow for the flow velocity (Equation (4)), the heat conduction equation (8) and the boundary condition equations (11) and (12) are solved by calculation to calculate the temperature distribution and the heat flux in the y - direction and the z - direction. Then, the Nusselt number of the target part is obtained by the following equation (Bird, R.B.; Armstrong, R.C.; Hassager, O. Fluid Mechanics. Dynamics of Polymeric Liquids, 2nd ed.; John Wiley and Sons Inc: New York, NY, USA, 1987; Volume 1.).

Number

[0028] In the simulation of the present invention, the average Nusselt number represented by the following equation was used.

Number

[0029] <Die> A die used in an embodiment described later, which has a hole with a circular cross - sectional shape orthogonal to the z - direction, and a through - hole will be described. The equation of motion in the die is shown below.

Number

[0030] The boundary conditions are shown below.

Number

Number

[0031] The equation of motion is shown below.

Number

Number

Number

[0032] <Viscosity reduction model> At high rotational speeds and high barrel temperatures, the resin (polymer) thermally degrades due to increased shear heating and heat conduction. Although various studies have been conducted on the thermal degradation of resins (Kim, B.; White, J.L. Simulation of Thermal Degradation, Peroxide Induced Degradation, and Maleation of Polypropylene in a Modular Co-Rotating Twin Screw Extruder. Polym. Eng. Sci. 1997, 37, 576, etc.), the simplest model is adopted in this simulation. That is, it is assumed that the resin is composed of linear polymers and that the thermal degradation of the polymers follows a random cleavage process.

[0033] The polymer was modeled as a long chain with the number of nodes N. N represents the backbone carbon atoms (Rubinstein, M.; Colby, R.H. Polymer Physics; Oxford University Press Inc: NY., 2003). Let the number of polymers with the number of nodes N be n N Then, all the number of nodes in the polymer is given by the following equation.

Equation

[0034] Assuming that the cleavage of the main chain follows a first-order reaction with a reaction rate k and that no re-polymerization occurs, the following relationship holds.

Equation

Equation

[0035] Ignoring the volatile content of the resin, the number of all nodes in the resin, as shown by the following equation, does not change with time.

Number

[0036] Since the number-average molecular weight is given by the following equation (26), the equation (27) for the time evolution of the number-average molecular weight can be obtained (Suehiro, T.; O'shima, E. A kinetic study on the random scission of a polymer. Kobunshi Ronbunshu. 1977, 34, 3, 241-248.).

Number

[0037] When the number-average molecular weight is sufficiently large, equation (27) becomes as follows.

Number

[0038] Since the zero-shear viscosity is known empirically to be proportional to the 3.4th power of the number-average molecular weight, the following equation (29) holds. In equation (29), the proportionality coefficient between the zero-shear viscosity and N is absorbed into the frequency factor A in the viscosity reduction rate model.

Number

[0039] When the resin is flowing, the time derivative can be replaced by the material derivative, and in the steady state, the following equation (30) holds.

Number

[0040] <Calculation method> FIG. 1 is a flowchart of the simulation method of the present embodiment. In the present embodiment, when resin temperature and viscosity data at the extruder inlet are given, for all positions in the axial direction of the extruder, pressure p, temperature T, and reference zero-shear viscosity η at the reference temperature (hereinafter, also referred to as viscosity as appropriate) will be calculated. Hereinafter, the axial coordinate in the extruder is denoted by z. Note that the order of each step shown below is an example, and each step may be performed in an order different from that in FIG. 1, except when using the values obtained and calculated in the previous step. r First, the case where the Nusselt number Nu is calculated in the Nusselt number calculation step S10 will be described. For the calculation of Nu, when the part where the pressure, temperature, and viscosity of the resin are to be calculated is the screw, Equation (17) is used for the calculation, and when it is the die or the through-hole, Equation (23) is used. The simulation method of the present invention calculates the Nusselt number Nu in the screw for each combination of the screw rotation speed and the barrel temperature of the extruder. In S10, the average Nusselt number calculated using Equation (17) is used as the Nusselt number in the screw, and the Nusselt number calculated using Equation (23) is used as the Nusselt number in the die or through-hole, which is a part other than the screw.

[0041] Subsequently, an estimated value setting step S11 is performed to set estimated values of the resin pressure, temperature, and viscosity with the extruder outlet as the target part. In S11, the part z to be calculated is set as the extruder outlet z (z = z). Since the pressure p at z is the atmospheric pressure (ambient pressure), the estimated value p is set to 0 (p = 0). Then, as the estimated values T and η of the temperature T and viscosity η, the temperature T and viscosity η at z are set (T = T, η

[0042] Next, with the extruder outlet as the target part, an estimated value setting step S11 for setting estimated values of the resin pressure, temperature, and viscosity is performed. In S11, for the part z to be calculated, O is set as the extruder outlet z f (z O = z f ). Since the pressure p at z is the atmospheric pressure (ambient pressure), the estimated value p f is set to 0 (p O = 0). And for the estimated values T and η O of the temperature T and viscosity η r , the temperature T O and viscosity η r O at z f are set as the estimated values T f and η rf (T O = T f0 , ηr O = η rf0 )。

[0043] Subsequently, a target part determination step S12 is performed to determine whether the target part is a screw or other part. In the case of an extruder equipped with a screw, a die, and a through-hole, in S12, it is determined whether the target part z O is a screw, a die, or a through-hole.

[0044] In S12, if the outlet z f is determined to be a die or a through-hole, the process proceeds to S13, and the flow rate v z of the resin and the pressure gradient ∂p / ∂z are calculated. These calculations are performed by an iterative method by giving appropriate estimated values to the flow rate v z , the pressure gradient ∂p / ∂z. In this embodiment, the analytical solution for the case of a power-law fluid is selected as the estimated value. By solving equations (18) and (20), the actual resin extrusion rate (extrusion amount) Q from the extruder and the calculated resin extrusion rate Q th are made to match, and the flow rate v z of the resin and the pressure gradient ∂p / ∂z are calculated.

[0045] In the flow rate - pressure gradient calculation step S14, using the physical properties of the resin, the configuration of the extruder, and the operating conditions, the flow rate v z of the resin and the pressure gradient ∂p / ∂z at the target part are calculated. In FIG. 2, based on the results calculated in S13, the flow rate v z and the pressure gradient ∂p / ∂z are calculated. Note that when the target part is a die or a through-hole, the filling ratio f of the resin filling region is 1.

[0046] In the temperature gradient - viscosity gradient calculation step S15, using the Nusselt number Nu calculated in S10, the flow rate v z calculated in S14, and the pressure gradient ∂p / ∂z, the temperature gradient ∂T / ∂z and the viscosity gradient ∂η O / ∂z at the target part z = z r are calculated. When z O is a die or a through-hole, ∂T / ∂z and ∂η rTo calculate ∂z, equations (21) and (30) are used.

[0047] In S12, when the target part z O is determined to be a screw, the process proceeds to the filling degree determination step S20. In S20, it is determined whether the pressure p O > 0, that is, whether the pressure p O is positive or zero or less.

[0048] p 0 > 0 (positive), all the target parts of the screw are filled with resin. Therefore, similar to the case of the die through-hole described above, the resin flow velocity v z and the pressure gradient ∂p / ∂z are calculated by S13 and S14. Then, in the temperature gradient - viscosity gradient calculation step S15, using the Nusselt number Nu calculated in S10, the v z in S14 and ∂p / ∂z, ∂T / ∂z and ∂η O / ∂z at z = z r are calculated. However, when the target part is a screw, in S13, equations (1) and (3) are used instead of equations (18) and (20), and in S15, equations (13) and (30) are used instead of equations (21) and (30). In this case as well, the filling ratio f of the resin filling area is 1.

[0049] p O is not > 0 but 0 or negative (p O ≤ 0), the target part of the screw is a non - filled area partially filled with resin. Therefore, in S21, the pressure p O of the target part is reset to 0, and the pressure gradient ∂p / ∂z is also set to 0. In the non - filled area, the resin flow velocity v z is given by equation (4), and the filling ratio f is given by equation (5). Based on these, in the flow velocity - pressure gradient calculation step S22, the resin flow velocity v z , the pressure gradient ∂p / ∂z and the filling ratio f are calculated. Then, in the temperature gradient - viscosity gradient calculation step S15, using the Nusselt number Nu calculated in S10, the v z calculated in S22 and ∂p / ∂z, at z = z OCalculate ∂T / ∂z and ∂η r / ∂z. In S15, similar to the full region, equations (13) and (30) are used.

[0050] Subsequently, move to the pressure - temperature - viscosity calculation step S16. In S16, using the pressure gradient ∂p / ∂z in S14, the temperature gradient ∂T / ∂z and the viscosity gradient ∂η r / ∂z, from the target site z O to the adjacent site z O -δz which is a predetermined distance δz away from the inlet side of the extruder, calculate the pressure p = p O -(∂p / ∂z)δp, the temperature T = T O -(∂T / ∂z)δz, and the viscosity η r = η r O -(∂η r / ∂z)δz. Here, δz is the discretization size on the z - axis.

[0051] In the site determination step S17, determine whether the adjacent site z = z O -δz is 0, that is, whether it is the inlet of the extruder. In S17, if it is determined that the adjacent site z O -δz is not the inlet of the extruder, move to S18. In S18, set the adjacent site z O -δz as the new target site z O (z O = z), the pressure p O , the temperature T O and the viscosity η r such that p = p O , T = T O and η r = η r O respectively, and move to S12. Then, using the calculated values of pressure p, temperature T, and viscosity η r calculated in the pressure - temperature - viscosity calculation step S16, perform the flow rate - pressure gradient calculation step S14, the temperature gradient - viscosity gradient calculation step S15, the pressure - temperature - viscosity calculation step 16, and the site determination step S17 again.

[0052] In the above manner, until it is determined in S17 that z = 0, that is, the target part is the inlet of the extruder, the process returns to S12 via S18, and the steps of calculating the pressure, temperature, and viscosity for each part of the extruder are repeated.

[0053] If it is determined in the part determination step S17 that z = 0, that is, it is the inlet of the extruder, the process proceeds to the comparison step S23, and the calculated values in the pressure·temperature·viscosity calculation step S16 are compared with the measured values at the inlet. In S23, the calculated values of the temperature T and viscosity η r at the inlet, and the temperature T i and viscosity η ri of the measured values are used to determine whether they match. Here, "match" means that the calculated value and the measured value are sufficiently close, for example, the difference between the two is equal to or less than a predetermined threshold value. The threshold value can be set as appropriate. For example, the relative error between the calculated value and the measured value can be set to about 10 -6 .

[0054] If the calculated value and the measured value do not match in the comparison step S23, the process returns to the estimated value setting step S11, and different estimated values are set for the pressure, temperature, and viscosity of the resin, and the above steps are repeated until the calculated value and the measured value match. The different estimated values are calculated using a root-finding algorithm so that the residual becomes small. An example of the root-finding algorithm is the Newton method.

[0055] If the calculated value and the measured value match in the comparison step S23, the pressure, temperature, and viscosity of the resin set as the estimated value in the estimated value setting step S11 are used as the simulation results.

[0056] In the above manner, along the z-axis of the extruder, the calculations of p, T, and η O at z - dz are repeated to obtain p, T, and η r at the inlet of the extruder where z = 0. The T and η r obtained as the calculated values at z = 0, which are set as the estimated values in S11, and the T r obtained as the measured value, iand η ri so that they approach, T at the outlet of the extruder f0 and η rf0 are repeatedly updated. After the calculation is repeated, the calculated values T, η r and the measured value T i , η ri When they match, as the predicted values of the simulation results, p, T, η at each position along the outlet of the extruder and the z-axis r are obtained.

[0057] In addition, in the embodiment, as an example, the case of obtaining p, T, and η at each position along the outlet of the extruder and the z-axis as simulation results has been described. However, in addition to the pressure, the viscosity and temperature of the resin in the extruder and after processing, the residence time (cumulative residence time) and the filling rate of the resin can be obtained. r The present invention can also be implemented as a program that causes a computer to execute the above-described simulation method of the single-screw extruder.

Example

[0058] <Apparatus> FIG. 3 schematically shows an overall view of the apparatus used in the example. As shown in the figure, an apparatus in which two different extruders are connected in series via a single pipe having a diameter of 10 mm and a length of 150 mm was used. The resin supplied from the resin supply section is melted by a twin-screw extruder and then supplied to the inlet of a high-shear extruder which is a single-screw extruder. The first extruder is a co-rotating twin-screw extruder (L / D = 48.5, D = 26 mm, manufactured by Shibaura Machine Co., Ltd.) and was used to melt the resin. The resin temperature at the outlet of the twin-screw extruder was 468 K (195 ° C) in all examples.

[0059] FIG. 4 is a schematic diagram showing the configuration and temperature conditions of the twin-screw extruder, and the arrows in the figure indicate the direction of the resin flow. As the twin-screw extruder, one having a length of 1260 mm and an inner diameter of the barrel of 26 mm was used. The extrusion speed (resin supply speed, extrusion amount) and the rotation speed N in the example are shown in Table 1.

Table 1

[0060] The second extruder is a single-screw high-shear extruder with a barrel diameter of 48 mm and a maximum rotational speed of 3,600 revolutions per minute. In the high-shear extruder, the polymer's molecular chains are thermally cut due to shear heating. The screw is composed of a plurality of screw elements, similar to a normal twin-screw extruder. In the screw used in the examples, since the difference in the shape of the screw elements constituting the screw has little effect on the melt flow rate, for screws with different screw elements, the shape of the screw element on the most upstream side of the screw, that is, the resin's most upstream side, was used. And the melt flow rate of the screw was calculated using the total length of the plurality of screw elements. Also, when there is a through-hole in the screw, it was replaced with one without a through-hole to evaluate the melt flow rate of the screw.

[0061] Figure 5 schematically shows a part of the high-shear extruder. As shown in the figure, the screw element has a through-hole with a circular cross-section. The arrow in the figure indicates the direction of the resin flow. The resin is blocked by the reverse screw and flows into the through-hole. The role of these elements is to form a region completely filled with resin in front of the reverse screw while preventing excessive shear force from being applied to the resin to prevent excessive low molecular weight. The resin discharged from the die of the high-shear extruder was immediately cooled with water and then dried.

[0062] <Raw material> Two different grades of homopolypropylene (F-704NP and J107G, manufactured by Prime Polymer) were used. The melt flow rates were 7.0 and 30 g / 10 min, respectively. The measurements were carried out in accordance with ISO1133-97. Hereinafter, F-704NP is denoted as PP1 and J107G as PP2. To evaluate the parameters of equations (6) and (7) of the viscosity model, the shear viscosity was measured with a modular compact rheometer (MCR 102 Anton Paar, Graz, Austria). The measurement range of the shear rate was 0.01 - 100 / s, and the measurement temperatures were 463, 473 and 483 K (190, 200, and 210 °C). The reference temperature was set at 473 K (200 °C). The model parameters of PP1 and PP2 obtained as a result of curve fitting are shown in Table 2. Figures 6 and 7 show the viscosity data and curves of PP1 and PP2.

[0063]

Table 2

[0064] To evaluate the activation energy of PP, Kissinger's method was used (Chan, J.H.; Balke, S.T. The thermal degradation kinetics of polypropylene: Part III. Thermogravimetric analyses. Polym. Degrad.Stab. 1997, 57, 135-149.). To obtain the weight loss data due to thermal decomposition of PP, PP1 was measured in an air atmosphere using a simultaneous thermogravimetric analyzer (STA7200, manufactured by Hitachi High-Technologies Corporation). The heating rates were 2, 4 and 8 K / min. In each measurement, the sample weight was approximately 10 mg. Figure 8 is a graph showing the results of thermogravimetric analysis (TGA) of PP1. For each heating rate β (K / min) in the TGA analysis, the temperature at the weight fraction X was measured. The following equation was used in Kissinger's method.

[0065]

Number

[0066] <Example 1: Examination of the Nusselt number> Figure 10 shows an overview of the screw configuration of the high-shear extruder used in this example. Note that the arrows in the figure indicate the direction of resin flow, and the resin flow is indicated by arrows in the following figures as well. A screw element with a groove having a depth of 3 mm, a lead of 15 mm, and a length of 45 mm was used. For the high-shear extruder, a die with a hole diameter of 4 mm and a length of 25 mm was used, and the extrusion speed was 4.8 kg / hour. The barrel temperatures were 468 K and 573 K (195 °C and 300 °C). The screw rotation speeds were 100, 1000, and 2000 revolutions per minute. PP1 was used as the resin, and the temperature of PP1 at the die outlet was measured.

[0067] <Molecular chain scission of PP by a high-shear extruder> <Example 2> Figure 11 is a schematic diagram showing the screw configuration of the high-shear extruder. A screw element with a groove having a depth of 3 mm, a lead of 22.5 mm, and a length of 45 mm was used. The last screw element in the resin flow direction is different from the previous screw element in that the groove depth is the same, but the lead is 15 mm and the length is 30 mm. Regarding the Nusselt number of the screw in this example, the shape of the last screw element was replaced with the shape of the screw element on the most upstream side of the resin for evaluation. However, other calculations related to flow rate calculation, etc. were performed considering the geometry of the last screw element.

[0068] In Figure 11, the shaded part shows a reverse-thread element with through-holes (see Figure 5). This element has four through-holes with a diameter of 2 mm and a length of 45 mm. The high-shear extruder is equipped with a die with a diameter of 2 mm and a length of 25 mm. The barrel temperature was set at 468 K (195 °C), and the extrusion speed was 4.8 kg / hour. The screw rotation speeds were 2000, 2500, 3000, and 3600 revolutions per minute. PP1 was used as the resin. The temperature of PP1 was measured at point P in Figure 11 and at the die outlet. The zero-shear viscosity of PP1 after high-shear treatment was measured at a reference temperature of 473 K (200 °C).

[0069] <Example 3> Figure 12 is a schematic diagram showing the screw configuration of the high-shear extruder used in this example. A screw element with a groove depth of 3 mm, a lead of 15 mm, and a length of 45 mm was used. The shaded part in Figure 12 is the same as in Example 2. A high-shear extruder equipped with a die with a diameter of 3 mm and a length of 25 mm was used. PP2 was used as the resin. The extrusion speed was fixed at 10 kg / hour and the screw rotation speed was fixed at 3600 revolutions per minute, and the barrel temperature was set at 578 K or 628 K (300 °C or 350 °C). The resin temperature was measured at the die outlet. The zero-shear viscosity of PP2 after high-shear treatment was measured at a reference temperature of 473 K (200 °C).

[0070] <Results> Table 3 shows the predicted values and measured values obtained from the simulation of Example 1. Here, since only heat conduction is focused on, the influence of viscosity reduction is not considered. When the screw rotation speed was fixed at 100 revolutions per minute and the barrel temperature was increased from 473 K to 578 K, the calculated value of the Nusselt number became slightly larger. As a result, the calculated value T of the temperature at the outlet of the high-shear extruder f Similarly, it also changed from the calculated value obtained using Nu = 8.92 when N = 100 revolutions per minute and the barrel temperature Tb = 473 K. It was clarified that by optimizing the Nusselt number, the predicted value by simulation approaches the measured value.

Table 3

[0071] When the barrel temperature was fixed at 468K (195°C) and the screw rotation speed was increased from 100 rpm to 1000 rpm or more, the value of the Nusselt number obtained by calculation increased. This is because the heat transfer coefficient in the case of forced convection depends on the flow velocity, and the resin flowing at high speed is cooled to a large extent by the barrel. As a result, the T predicted by the simulation method of the present invention f The predicted value of is the predicted value T obtained using Nu=8.92. f From this, it can be said that the simulation method of the present invention incorporates the effects of the screw rotation speed and barrel temperature, which were not considered in the past, into the predicted value as the Nusselt number. f The large difference in viscosity is believed to be due to the decrease in resin viscosity caused by thermal decomposition.

[0072] <Decomposition of PP using a high shear extruder> 13A and 13B are graphs showing predicted and measured values ​​obtained by the simulation results at 3600 rpm in Example 2. As shown in Figs. 13A and 13B, when the frequency factor A is set to 0 (not considering viscosity reduction), the predicted temperature and the reference zero shear viscosity at the outlet of the high shear extruder do not match the measured values. This is because the reference zero shear viscosity η r This is because A does not decrease and shear heat is overestimated. 5 The predicted values ​​from the simulation with A set to 5.7×10 were in good agreement with the measured values. 5 Fixed to.

[0073] Table 4 shows the predicted values ​​and the measured values ​​obtained by the simulation of Example 2. At all rotation speeds, the predicted values ​​of Tp and ηrf were in excellent agreement with the measured values. [Table 4]

[0074] Figures 14A and 14B show the simulation results of temperature and reference zero-shear viscosity in Example 2. As the screw rotation speed increased, the temperature increased due to shear heating, and the viscosity decreased due to thermal decomposition (molecular chain scission) of the resin. The viscosity decreased significantly at the positions in front of the through-hole and the die. This is because at this position, the screw is completely filled with the resin, so a large shear force is applied to the resin, and the residence time is also longer compared to the non-filled state. Inside the through-hole and the die, the shear force applied to the resin is small, and the residence time is short, so the thermal decomposition of the resin is suppressed. In the through-hole, the temperature did not change significantly because it was in a heat-insulated state, but since the die was maintained at 568 K (195 °C), the temperature of the resin decreased at the die.

[0075] After the resin was discharged from the through-hole, despite the high screw rotation speed, the temperature of the resin gradually decreased. This is because the shear heating generated in the resin decreased due to the decrease in viscosity in front of the through-hole (upstream side of the resin flow), and heat conduction to the barrel became dominant.

[0076] In Example 3, the barrel length was increased and the barrel temperature was changed to 573 K (300 °C) or higher. The screw rotation speed was fixed at a maximum value of 3600 revolutions per minute. A screw with four stoppers having four through-holes was used.

[0077] Table 5 shows the simulation and measured values of the outlet temperature and the reference zero-shear viscosity at the outlet in Example 3. The predicted value of the outlet temperature by simulation was slightly lower than the measured value as predicted from Example 2, but the simulation results of the reference zero-shear viscosity were in good agreement with the measured values.

[0078] Figure 15 is a calibration curve (calibration line) created to specify the MFR value of the resin. The MFR values of Tb = 573 K and 623 K (300 °C, 350 °C) obtained using this calibration line were 938 g / 10 minutes and 2411 g / 10 minutes, respectively. In this way, various low-molecular-weight PPs having an MFR value of 1000 g / 10 minutes or more were successfully produced using a high-shear processing apparatus.

[0079]

Table 5

Industrial Applicability

[0080] The present invention can be used, for example, to predict the pressure, residence time, resin filling rate, resin viscosity, and temperature in an extruder and after treatment when a shearing force is applied to a commonly used polypropylene resin to produce a low-viscosity polypropylene resin that can be used as a raw material for nonwoven fabrics.

Claims

1. A Nusselt number calculation step of calculating the Nusselt number in the screw for each combination of the screw rotation speed and the barrel temperature of the extruder; An estimated value setting step of setting estimated values of the pressure, temperature, and viscosity of the resin with the outlet of the extruder as the target part; A flow velocity and pressure gradient calculation step of calculating the flow velocity and pressure gradient of the resin at the target part using the physical properties of the resin, the configuration of the extruder, and the operating conditions; A temperature gradient and viscosity gradient calculation step of calculating the temperature gradient and viscosity gradient at the target part using the Nusselt number, the flow velocity, and the pressure gradient; A pressure, temperature, and viscosity calculation step of calculating the pressure, temperature, and viscosity of an adjacent part located at a predetermined distance from the target part on the inlet side of the extruder from the target part using the pressure gradient, the temperature gradient, and the viscosity gradient; A part determination step of determining whether the adjacent part is the inlet of the extruder, comprising: In the part determination step, when the adjacent part is determined not to be the inlet of the extruder, the adjacent part is set as a new target part, and using the calculated values calculated by the pressure, temperature, and viscosity calculation step, the flow velocity and pressure gradient calculation step, the temperature gradient and viscosity gradient calculation step, the pressure, temperature, and viscosity calculation step, and the part determination step are performed; In the part determination step, when the adjacent part is determined to be the inlet of the extruder, a comparison step of comparing the calculated value calculated by the pressure, temperature, and viscosity calculation step with the measured value at the inlet is performed; In the comparison step, when the calculated value and the measured value do not match, return to the estimated value setting step, and for the pressure, temperature, and viscosity of the resin, set another estimated value using a root-finding algorithm so that the residual is reduced, and repeat the above steps until the calculated value and the measured value match; In the comparison step, when the calculated value and the measured value match, the pressure, temperature, and viscosity of the resin set as the estimated value in the estimated value setting step are used as the predicted values; A simulation method for an extruder.

2. A target part determination step of determining whether the target part is the screw or another part, and In the target part determination step, when the target part is determined to be the screw, a fullness determination step of determining whether the pressure is positive or zero or less is further provided. The simulation method of an extruder according to claim 1.

3. The Nusselt number calculation step is as follows: The Nusselt number Nu in the screw is calculated using the following formula (17): 【Number 1】 (In formula (17), L p is the path length of the screw, z is the coordinate in the extension direction of the screw path, and Nu Z is represented by the following formula (16).) 【Number 2】 (In formula (16), H is the height of the screw groove, q is the heat flux, z is the coordinate in the extending direction of the screw path, y is the coordinate in the depth direction of the screw groove, κ is the thermal conductivity of the resin, Tb is the barrel temperature, and T(z) is represented by the following formula (14).) [Number 3] (In Formula (14), H is the height of the screw groove, y is the coordinate in the depth direction of the screw groove, v z is the flow rate of the resin in the extending direction of the screw path, and T is the temperature of the resin.) The Nusselt number Nu at a part other than the screw is calculated using the following formula (23). 【Number 4】 (In formula (23), κ is the thermal conductivity of the resin, l is the length of the die or the through hole, n is the viscosity index when assuming a power-law fluid, ρ is the melt density of the resin [kg / m 3 , C p is the specific heat of the resin [J / (kg·K)], and Q is the extrusion rate of the resin (m 3 / second).) The simulation method of an extruder according to claim 2.

4. A Nusselt number calculation step of calculating the Nusselt number of the screw for each combination of the screw rotation speed and the barrel temperature of the extruder; An estimated value setting step of setting the pressure, temperature, and viscosity of the resin with the outlet of the extruder as the target part; A flow velocity and pressure gradient calculation step of calculating the flow velocity and pressure gradient of the resin at the target part using the physical properties of the resin, the configuration of the extruder, and the operating conditions; A temperature gradient and viscosity gradient calculation step of calculating the temperature gradient and viscosity gradient at the target part using the Nusselt number, the flow velocity, and the pressure gradient; A pressure, temperature, and viscosity calculation step of calculating the pressure, temperature, and viscosity of an adjacent part at a predetermined distance from the target part to the inlet side of the extruder using the pressure gradient, the temperature gradient, and the viscosity gradient; A part determination step of determining whether the adjacent part is the inlet of the extruder, and In the part determination step, when it is determined that the adjacent part is not the inlet of the extruder, the adjacent part is set as a new target part, and the flow velocity and pressure gradient calculation step, the temperature gradient and viscosity gradient calculation step, the pressure, temperature, and viscosity calculation step, and the part determination step are performed using the calculated values calculated by the pressure, temperature, and viscosity calculation step. In the part determination step, when it is determined that the adjacent part is the inlet of the extruder, a comparison step of comparing the calculated values calculated by the pressure, temperature, and viscosity calculation step with the measured values at the inlet is performed. In the comparison step, if the calculated value and the measured value do not match, return to the estimated value setting step, and for the pressure, temperature, and viscosity of the resin, set another estimated value using a root-finding algorithm so that the residual becomes small, and repeat the above steps until the calculated value and the measured value match. In the comparison step, when the calculated value and the measured value match, the pressure, temperature, and viscosity of the resin set as the estimated value in the estimated value setting step are used as the predicted values. A simulation program that causes a computer to execute a simulation method for an extruder.

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