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Prediction of Vinyl Chloride Monomer Migration from Rigid PVC Pipe A R. BERENS Corporate Research The B. F. Go<xIrieh Company Research and Dexelopment Center BrecisviUe. Ohio 44141 and C. A. DANIELS B. F. Goodrich Chemical Company Aocm Lake Technical Center Aeon Lake. Ohio 44012 Data on the solubility az.d diffusion of vinyl chloride monomer (VCM) in PVC resur powders have been combined with published solutions of Fsck's diffusion equation to yield predictions of the amount ac-d rate of loss of residual VCM (RVCM) from rigid PVC pipe under storage and serv ice condi tions. The principal factors comtrolling VCM migration are the initial VCM content thickness of the PVC section, tempera ture. and the age of the PVC product. Analytic solutions are presented for RVCM loss froc= freshly extruded pipe (uniform VCM concentration' into either the storage environment or the pipe contents. From these sotat.ons, estimates are made for the real-world situation of closetd-svstem service following vari able storage periods. The validity of this approach for rigid FYC pipe in water-service is supported by reasonable agree ment between its predictions and experimental laboratory data on the VCM content of water stored in PVC pipes. Both the predictive model and experimjer.tal data indicate that PVC pipe containing si mg kg (1 part per million) residual VCM will result in VCM concentrations ir. water of less than 0-002 mg^kg under anv expected serv ice conditions. INTRODUCTION A subject of continuing concern sincr the discovery of th* potential toxic hazard of vinyl chloride monomer iVC'M1 has U-en the migration of residual VCM from finished PVC products into the environment or into liquid' transported in PVC vessels. Many efforts have l>een made to investigate this problem bv direct analysis for VCM in media in contact with PVC vessels Earls efforts in 1973 were questionable because of the impre cise analytical methods then available. As analytical pr*cedures have been improved, the residual VCM levels m commercial PVC products have been sharplv rrduced mi the direct analysis for VCM migrating from todav s PVC products remains a very difficult problem. Recent data (1) show that sensitivity in the thousandths ol a milligram per kilogram range is needed to analyze lor VCM in water contained in PVC pipe even at the residual VCM level of 20 mg per kilogram. A reliable model for predicting the amount and rate ofVCM migra tion from available basic transport data and theory thus wuuld l>e very' useful. Our approach to the development of a predictive model has been to combine the solubility and diffusion data we hav e obtained for VCM in unrompounded PVC resin powders (2. 3) with the solutions of the Fiokean diffusion equations given by Crank <41. This report sum'marizes the assumptions and approximations ii* volved in applying these diffusion equations to the VCM migration problem and illustrates the possible calcula tions with some numerical examples. The predictions of our model are compared with experimental data on VCM content' >1 water stured m PVC pipe. CALCULATIONS OF VCM MIGRATION Background and Assumptions On the basic assumption that migration of VCM thru PVC is controlled by the diffusion of VCM in the PVC phase, this process may be treated by well-known theory. The basis of classical diffusion theory is the simple differential equation known as Ftck s First law, f C -Q -- ex (1) which states that the amount ofdiffusing substanie cross ing a unit plane area in unit time. F, is proportional to -- - C'-.V'x-o ,rt T* P - 10-r AP00055814 Prediction of IVny/ Cftlorrdc Monomer Migration from Rigid PVPC Pip-c the concentration gradient ten s$ the plane. --. The proportionality constant. D, is called the diffusion coefficient. The minus sign indicates that diffusion al ways occurs toward the region oflower concentration, i.e.. "downhill Net diffusive transport ceases when the concentration gradient becomes zero, i.e., when the concentration becomes uniform. The use of Fick's law to calculate useful quantities, suc-h as the rate at which a diffusing substance escapes from a solid object, or the concentration profile within the object, involves some very complicated mathemat ics Enact mathematical solutions are generally possible only for geometrically simple shapes and for certain specified initial and boundary conditions. Many of the useful solutions are presented in Crank's text (41, and fortunate!) it seems that some of the most important problems in VCM migration from PVC can be handled with a feu of these equations. Our application of these equations and our diffusion data to VCM migration from PVC products involves several assumptions: (1) The diffusion of VCM in PVC obeys Fick's law. (2) The diffusion coefficient is independent of VCM concentration. (31 The value of the diffusion coefficient in rigid PVC products is the same as we have determined for pure PVC resins. (4) The diffusion coefficient is independent of the medium surrounding the PVC; i.e., values we have determined bv vapor sorption/desorption also apply to migration into a liquid phase. Assumptions (1 > and t2) have been demonstrated to be ven satisfactory approximations at quite low RVCM concentrations by our work on PVC powders (3). More limited e^jH-nments on thin, rigid PVC films also sup port assumption (3>, although some variation of D might be expected for varving amounts and types of com pounding additives. The use ofassumption (4) should be considt red a tentatively useful approximation, we shall see that it does seem justified by experimental data on \ CM migration into water from PVC pipe. To describe the diffusion of RVCM from PVC prod ucts through Crank's equations, three situations have been considered: Case I: RVCM loss during storage of a freshlymanufactured PVC product. Case II: RVCM loss from freshly formed PVC products into a closed medium. Case III: RVCM loss into a closed medium from previously aged PVC products. In l*>tb Cases I and II. the initial RVCM concentra tion is assumed to be uniform through the thickness of tin- PVC product, this is probably a valid assumption only at the time of extrusion, as the surface concentra tion ol H\ CM will quickly decrease upon exposure to a lim-VCM environment. Cases 1 and II differ in the time-drpendcnce of the surface concentration: in Case 1. the surface concentration ofVCM remains essentially zero, as any RVCM escaping is carried away in the eris imoment. this case mav represent slot age or service in a continuously renewed en\ imnment. such as flowing water. In Case II, the VCM concentration in the medium builds up with time, and consequently so does the VCM concentration in the surtace ofthe PVC. Case III is the genera] situation in a real-world application; VCM loss into a closed medium follows a variable stor age period and thus proceeds from a product in which the surface VCM concentration is already depleted. He will see that the agingperiod between manufacture and closed-system service is quite important in determining the rate of VCM migration into the contents of a PVC pipe. Now let us consider the detail* and some numerical examples of each of these three cases. Case 1--VCM Loss During Storage Consider a freshly extruded PVC product, quicldv cooled to ambient temperature and stored in an atmo sphere of essentially zero VCM content. The initial RVCM concentration in the product is C, and may be assumed to be uniform through the product. At the surface, equilibrium is quickly established with the environment and the RVCM concentration is zero. W e assume that VCM leaving the PVC is carried away (e.g., good air circulation) so that the surface concentration remains zero. W e want to calculate (a) the amount of VCM which leaves the PVC and .b) the concentration profile within the PVC. both as functions of time, tem perature. and sample thickness. Crank gives solutions to this problem for several sim ple geometries---plane sheets, solid and hollow cylin ders and solid spheres. The predictions for hollow cylin ders are virtually identical to those for plane sheets, provided the wall thickness is less than the inside diame ter. Thus for all practical PVC products {pipes. bottles, sheets, films), we need consider onlv the mathematical solutions for plane sheets. Equations for the amount uf VCM escaping from the sheet may be written in terms uf Af, the fraction of the original VCM which escapes in time t. The general expression, valid at all times. *c M - 1 -- V --------------f -tAt* - !**: mi . + 1 >* -- tJ where n is the series of integers {0. 1. 2--). D tin diffusion coefficient, and L the sh*-et thickness. Fur tin late stage*, of the process (SI >--*?*. terms beyond i = 0 bccoui. insignificant, and </ 2 become* Fnr Af M=1 ir t3i --0.6 a very good approximation is given In Titus tin initui hiss ofVCM is proportional to the square root of the vl *ruge time after extrusion. For nurm ru ol calculations, v.c need only tin* sheet thickness and the diffusion co*. tfiuVnt values. From our measurements on PVC resins v). the value of D at various temperatures is given bv AP00055815 A. R. Berent and C. A. Daniels D 3.7exp -17.000 RT (5) for D in em*/*ec, T in *K, and R 1.987 cal/moleK. Equations 3, 4 and 5 permit prediction of the frac tional loss of RVCM from rigid PVC products for different sheet thicknesses, times and storage temperatures. Examples of numerical results are given in Figs. 1 and 2 as plots a M vs /*. Figure 2 shows such RVCM-loss curves for several sheet thicknesses at 30C, where D * 2 x 10"ucm*/iec * 1.73 X 10-7cm*/day, andFig.2,for a 1 mm sheet thickness at several temperatures. The concentration of RVCM remaining at time t at various distances from the sheet surface (i.e., the con centration profiles) can also be calculated from the same parameters. Crank gives the general solution as c-c, c,-c. & ^l-Wj t \* . j.f (2fl + 1) 1 + X1 4 ,?0 {~1} erfcl 2(Pr)i J (6) where C is the concentration at time t at distance i from the center of the sheet, C, is the initial (uniform) con centration, Ct is the constant concentration at the sur face (zero in our caseand / is the half-thickness of the sheet; "erfc" stands lor error function complement, de fined as trfc *= 1 -- erf z (7) The error function. "erf\ also called the probability t ^, doyi Fig. 2. Fraction ofinitial VCM content loti ($f) w square root of time (ti)for TVC heet l mm tfucJe, calculated for itinoui tem peratures, Cote l. integral, is tabulated in standard mathematical tables. For times short enough that the concentration at the center ofthe sheet does not decrease significantly below C,,, only the first term ofEq 6 is necessary, then, using Eq 7, we have simply -7`erfH^r] ,s' IMCLtW. f> 10 20 50YR& tl/\ day. 1/1 Fill /. Fraction ofitiitiuf VCM nmirut tost t\t J t * * ....* ..r UsincE^ 6.'orEq 6 where necessarv. we have i-uJuilated concentration profiles at 30SC (D = 1.73 x 10`5 cnrvday i for a PVC sheet Vi in. thick (or pipe with Js in. wall). The results at various times are plotted in Fig 3. Note that the VCM lost in the first month comes tmlv from the 100 microns of PVC near the surface. It take', over 2U years in this case for the VCM concentration near the tenter of the sheet to decrease appreciably. CASE II--VCM MIGRATION FROM FRESHLY/FORMED PVC PIPE INTO CONTENTS The Case ) calculations may lx* applied whem-wr WVf leaving the PVC product is carried away b\ tin- environment istorage in circulating, air. water-pipe notvRv with flowing water, etc.), so that the surface con centration of RVCM remains essentially zero. For PY<) pipes in ordinary serv ice, the outer surface is generally exposed to a low-VCM environment, i.e.. a Cave 1 situa tion. On the inside ofpipes with stagnant contents, on the other hand. VCM leaving the PVC builds up in coiitvn- (ration in die contents. Consequently, the instdr surface concentration of RVCM in th* PVO .......... AP00055816 Prediction of Vn^/ Chloride Monomer MigfOtion from Rigid PVC ;* Fig. 3. Relative VCM concentration (C/C*) vi depth below sheet surface (l -- j) at carious times, calculated for to in. thick F\rC sheet at 30*C (D -- 1.73 x 1Q~' cmVtec). Case i. PVC wall and in the contents will diffuse outward to the environment. This net outward diffusion of VCM will onJv occur after the VCM concentration at the midiine of the wall falls below its initial value; the time at which this occurs car. be estimated from concentration profiles such as those in Fig. 3. Since this effect occurs at such long times for pipes of norma) wall thickness, we have not considered it in our model, but instead have applied Case I and Case 11 calculations independently to the outer and inner halves ol the PVC walls, respectively. The rate and amount of VCM entering the pipe con tents may be calculated through equations given by Crank. The maximum amount of VCM which will enter the contents is that required to establish equilibrium between PVC and contents, and is governed bv the partition ci efficient and t)w ratio ofvolumes of PVC and contents. The partition coefficient, K, is defined as the ratio ol HVCM concentration in the PVC to that in the contents at equilibrium Imth expressed in the same units, e.g , g liter). The volume of PVC supplying VCM to the container contents Vr,Y. is one-hali the total PVC volume, as HVCM in the outer half diffuses outward in the situation we are considering. It can be shown that the maximum VCM concentration. (ppm by weight) in the liquid contents of a PVC pipe originally containing C',, ppm VCM. is --^4^-- tyi r r where dn, and dm are densities eff the PVC and con tents. and V*. is the volume of the contents. From our data (2) on VCM solubility as a function of VCM pressure over PVC and water, we havcestimati J a value oFIC -- 49 inr the distribution coefficient of VCM betw een PVC and water at 306C. It should be noted th. t this estimate off! assumes that the solubility of VCM in PVC is not affected bv contact with water. It also in volves a somewlut arbitrary selection ofa value for VCM solubility in PVC. since we have shown (2) that this rcslem shows non-ideal and histon-dependent solubil ity- Using this value of K> Eq V predicts that the maximum VCM concentration in water in a J in. J.D., Vi in. wall, PV'Cpipe containing 1 mg'lcg residual V'CM will be 0.027 mg/kg. Hie rate of VCM desorption into the pipe contents may be obtained from another of Crank's equations: M * or[l erfc\Tlc?)i\ (10) where T * Dt//*. A( is the fraction of the original RVCM desorbed at time t, and o *= VJWpyC- To uJustrate. we have applied tq/O to the l in. I.D.. H in. wall. PVC pipe filled with standing water. Figure 4 shows the results, with scales showing both Af, the fraction of original RVCM desorbed, and the VCM concentration in the water per original ppm RVCM. Also shown in Fig. 4 is the M vs t* plot tor Case I. Note that die initial rate of VCM desorption is the same for both Cases I and 11, but the buildup of VCM in the water in Case II causes the desorption to slow down as equilibrium is approached. Case IB---VCM Migration in Closed-System Service from Previously Aged PVC Products When a PVC product is put into closed-system serv ice some time after manufacture, the RVCM distribution through the PVC at the time of tiling and closing the container will not be uniform. a` was assumed in the Case II calculations. Rather. RVCM wilt already be depleted near the surface, and VCM migration into the pipe contents will start from a VCM distribution as calculated in Case I le.g.. Figure 3 . An analytical solu tion for this situation has been obtained bv Daniels and Proctor (5). but a useful and simpler estimate of the rate Fip 4. Frectum ofnriglnalVCM sontentloti/M/ur^umr root oftime it*jfor / in. l-O., V*(n. mail PVC pipe,calculatedfor 3fCC (D 1.72 k JO' 'em 'idayl, Cate l andCate II with water in pipe. Right-hand scale fiiecsppb VCM tit tt-ater per ppm ini/iW I'CM in pipr. AP00055817 A. R. Brrrnt end C. A. Donielt of VCM migration can be made by combining results of our Case 1 and Case II equations. For Case 1 during desorption of the first 60^ ofthe VCM, Eq 4 shows that the amount of VCM desorbed is proportional to the square root of storage time. Differentiating!^ 4 give* Thus the rate of VCM loss is inversely proportional to the square root ofstorage time. For Case II, we saw that the initial rate of VCM migration into the medium in a closed system is the same as id Case I. Thus Eq 11 also gives the initial rate of VCM migration into the closed system when t is the storage age of the PVC product at the start of clused-tvstem service. Applying 9 JJ to a PVC product with W in. wall thickness at 30C (D = 1.73 x 10"T cm*/day) gives the curve shown in Fig. 5. We see that the rate of RVCM desorption drops very sharply in the first few weeks of storage after manufacture. It is also possible to estimate die amount of VCM w hich will migrate from a PVC product during a given period ofa closed-system service following various Case I storage periods. This estimation may be explained with reference to Fjg. 6, which illustrates the VCM-loss (M) vs t* curves for the three cases. Case 111 is approximated by shifting the origin of the Case II curve to point t, along the Case I line, where t j is the age of the PVC product at the start of closed-system service. Then the VCM lost from the PVC in the time interval a during continued open-system storage would be, from Eq 4 AM <( ^r)1 l(, +)*-!*) U2) The VCM lost, and entering the contents of a PVC container, in Case 111 service, will be approximately equal to AM for relatively short service periods, and always less than AM. Equation 12 thus is useful for calculating the maximum fraction ofthe original RVCM which will migrate into the contents ofa PVC container during closed-system service lor any time period as a Junction of the age of the container at the time of filling and closing. Figure T illustrates results calculated from Lq 12 for 7 and 30 day service periods for a V& in. wall thickness at 30C as functions of f,. Again we see the important effect of a few weeks prior aging in reducing the amount of VCM migration into the contents. Comparison of Predictions with Experimental Data The foregoing analysis clearly shows that the age ofa PVC product at the start of an extraction test is an* important factor in determining the amount of VCM extracted. Since this information is seldom available in reported extraction data, direct comparisons between our predictions and experimental data are possible for only a few cases. For the data recently obtained by O'Mara and DeCapita (1) on the VCM content of water stored in I in. I.D. M in wall PVC pipes at 23"C. thr approximate age I* days Fig 5. Rate of VCW loir (dM/dt) ci time for H in thick PVC sheet, eeladett-J for 30*C, Cate 1. Fig 6 Scfw-meri: (wnperiron offraetiotutl VCM lost (Mt tt M curve* for Cent* I. II. end 111extraction test, w-as known. A "headspace" GC analytical method was used to provide sensitivity to low VCM levels in the water (on the orderof 1 or2 thousandths ol a milligram per kilogram). We have calculated the \ CM content expected in the water, using Eq 12 with the parameters appropriate to the experimental conditions; D was obtained from Eq 5. Table J compares the calcu lated and experimental results. Die agreement must be considered qtoie satisfactory, especially in view ofa) our application of D values obtained from resin powders to AP00055818 iPrtdwlum of Vinyl Chlvnde hionurier Migration from Rigid Pl'C Pipe Fig. 7. Fraction of originalVCH content enteringpipe contenti (AM)for 7 and 30-day extraction periods vtpipe age at start of ertroetkm (t,), calculated for H in. wall thickness and 3CFC, Case ID. storage conditions of the pipe samples, and c) the diffic ulty of analysis of water for extremely low levels rf VCM. DISCUSSION While further experimental verification would be de sirable. it appears that the simple approach discussed abo\ e is quite adequate for describing and predicting the migration of KVCM from PVCpipe into water. Thr reasonable agreement between predicted and observed migration data for this application ofrigid PVC supports the premises that, a) the diffusion coefficient deter mined lor pure PVC resins is applicable to rigid PVC pipe compound*. and b- contact of PVC with water produces little cliange m the dUFu.sivit) of VCM com pared to that measured l>v vapor sorption-desorption technique*, further, lor such relative!v thick waJh*d product* as pipe*, the diffusion into the environment Tabic 1. Comparison of Predicted and Experimental Extraction Result*, Water-Filled t In. t.D. W in. Wall PVC Pipe Sample*, 2J*C hvcm Extraction tn pipe, Pipe age, Time, VCM Inwalar, (mg/kg) l t*ley* Experimental Calculated- 292 --6 mo. 292 --6 mo 292 -6 mo 3 7 14 0.021 0 0414 0 113 0 0257 0 0596 0.116 177 -6 mo. 177 -6 mo. 177 --6 mo. 3 7 14 00173 00335 0 056 0.0156 0.0362 00717 22 -4mo. 22 -6 mo. 22 -- mo. 3 7 14 0 0006 0 0022 00046 0.0019 0.0045 0.0069 29 -lyr. 14 0 0105 0.0064 from the outer halfof the wall and into the contents from the inner half may be treated as independent processes over normal service lifetimes. Our simple predictive model may thus be used with some confidence for estimating the concentrations of VCM in water which might arise during actual service of FVC water pipe systems. To illustrate. Eq 12 has been used to calculate the VCM concentrations resulting from various stagnant exposure times ofwater in PVC pipes of I mg/kg original VCM content and varied diameter, warehouse age before installation and service age. Some results or such calculations are given in Table 2 for 2, 6 and 8 in. SDR21 pipes in service at room temperature <--23C h While these data are presented as though they represent stagnant water situations, from known use conditions (flow rates, pipe dimensions and resultant residence time), these calculations can be shown to model dynamic flowing systems. The figures in Table 2 clearly show that the highest VCM concentrations would be found in new installa tions of recently manufactured small diameter FVC pipe after long stagnation periods. Yet even for these most extreme conditions, the predicted VCM-in-water con centrations are well below the level of 0,002 mg VCM/kg HjO when the original residual VCM content ofthe pipe is 1 mg.'kg or less. In actual installations, stagnation times of more than a few davs are rarely encountered. A typical residence time for water in PNC pipes is believed to be about 2 days (6-8) and in this situation, the pre dicted VCM-in-water concentration falls in the partsper-trillion range. Thus we may conclude that PVC pipe containing si mg/kg residual VCM will result in VCM concentrations of less, than 0.002 mg VCM/kg H2t> under anv expected service condition*, and. therefore, non-detectable by present analytical methods. Table 2. Calculated VCM In H.O Concentration* tor Stagnant Storage ol Water In FVC Pipes of Varied Size and Age and Original 1 mg kg Rtaidual VCM Content Pipe size CSOR21) Ware house Sc. days Service 8. yurt VCM in water after erven itoraoe times, mg ka 2 days 2 weeks 1 month 2 in. . j y 30 0(ne w) 00007 .00044 .00087 60 0 .00005 .00033 .00067 90 0 .00004 .00027 .00056 90 1 .0000160 .000125 000265 90 2 .00001 .00009 000199 90 5 .00001 .00006 .00013 0 in 30 0 60 0 90 0 90 1 90 2 90 5 .00002 .00002 .00001 000006 .000004 .000003 .00015 .00011 .00009 .000042 00003 .00002 .00029 .00022 .00019 . .000088 .000066 .00004 6 n. 30 0 60 0 90 0 90 1 90 2 90 S .00002 .00001 .00001 .0000045 .000003 .000002 .00011 .00006 .00007 .000031 .00002 .00001 .00022 00016 .00014 .000066 .000050 .00003 AP00055819 REFERENCES 1 M M O'Mara and C- DeCapita. Internal Report, B. T. Goodrich Chemical Compun>, &4/7S, 2 A R. Berens. Am. Cbcm. Soc- Po/ynt. Prtpr., 15, 197(1974), Angru. tJakrvmoI. Chem., 47, 97 (i975). 3 A. R. Berrns.Am. CArm. Soc., Pi/lvm. frrpr15.203(1974). 4 j Crank. "The Mathematics ofDiJiYuricm.''0*ford University Frets. London 2956). 5. C. A- Daniels and D. E. Proctor, iindem PscLefine p 45 (April 1975). 6. American Waterworks Association, C 601 *54. Sec 1). Reten tion Period. 7. "Design Parameters for Rural "-^er Dj-:-1 ` .nV J. Amer. Water Work* Assoc., p. 1595 11\ !kt i ,-s*v. - "A Study of Residential Water Use," l'.s l5.H.U.1>. .Feb ruary, 1967) \ AP00055820