PI I:
Joumul of Food Engineering 32 (1997) 179- 198 0 1997 Elsevier Science Limited. All rights reserved Printed in Great Britain 0260-8774197 $17.00 + 0.00 SO260-8774(97)00022-S
Cheese Manufacture as a Separation and Reaction Process Ken R. Morison Department
of Chemical
and Process Engineering, University New Zealand
(Received
11 January
of Canterbury,
Christchurch,
1996; accepted 25 March 1997)
ABSTRACT This paper defines the separations and chemical reactions in the cheesemaking process as a system of equations. Mass balances are formally defined for milk separation and cheesemaking in terms of input and output streams, each with a number of components. Pasteurisation and the coagulation of milk during curd production are discussed as chemical reactions. From the model, expressions are derived for cheese yield. The modelling process reveals a number of assumptions which require testing and verification by experimentation. The model provides a means by which process engineers can more easily understand and analyse the cheesemaking process and it also provides a framework which enables comparison of research on cheese yields. The sensitivities of cheese yield to some of the assumptions are calculated and discussed. 0 1997 Elsevirr Science Limited
INTRODUCTION Some types of cheese are now mass produced in quantities of tens of tonnes per hour. On this scale the process becomes of greater interest to process engineers and technologists. In chemical engineering the standard approach for analysing systems has involved the use of unit operations, each explained in terms of heat and mass balances, physical separations, reactions and equilibria (e.g., Coulson et al., 1983). Historically mass balances for cheese production have been reported in numerical terms, e.g., Emmons (1994), or perhaps as a single yield equation (Emmons et al., 1990, 1993a, 1993b). It can be more useful to express the mass balance as a system of equations, thus enabling the use of process flow-sheeting tools to evaluate the effect of various parameters on the process and its yield. The scope of this paper is limited to the processes which affect the mass balances of the cheesemaking. Cheddar cheese is used as the example on which specific details are based but the 179
K. R. Morison
180
framework can be changed easily to suit other mass-produced cheeses. Changes in the energy of the streams are not be considered here. The yield of the cheesemaking process is usually defined as the mass of cheese produced from a given mass of standardised cheese milk. It is expressed in units of kilograms of cheese per 100 kg of milk (e.g., Emmons, 1993). Yield calculation has been a useful control tool to monitor the effectiveness of the process but some have argued that the natural variability in composition, causing variability in yield, is so great that yield is not a useful control tool, but rather measurements of losses are more effective (Parkin, 1982).
ELEMENTS
OF UNIT OPERATIONS
For any unit operation a number of elements must be defined. The system boundary is the first element which must be defined. In the case of cheesemaking the process is defined as starting at the pipe exiting from of the raw milk silo. The end of the process will be defined as the end of the cheese curd draining and salting system. Auxiliary operations such as the supply of energy, chemical and water utilities will not be included. Thus we can consider the process as shown in Fig. 1. It is useful to divide any process into a number of unit operations, each of which can be described by a system of equations. In this case, the unit operations are those shown in Fig. 1. While it is possible to integrate the pasteurisation, separation and standardisation operations so as to achieve better energy efficiency, the three operations will be considered independently in this work. The results of the analysis are identical to those of the integrated process. The last two operations of curd production and curd draining and salting will be considered together to avoid the need to define the composition of the intermediate product. Each unit operation will have streams flowing into and out of it and each stream will have a number of components, each component being a defined mass fraction of the total. In general the overall flow rate of the stream may be defined as a constant or as a variable. Each unit operation consists of some physical and/or biochemical process for which a mathematical model is written. The simplifications and assumptions used in the model are an essential component in defining the scope and accuracy of the model.
Desludge
Fig. 1. The Cheddar
cheesemaking
Excess Cream
Whey
process showing the defined operations.
Whey
system boundary
and unit
Cheese manufacture as a separation and reaction process
The processes of interest to us in the cheesemaking
181
process are:
(1) Heating and (2) Liquid phase
cooling (pasteurisation) separation (cream separation) Chemical reaction (of casein protein) Chemical equilibrium (of protein and minerals) Solids/liquid separation (of curd from whey)
[a{ (3
NOMENCLATURE The following symbols will be used: Flow rate of stream j (kg/s) 6 Mass fraction of component i in stream j $.I II Number of components m Number of streams
GENERAL
MASS BALANCE
In any process a steady state mass balance can be defined. Consider a process with a number of streams in and out (Fig. 2). An overall mass balance applies to the process, and if all flows are defined to be positive; CFin
=
CF,,ut
(1)
In an aqueous system we might say there are n components of which n - 1 are dissolved or suspended components and component II is water. A component mass balance applies within each of m streams and it may be expressed as x /.,,=
I-
c
,=l.Iz+ I
x,. , for each stream ,j = 1. m
(2)
Thus there will be m individual equations defined by eqn (2). A component balance applies over the process for each component: X
X,.,Fi,l,,=
, = I. 111,,,
C
x,.;F,,,,~.,
i= I. u,,.l,,
There will be n - 1 individual equations
i=l.n-1
(3)
defined by eqn (3).
.-___..-._..---
..___..-__.a_._)
Fin
_)
.~__._._..__..-
F out
Process
e
..___---_______)
Fig. 2. A general process.
mass
K. R. Morison
182
DEGREES
OF FREEDOM
Within a process, there are usually some variables which are free to be set. The number of such variables is the number of degrees of freedom, which is well defined by Co&on et al. (1983) as the total number of variables minus the number of unique equations which define the process. One variable is defined for each component fraction in each stream and for the stream flow rate. Thus the number of variables for a mass balance only is given by Variables = Streams x (Components+ and hence the number of degrees of freedom is defined.
1)
MILK: THE FEED MATERIAL For the process of cheesemaking the feed material is generally cows’ milk. The basic components and typical mass fractions in cows’ milk are given in Table 1. More detailed explanation of the components can be found in Walstra & Jenness (1984). Casein protein is defined as the protein which precipitates when the pH is reduced to 4.6. The remaining protein in the milk or whey stream is referred to as whey protein. Fat, casein protein and whey protein do not have fixed molecular structures and thus there may be variation within these species. The composition of milk has been found to vary between species, within a species, from day to day and from month to month (see, for example, Walstra & Jenness, 1984). Banks & Tamine (1987) showed that the seasonal variation in the composition of milk affected cheese yields in that the proportion of casein retained in the cheese varied from 95% to 99% and the proportion of fat retained varied from 89% to 93%. This indicates that some of the reactions and separations in the process are affected by composition. Other components of milk will be introduced in the discussion on cheesemaking. PASTEURISATION Pasteurisation may be carried out before or after separation and standardisation but it is considered first here. Within the pasteurisation process, the raw milk is heated
The Basic Components Component
Fat Lactose Casein protein Whey protein Minerals Miscellaneous Water
TABLE 1 of Milk (Walstra & Jenness,
1984)
Typical mass fraction (TO)
Range
3.9
2.4-5.5 3.8-5.3 1.7-3.5 0.6-0.9 0.53-0.80
;.: 0:65 0.65 0.32 87.3
85.5-88.7
Cheese manufacture
as a separation and reaction process
183
from about 10°C to at least 72°C is held for 15 s, and then is usually cooled to the separation temperature of about 55°C. Pasteurisation is carried out to kill bacteria in the milk. The mass of bacteria in milk is so small that it will be considered insignificant in this analysis. Reactions
during
pasteurisation
There is an anecdotal belief that higher pasteurisation temperatures cause an increase in yield and this is supported by findings that during the pasteurisation heating step some of the whey proteins form a complex with the casein proteins. Lau et al. (1990) reported that when milk was pasteurised at 63°C for 30 min, 5% of the whey protein, which they presumed to be fl-lactoglobulin, became associated with the casein protein. De Jong & van der Linden (1992) considered the denaturation of /Hactoglobulin as a reaction process, especially as part of the fouling process. The denaturation of fl-lactoglobulin (variants A and B) and a-lactalbumin during heating to 70-150°C for 2-5400 s was examined by Dannenberg & Kessler (1988). They found that /I-lactoglobulin B had the highest rate of denaturation so this protein is used here as the worst case. The data they obtained for temperatures in the range 70-90°C will fit a rate equation for the denaturation of fi-lactoglobulin (P-LG) with an order of between 1.5 and 2.0. The best fit for the data given was found by the current author to be - r = kC/;?9LG B where C is the concentration (kmol m-‘), r is the rate of reaction and k ((km01 m-3))0.79 ss’) is given by the Arrhenius law: In (k) = 100.4-
(4)
(kmol me3 ss’)
s
where the activation energy, E A, is 291.5 kJ/mol. Thus the extent of reaction is dependent on the temperature and duration of the heat treatment.The concentration of all variants of P-lactoglobulin in whey is about 180 x lo-’ kmol/m” (3.2 g/kg) (Walstra & Jenness, 1984). Using this information it was predicted that for a 73”C, 15 s holding time, pasteurisation would denature 0.7% of the fl-lactoglobulin (0.02 g/ kg milk). This is less than 0.1% of the amount of casein in the milk (26 g/kg), so at typical pasteurisation temperatures the denaturation of [&lactoglobulin and other whey proteins can be considered insignificant. There is some discussion in the literature about the effectiveness of coagulation of the /I-lactoglobulin-casein complex, possibly leading to lower yields (see Banks & Muir, 1985). For the purposes of this paper it will be assumed that a small amount of denatured P-lactoglobclin acts in the same manner as casein. Lau et al. (1990) did not find any evidence that pasteurisation affected the fat in the milk but Sharma & Dalgleish (1994) showed that during heat treatment whey proteins can be incorporated into the fat globule membrane at a level of up to 0.5 mg/m*. At 75°C for 15 s, the data indicates that 0.01 mg/m’ would b$- incorporated. Using their fat globule size, after homogenisation, of 300 pm the total incorporation can be calculated to be 0.00024 g of whey protein per gram c;f fat. Assuming that all this protein is retained in the cheese we can estimate that neat treatment may cause an increase in yield of less than 0.01%. Thus we can conclude
184
K. R. Morison
that the incorporation of whey protein in the fat globule membrane is not significant. It will also be assumed that no other components of milk are altered during pasteurisation. We conclude that, despite the anecdotal belief, it seems unlikely that typical HTST pasteurisation will increase cheese yield.
SEPARATION Centrifugal separators are used to remove fat from whole milk. Practically all the fat in milk is contained within fat globules which are surrounded by a protein-based fat globule membrane. It is more accurate to consider that separators remove fat globules, rather than fat, from whole milk. The entire fat globule is less dense than the remainder of the milk. Within the separation process skim milk can be considered as the heavy component and fat globules as the light component. The heavy stream contains only about 0.06% of the light component while the light stream (cream) contains a mixture of light and heavy components. There is a further stream in the separation process, which is the desludge material containing unwanted particulate matter. Thus there is one stream flowing into the separator and three streams leaving the separator, as shown in Fig. 3. The overall mass balance for separation is F,,
= Fsm+F,r+Fdesi
(6) where the subscripts wm, sm, cr and desl refer to whole milk, skim milk, cream and desludge respectively. Component mass balances for the milk solids components are F,,x,,,
i = F,,-G,,
i+F,,x,r, i+Fdes&esl,
i i = 1, n - 1
(7)
The water fraction is defined by eqn (2) for each of the four streams: X ,. II= 1 -
;=,J$_,
XJ,;
j=
bm,
sm,
cr,
desll
(8)
The three equations (6) (7) and (8) p rovide between them n+4 individual equations. The variables include the four flow rates and IZ mass fractions in each of the four flows, i.e., a total of 4(n+l) variables. In this system there are 3n degrees of freedom so 3n variables need to be specified in some manner.
whole milk
Fig. 3. The separation
@ci
process has one feed stream and three outlet streams.
Cheese manufacture a.s a separation and reaction process
1x5
Whole milk stream The separation process is usually the first separation process in a dairy factory, so the whole milk is defined by the average of what is delivered to the factory. The composition given in Table 1 will be used here. From this we shall use seven components (n = 7). This provides six mass fractions of the whole milk components; the fraction of the seventh component, water, being specified by eqn (8). The whole milk flow rate is not always specified. Desludge The amount of desludge is set by the operator or manager depending on the quality of the milk. A typical separator desludges about every 10 min with a mass of about 20 kg per desludge. It is convenient to consider this as a continuous flow of 120 kg’h or about 0.3% of a typical feed flow. When a desludge occurs, the contents of the separator bowl are emptied complete with any particulate matter which has collected within the separator. The amount of particulate matter in this stream is very small on a mass basis so it is normally assumed the particulate matter is insigniiicant. It is further assumed that the desludge stream has the same composition as the feed as any differences will have an insignificant contribution to the mass balance, i.e.: -Y
i=l,n-1
(‘4
Skim milk By design, and when used within the specified operating range, the amount of fat in the skim milk is in the range 0.04 to 0.10%. The amount of fat in the skim milk depends on the fat globule size distribution, the milk temperature (and hence viscosity), the separator speed, fat globule damage before separation and the physical design of the separator. Details of the centrifugal separation can be found in Kessler (1981). A value of 0.06% fat in the skim milk was used for the mass balance in this paper. Separators can be operated as skimmers, where the cream flow is adjusted so that only a fraction of the fat is removed from the skimmed milk stream. That use of separators will not be considered here. Cream The amount of fat in the cream is usually specitied by the manager in charge of the separator. Separators are capable of producing cream with a fat content ranging from that of whole milk to about 45%. Above this the fat content of the skim milk increases excessively. Typically the manager will specify 40% or 41% as being a level which can be achieved consistently, while still giving low fat contents in the skim milk. During separation, it is assumed that there is no significant separation of components other than the fat globules. For accuracy, the protein and other minor non-fat components associated with the fat globule membrane in cream should be accounted for. About 98.7% of the fat globule mass is milk fat, about 0.9%) is
K. R. Morison
186
protein and 0.3% is water (Walstra & Jenness, 1984). The proteins have not been well identified but we will assume that all the milk fat globule membrane protein is incorporated in cheese curd, so we can consider it to be the same as casein protein for the mass balance. No special consideration will be given to the water in the fat globule. A similar correction for the fat globule components in skim milk is unnecessary because of the very low levels of fat in skim milk. Thus, as a good approximation, the composition of cream on a fat globule free basis is the same as the composition of skim milk on a fat-free basis:. &,, (1 -&r,
xsm,
i
fat globules
>
=
i
for i = (whey protein, lactose, minerals, misc.}
(1 -&n,fat) (10)
but for casein the extra protein in the fat globule membrane &r,
-O-Oo9xcr,fat
casein
(1 -
xc,, fat globules
globules
xsm, =
1
where the fraction of fat globules is calculated tion given above:
is taken into account:
casein
from the typical fat globule composi-
xc,,fat xc,, fat globules
-
(11)
(1 -hll,fat)
o.987
(12)
It is assumed here that, within cream, fat exists only within fat globules but in fact a small amount of fat (0.015%) exists outside of the globules. In eqns (10) and (11) the fat content, rather than the fat globule content, of skim is used. At the low levels in the skim the difference is negligible and is ignored.This provides an additional n - 1, (i.e., 6), equations and one additional variable (x,,, fat giObuies). THE SEPARATION Thus we have, for a seven-component Variables
SYSTEM
separation: Compositions Fat globule fraction Flows Total
Equations
Mass balance (6) Components (7) Component balances (8) Desludge (9) Skim components (10) Skim casein (11) Fat globule fraction (12) Total
Variables specified
28 1 4 33 1 4 : 4 1 1 23
Desludge flow rate Skim milk fat content
1 1
Total
2
Cheese manufacture
as a separation and reaction process
SqiiiJzq
czs;;
18’7
)
Fig. 4. Milk standardisation.
From this we see that there are eight degrees of freedom (33-(23+2)) in the system as it has been specified. It is normal to specify the fat content of the cream and the flow rate of the whole milk or skim milk. The composition of either the raw milk or the standardised milk is then specified and the system can be solved.
STANDARDISATION Within the standardisation operation, cream and skim from the separation step are mixed together to produce cheese milk with the required fat content, or fat to casein ratio (Fig. 4). The operation consists of miscible mixing only. Simple overall and component balances as specified by eqns (1) (2) and (3) apply. Some standardisation systems use ultrafiltration to enrich the amount of protein in the milk and hence are able to independently standardise both the fat and protein fraction in cheese milk. These systems will not be considered here. The system of equations for separation and standardisation can be solved together to give standardised cheese milk with the composition specified in Table 2. The system can be solved using any standard algebraic equation solver. For this analysis the Microsoft package Excel Solver was used. The sum of the squares of residuals from each equation was minimised until it was less than 10e9. Typical values for the compositions and flow rates of the streams are given in Table 3.
Components
Typical fraction in standardised cheese milk’
Components
Fat Lactose Casein Whey protein Casein-bound minerals Soluble minerals Miscellaneous Sodium chloride Water ‘Based on Emmons
TABLE 2 of Standardised Cheese Milk and Cheese
et al. (1990).
0.036 0.045 0.02464 0.0065 0.002 0.0045 0.0032 0.0 0.878
188
Calculated Stream
K. R. Morison
Compositions
Separated cream
Feed Mass fraction
TABLE 3 and Flow Rates in Separation and Standardisation. fied a @on’ are Shown in Italics
Flow rate
Mass j-action
(kgls) Fat Lactose Casein Whey Minerals Misc. Water Total
0.0450 0.0446 0.0245 0.0064 0.0064 0.0032 0.8699
Skim milk
Flow (ran)
Mass fraction
S
0.463 0.458 0.252 0.066 0.066 0.033 8.948 10.287
0.4000 0.0278 0.0187 0.0040 0.0040 0.0020 0.5436
Mass
Flow rate
fraction
&IS)
0.456 0.032 0.021 0.005 0.005 0.002 0.620 1.140
0.0006 0.0467 0.0252 0.0067 0.0067 0.0033 0.9107
Mass fraction
(WS)
0.005 0.425 0.230 0.061 0.061 0.030 8.300 9.114
0.0450 0.0446 0.0245 0.0064 0.0064 0.0032 0.8699
Speci-
Standardised milk
Desludge
Flow rate
Variables
0.0015 0.0015 0.0008 0.0002 0.0002 0.0001 0.0287 0.0330
Flow rate MS)
0.036 0.045 0.02464 0.0065 0.0065 0.0032 0.87816
0.360 0.450 0.246 0.065 0.065 0.032 8.782 1o.ouo
CURD PRODUCTION The unit operation for curd production in the Cheddar process is shown in Fig. 5. There are three streams flowing into the process and two streams coming from the process. Cheese milk (from the standardisation process) is fed to a cheese vat. Starter culture and rennet enzyme are added to the cheese milk by flow ratio. Without loss of accuracy we combine the rennet and starter culture streams. Within the vat, the milk is coagulated by the action of the rennet and then the coagulum is cut and heated to form the curds and whey. The curds and whey are then separated by a flat screen and draining belt. In the case of dry-salted cheeses, salt is added to the milled curd on the belt. The end of curd production is defined as the end of the curd drainage and salting belt, just before packing. OVERALL The usual overall mass balances mass balance is given by
BALANCES
and component
mass balances
apply. The overall
Fstan+Fcu~t+Fsait= Fch+Fwt,ey
(13)
salt cheese milk
total feed
cheese curd
+ starter culture and rennet Fig. 5. Cheddar
draining belt
whey
cheese curd production.
+
Cheese manufacture
as a separation and reaction process
IX9
where F is the mass flow rate of standardised cheese milk (Stan), starter culture and rennet (cult), salt, cheese (ch) and whey. It is useful to define the feed stream as the combined standardised cheese milk, starter culture and rennet:
Ffeed= Fstan+Fcu~t The compositions
in the feed stream can be defined as xst, iFs+xcult, Gxd, i =
Component
(14)
#‘cult
i=l,n-I
FfWJ
balances for the milk solids components
(l-5)
are defined:
Ffcedxfeed, ,+F\altxsalt,, = Fch&h, r+Fwhry.hhey,,
(16)
for components except casein, whey, soluble minerals and water, which are defined later. The water fraction is defined by one equation for each of the five flows: Xl.,,
=l-
c ,‘l.II~I
j = (Stan, cult, ch, whey, feed}
THE SETTING
(17)
PROCESS
Before defining all the components of milk, it is useful to understand the coagulation processes. During coagulation the casein protein is hydrolysed by the action of rennet following the reaction: casein ‘para-casein
+glyco macro peptide (GMP)
where casein can be thought of as a complex of sr,-casein, /3-casein and ti-casein. The K-casein molecules exist predominantly on the exterior surfaces of the casein micelle (a casein micelle is a group of casein molecules with associated calcium phosphate) and give a structure that inhibits interaction between micelles. During the reaction the k--casein is hydrolysed by chymosin in a rennet solution allowing casein micelles to interact and coagulate. The hydrolysed part of k--casein is soluble and is known as glyco macro peptide. It does not coagulate but becomes part of the whey protein. It is estimated that the mass of glyco macro peptide formed during cheesemaking is 5.5% of the mass of the original casein (Van Boekel, 1994). The remainder of the casein is usually known as para-casein. In this paper we will refer to para-casein as casein. Van Hooydonk et al. (1984) found that the hydrolysis reaction could be described bY ds = kC,C,,,, dt
(IT')
where s is the substrate, which in this case is h--casein, C, is the concentration of the of the rennet solution containing substrate in gmol/l and C,,, is the concentration the chymosin enzyme (as percentage of rennet solution added to the milk). It was found that k had a value of 0.078 s-’ %,A,,, and that k followed the Arrhenius law with an activation energy of about 26 kJ/mol. The temperature history and type of milk used affected the reaction kinetics. Typically the concentration of rennet used
K. R. Morison
190
is 0.03% (vol./mass). The proportion of rc-casein in all casein is about 9-Z% and thus the concentration is typically 3.3 g/l. Using a molecular mass of about 19000 the concentration is about 0.000180 kmol/m3 (Walstra & Jenness, 1984). The casein micelles start to aggregate when the reaction is about 85% complete (Dalgleish, 1982) and continue to aggregate over several minutes. The reaction is allowed to continue until effective completion at about 50 min before the enzyme is inactivated by raising the temperature above 40°C. There is an additional complication in that one of the whey components, proteose peptone, precipitates with the casein, essentially becoming casein. Van Boekel & Crijns (1994) found that 0.9 g of proteose peptone per kilogram of milk precipitates as curd, but they reported considerable uncertainty in this value. We can write the precipitation reaction as proteose
peptone+casein-+casein
and we can write the casein mass balance: -&hey,
casFwhey+&h,
casFch
=
(0.945+,d,
cas.+@0009)Ffeed
(18)
A mass balance applies for total casein and whey protein: @whey,
whey+-%hry,
whey+&h,
cas > Fwhey+(&h,
.a,> Fch
= bfeed,
whey+-1Cfeed,
.a,>
Ffeed
(19)
While cheese is setting, the starter bacteria grow and produce lactic acid, which reduces the pH of the curd. The proportion of calcium, magnesium, phosphate and citrate which is associated with the casein reduces as the pH drops, essentially following the reaction: casein.CaH,P04+casein+CaH,P0, Davies & White (1960) found that 30% of the calcium in milk was in solution at pH 6.77, 68% was dissolved at pH 5.60 and 97% was dissolved and at pH 4.6. The relationship between pH and calcium solubility is not a simple equilibrium. Interpolating their data, it was assumed here that when the curd and whey are separated at a pH of about 6.3, 31% of th e minerals are retained in the curd. This can best be expressed as 0.065 kg of bound minerals per kilogram of casein. Van den Berg (1994) states that further research is required to find a more accurate value. Thus xch, bound
-&hey,
and the component
hound
min = O.O65Xch,
min =O.O65&hey,
cas
cas
(21)
balance for the minerals is
(~~/,,so,u,, ,,ri,,+~,./r.t,r,ur,~/ ,,rirr)F,.,r+(x,,.,r~,?..v~,,uh rrr;,,+~~/,~~.~,~,~lrlrl ir,irr)F,.,,,, = (x /rr
PO)
(22)
cheese milk stream
Given a good model of the cheese process, a designer may specify the standardised cheese milk composition required to achieve a desired cheese composition. Any composition may be achieved by using ultrafiltration, reverse osmosis, fat separation or chemical addition. It is useful to use the nine components (n = 9) in Table 2. It is assumed that all of the miscellaneous fraction is soluble. The sodium chloride is
Cheese manufacture
as a separation and reaction process
191
considered separately from the soluble minerals normally in milk and thus is zero for all the streams except the salting stream and the cheese. Starter culture and rennet At a rate of 300 ml/m’ (0.03%) the rennet addition can be considered to be negligible for the mass balance though not for the chemical reaction which occurs. Starter culture generally consists of skim milk which has been sterilised by heating and in which starter bacteria have been grown (see, for example, Heap & Lawrence, 1988). The rate of starter culture addition is usually set at about 0.4% of the standardised cheese milk flow. If necessary the starter cell concentration can be altered by varying the starter growth conditions so that the 0.4% ratio can be maintained. Thus Fcult = O.O04F,,,,
(23)
The mass fraction of cells in the starter culture is small enough to be negligible in the mass balance. The bacteria consume an unknown proportion of the lactose and some protein and produce lactic acid which reduces the pH of the cheese. For this model, it is assumed that the amount of lactose and protein consumed in the starter milk is negligible in the overall mass balance. The heat sterilisation step is sufficient to destroy all bacteria and is likely to denature all of the whey protein in the starter milk. Banks & Muir (1985) found that about 84% of the nitrogen in skim milk (about 88% of the whey and casein protein) used for starter was retained in the cheese but for this model denaturation is not taken into account. Cheese The fat, casein and moisture content of the cheese can be defined for a particular type of cheese. The moisture content of the curd can be affected by changes in cutting, stirring, cooking, chipping and salting and these can be adjusted by the cheesemaker to obtain the required moisture content. The protein and lactose content of the cheese will change from the time starter bacteria are added until the cheese is consumed. All the lactose in the Cheddar cheese will be consumed by the bacteria within about seven days of making and protein will be hydrolysed over longer periods. These changes are critically important to the flavour and texture of the cheese but for the purposes of the mass balance it will be assumed that loss of protein and lactose within the curd production process is negligible.
The amount of fat in the whey depends on the firmness of the coagulum at cutting and on the amount of cutting. Phelan (1981) states that 85-93% of the fat is retained in the curd. This fraction is strongly influenced by processing conditions (Lawrence, 3993). A value of 90% will be used here. Hence &h.
fatFch
= ~~9kxd.
I.stFfced
(24)
Practically all the casein is retained in the cheese except for casein in ‘fines’, which are small pieces of curd that pass out with the whey. Emmons et al. (1990) indicates
192
K. R. Morison
that 0.9% of the casein is lost as fines in the whey, though Van den Berg (1994) gives an estimate of 0.4%. The second value will be used here. Hence &h,
casFwh
= @004xfeed,
NON-SOLUTE
casFfeed
(25)
MOISTURE
The remaining components (whey, lactose, minerals, water) are water soluble and we must make assumptions about their separation during curd formation. Not all the water in milk is available as a solvent. Some is contained within or on the surface of the casein protein and is not available as a solvent for whey, lactose and minerals. The whey proteins are sufficiently large and are electrically charged in such a way that they are repelled by the casein particles and thus some water, known as steric exclusion water, is not used as a solvent for whey. Geurts et al. (1974) found that 0.55 g of water per gram of casein is non-solvent for lactose. Van Boekel & Walstra (1989) found that for every gram of casein protein in solution, 2.6 g of water is not available as solute water for whey proteins. Emmons et al. (1993b) state that 0.1 g of water per gram of casein is not available as a solvent for sodium chloride. In this paper this value will be used for all soluble minerals and the miscellaneous fraction. It is useful to define some new variables to specify the separation. We define x’ as the mass fraction of the soluble components in the appropriate solute water for the feed, cheese and whey streams. In general
x.j.i
Xi.;'
x,j,solute
water
for i
for components i = {lactose, soluble minerals, streams j = {cheese, whey}. For example: &vh, xwh,
lactose
whey proteins,
miscellaneous}
and
lactose
=
(26) xv/h,
solute
water for lactose
where
x.i.SOlUttT Water
for lactose
= X,j,
water-0.55Xj.
cas
(27)
Likewise:
Xj,
X,,
solute
solute
water
x,j,
solute
waterfor whey for soluble
= X.j, water -
minerals
water for misc. = xj,
= XI.
2.6x.j.
cas
water -O.lxj,
Water -O.lxj,
P-9
cas
cas
(29)
(30)
Now we make the assumption that there is no significant separation of the watersoluble components in the cheesemaking process, though it is not clear that this assumption is valid (Emmons et al., 1990). With this assumption we state that the fraction of the soluble components in solute water is the same in the cheese and as in the whey.
Cheese manufacture
Gley, i = L.
for components
i =
193
as a separation and reaction process
(31)
I
{lactose, soluble minerals, whey proteins, miscellaneous}. SALT ADDITION
In the dry-salted cheese process (e.g., for Cheddar production) the salt stream is pure sodium chloride. The salt is blown onto the cheese as it passes along the belt. Some of the salt is lost as whey is exuded by the curd after salting but for the purposes of this paper we will consider only the salt that is absorbed by the cheese. Thus there is no salt in the whey stream. Typically salt is added to achieve a salt to moisture ratio in cheese of about 4.5. In this analysis the salt content of the cheese will be set at 1.7%. THE CHEESE
SYSTEM
We have for a nine-component system with five streams (standardised starter culture, feed, cheese, whey) and a pure salt stream: Variables
Equations
Variables specified
cheese milk,
Compositions Flows Salt flow Solute water component fractions Solute water total fraction
54 5 1 8 8
Total
76
Overall mass balance (13) Feed flow rate (14) Feed stream (15) Stream components (16) Component balances (17) Casein balance (18) Whey protein balance (19) Minerals in cheese (20-22) Starter culture flow rate (23) Whey fat (24) Whey casein (25) Solute water fractions (26) Solute water total fraction (27-30) Cheese-whey solute components(31)
1
3
Total
8 8 4 46
Starter culture composition Zero salt in feed and whey Salt stream is pure salt
7 4 9
Total
20
From this we see that there are 10 degrees of freedom (76-(46+20)) in the system as it has been specified. It is normal to specify the flow rate of either the
194
K. R. Morison
cheese or standardised cheese milk stream and to specify the salt content of the cheese. The choice of other variables depends on whether we are interested in simulation of a known process or design of a new one. For example, for an existing cheese plant we are likely to specify the flow rate of standardised cheese milk, the seven solids components in the standardised cheese milk and perhaps the cheese moisture content. With this information the system can be solved.
CHEESE
YIELDS
In the cheese industry yield is defined as ‘kilograms of cheese per 100 kg of milk’ (Emmons, 1993) Industry Cheese Yield =
Mass of Cheese Mass of Standardised
Milk
x 100
(31)
He points out that comparisons between values of yield require correction for the composition of milk and cheese. Emmons does not, however, mention the starter culture flow and it appears from Banks & Muir (1985) that the starter culture stream is not included in the yield equation. The yield could be expressed better as the mass of cheese produced per mass of ingredients on a wet basis. The ingredients would standardised cheese milk, starter culture and salt. Thus wet basis yield is defined as: Wet Basis Cheese Yield =
Cheese Standard
Flow
Milk Flow+Starter
Flow+Salt
Flow
(31)
It has no dimensions as it would normally be expressed as a fraction or percentage. Given the natural variability in the moisture content of the standardised cheese milk a dry basis yield would probably give the best indication of the efficiency of the cheesemaking process. Cheese
= Standardised Comparisons
solids
Milk Solids + Starter
of the yield formulae
Solids + Salt
(31)
are given below.
MODEL SOLUTIONS The system defined above can be solved using any standard algebraic equation solver. For this analysis the Microsoft package Excel Solver was used. The sum of the squares of residuals from each equation was minimised until it was less than 10-9. The standardised cheese milk composition used was that given in Table 2. In addition to this, the cheese moisture content was set at 37%, the salt content at 1.7% and the standard milk flow rate 10 kg/s. Yields were calculated for the base case and are shown in Table 4. The yields obtained here are within the range
Cheese manufacture as a separation and reaction process
1Y5
TABLE 4 Yield Results -9.73% 9.h8% 49.5% --
Industry yield Wet basis yield Dry basis yield
reported by Emmons ef al. (1990) of between 9.4% and 10.1% for similar conditions. The composition and flow rate of each stream are shown in Table 5. Many of the model parameters and variables were then altered, one at a time. and the effect on yield was calculated. The choice of size of perturbation was somewhat arbitrary within the bounds of likely variation or uncertainty. The results, shown in Table 6, show that composition of the standardised cheese milk and the final cheese moisture affect yield as expected. The fat recovery and the amount of minerals bound to the casein in the cheese have a large influence on yield.
DISCUSSION One of the surprising results from the model was that there was no whey protein in the cheese. This occurred because the amount of non-solvent water for whey is greater than the amount of water in the cheese. Emmons et al. (1990) used a general value of 0.5 g of non-solvent water for every gram of casein, compared with 2.6 g/g used here for whey proteins. The value needs to be less than 1.5 g/g for the
Calculated
Composition Srundardi.wl rnrlk
and
Flow
TABLE 5 Rates in the Cheesemaking priori are Shown in Italics C’uhm
Suit
Process. Variables Cheesr
Specified a WW
K. R. Morison
196
TABLE 6
Effect of Model Variables
and Parameters
on Calculated
Cheese Yield
Relative change in yield Variation/parameter Fat in standardised milk Casein in standardised milk Cheese moisture Casein conversion Proteose peptone Bound mineral ratio Starter culture flow ratio Fat recovery Casein fines loss Lactose exclusion factor
Eqn
18 18 20,21 23 24 ;57
Basis
Variation
Industry
Wetbasis
Dly basis
0.036
0.037
1.6%
1.6%
0.7%
0.02464
0.0253
1.1%
1.1%
0.6%
0.37 0.945 0.0009 0.065 0.004
0.38 0.95 0.0005 0.08 0.008
1.8% 0.2% - -0.7% 0.6% 0.2%
1.8% 0.2% -0.7% 0.6% -0.2%
0.2% 0.2% -0.7% 0.6% -0.1%
Eo4 0:55
0.091 0.002 0.5
0.6% 0.1% 0.1%
0.6% 0.1% 0.1%
0.6% 0.1% 0.1%
to predict whey incorporation in cheese. Given that cheese initially forms as a coagulum with no volume change, then contracts as the casein binds the curd together, it seems very likely that some whey protein will be trapped within the cheese. Thus it seems that the amount of non-solvent water for whey proteins found by Van Boekel & Walstra (1989) does not apply directly to cheesemaking. The definition of cheese yield in all the papers reviewed does not seem to include the milk which enters with the starter culture. The wet and dry basis definitions used here better reflect the ingredients of the cheese. This is particularly obvious in the case of starter culture flow ratio. As the ratio is increased the industry yield increases, but the wet and dry basis yields decrease. The fraction of cheese solids in the starter culture is less than in the cheese milk so a decrease in yield is sensible from a chemical engineering point of view. No attempt was made here to reduce the system to a single yield equation as has been the practice in the literature. In the form that the mass balance is presented in this paper, the assumptions, constituent equations and parameters can be easily identified and changed. The same equations can be used to calculate the standardised cheese milk composition required to achieve a desired cheese composition. This model and previous studies show the need for more experimental data relating to the effect of pH on the bound minerals. It also shows the need for better data on non-solute water in the cheesemaking process especially relating to the physical incorporation of whey proteins in cheese. model
REFERENCES Banks, J. M. & Muir, D. D. (1985). Incorporation of the protein from starter growth medium in curd during manufacture of Cheddar cheese. Milchwissenschaft, 40, 4 209-212.
Cheese manufacture
as a separation and reaction process
107
Banks, J. M. & Tamine, A. Y. (1987). Seasonal trends in the efficiency of recovery of milk fat and casein in cheese manufacture. J. Sot. Dairy Technol., 40, 3 64-66. Coulson, J. M., Richardson, J. F. & Sinnott, R. K. (1983). Chemical Engineering. Vol. 6. An Introduction to Chemical Engineering Design. Pergamon. Oxford. Dalgleish, D. G. (1982). The enzymatic coagulation of milk. In Developments in Dairy Chemistry. I: Proteins, ed. P. F. Fox. Applied Science, Essex, pp. 157-187. Dannenberg, F. & Kessler, H. G. (1988). Reaction kinetics of the denaturation of whey proteins in milk. J. Food Sci., 53, 258-263. Davies, D. T. & White, J. C. D. (1960). The use of ultrafiltration and dialysis in isolating the aqueous phase of milk and in determining the partition of milk constituents between aqueous and disperse phases. J. Daity Rex, 27, 171- 190. Dc Jong, P. & van der Linden, H. J. L. J. (1992). Design and operation of reactors in the dairy industry. Chem. Eng. Sci., 47, 13114 3761-3768. Emmons, D. B. (1993). Definition and expression of cheese yield. In Factors Aflecting rhe Yield qf Cheese: IDF Special Issue 9301. International Dairy Federation, Brussels. Emmons. D. B. (1994). Does the addition of components of cheese equal 100%~‘~Clleese Yield and Factors Afiecting its Control, IDF Seminar; Cork 1993. International Dairy Federation. Brussels. Emmons, D. B., Ernstrom, C. A., Lacroix, C. & Verret, P. (1990). Predictive formulas for yield of cheese from composition of milk: a review. J. Da@ Sci., 73. 13651394. Emmons, D. B., Ernstrom, C. A., Lacroix, C. & SauvC, P. (1993a). Further considerations in formulas for predicting cheese yield from composition of milk. J. Dairy Sci., 76, 914-920. Emmons. D. B., Ernstrom, C. A.. Lacroix. C. & Verret, P. (1993b). Yield formulae. In Factws Aflecting the Yield qf Cheese: IDF SL)ecial Issue 9301. International Dairy Federation. Brussels. Gcurts, T. J., Walstra, P. & Mulder, H. (1974). Water binding to milk protein, with particular refercncc to cheese. Neth. Milk Dairy J., 28, 46 Heap. H. & Lawrence R. C. (1988). Culture systems for the dairy industry. In De~&~pntenr.s irz Food Microhiolog);, Vol. 4, ed. R. K. Robinson. Elsevier, London. Kessler, H. G. (1981). Food Engineering and Dai? 7&hrloloD. Verlag A. Kessler. Freicing, Germany. L~LI. Kum Y.. Barbano. David M. & Rasmussen, Rohcrg R. (1990). Influence of pasteurization on fat and nitrogen recoveries and cheddar checsc yield. J. Daiq’ Sci., 73. 561-570. Lawrence, R. C. (1993). Processing Conditions. In Factors A,jfectirlg the Yield of Cheese: IDF Special Issae 9301. International Dairy Federation, Brussels. Parkin, M. F. (1982). Review. Conservation of resources: product loss management. In Proceedings qf the 2nd Australian Daity Technology Relieu Conference, 1982. Phclan. J. A. (1981). Standardisation of milk for chcesemaking at factory level. J. Sot,. Da& khr10l.. 40, 64-66. Sharma, S. K. & Dalgleish, D. G. (1994). Effect of heat treatments on the incorporation of milk serum proteins into the fat globule membrane of homogcnised milk. J. Da& Res.. 61, 375-384. van Boekel, M. A. J. S. (1994). Transfer of milk components to cheese: scientific considerations. In Uleese Yield arui Factors A,@ecting its Control. IDF Seminar; Cork. 199.7’. lntcrnational Dairy Federation, Brussels. Van Boekcl, M. A. J. S. & Crijns, C. L. (1994). Behaviour of the protcose-peptone fraction during rcnneting of milk. Net/z. Milk Dairy .I., 48, I 17-116. Van Boekel, M. A. J. S. & Walstra, P. (1989). Steric exclusion of serum proteins with respect to (para)casein micelles. Neth. Milk Dairy J., 43. 437-446. Van den Berg, M. G. (1994). The transformation of casein in milk into the paracasein structure of cheese and its relation to non-casein milk components. In Qleese Yield a&
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K. R. Morison
its Control, IDF Seminar; Cork 1993. International Dairy Federation, Brussels. Van Hooydonk, A. C. M., Olieman, C. & Hagedoorn, H. G. (1984). Kinetics of chymosincatalysed proteolysis of K-casein in milk. Neth. Milk Dairy J., 37, 207-222. Walstra, P. & Jenness, R. (1984). Dairy Chemistry and Physics. Wiley, New York.
