Pierre Blanchard

Huiban Jean-Pierre
email: huiban@ivry.inra.fr

Mathieu Claude

THE DYNAMICS OF FRENCH FOOD INDUSTRIES: PRODUCTIVITY, SUNK COSTS AND FIRM EXIT*

Keywords: FIRM PRODUCTIVITY, SUNK COSTS, EXIT, FOOD INDUSTRIES JEL Classification: C23, D24, L25

A semi-parametric approach is used to estimate the unobserved individual productivity of firms. This productivity is then introduced in a model of firm exit.

We also introduce the firm's level of sunk costs as an expected barrier to exit. By using an unbalanced panel of 4818 firms in French food industries from 1999 to 2002, we find a significantly negative relationship between the probability of exit of the firm and its individual efficiency, age and sunk costs level. At the opposite, the intensity of competition in an industry increases the propensity to exit for firms in that industry.

Introduction

In France, 63,024 firms failed between August 2008 andAugust 2009, 19,1% more than the number of failed firms during the same period the previous year (Banque de France, 2009). However, regardless of the period under consideration, firm demography (including both firm entry and exit) is a major component of industry dynamics. [START_REF] Bartelsman | Comparative analysis of firm demographics and survival: Evidence from micro-level sources in OECD countries[END_REF] show that the firm turnover rate (calculated as the national average rate of entry plus exit, over the period [1989][1990][1991][1992][1993][1994] varies from 16% in the Netherlands to 23% in the United States. Behind the apparent inertia of the stock (the number of existing units at a given date), these important flows deeply modify the distribution of industries by size, location and performance.

There is a large body of empirical literature devoted to firm exit, as shown by [START_REF] Caves | Industrial organization and new findings on the turnover and mobility of firms[END_REF]. Until recently, most studies have highlighted the influence of a particular set of determinants (such as firm characteristics, industry, and period), but without replacing exit as a structural component within a theoretical model of industry dynamics. However, following the theoretical contributions of [START_REF] Jovanovic | Selection and the Evolution of Industry[END_REF], [START_REF] Hoppenhayn | Entry, exit, and firm dynamics in long run equilibrium[END_REF] and [START_REF] Ericson | Markov-Perfect Industry Dynamics: A Framework for Empirical Work[END_REF] (EP95 hereafter), among others, some empirical methods have proposed to assess the contribution of firm exits to the industry dynamics. The one by [START_REF] Olley | The Dynamics of Productivity in the Telecommunications Equipment Industry[END_REF] (OP96 hereafter) is one of the most widely used. The study of productivity growth is often the first and main goal of such studies. But, it also permits to implement more complete exit models, where the unobserved individual efficiency of the firm is introduced as a determinant of the firm's probability of exit. Clearly, if exit is the expression of a market selection process, the less efficient the firm, the higher its probability of exiting. Such a prediction is widely confirmed by empirical results. [START_REF] Farinas | Firm productivity, heterogeneity, sunk costs and market selection[END_REF] focus on Spain and find that exiting firms exhibit significantly lower productivity levels than other firms. [START_REF] Bellone | Productivity and market selection of French manufacturing firms in the nineties[END_REF] analyze post-entry and pre-exit performances of French manufacturing firms and also show that exiters are less efficient than firms still in activity. [START_REF] Frazer | Which Firms Die? A look at manufacturing Firm Exit in Ghana[END_REF] and [START_REF] Shiferaw | Survival of Private Sector Manufacturing Establishments in Africa: The Role of Productivity and Ownership[END_REF] find similar results in the case of developing countries (namely Ghana and Ethiopia): only the more efficient firms can survive. [START_REF] Griliches | Firm productivity in Israeli industry 1979-1988[END_REF] and [START_REF] Almus | The shadow of death: An empirical analysis of the pre-exit performance of new German firms[END_REF] suggest that this relationship between efficiency and exit may reflect what is called the "Shadow of Death" effect: a lower (and lowering) efficiency would be a symptom of the imminent exit of the firm.

Following this line of research, the aim of this study is to analyse the exit process of the firms in French food industries, by using a large unbalanced panel data set of 4,818 French firms over the period 1999-2002. We start with the EP95 model and use the semi-parametric method initially developed by OP96 to estimate unobserved individual firm efficiency. Then, this measurement of efficiency is used as a determinant of the probability of exit, in addition to the usual state variables, such as age. But, the major interest of the study is the introduction of two new variables, the level of sunk costs and the intensity of industry competition.

Sunk costs play an important role in the theoretical models of industry dynamics (as EP95), but are rarely introduced in empirical tests, presumably because of the difficulty of measurement. Being non recoverable in the case of exit, sunk costs have an engagement value for incumbents and consequently create barriers to entry for new firms but also barriers to exit for incumbents (see for example [START_REF] Dixit | Entry and exit decisions under uncertainty[END_REF]Lambson, 1992;[START_REF] Sutton | Sunk Costs and Market Structure[END_REF]Hopenhayn, 1992;[START_REF] Cabral | Sunk costs, firm size and firm growth[END_REF]. The corresponding empirical tests of this claim are less conclusive. Some authors [START_REF] Kessides | Market concentration, contestability, and sunk costs[END_REF][START_REF] Dunne | Variation in producer turnover across US manufacturing[END_REF][START_REF] Fotopoulos | Entry and exit from manufacturing industries: Symmetry, turbulence and simultaneity -some empirical evidence from Greek manufacturing industries[END_REF] find that capital requirements are barriers to exit, while others [START_REF] Rosenbaum | Profit, entry and changes in concentration[END_REF][START_REF] Roberts | Entry and exit in a transition economy: the case of Poland[END_REF] find no evidence of this. Two complementary reasons may explain such mixed findings, namely definition and measurement. Following [START_REF] Sutton | Sunk Costs and Market Structure[END_REF], a distinction must be made between exogenous (passive) and endogenous (active) sunk costs. Exogenous sunk costs (as the cost of "acquiring a single plant of minimum efficient scale" (Sutton, 1991, p.28) mainly depend on the industry and affect the capital variable. Such costs represent both entry and exit barriers. Endogenous sunk costs (R&D or advertising expenses, for instance) are linked to firm's own strategy. This certainly represents entry and exit barriers, but in a more complex way, as it may increase the individual efficiency of the firm.

In this way, endogenous sunk costs reduce the probability of exit even without being directly observed. In this study, we exclusively use exogenous sunk costs, for which an original measure is proposed. This measure is mainly based on the amount of investment and capital, but weighted with several coefficients. Such coefficients take into account leasing, capital depreciation and the resale of second hand equipment.

Our main findings are the following. First, our summary statistics are consistent both with the literature results and with expected patterns. When considering the all food industry, the annual entry and exit rates vary between 5.6% and 8.0% depending on the year, providing a turnover rate between 11.5% and 15.5%. Such a value is close to, but slightly lower than those obtained previously in the literature [START_REF] Bartelsman | Comparative analysis of firm demographics and survival: Evidence from micro-level sources in OECD countries[END_REF], which are around 20%. The difference may be explained by several reasons linked to our population, which is composed of manufacturing firms, and excludes very small units of less than 20 employees. First, firm turnover is lower in manufacturing (including food industries) than in services. Second, very small firms, which are not included in our sample exhibit generally high turnover rate. Third, turnover is lower when it is measured at the firm level than at the plant level, because of multiplant firms. When comparing the different component of the food industry, we find that both entry and exit rates vary greatly across industries. For example, exit rate is very low in the Oils and fats industry at around 2% and very high in the Bread and pastry goods and cakes shops industry at more than 16%. Some interesting correlations may be found between variables when they are observed at both 3 and 4digit mean levels. A well-known positive correlation in firm demography is between entry and exit rates, as shown among others by [START_REF] Fotopoulos | Entry and exit from manufacturing industries: Symmetry, turbulence and simultaneity -some empirical evidence from Greek manufacturing industries[END_REF]. But some other patterns are more directly related to our model, such as the apparent negative correlation between the level of sunk costs and the competition intensity on the one hand, and the intensity of flows (both entry and exit) on the other hand.

The estimation results first provide some presumably unbiased estimates of the production function. Compared to the OLS results, the estimates obtained by using the OP96 method are significantly different: the estimated capital elasticity is higher (0.317 versus 0.251), while the labor elasticity is lower (0.579 versus 0.704). The OP96 values of estimates lie between the OLS and the Within values, clearly suggesting that simultaneity bias, which is corrected by the OP96 and Within estimators, and selection bias, corrected only by the OP96 estimator, exhibit opposite signs. But our more important findings concern the exit function; the exit probability of firms is negatively and significantly correlated with the individual firm productivity, the firm age and positively correlated with the intensity of competition in the industry. These results are consistent with the predictions of the theoretical model and, more generally with previous studies using similar methods. The specific result offered by this study is that sunk costs also play a significant and negative role: the higher the sunk costs level, the lower the exit rate.

The low magnitude of this effect, which is associated with the large dispersion of the variable value between firms, suggest that this effect is generally light but may become very strong in some particular industry cases. In summary, competition intensity and sunk costs may explain differences in exit rates between industries, opposing "inert" versus "turbulent" industries, while age and individual efficiency may explain the variability observed between firms within an industry.

The rest of this paper is organized as follows: Section 2 introduces the economic model, and Section 3 presents the econometric methods. Data and some summary statistics are introduced in Section 4, while in Section 5, estimation results are provided and analyzed. Section 6 concludes.

The economic model

EP95 provide the theoretical model underlying the OP96 approach. Their aim is to explain the great variability observed between firms in terms of their performance level, including entry and exit processes.

To do so, these authors first incorporate "idiosyncratic or firm-specific sources of uncertainty (that) can generate the variability in the fortunes of firms observed in (...) data" (p. 53). In addition to the usual state variables (i.e. capital, labour and age) they use a new variable: ω it . This variable is defined as follows. A firm (or an entrepreneur) exploits "an opportunity (technology) provided by the industry, which is open to all, so that the only distinction among firms is their achieved state of "success" (index of efficiency),ω ∈ t Z , in exploiting it."(p. 55). As defined,ω it , the individual efficiency of the firm i observed at the period t, explains all the unobserved heterogeneity between firms.

In such a model, entry and exit processes are a natural component of industry dynamics. Entrants must invest, in order to explore and then exploit an opportunity offered by the industry. At the same time, at the beginning of any period t, the incumbent firm must make two decisions. First, it must decide to continue or exit the industry. Second, if it decides to stay, it must decide how much to invest.

To make the first decision, the firm comparesφ , which is the cost to remain in activity (the selloff value) and (EDP), which is the expected present discount value of activity profit, according to optimal future decisions concerning investment. The Bellman equation is:

} { ω φ = ( , , ) max , it it it it it it V K a EDP , (1) with:
π ω ω

+ + + +   = - +   1 1, 1 1 max ( , , ) ( ) ( , ) it it it it it it it it it it it I EDP K a c I rE V K a J , (2)
where π (.) is the profit of the current period, gross of the investment cost ( )

it c I , it K is the capital, it a is
the age of the firm and ω it its individual unobserved efficiency. (.) E is the expectation operator, r is a discount factor and it J is the information set available at time t .

ω + + + 1 1 1 ( , ) it it it V K
δ + = - + 1 (1 ) it it it K K I , (3)
The exit rule is based on the comparison between the sell-off valueφ and the optimal expected discounted profits it EDP , depending on the value of ω

( , , ) it it it it V K a .
If the first term is greater than the second, the firm leaves the industry otherwise it stays in. Let z be a decision variable such that = 1 z = ( 0) z if the firm decides to exit (stay on) the market. Then, the exit rule can be written as,

φ >  =   1 0 otherwise it it if EDP z , (4)
Second, if the firm decides to stay in the industry, it has to choose the level of its investment it I that maximizes it EDP , in relation to the usual state variables capital and age, but also to the unobserved individual efficiency:

ω = ( , , ) it it it it I I K a , (5)
Our specific contribution consists of introducing two new variables in this well known model, namely sunk costs and competition intensity. Concerning the first variable, EP95 assume: "Investment to enter is a sunk cost, perhaps partially recoverable if there is some scrap value realizable on exit" (p. 55). Such costs are present first when the firm enters to explore the opportunities that are offered in the industry and second as a part of the investment cost for each period t:

4 Note that this last function can be expressed as the following Bellman equation:

{ } ω φ + + + + + = 1 1, 1 1 1 ( ) sup , it it it it it V K EDP [ ] [ ] α α α α - = + ∈ 1 , 0,1 it I it K t I K SC I K , (6)
This definition which is further developed when presenting our empirical measurement of this variable is consistent with the definition of sunk costs, more precisely of what J. [START_REF] Sutton | Sunk Costs and Market Structure[END_REF] calls "exogenous" sunk costs: "We identify the set-up cost incurred by firms on entering (…) with the cost of acquiring a single plant of minimum efficient scale, net of any resale value" (p. 28). We introduce it in the exit equation which then becomes:

} { ω φ = - ( , , ) max , t t t t it t V K a SC EDP , (7)
This exit rule suggests that the higher the sunk costs, the lower the propensity to exit. Sunk costs appear then to be barriers to exit as well as barriers to entry.5

The intensity of competition in the industry should also be included in the model. In the Bellman equation, the expected profit EDP is a function of ω it which is the individual efficiency of the firm. The level of ω it should be compared with ϖ st which is the efficiency level cutoff in the industry during the same period. This average efficiency is a function of competition intensity in the industry. It seems consistent to assume that the more intense the competition, the higher the value ofϖ st , and the higher the probability of exit, for firm i. Thus, we obtain: ,,,, )

} { ω φ ω = - = ( , , ) max , (
it it it it it it it it it it it it V K a SC EDP f K a Comp SC , (8)
The inclusion of sunk costs and competition intensity completes the theoretical model and allows a more precise identification of resulting firm heterogeneity through the non-observable individual efficiency ω it .

One may consider this efficiency to further depend on many non-measurable arguments, such as manager's ability, skill level of the labour force, the agglomeration effect due to location or the other kind of sunk costs, namely endogenous costs such as advertising or R&D expenses.

The econometric model

Our goal is to estimate the exit model of firm i observed during period t:

ϖ = Pr( ) ( , , , , ) it it it it it it Exit f a Comp SC X , (9)
The probability of a firm's exit depends on the individual firm's efficiency, age, level of sunk costs, the intensity of industry competition and some control variables, such as industry and time dummies. Butϖ it , which is individual efficiency, cannot be directly observed but has to be estimated by using a production function. Such a function has the following form, in the case of a Cobb-Douglas technology:

β β β β ϖ ε = + + + + + 0 log log log it l it k it a it it it Y L K a , ( 10
)
where it Y is the output of firm i observed at period t , it L is the labor input, it K is the capital input, it a is the age of the firm, and ϖ it is the individual efficiency. ϖ it is a state variable for the firm's decision, which is known by the firm even if it is non observed by the econometrician, while ε it is the usual error-term, associated for instance with a non-predictable productivity shock.

It is well known that standard econometric methods, such as OLS, provide biased and inconsistent estimates of the previous production function for (at least) two reasons: simultaneity between output and inputs and selection bias resulting from the exit process. 6 Several methods exist to address these problems, (or at least one), including current panel data estimators, such as within estimator, IV and GMM estimators, and semi-parametric methods, such as the OP96 method, or some extensions of it [START_REF] Levinsohn | Estimating production functions using inputs to control for unobservables[END_REF][START_REF] Ackerberg | Structural identification of production functions[END_REF]. 7 In this study we use the OP96 approach, modified as suggested by [START_REF] Levinsohn | Estimating production functions using inputs to control for unobservables[END_REF]. Their argument is as follows. In the standard OP96 method, the investment is a proxy for unobserved efficiency:

ω = ( , , ) it it it it I I K a , (11)
Under the assumption that it I is strictly positive, one can write the inverse function of the unobserved shock, and obtain:

ω - = 1 ( , , ) it it it it I I K a , (12)
However, especially from the perspective of a coming exit, a firm may stop to invest while it always requires intermediate consumptions to produce. Consequently, we follow [START_REF] Levinsohn | Estimating production functions using inputs to control for unobservables[END_REF] and substitute intermediate consumption it M to investment it I . Under the assumption that it M is strictly positive the inverse function of the unobserved shock is now:

1 ( , , ) ( , , ) it it it it it it it M M K a h M K a ω - = = , (13)
Following this and taking into account the introduction of two new variables (namely sunk costs and competition intensity) the OP96 method may be implemented as follows. At the first step, one estimates a reduced exit equation (that, of course, does not include firm efficiency at this cannot be yet be estimated):

= Pr( ) ( , , , , ) it it it it it it Exit f K a Comp SC X , (14)
This provides it p which is the predicted exit probability of firm i during period t. The second step consists of the estimation of the labor coefficient β l , which is the only flexible input. The third step consists in writing:

β η = + + log log ( , , log , , log , ) it l it it it it it it it it Y L g Comp SC M a K p , (15)
Being non-parametric, g is estimated using a second-order polynomial series. At this step β β β β

, , and

k a comp
SC are estimated and the difference between output and its fitted value from the second and third steps yields an estimate of the individual firm's efficiency, ϖ i t . The fourth and final step is the estimation of the exit model from the equation 9, including the estimated value of the individual firm's efficiency:

ϖ = Pr( ) ( , , , , ) it it it it it it Exit f a Comp SC X , (16)

Data and summary statistics

Our database contains 15,110 observations. This is an unbalanced panel of 4,818 firms from the French

The construction of the variables

Using the standard definitions of exit, an incumbent at period t is a firm that is present both during the current year t and the next year 1 t + , while the exit firm at period t is in the market in year t but not in 1 t + . 8 The EAE survey suffers from several limits with respect to this measurement, because of its own selection rules. According to these rules, a firm may exit for three reasons, two "good" reasons, according to this paper's topic, and one "bad" reason. The first reason is closure, which occurs when a firm is liquidated, which is a first kind of exit. Merging or acquisition may also happen. In this case, the firm identity has changed, and the initial unit is considered as exiting, even if the concrete firm is still active.

Those two cases, the "failure" and the "successful closure", to use Bates' (2005) term, are both consistent with the theoretical model. They simply correspond to a different sell-off valueφ , which is about 0 for the first case, and largely positive in the second case. But, in addition a firm may be unfortunately excluded from the data set without exiting, because its number of employees has fallen under the threshold or because its main activity has changed. This last reason should lead to an upward bias for our measurement of exit.

Concerning the other variables, we deflate the value-added by firm i operating in sector j at time t by the annual price index of value-added. As a measure of capital used by firm i, we compute the sum of the value of fixed assets at the end of the year and the leased capital. This sum is deflated by the annual price index of capital. Intermediate consumption is deflated by the annual price index of intermediate consumption. Labour input in firm i at time t is the number of its employees at the end of the year. The investment deflated by the annual price index of gross fixed capital formation is used to build the capital series when the value of fixed assets is only available either at the beginning or at the end of the period.

To measure the intensity of competition, we first compute the Herfindhal index ( Herfindhal ) calculated from the initial database for each industry s (at the NACE 2 3-digit level) observed at period t:

= = = = = ∑ ∑ 1 1 ( )² st st i N it st i N i it i VA Herf VA , ( 17
)
We then use the following indicator:

= 1 ln( ) st st LCOMP Herf , ( 18
)
Given this, the higher is the indicator value and the more intense is the competition within the industry.

8 Our database ends in the year 2002 but information about the presence of a firm in an industry is available for 2003.

We pay particular attention to the sunk costs variable. We come back to equation ( 6) and propose the following indicator:

( ) ( ) ρ δ α -   = - + - -     1 1 1 (1 ) st it st it st st t s Sunk cI c K c , (19)
During the current period, the sunk cost of a firm is a linear function of its current investment it I and the lagged value of physical capital -1 it K , with several underlying assumptions. First, the firm may lease ρ st percent of its current physical capital it K , such that only the fraction ρ -1 st is related to sunk costs.

Second, physical capital is affected by a depreciation rate of δ st percent each period. Third, a firm may sell α st percent of its physical capital on the second-hand market at the end of each period at a price of st s .

From the information available in our database, we can build some proxies for δ st , ρ st andα st st s c . Thus, δ st is built as the ratio between the destructed capital during the current period over the capital stock available at the beginning of the period 1 t K -. ρ st is approximated by the rental payments divided by the capital in value while α st st s c is the ratio of the value of used capital sold on the second-hand market over the value of capital. These three variables are assumed to vary over time but not within a given industry.

To sum up, sunk costs will be low for firms (and industries) using assets that can be easily leased, have depreciation rate and are present on a large second-hand market. Such measurement suggests that the more specific the assets, the higher the sunk costs.

Summary statistics

As shown in Table 1, the exit rate in French food industry varies between 5.66% and 7.56%, between 1999 and 2002, depending on the year. These values are in accordance with findings in the literature of firm demography, though they lie in the lowest part of the range. Studying France, [START_REF] Bartelsman | Comparative analysis of firm demographics and survival: Evidence from micro-level sources in OECD countries[END_REF] report an exit rate of 11% per year between 1989 and 1994, which is one of the highest values among OECD countries. This difference relative to our results may be explained by the absence of very small firms in our sample, where there is a well known negative relationship between the size of firms and both entry and exit rates. The industry is another reason: firm's turnover is traditionally higher in services than it is in manufacturing (including food industries). The observation level is the last reason. Exit rates would be higher at the plant level because of the high number of multi-plant firms as a plant may be closed while the firm itself is still active. The same analysis may also be applied to the entry rate, which ranges between 5.67% and 7.97%, and to the resulting turnover rate, which ranges between 11.44% and 15.53%.

[Table 1]

Table 1 suggests the existence of a positive correlation between entry and exit rates. Such a result is strongly confirmed when considering food industry at a disaggregated level. Food industry corresponds to class 15 of the NACE 2-digit level but also to 45 different industries at the NACE 4-digit level and to 9 positions at an intermediate 3-digits level that we have built specifically for this study. Table 2 provides a list of industries, the corresponding number of firms in our sample and, finally, entry and exit rates.

[Table 2]

As shown in Table 2, a great variability in terms of the entry and exit rates exists between the sectors composing the food industry. This is even true, first with respect to the NACE 3-digit level. While the average exit rate between 1999 and 2002 equals 6.62% for the all population, this rate varies between 2.02% and 8.56%, with the upper bound being more than four times the lower bound. A brief distinction can be made between:

-The set of industries with a low exit rate (smaller than 5 %): Oils and fats, Fish, Dairies and Beverages;

-The set of industries with a medium exit rate (between 5 and 7 %): Grain products, Meat, Fruits and vegetables products and Animal feeds; -An industry with a very high exit rate: Other food products.

However, this last 3-digit level class Other food products is a very heterogeneous one, composed of very different 4-digit level industries such as Manufacture of Sugar and Bakeries or Pastry shops. For this reason, Table 2 presents some results that are computed at the infra-level that is the NACE 4-digit level. When observing the results of the industries composing the 15.8 class (Manufacture of other food products) at the 3-digit level, we find that only three 4-digit sectors exhibit high entry rates, among which two (Cooking and Bakeries products and Bread and pastry goods and cakes shops) are closer to service activities than to manufacturing both in terms of products and firm's size. In such industries, the exit rate is very high (16.11% and 14.80% respectively). To a lesser extent, this is also the case for the exit rate observed in Sugar manufacturing, which equals 10.14%. When considering the other 3-digit level classes, one may observe that within heterogeneity, as revealed by the 4-digit level, is more limited. Therefore, most heterogeneity is captured at the 3-digit level of the NACE, with the exception of the class Manufacture of other food products that has to be disaggregated.

[Table 3] The main result is the positive correlation between exit and entry rates, which equals 0.707 at the 3-digit level of the NACE, and 0.582 at the 4-digit level of the NACE, with both coefficients being significant at the 5% level. This positive correlation confirms a well-established result [START_REF] Caves | Industrial organization and new findings on the turnover and mobility of firms[END_REF]: the relevant distinction is not (or not first) between creative and destructive industries but rather between turbulent and inert ones. Another interesting result is the apparent negative correlation between, on the one hand, both exit and entry rates, and, on the other hand, sunk costs and competition. These results are consistent with the expected results of estimations. One may note that the two variables that we introduce competition and sunk costs are more strongly correlated to exit rate than size and age which are commonly in the literature.

[Table 4] [Table 5]

The estimation results

Estimation of the production function

A primary interest of the OP96 approach is to provide unbiased estimates for input coefficients in the production function, in contrasts to OLS estimates which suffers from both endogeneity and selection biases, as well as to the Within estimator, which corrects the simultaneity bias but not the selection one.

Accordingly, Table 6 proposes estimation results using the OLS, Within , and OP96 estimators.

[Table 6]

The first point is that significant differences appear between the results obtained with the different estimators. 9 If we first consider simultaneity bias, one may consider that biased estimates (such as the OLS) capture both the real effect of the variable and that of the omitted variable, which is the unobserved individual productivity in this case. Because productivity is expected to be positively linked with labor and age, when comparing the OLS to Within or OP96 estimates 10 , one should find upward-biased values. This is the case with our results: the estimate of labor equals 0.704 using the OLS and 0.376 using the Within estimators, while the estimate for age is not significant with the OLS estimator and equals -0.033 when using the Within estimator. In the case of capital, [START_REF] Levinsohn | Estimating production functions using inputs to control for unobservables[END_REF] suggest that, if there is a positive correlation between the two inputs, then the simultaneity bias will lead to underestimate the coefficient β k . This seems to be the case, as the value when this bias is corrected is 0.278 (Within) versus 0.213 (OLS).

When considering selection bias, the exit decision is not taken into account in OLS or Within estimators, while the OP96 estimator includes the estimated probability of exit at the next period as an 9 Such differences are consistent, in value and sign, with those found in [START_REF] Olley | The Dynamics of Productivity in the Telecommunications Equipment Industry[END_REF] in the case of the Telecommunications Equipment Industry.

10 One should also note that Within and OP96 corrections of simultaneity differ (time-invariant versus time-varying individual effects).

argument. Once again, the biased estimates add to the "true" unbiased value of the correlation between the variable and the omitted variable, which is this time the probability of exit. As this probability is negatively related to age, capital and labour, selection biases are expected to be negative. The direct comparison of OLS to OP96 results is uneasy because of the opposite signs of the biases. However, when comparing Within to OP96 results, one should obtain higher values in the second case. In the case of labor, we obtain 0.579 when using the OP96 estimator against 0.376 when using the Within estimator, 0.317 against 0.278 for capital and, for age, a non significant estimate when using the OP96 estimator against -0.033 when using the Within estimator.

Estimation of the exit equation

Individual firm productivity ˆit ω , as estimated in the previous step, is now included as a regressor in the exit equation. The results of this estimation are presented in Table 7, which provides both coefficient estimates and marginal effects, allowing for a direct (but cautious) comparison of the impact of the different variables on the probability of exit.

[Table 7]

First, the coefficient of ˆit ω is significantly negative and equal to about -0.12: the more efficient the firm, the more protected against the risk of exit. This result is consistent with theoretical predictions. As exit process is the result of market selection, the least efficient producers are the first to be eliminated.

Similar results may be found in previous empirical studies. OP96 obtain a significant value of -0.16 in the case of the American telecommunications equipment industry, observed during the 1980s. Exploring a very different context, namely the Ghana, Kenya and Tanzania manufacturing firms, Söderbom et al.

(2006) obtain a negative estimate equal to -0.239. Using the hazard survival rate, Shiferaw (2009) finds a positive estimate for the productivity variable in the case of the private manufacturing sector in Ethiopia, during 1996-2002. Our results also show that the probability of exit is negatively and significantly correlated to the age of the firm. Such a result is consistent both with numerous empirical results and with theoretical models based on the effect of "learning by doing" [START_REF] Jovanovic | Selection and the Evolution of Industry[END_REF]. However it is interesting to compare the marginal effects of individual efficiency and age. The effect of the former is clearly stronger; a 1% increase in efficiency leads to a 1.47% decrease in exit probability, which is about 10 times more than the effect of one additional year of existence of the firm. One may conclude that most of this experience effect is captured by unobserved individual efficiency, with age being a poor proxy. As in R&D models, the absorption capacity of the firm which is largely based upon unobserved characteristics, would greatly improve the effect of experience and then represent a component of unobserved firm efficiency.

One now must consider the effect of industry variables, namely competition intensity. A positive estimate is obtained, as a higher intensity of competition leads to a higher probability of exit. This result is consistent with findings about industry life cycles, and more precisely with the so-called "Shakeout" literature [START_REF] Klepper | Entry, exit, and shakeouts in the United States Market in new manufactured Products[END_REF][START_REF] Klepper | Industry shakeouts and technological change manufactured Products[END_REF]. When competition is the more intense in an industry, a great number of exits occur, as in Production and processing of meat industry. Once this Shakeout period ends, the industry is more concentrated, as in Manufacture of oils and fats, and the exit rate decreases. Using a different approach based on spatial patterns, [START_REF] Huiban | The spatial demography of new plants: urban creation and rural survival[END_REF] empirically obtains the same result: a negative relationship between a firm's survival probability and the intensity of local competition.

The effect of sunk costs on exit probability is clearly significant and negative. Sunk costs are barriers to exit for French firms because they limit the mobility of incumbents outside the market, other things being equal. The intensity of this effect seems lower than the effect of competition, as shown by the marginal effect. However, at the same time, one has to recall that there is a huge dispersion of sunk cost levels between industries, even if not speaking of the firm level. One may conclude from this that sunk costs play a poor role for most firms and in most industries, but may serve as very important barrier to exit in particular cases.

In summary, competition increases the probability of exit, while sunk costs act as exit barriers. These variables may mostly explain the differences between industries. Recall that competition is measured at the industry level. Sunk costs is observed and measured at the firm level but defined in a way (as exogenous sunk costs) that tends to favour inter-industry dispersion and reduce intra-industry dispersion. Together with the variable age, the individual efficiency explains most part of the differences observed between firms of a given industry, in terms of propensity to exit.

Conclusions

This study uses the OP96 method to estimate the effects of several determinants of a firm's probability of exit. As in previous works using a similar approach, some robust estimates are obtained for the production function arguments. Capital and labor estimates are both different from those obtained when using methods that do not correct for simultaneity and selection biases. Once the unobserved individual efficiency has been estimated for each firm, it is introduced as a regressor in the exit model. As a result, the firm's probability of exit is negatively and significantly correlated with the individual firm' productivity, its age and positively correlated with the intensity of competition that exists in the firm's industry.

However, this study also provides an original measurement of sunk costs at the firm level which is then introduced in the empirical model. Thus, sunk costs appear to play a significant and negative role: the higher the level of sunk costs, the lower the exit rate. The low value of the marginal effect and the large dispersion of the variable value suggest that this determinant effect is generally light but may become very strong in some particular industries. In summary, competition intensity and sunk costs may explain differences in exit rates between industries, while age and individual efficiency may explain the variability observed between firms within an industry.

Several extensions and improvements can be made with respect to the present study. Some concern the measurement of exit rates. It would be useful to introduce a distinction between exits that correspond to a failure situation (i.e. closure) and that signify a success (i.e. selling, merging and acquisition). Actually, one may posit that both the determinants and effects of exit differ between these two kinds of situations. The present classification of food industries is a second problem. The complete 4digit level classification is not a very tractable one, as some classes of the 3-digit level classification are too heterogeneous. A specific classification should be developed to provide a more efficient measurement of both the intensity of competition and sunk costs.

  food industry, observed during the period 1999-2002. The data are obtained from annual surveys about firms' activity ("Enquête annuelle d'entreprises", EAE thereafter) which is the official French business-level data collected by the French Office of National Statistics (INSEE), and, in the case of the food industry, by the Statistical Department of the French Agriculture Ministry. This survey only includes firms that employ at least 20 employees. The affiliation of firms with an industry depends on their activity in terms of product turnover by products.

Table 3

 3

reports the average value of the different variables by 3-digit level industry. Table

4 (and Table 5

) shows the correlation matrix at the 3-digit NACE level (and 4-digit NACE level), respectively.

Table 1 :

 1 Exit and entry rates by year

	Year	Number of Observations	Entry Rate	Exit Rate	Turnover
	1999	3725	5.80	5.66	11.46
	2000	3822	7.64	7.22	14.86
	2001	3738	5.67	5.99	11.66
	2002	3825	7.97	7.56	15.53
	Average Rate	15110	6.78	6.62	13.40

Table 2 :

 2 Exit by industry, average annual rate, from 1999 to 2002 Nace, 2,3 and 4-digit levels

	Industry code and name Number of	Number of	Entry Rate	Exit Rate
		Firms	Observations	(%)	(%)
	15 Manufacture of	4818	15110	6.78	6.62
	food products and
	beverages
	15.1 Production and	1524	4822	6.43	6.64
	preserving of meat
	and meat products
	15.1A Production,	509	1740	4.89	5.63
	processing and preserving of
	meat
	15.1C Production of	207	707	5.23	4.67
	poultry meat
	15.1E Production of	520	1702	6.46	6.23
	meat and poultry meat
	products
	15.1F Cooked pork meats	288	673	11.59	12.33
	15.2 Processing and	198	637	5.97	4.55
	preserving of fish and
	fish products
	15.2Z Processing and	198	637	5.97	4.55
	preserving of fish and fish
	products
	15.3 Processing and	186	608	6.58	5.26
	preserving of fruits
	and vegetables
	15.3A Processing and	12	41	2.44	4.88
	preserving of potatoes
	15.3C Manufacture of fruit	21	63	6.35	7.94
	and vegetable juice
	15.3E Processing and	92	302	7.62	4.64
	preserving of vegetables
	15.3F Processing and	61	202	5.94	5.45
	preserving of fruit
	15.4 Manufacture of	27	99	4.04	2.02
	vegetable and animal
	oils and fats
	15.4A Manufacture of	15	53	1.89	1.89
	crude oils and fats
	15.4C Manufacture of	10	39	7.69	2.56
	refined oils and fats
	15.4E Manufacture of	2	7	0	0
	margarine and similar edible
	fats
	15.5 Manufacture of	318	1082	3.70	3.70
	dairy products
	15.5A Operation of	54	192	4.17	3.65
	dairies and cheese making
	15.5B Production of butter	13	40	0	7.50
	15.5C Production of	188	665	3.61	3.31
	cheeses
	15.5D Production of other	39	108	2.78	2.78
	dairy products
	15.5F Manufacture of ice	24	77	6.49	6.49

Table 3 :

 3 Average annual values by industry,(1999)(2000)(2001)(2002) Nace, 3-digit level

	Industry code and name	Size	Age	Sunk Cost	Herfindahl
		(Number of	(Years)	(€ millions)
		Employees)
	15.1 Production and	106.95	11.50	5.05	0.54
	preserving of meat
	15.2 Processing and	94.38	10.21	5.77	3.80
	preserving of fish and fish
	products
	15.3 Processing and	144.52	11.88	14.52	2.34
	preserving of fruits and
	vegetables
	15.4 Manufacture of	126.59	13.77	20.49	24.43
	vegetable and animal oils and
	fats
	15.5 Manufacture of dairy	183.99	14.02	20.09	3.58
	products
	15.6 Manufacture of grain	95.91	13.24	26.03	13.46
	mill products, starches and
	starch products
	15.7 Manufacture of	76.64	13.38	7.99	4.34
	prepared animal feeds
	15.8 Manufacture of other	94.25	10.71	9.09	1.73
	food products
	15.9 Manufacture of	96.77	13.21	19.23	3.58
	beverages

Table 4 :

 4 A correlation table at the industry level(1999)(2000)(2001)(2002) Nace, 3-digit level (9 industries)

	Variable	Size	Entry rate	Exit rate	Sunk costs	Herfindahl	Age
	Size	1	-0.43286	-0.50693	0.37953	0.04297	0.35715
			(0.2445)	(0.1637)	(0.3137)	(0.9126)	(0.3454)
	Entry rate	-0.43286	1	0.70672	-0.51151	-0.57954	-0.74389
		(0.2445)		(0.0333)	(0.1593)	(0.1019)	(0.0216)
	Exit rate	-0.50693	0.70672	1	-0.56788	-0.64167	-0.52457
		(0.1637)	(0.0333)		(0.1107)	(0.0107625)	(0.1471)
	Sunk costs	0.37953	-0.51151	-0.56788	1	-0.52457	0.72457
		(0.3137)	(0.1593)	(0.1107)		(0.1471)	0.47070272
	Herfindahl	0.04297	-0.57954	-0.64167	-0.52457	1	0.49744
		(0.9126)	(0.1019)	(0.0107625)	(0.1471)		(0.1730)
	Age	0.35715	-0.74389	-0.52457	0.72457	0.49744	1
		(0.3454)	(0.0216)	(0.1471)	0.47070272	(0.1730)

Table 5 :

 5 A correlation table at the industry level(1999)(2000)(2001)(2002) Nace, 4-digit level (45 industries)

	Variable	Size	Entry rate	Exit rate	Sunk costs	Age
	Size	1	-0.2470	-0.13457	0.81210	0.18154
			(0.106)	(0.3782)	(0.0001)	(0.2327)
	Entry rate	-0.2470	1	0.58179	-0.15282	-0.78027
		(0.106)		(0.0001)	(0.3162)	(0.0001)
	Exit rate	-0.13457	0.58179	1	-0.01643	-0.53618
		(0.3782)	(0.0001)		(0.9147)	(0.0001)
	Sunk costs	0.81210	-0.15282	-0.01643	1	0.11031
		(0.0001)	(0.3162)	(0.9147)		0.4707
	Age	0.18154	-0.78027	-0.53618	0.11031	1
		(0.2327)	(0.0001)	(0.0001)	0.4707

Table 6 :

 6 Estimates of the production function FoodIndustry, 1999Industry, -2002 Standard errors are in parentheses and computed using 50 bootstrap replications (OP96). Time and industry (Nace3 level) dummies are included in each regression but are not reported.

	Variables	OLS	Within	Olley-Pakes
				96
		0.704	0.376	0.579
	L	(0.0063)	(0.0014)	(0.0068)
	K	0.251	0.278	0.317
		(0.0041)	(0.0081)	(0.0367)
	Age	Ns	-0.033	Ns
			(0.0023)
	N	15110	4818	15110
	R²	0.8040	0.2038	0.5801

Table 7 :

 7 Estimates of the exit probit model (marginal effects) FoodIndustry, 1999-2002 (Including Lcomp3 and Lcomp4)

	Variables	(1) Estimates	(2)Marginal Effects
	ˆit ω	-0.1233	-0.0146
		(0.0238)	(0.0028)
	Age	-0.0146	-0.0017
		(0.0026)	(0.0003)
	Competition	0.7387	0.0877
		(0.1734)	(0.0205)
	Sunk Costs	-0.0586	-0.0070
		(0.0116)	(0.0014)
	Intercept	-5.5061
		(0.9108)
	N	15110	15110
	Log Likelihood	-3539

Standard errors are in parentheses. Time and industry (Nace3 level) dummies are included in each regression but are not reported.

Interestingly, one may note point may be that a potential buyer should implicitly include such costs in the value accorded to the firm. Unfortunately the structure of the data does not allow us to test this assumption.

Some other reasons may exist, that are not taken into account in this study. As one example,[START_REF] Katayama | Firm-level productivity studies: illusions and a solution[END_REF] claim that severe measurement errors of both output and inputs occur, when applying to differentiated products industries.

Many surveys have been proposed regarding the way to estimate total factor productivity.[START_REF] Van Beveren | Total factor Productivity Estimation: A Practical Review[END_REF] proposes an empirical application to the case of Belgian food industries.

Acknowledgements

We gratefully acknowledge financial support from the MICRO-DYN project of the Sixth Framework Research Program of the European Union.


Juan-David Llamas

François Lesage

Gabriel Wild

Influence of gas flow rate on liquid distribution in tricklebeds using perforated plates as liquid distributors

Influence of gas flow rate on liquid distribution in trickle-beds using perforated plates as liquid distributors.

Introduction

Trickle-beds reactors are widely used chemical reactors in which a gas and a liquid flow cocurrently downwards through a fixed bed of solid particles. Along with their advantages in terms of cost and simplicity, trickle-beds reactors have two main handicaps: they are unable to evacuate big amounts of heat and it is difficult to properly distribute the fluid phases over the catalyst particles. While the first of these two problems will mostly restrain the application field of trickle-beds reactors, the second will directly affect its performances. Indeed, a bad liquid distribution will not only lead to an inefficient utilization of catalyst but could also be the cause of hot spot formation.

Among the factors affecting liquid distribution in trickle beds one will find the initial liquid distribution (ensured by the use of a proper distributor), the packing and fluids characteristics, the pre-wetting conditions and the flow rates. Those factors have been widely studied by numerous authors (e.g. [1][START_REF] Sylvester | Radial Liquid Distribution in Cocurrent Two-Phase ownflow in Packed Beds[END_REF][3][4][5][6][7][8][9][10] ). Many of their studies however, dealt mostly with small sized columns and/or were performed using liquid collectors; so, in a very recent investigation, Babu et al. 10 used a column with 50 mm i.d.. Note that these authors compared collector data with radial spreading data issued from a radial heat transfer model. Although simple to use and quite valuable in many circumstances, the liquid collector can only give access to the macroscopic flow rate distribution at the exit of the reactor. As the flow distribution inside the reactor is not necessarily reflected by the exit distribution, the use of a liquid collector could lead to improper conclusions. For this reason, the present work tries to complete the information obtained with a liquid collector by using two wire-mesh tomography devices that allow studying liquid distribution at two different bed depths. Using two different perforated plates for fluid distribution and operating under different gas and liquid flow rates, the present work focuses on the influence of the gas flow rate on liquid distribution when this kind of distributor is used.

2.

Experimental setup

The reactor

The experiments were performed using a 0.3 m diameter trickle-bed reactor. The fixed bed, of 1.3 m height, was composed of porous alumina cylinders whose mean length and diameter were 4.3 mm (with a standard deviation of 1.5 mm) and 1.2 mm (with a standard deviation of 0.16 mm) respectively. The internal porosity of the solid particles, measured by helium pycnometry, was 0.46, while the external porosity of the fixed bed, which was sock packed, was 0.47.

Air and water were used as fluids. The superficial velocities considered varied from 0 to 0.34 m/s for the gas and from 0.0016 to 0.0047 m/s for the liquid. All experiments were performed at room temperature (22°C) and pressure (1 bar) and using a pre-wetted bed.

For fluid distribution, two perforated plates were used: perforated plate "A" which had 24 liquid inlets and 4 gas inlets and will be referred to as "uniform distributor" and perforated plate "B" which had 5 liquid inlets and 4 gas inlets and will be referred to as "cross-shaped distributor" (Figure 1). The second distributor is used to mimic an imperfect initial distribution, while the first one is a design actually used in industry a dozen years ago. Between the perforated plate and the solid particles, 3 layers of "inert" spherical particles were disposed: a first layer of 3 mm steel spheres that were in contact with the catalyst, a second layer of 5 mm steel spheres over the previous ones and a third layer of 6 mm ceramic beads in contact with the perforated plate. These inert particles occupied about 30 mm of the fixed bed.

Further details on the experimental plant may be found in Llamas 11 .

The measuring devices

Two different measuring techniques were used for the experiments: a liquid collector and two wire-mesh tomography devices. The liquid collector, placed at the exit of the reactor, was divided in 9 collecting zones of the same surface (Figure 2) and allowed measuring the macroscopic liquid distribution in terms of flow rate at this point; it is the same as the one proposed by Marcandelli et al. 6 . The quantification of the results obtained with this device was done by means of the maldistribution factor (M f ) defined according to Marcandelli et al. 6 .

( ) ∑ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - - = i i f Q Q Q N N M 2 1 1 ( I )
where N is the number of collecting zones (9 for the present work), Q i is the flow rate measured in zone i and Q is the mean liquid flow rate. The wire mesh tomography devices were placed 0.33 m and 0.96 m from the distributor and allowed measuring the liquid distribution in terms of liquid saturation at those two bed depths. More precisely, each wire mesh tomography device is composed of two horizontal planes of parallel wires placed at a short distance between them (4 mm in the present case). The angle between the wires of both planes is 90°, forming thus a square grid where the wires do not touch each other and allowing, by local conductance measurements, to detect the presence of a conductive fluid between them. Each plane contains 19 stainless steel wires of 2 mm diameter, resulting in 313 measurable crossing points per device. The operating principle of wire mesh tomography is simple: if a current is applied to one of the wires of the first (transmitter) plane, it will not be measured on the second (receiver) plane, unless a conductive fluid makes the connection between them. As the conductance of a liquid filament is proportional to its section, for each of the crossing points, the local liquid saturation can be estimated as:

i column filled liquid i i L i L C C = = ε ε β ( I I )
Where C i is the measured conductance for crossing point i and is the local liquid saturation which is the ratio of the local liquid holdup to the bed porosity ε. More detailed information about the working conditions, advantages and possible pitfalls of this device can be founded elsewhere

i L β i L ε 12 .
It is important to state that, as the measuring principle of wire mesh tomography reposes on conductance measurements, the use of this technique inside a bed of porous particles is quite complicated. Indeed, once wetted, porous particles remain filled by water and can conduct electricity. In this case, it is thus difficult to make any difference between a set of wetted particles and a real water filament flowing through the reactor. For this reason, between the wires of the tomography device, porous particles were replaced by 2 mm glass beads. However, radial spreading in a bed of glass beads is slow, as shown in 11 , and it can safely be assumed that the influence on liquid distribution of a length of 50 mm of glass beads (which corresponds to about 3.8% of the total bed height) is negligible.

Results

Results were obtained using the two measuring techniques described earlier for two perforated plates and five different liquid superficial velocities ranging from 0.0016 to 0.0047 m/s. For each of the liquid flow rates considered, five gas superficial velocities between 0 and 0.34 m/s were studied.

Uniform distributor

With 24 liquid inlets (equivalent to 340 inlets per m 2 of reactor cross-section), perforated plate "A" can be considered as a good liquid distributor. Some of the images obtained using this perforated plate at U L = 0.0082 m/s are presented in Figure 3. From those images, and the ones obtained for the others gas-liquid superficial velocities combinations, two well know consequences of the gas flow on the reactor hydrodynamics were evidenced. The first one is the logical reduction of the mean liquid saturation as the gas flow rate increases. The second is that, while the entrance of gas inside the reactor modifies deeply the liquid distribution, further increase of its flow rate has only a limited effect on the liquid flow pattern. This is not surprising as in absence of gas flow the mechanisms governing the single phase liquid motion are not the same: with a gravity-driven liquid flow, the distribution is mainly affected by packing topology and capillarity forces. The obtained results show that, from a liquid saturation point of view and for U G ≠ 0, the quality of the liquid distribution does not seem to be severely affected by the gas flow rate (Figure 4). Liquid superficial velocity, however, seems to play an important role as, as it can be seen in Figure 5, the MSD value decreases notably when U L increases. The predominant effect of the liquid flow rate on liquid distribution compared to that of the gas had already been reported, among others, by Sylvester and Pitayagulsarn 1 and Kundu et al. 7 . Measurement were also realized with the liquid collector. The maldistribution factor M f was calculated for all liquid-gas flow rate combinations. Although not of the same intensity for all liquid flow rates, an improvement of the liquid distribution was observed at increasing gas flow rate. The former statement can be easily appreciated from Figure 6, where M f is plotted against U G for all the experiments regardless of the liquid flow rate. In this figure, the maldistribution factors for U G = 0 were omitted because their dependence on U L seems to be stronger. Those M f values were comprised between 0.15 and 0.26 which shows, as already reported by authors like Marcandelli et al. 6 and Møller et al. 4 , the beneficial effect of having a flowing gas inside the reactor. The results obtained with both measuring techniques lead to a first hypothesis about the fluid flow inside the reactor. Indeed, while wire mesh tomography showed that liquid distribution quality is not deeply affected by gas flow, the liquid collector showed that the flow rates at the exit of the reactor gain in uniformity as gas flow rate increases. That could mean that the gas follows preferred paths inside the reactor. The zones of the column concerned by those paths, probably because gas and liquid are injected separately into the column (as perforated plates are used), will have lower liquid saturation than others but, as gas velocity is higher and liquid droplets can be carried along by gas flow, the flow rates at the exit of the reactor will be macroscopically similar for those zones that for zones where liquid saturation is higher but the amount of gas is lower. Flow rates measurements inside the reactor (if possible near the wire mesh tomography devices) would be necessary to get information concerning the validation of the stated hypothesis.

Cross-shaped distributor

With 5 distant liquid inlets, the cross shaped distributor allows getting an insight about the influence of gas flow over individual liquid filaments. Figure 7 shows typical images obtained with this perforated plate. The presented results concern a liquid superficial velocity of 0.0082 m/s at 3 different gas flow rates. With this set of images, the influence of gas flow rate on liquid distribution becomes clearer. Indeed, when no gas is flowing through the reactor, a liquid flow pattern similar to the one obtained with the uniform distributor is observed: the liquid manages to occupy the whole reactor cross-section before the first tomography device. When the gas flow rate is larger than 0 however, liquid flow pattern changes radically to adopt, at least for a distance superior to one reactor diameter, the flow pattern imposed by the distributor. According to the obtained images, this low quality liquid distribution is emphasized by the increase in gas flow rate.

The effect of gas flow reported previously is more pronounced for high liquid flow rates without completely disappearing for the lowest ones (Figure 8). For the latter, even if the cross-shaped pattern is less evident, the increase of poorly irrigated zones leads to an increase of MSD values. It is important to notice that, in order to avoid appreciation errors issued from the increase of liquid saturation with liquid flow rate, the colours assigned to each of the images in Figure 8 are a function of the mean liquid saturation of the concerned image. The comparison between the results obtained using the wire mesh tomography and those obtained with the liquid collector is quite interesting. Indeed, as presented in Figure 9 where the maldistribution index (M f ) and the MSD are both plotted against U G for U L = 0.0082 m/s, the effect of gas obtained with both techniques is not the same. While the collector shows an improvement in liquid distribution quality with gas in terms of liquid flow rate at the exit of the reactor, the tomography measurements show (as discussed early) a deterioration of liquid distribution quality with the increase of gas flow rate in terms of liquid saturation. In order to avoid scale problems, local liquid saturation values were averaged to match the 9 measuring zones defined by the liquid collector. The 9 liquid saturation values thus obtained were then used to calculate a M f kind of parameter (using, evidently, liquid saturation instead of liquid flow rates in equation I) that could be compared to the M f values measured using the liquid collector. As the M f values obtained with the wire mesh tomography device were significantly lower than those obtained with the liquid collector, all values were normalized by dividing them by the largest measured value (0.23 for the liquid collector and 0.06 for wire mesh tomography). Results obtained (Figure 10) show a similar behaviour as that evidenced in Figure 9. An explanation of this behaviour is difficult to establish. On the one hand, this could be a consequence of the hypothesis proposed earlier, according to which the gas will follow preferred paths while carrying along liquid droplets (especially when taking a look of the images obtained 0.33 m from the distributor). On the other hand, it is true that liquid distribution seems to improve with the distance from the distributor. Indeed, in Figure 9, the increase in MSD with gas flow is mostly the consequence of the increase of the standard deviation measured for the first tomography device, 0.33 m from the distributor. For the second device, the standard deviation does not seem to be altered by gas flow and remains mostly constant. Following this behaviour, it is possible to imagine that the liquid distribution could improve near the exit of the bed to give the results obtained with the collector. Anyhow, and even if the first of the two explanations seems more reasonable, the obtained results do show the limitations of the liquid collector and the effects of gas on liquid distribution.

Conclusions

The use of two different measuring devices allowed studying the influence of gas flow rate on liquid distribution when perforated plates are used for fluid distribution. When using a good liquid distributor, the results showed that, as stated by authors like Marcandelli et al. 6 and Møller et al. 4 , it is the presence of a flowing gas, more than its flow rate, which has a clear positive impact on the liquid distribution inside the reactor. It was also observed that in general terms, increasing the gas flow rate enhances the quality of the liquid distribution. This kind of behaviour has already been reported, among others, by Weekman and Myers 1 , Saroha et al. 5 , or more recently by Kundu et al. 7 . However, in contrast with the results reported by those authors, the measurements showed that the gas can also have a negative impact on liquid distribution. Indeed, when a bad liquid distributor is used (cross-shaped distributor), although the liquid collector shows an improvement in liquid distribution quality, this is not the case of the overall liquid distribution measured in terms of local liquid saturations.

According to these results, two main conclusions can be proposed:

• For a distance superior to one reactor diameter, the introduction of gas flow rate causes the liquid to follow the flow pattern imposed by the distributor. If a good liquid distributor is used, the overall influence of the gas will be positive. If a bad liquid distributor is used, however, the presence of the gas will have a negative impact over liquid distribution.

Although simple to use and quite valuable in many circumstances, the known limitations he presented results show also the importance of considering liquid maldistribution as a inally, it is important to keep in mind that the results presented here concern only reactors in cknowledgment he authors wish to thank "Total Raffinage" not only for financial support, but also for

Notation i = Conductance at crossing point i [Siemens] uid collector. D ty of phase i [m/s]

) Weekman, V. W. J.; Myers, J. E. (1964). Fluid-flow characteristics of concurrent gasliquid flow in packed beds. A.I. Ch.E. Journal 1964, 10(6), 951.

•

of the liquid collector were exposed here as it was showed that the sole consideration of exit flow rates can lead to incomplete distribution quality impressions. Indeed, the use of the cross shaped distributor showed that while the overall liquid distribution deteriorates with gas flow (in terms of liquid saturations), the results obtained with the liquid collector showed the opposite behaviour (in terms this time of liquid flow rates).

T function of the quantity that is being measured. It is obviously not the same to consider liquid maldistribution in terms of liquid saturation as liquid maldistribution in terms of liquid flow rates or liquid velocities. Neither the results obtained with the collector nor those obtained with the tomography can be considered as wrong. Those results however, are incomplete if there are considered separately because, at it was expressed before, maldistribution can manifest itself differently depending of the measured quantity.

F which perforated plates are used for liquid distribution. This consideration could explain up to some extent the differences between the results present here and the behavior reported by other authors. In the case of distributors where gas and liquid are mixed before entering the reactor (e.g. gas chimney trays) the influence of gas flow rate will probably manifest itself in a different way.

A

T providing the catalyst support particles, and for numerous discussions.

Figure 1 .

 1 Figure 1. Perforated plates used for fluid distribution.

Figure 2 .

 2 Figure 2. Liquid collector used for the experiments.

Figure 3 .

 3 Figure 3. Uniform distributor: images obtained at U L = 0.0082 m/s.

Figure 4 .

 4 Figure 4. Influence of U G on MSD for different liquid superficial velocities.

Figure 5 .

 5 Figure 5. Influence of U L on MSD at different values of the gas superficial velocity.

Figure 6 .

 6 Figure 6. Evolution of M f with gas superficial velocity for all liquid flow rates.

Figure 7 .

 7 Figure 7. Cross-shaped distributor: images obtained at U L = 0.0082 m/s.

Figure 8 .

 8 Figure 8. Cross-shaped distributor: images obtained at U G ≈ 0.17 m/s.

Figure 9 .

 9 Figure 9. Comparison between the results obtained with the liquid collector and the wire mesh tomography devices.

Figure 10 .

 10 Figure 10. Maldistribution factors obtained with wire mesh tomography and with the liquid collector at the same scale.

  Saroha, A. K.; Nigam, K. D. P.; Saxena, A. K.; Kap T (7) Marcandelli, C.; Lamine, A. S.; Bernard, J. R.; Wild, G. B (8) Kundu, A.; Saroha, A. K.; Nigam, K. D. P. Liquid distribution stud re (9) Atta, A.; Roy, S.; Nigam, K. D. P. In re (10) Babu, B. V.; Shah, K. J.; Govardhana Rao, V. Lateral mixing in trickle C (11) Llamas, J. D. Etude expérime fi National Polytechnique de Lorraine, Nancy, France. (12) Llamas, J. D. ; Pérat, C. ; Lesage, F. ; D'Or to Proc. -Process Intensification, 2007, (to be published: doi:10.1016/j.cep.2007.09.017).

Département de Chimie Physique des Réactions, Nancy-Université, CNRS, 1, Rue Grandville, 54000 NANCY, France. * Corresponding author : E-mail : gabriel.wild@ensic.inpl-nancy.fr