METHOD AND DEVICE FOR DETERMINING THE AIR CHANGE RATE OF A ROOM OR BUILDING

Abstract

A method, which seeks to determine the air change rate of a space, includes, over at least two successive time periods corresponding to distinct given-gas flow rates applied in the space, carrying out a campaign of measurements to determine the concentration of the gas inside the space at closely-spaced time intervals, and the concentration of the gas outside the space is determined at closely-spaced time intervals. The value of the air change rate of the space is determined by causing the convergence of a diffusive model expressing the temporal variation of the concentration of the gas inside the space as a function of the concentration of the gas outside the space and of physical parameters of the space from which parameters the air change rate of the space can be calculated, and the measured change in the concentration of the gas inside the space as a function of time.

Description

The present invention relates to a method and a device for determining the air change rate of a space.

Within the meaning of the invention, a “space” means any space delimited by a physical boundary, particularly a living or storage space. It may be a fixed living or storage space, such as an individual home or a building, notably for habitation or tertiary use, a part of such a building, for example an apartment in a multistory building, or even a storage tank. It may be a mobile living or storage space, such as a cabin or a storage tank in a vehicle, notably in a motorcar, a truck, a train, a ship, a submarine, an airplane, a spacecraft.

The air change rate of a space, denoted ACH, is the volume of air inside the space which is changed per hour, expressed in m³·h⁻¹. This may be a rate of air change by natural ventilation, or a rate of air change by forced ventilation (namely using controlled mechanical ventilation). For an old building that is to be renovated, determining the rate of air change by natural ventilation, without mechanical ventilation, is of use in assessing whether the air flow rate is high enough with regard to the interior air quality and in order to determine the impact that natural infiltration will have on the energy balance of the building. For a new-build comprising a mechanical ventilation system with heat recuperation, it is possible to determine the rate of air change by natural ventilation, in a configuration in which the mechanical ventilation is deactivated, this making it possible to evaluate the airtightness of the building; the rate of air change by forced ventilation, with the mechanical ventilation in the active configuration, may also be determined making it possible to evaluate the flow rate of the mechanical ventilation system and to verify that it is operating optimally.

It is known practice to determine the air change rate in a building using a test of the “blower door” type, in which test mechanical pressurization or depressurization of the building is obtained and the resulting air flow rates are measured in a range of static pressure differences between the inside and the outside of the building. One coefficient conventionally measured is the air leakage rate at 50 Pa divided by the heated volume, denoted n₅₀, which corresponds to the volume of air changed per hour in the building subjected to a 50 Pa difference in pressure between the inside and the outside of the building.

In this “blower door” method, a false door formed of an airtight tarpaulin in which a blower is fixed is installed in an opening of the building, then the blower is switched on in order to create a difference in pressure between the inside and the outside of the building, and the air flow rate and the pressure difference are measured over a range of pressure differences generally ranging from 20 Pa to 70 Pa. These large pressure differences do not make it possible to take account of the effect of external conditions on the building. It is necessary to use physical models to extrapolate the results to smaller pressure differences and to work back to realistic physical parameters, one example being the Persily-Kronvall model. However, it is difficult to obtain a satisfactory result in a simple way as the simplified physical models are not suited to all types of building and the more elaborate physical models are complicated to use. In addition, with this method, it is necessary to conduct the measurements under conditions of low wind, something which is not always possible.

Furthermore, in building physics, it is known practice to determine the air change rate using the tracer gas method, which has the advantage of taking natural measurement conditions into consideration. In the most conventional variation of this method, a large quantity of a specific gas such as SF₆ or CO₂ is injected into the building, and the decrease in the concentration of this gas in the air over several hours is measured. The air change rate is then estimated using the ratio of the temporal variation of the concentration of the gas inside the building and of the difference in absolute quantity thereof between the inside and the outside. However, this method is not very widely used on building sites after construction, chiefly because of its cost and because of the lengthy measurement durations.

It is these disadvantages that the invention more particularly intends to overcome by proposing a method and a device that make it possible to determine the air change rate of a space simply and quickly, notably over a period of a few hours, at a moderate cost and with reasonable precision, for any type of space.

To this end, one subject of the invention is a method for determining the air change rate ACH of a space, characterized in that it comprises steps in which:

• • over at least two successive time periods D_k corresponding to distinct given-gas flow rates {dot over (q)}_k applied in the space, a campaign of measurements is carried out to make it possible to determine the concentration of the gas inside the space c_ik at closely-spaced time intervals, and the concentration of the gas outside the space c_ek is determined at closely-spaced time intervals;
  • the value of the air change rate ACH of the space is determined by causing the convergence of: on the one hand, a diffusive model expressing the temporal variation of the concentration of the gas inside the space c_ik as a function of the concentration of the gas outside the space c_ek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and on the other hand, the measured change c_ik (t) in the concentration of the gas inside the space c_ik as a function of time.

Within the meaning of the invention, the “concentration of the gas” may be the gas content in the air in grammes of gas per cubic meter of air (g/m³), which in the case of the gas H₂O corresponds to the absolute humidity, or the gas content in the air in grammes of gas per gramme of air (g/g of air) which, in the case of the gas H₂O, corresponds to the specific humidity. The air change rate ACH of the space can therefore be given either in m³/h, or in g of air/h.

In addition, in the context of the invention, “the inside of the space” and “the outside of the space” denote the two masses of air which are separated by the physical boundary of the space and situated respectively inside and outside the physical boundary of the space.

The gas used in the context of the invention, of which distinct flow rates {dot over (q)}_k are applied in the space and the change in concentration of which is monitored, may be chosen, notably from H₂O, CO₂, He, SF₆, H₂, N₂, or other refrigerant tracer gases, this list not being exhaustive. There are a number of important criteria to consider for the choice of the gas; in particular, the gas needs to be easily identifiable and measurable in the atmosphere; the gas must not be dangerous if inhaled at length or frequently, even if the method does not require a human presence throughout the measurements; for preference, the gas is not harmful to the environment. In addition, the use of a gas which is present in the atmosphere, such as H₂O or CO₂, entails taking the concentration thereof in the atmosphere into consideration and correcting for this when calculating the air change rate. The use of water vapor H₂O in the context of the invention, as a gas to which the distinct flow rates {dot over (q)}_k in the space are applied and the change in concentration of which is monitored, is advantageous because of its low cost, its innocuousness, and the ease with which a flow of water vapor can be generated.

The invention allows an in-situ determination of the air change rate of a space. The principle underlying the invention is that of using the transient variations in the concentration of a given gas inside the space when the space is subjected to controlled internal influences and in a measured external environment. Quantitative analysis of the variation in the concentration of the gas inside the space makes it possible quantitatively to determine the air change between the inside and the outside of the space over a short period, of the order of a few hours, by limiting the number of parameters liable to influence the way in which the space behaves. In particular, the briefness of the measurements makes it possible to get around the influence of the conditions of use of the space, of the variations in external conditions, and of the phenomena of absorption or desorption of the gas by the building materials and/or furnishings of the space.

Within the context of the invention, what is meant by “flow rate of the gas applied in the space” is any operating condition that generates a variation in the concentration of the gas inside the space, for given conditions of gas concentration outside the space. It will be appreciated that the flow rate of the gas applied in the space may be positive, zero or negative. A positive gas flow rate corresponds to an injection of the gas into the space, whereas a negative gas flow rate corresponds to an extraction of the gas from the space. In the case of a zero or substantially zero gas flow rate applied to the space, the variation in the concentration of the gas inside the space may be the result of an imbalance between the initial concentrations of the gas inside and outside the space. According to the invention, provision is made for at least one of the given-gas flow rates {dot over (q)}_k to be non-zero.

In the context of the invention, the value of the air change rate ACH of the space is determined by causing the convergence of a diffusive model and the measured change c_ik(t) in the concentration of the gas inside the space as a function of time. In one advantageous embodiment, the diffusive model expresses the temporal variation of the concentration of the gas inside the space c_ik as a function of the concentration of the gas outside the space c_ek and of the gas flow rate in the space {dot over (q)}_k. When the temporal variation of c_ek is expressed as a function of c_ek only, it is possible to arrive at an evaluation of ACH/V, where V is the effective volume of the space, which means to say it is possible to arrive at a number of volumes changed per hour.

The diffusive model used to determine the air change rate of the space may be of any type known to those skilled in the art.

According to one aspect of the invention, the diffusive model used for determining the air change rate of the space may be an R-C model with a suitable number of resistors and capacitors. For preference, the diffusive model is a simple R-C model with one resistor and one capacitor. As an alternative, the diffusive model may notably be a more complex R-C model than the simple R-C model, such as a so-called “3R2C” model with three resistors and two capacitors.

According to another aspect of the invention, the diffusive model used to determine the air change rate of the space may be a parametric identification model (or system identification model), namely one in which a mathematical model of a system is obtained from measurements, such as the models described in the work “Time Series Analysis” by Henrik Madsen, Chapman & Hall, 2008 (ISBN-13:9781420059670 0).

In particular, the diffusive model used to determine the air change rate of the space may be an autoregressive model, notably an ARX model (autoregressive model with external inputs). As an alternative, other autoregressive models may be used, such as, for example, ARMAX models.

In the known way, an ARX model is an autoregressive model defining one output y(t) as a function of one or more inputs u(t), v(t) and a random modeling residual characterized by a zero mean white noise e(t), t denoting the sampling instant considered. The ARX model, if the delay is taken into consideration, can be written:

A(p⁻¹)y_k=B(p⁻¹)u_k+D(p⁻¹)v_k+e_k

with:

A(p⁻¹)=1+a₁p⁻¹+ . . . +a_np⁻ⁿ

B(p⁻¹)=b₁p⁻¹+ . . . +b_np⁻ⁿ

D(p⁻¹)=d₁p⁻¹+ . . . +d_np⁻ⁿ

and:

p⁻¹u_k=u_k-1

p⁻¹v_k=v_k-1

p⁻¹ is referred to as the delay operator and takes into consideration past states that influence the system in the present time. n is the order of the ARX model. Regarding the choice of the order n of the ARX model, the value of n needs to be high enough to take the inertia of the system into consideration, but low enough to avoid overparametrizing the model.

The steps of identifying a model are known per se and are therefore not detailed further here. The coefficients that need to be identified by adjusting (fitting) the ARX model to the measured change c_ik(t) are the coefficients a_i, b_i, d_i, i=1, . . . , n, to which the air change rate ACH of the space is linked.

In particular, in the case where it is the diffusion of a gas in a space that is being modeled, it may be considered that the output y(t) of the ARX model is the concentration of the gas inside the space c_ik and the inputs u(t) and v(t) of the ARX model are, respectively, the concentration of the gas outside the space c_ek and the flow rate of the gas in the space {dot over (q)}_k. For identification, the procedure is one of analogy between the static state of the ARX model (p⁻¹=1):

A(1)c_ik=B(1)c_ek+D(1){dot over (q)}_k+e

• • and the physical-matter balance:

{dot over (q)}_k=ACH(c_ek−c_ik)+e

The physical parameters are then obtained simply by comparison between the previous two equations. In particular, through a conventional mathematical processing accessible in scientific literature, it is possible to arrive at the air change rate ACH of the space as being a weighted mean of the

$s\frac{\sum _{i=1}^n\mathrm{ai}}{\sum _{i=1}^n\mathrm{di}}$

and of the

$\frac{\sum _{i=1}^n\mathrm{bi}}{\sum _{i=1}^n\mathrm{di}}.$

It may be noted that the inputs and outputs of a parametric identification model can be exchanged. In particular, in the context of the invention, for processing the measurement data c_ik(t) using an ARX model, it is possible to consider that the output y(t) of the ARX model is the gas flow rate in the space {dot over (q)}_k and the inputs u(v) and v(t) of the ARX model are, respectively, the concentration of the gas outside the space c_ek and the concentration of the gas inside the space c_ik.

Within the meaning of the invention, the fact of making the diffusive model and the measured change c_ik(t) converge means that the value of physical parameters of the space that are used in the diffusive model are adjusted (fitted) in such a way as to minimize the discrepancy, at least over a time interval comprised within each time period D_k, between the temporal change in the concentration of the gas inside the space as calculated from the diffusive model and the temporal change in the concentration of the gas inside the space as actually measured c_ik(t). The fitting can thus be done over the entire extent of each time period D_k, or over one or more time intervals comprised within each time period D_k.

By way of example, in the case where the diffusive model is a simple R-C model with one resistor and one capacitor and in which, for each time period D_k there is a time interval Δt_k for which the measured change c_ik(t) in the concentration of the gas inside the space as a function of time is substantially linear, the simple R-C model and the measured change c_ik(t) can be made to converge over the time intervals Δt_k as follows: for each time period D_k, the gradient a_k of the tangent to the change c_ik(t) is determined over the time interval Δt_k and the value of the air change rate ACH of the space is deduced from the gradients a_k, from the gas flow rates {dot over (q)}_k applied in the space and from the difference in concentration of the gas between the inside and the outside of the space.

According to another example, in the case that the diffusive model is a more complex R-C model, such as a “3R2C” model or an ARX model, the diffusive model and the measured change c_ik(t) are made to converge by adjusting the value of the physical parameters of the space that are used in the model in such a way as to minimize the discrepancy (“fitting”), over all of the time periods D_k, between the temporal change in the concentration of the gas inside the space as calculated from the diffusive model and the temporal change in the concentration of the gas inside the space as actually measured c_ik(t).

Examples of parameters of the space that are liable to influence the way in which the space behaves with regard to the diffusion of gas notably comprise the total surface area of the physical boundary of the space, the number and size of joinery works, making it possible for example to determine an equivalent surface area of holes.

According to one aspect of the invention, the method comprises steps in which:

• • over at least two successive time periods D_k corresponding to distinct gas flow rates {dot over (q)}_k applied in the space, a campaign of measurements is carried out to make it possible to determine the concentration of the gas inside the space c_ik at closely-spaced time intervals, and the concentration of the gas outside the space c_ek is determined at closely-spaced time intervals;
  • for each time period D_k, starting from the measured change c_ik(t) in the concentration of the gas inside the space c_ik as a function of time:
  • either, if there is a time interval Δt_k for which the change c_ik(t) is substantially linear, the gradient a_k of the tangent at the change c_ik(t) is determined over this time interval Δt_k and the value of the air change rate ACH of the space is deduced from the gradients a_k;
  • or, if there is no time interval for which the change c_ik(t) is substantially linear, a time interval Δt_k′ in which the change c_ik(t) is substantially exponential of the type exp(−t/τ) is selected, where r is the time at the end of which the volume of air inside the space has been changed, and the value of the air change rate ACH of the space is deduced, this being the value such that the change

$\mathrm{Ln}\left[\left({\theta }_k\left(t\right)-\frac{{\stackrel{.}{q}}_k}{ACH}\right)/\left({\theta }_k\left(0\right)-\frac{{\stackrel{.}{q}}_k}{ACH}\right)\right]$

• •  is a straight line, where θ_k(t)=c_ik(t)−c_ckm′, where c_ekm′ is the mean of the concentration of the gas outside the space c_ek over the time interval Δt_k′.

Of course, the method according to the invention does not necessarily require a graphical representation of the change c_1k(t) to be put in place.

In particular, over each time interval Δt_k, the gradient a_k of the tangent to the change c_ik(t) is equal to the derivative of the change c_ik(t) over the interval Δt_k. Consequently, the step of determining the gradient a_k of the tangent to the change c_ik(t) over the interval Δt_k may be performed, in the context of the invention, by calculating the derivative of the change c_ik(t) over the interval Δt_k, without resorting to a graphical representation of the change c_ik(t).

The calculation steps of the method, particularly for determining the gradients a_k, may be implemented using any suitable calculation means. This may notably be a terminal comprising an acquisition system for acquiring the measurements required by the method and calculation means for executing all or some of the steps of the method on the basis of the measurements acquired.

In the context of the invention, the time periods D_k may be either disjointed from one another or immediately succeed one another. In the latter instance, the method may be considered to be performed overall over a continuous time period, formed by the succession of the time periods D_k.

For preference, the method is implemented with two successive time periods D₁ and D₂ corresponding to two distinct gas flow rate setpoints {dot over (q)}₁ and {dot over (q)}₂ applied in the space.

According to one aspect of the invention, the first gas flow rate {dot over (q)}₁ applied over the first time period D₁, and the second gas flow rate {dot over (q)}₂, applied over the second time period D₂, have values very different from one another. In one advantageous embodiment, the first gas flow rate {dot over (q)}₁ applied over the first time period D₁ is strictly positive or strictly negative, whereas the second gas flow rate {dot over (q)}₂ applied over the second time period D₂ is zero or substantially zero.

Advantageously, for each time period D_k, the gas flow rate {dot over (q)}_k applied in the space comprises a flow rate {dot over (q)}_impk imposed by means of at least one controlled-flow rate apparatus. What is meant here by a “controlled-flow rate apparatus” is an apparatus such that the quantity of gas injected or extracted by the apparatus can be determined precisely. For preference, the control of the or each controlled-flow rate apparatus is automated.

When the gas used is water vapor, the or each controlled-flow rate apparatus may be a humidifier, for example an ultrasound humidifier. One method for precisely determining the flow rate of water vapor injected over each time period D_k is then to weigh the humidifier at the start and at the end of the period D_k and, by knowing the duration for which the humidifier is on, to deduce the mean flow rate of water vapor applied to the space over the period D_k.

In the context of the invention, distinct gas flow rates {dot over (q)}_k applied to the space over the various time periods D_k may be various gas flow rate setpoints, which means to say that for each time period D_k the gas flow rate {dot over (q)}_k is constant over the entire period D_k. As an alternative, the gas flow rate {dot over (q)}_k may be non-constant over one or more periods D_k and vary about a mean gas flow rate value {dot over (q)}_km, provided that the mean gas flow rate {dot over (q)}_km over the period D_k is distinct from the (constant or mean) gas flow rates applied over the time periods surrounding the period D_k. In that case, the gas flow rate considered over the time period D_k is the mean gas flow rate {dot over (q)}_km. The variation in gas flow rate over each time period D_k needs to be small in comparison with the difference between the gas flow rates applied over two consecutive time periods, and for preference, the variation in gas flow rate over each time period D_k is less than 30%, more preferably less than 20%, more preferably still less than 10%, of the difference between the gas flow rates applied over two consecutive time periods.

If no source of the given gas other than the apparatuses used to apply the imposed flow rate {dot over (q)}_impk is active in the space during the time period D_k, the gas flow rate {dot over (q)}_k applied in the space is equal to the imposed flow rate {dot over (q)}_impk. By contrast, if, during the time period D_k, there is an additional gas flow rate {dot over (q)}_supk applied in the space in addition to the flow rate {dot over (q)}_impk, the gas flow rate {dot over (q)}_k applied in the space is equal to {dot over (q)}_impk+{dot over (q)}_supk. It is therefore necessary either to be capable of measuring the additional flow rate, or to cut off all sources other than the apparatuses used for applying the imposed flow rate.

In particular, when the gas used is water vapor, an additional flow rate of water vapor in the space may come from sources such as the respiration of the occupants, cooking, the presence of laundry that is drying, the use of a shower, the use of a tumble dryer. For preference, the method is implemented while the space is unoccupied. In addition, any household electrical appliances that may be present are preferably switched off.

The method according to the invention relies on the fact that the variation in the concentration of the gas inside the space is proportional to the quantity of air changed by infiltration. If the concentration of the gas inside the space is not homogeneous, there is a risk that a greater quantity of air than of gas will be exchanged, or vice versa, something which is liable to make the measurements imprecise. The same risk may result from stratification of the gas, caused by excessive temperature discrepancies within the space. In order to improve the homogeneity of the concentration of the gas and of the temperature inside the space, it is advantageous to open the communicating doors inside the space and to install an air agitation system inside the space. When the space has a high interior volume, several controlled-flow rate apparatuses are advantageously spread through the space, associated with a system for agitating the air.

According to one aspect of the invention, the measurements making it possible to determine the concentration of the gas inside the space c_ik are taken using one or more sensors of said gas which are placed in the interior volume of air of the space. In instances in which the gas used is water vapor, each sensor of said gas is a moisture sensor configured to measure the water vapor concentration, also referred to as absolute humidity, inside the space c_ik.

For preference, each sensor of said gas is associated with a temperature sensor able to measure the temperature of the air inside the space. The concentration of the gas inside the space c_ik, and the temperature inside the space T_ik can then each be considered to be the mean of the measurements of the various sensors distributed through the volume of air inside the space. The more imperfect the homogeneity of the concentration of the gas and of the temperature inside the space, the higher the number of sensors required. The use of several sensors at various points may also make it possible to locate air leaks, for example by identifying that a sensor positioned near a somewhat non-airtight joinery work behaves differently from a sensor positioned at the center of the volume of air inside the space.

For preference, over each time period D_k, the temperature of the air inside the space T_ik is stable. Variations in the temperature of the air inside the space may actually influence the concentration of the gas in the air inside the space. Consequently, it is preferable, over each time period D_k, to switch off sources of heat or cold in the space, notably heating or air conditioning devices, or keep them running at a constant setpoint. In particular, when the gas used is water vapor, an increase in the temperature inside the space may lead to a drying out of the materials inside the space, causing water vapor to evaporate into the air, whereas a drop in the temperature inside the space may cause water vapor present in the air to condense on the surface of the materials.

It is also preferable, over each time period D_k, to have low, preferably zero, solar radiation, in order to avoid the temperature increasing inside the space under the effect of solar radiation. Shutters, blinds or other elements that close off the space may be closed during each time period D_k, notably on the side of the space that faces south. For preference, the method according to the invention is implemented at night.

According to one advantageous aspect, with a view to limiting the time taken to implement the method while at the same time reducing the contribution made by solar radiation, the method is performed in its entirety continuously over a single night-time period.

In order for the change in absolute humidity inside the space during the implementation of the method to be associated solely with the change of air, it is necessary to operate under conditions such that the exchanges of water vapor contained in the air and in the building materials and/or the furnishings are negligible. Now, by way of example, a 50 m² surface area of unvarnished oak can store approximately 2 kg of water in 3 hours when the humidity inside the space varies from 60% to 80%. It is therefore preferable to apply the distinct water vapor flow rates and to take the measurements according to the invention over time periods D_k that are as short as possible, in order to limit these exchanges. For preference, each time period D_k lasts 2 hours or less, more preferably 1 hour or less.

If it is desired to measure the air change rate by natural infiltration of a space equipped with a mechanical ventilation system, the mechanical ventilation needs to be deactivated over each time period D_k, so as not to introduce an additional air flow. As an alternative, it is possible to keep the mechanical ventilation in the active configuration at a desired flow rate over the time periods D_k, the method according to the invention then making it possible to measure the air flow rate generated by the mechanical ventilation and thus verify operation thereof.

For preference, over each time period D_k, the concentration of the gas outside the space c_ek is stable.

The concentration of the gas outside the space c_ek may be determined by measurements using sensors of said gas which are placed in the air outside the space, notably humidity and temperature sensors when the gas used is water vapor. These humidity and temperature sensors are placed in the volume of external air, avoiding siting them close to heat sources or water vapor producing sources, so as to have measurements representative of the overall mass of air in the vicinity of the exterior surface of the physical boundary of the space.

As an alternative, when the gas used is water vapor and the space opens directly to the outside, the concentration of water vapor or absolute humidity outside the space c_ek can be determined by interpolating meteorological data for the site at which the space is situated.

In general, the outside air contains water vapor, particularly during damp periods. The method according to the invention is all the more reliable if the water vapor flow rates applied in the space according to the method of the invention are well suited to the external conditions and if the difference in absolute humidity between the inside and the outside of the space is large.

In the context of the invention, it is possible to use a simple R-C model to describe a space, with two homogeneous gas concentration (in g·m⁻³) nodes, one inside the space and the other outside the space, which are separated by a resistor representing the inverse of the air change rate ACH of the space (in m³·h⁻¹). The gas concentration node inside the space is connected to a capacitor which represents the effective volume of the space (in m³). The gas flow rate applied in the space (in g·h⁻¹) is compensated for by the exchange of gas across the physical boundary of the space and the quantity of gas stored up in the structure of the physical boundary, something which is described by the equation:

${\stackrel{.}{q}}_k=ACH\left(c_{\mathrm{ik}}-c_{\mathrm{ek}}\right)+V\frac{dc_{\mathrm{ik}}}{\mathrm{dt}}$

where {dot over (q)}_k is the total gas flow rate applied in the space, c_ik and c_ek are respectively the concentration of the gas inside the space and the concentration of the gas outside the space, ACH is the air change rate of the space and V is the effective volume of the space.

It is assumed that the response of the space is a simple decreasing exponential and that its time constant is the product of the air change rate ACH and of the effective volume V of the space. In actual fact, the response of the space is more complex and is the superposition of a great many decreasing exponentials, but it has been experimentally validated that, by adapting the test conditions, particularly the duration of the test and the value of gas flow rate applied in the space, only the largest time constant plays a part and the model described hereinabove is valid.

By applying two gas flow rates {dot over (q)}₁ and {dot over (q)}₂ with different values to the space over two time periods D₁ and D₂, it is then possible to determine the air change rate ACH of the space using the equation:

$\begin{array}{cc}ACH=\frac{a_1+{\stackrel{.}{q}}_2-a_2\times {\stackrel{.}{q}}_1}{a_1\times \Delta c_{2m}-a_2\times \Delta c_{1m}}& \left(1\right)\end{array}$

and the effective volume V of the space using the equation:

$\begin{array}{cc}V=\frac{{\stackrel{.}{q}}_1\times \Delta c_{2m}-{\stackrel{.}{q}}_2\times \Delta c_{1m}}{a_1\times \Delta c_{2m}-a_2\times \Delta c_{1m}}& \left(2\right)\end{array}$

where ({dot over (q)}_k)_{k=1 or 2} is the gas flow rate applied over the time period D_k, (a_k)_{k=1 or 2} is the gradient over the time interval Δt_k of the tangent to the change c_ik(t) in concentration of the gas inside the space as a function of time, and (Δc_km)_{k=1 or 2} is the difference between the mean gas concentration inside the space and the mean gas concentration outside the space over the time interval Δt_k.

According to one aspect of the invention, after the value V_calc of the effective volume V of the space has been calculated according to the method, a check is performed to verify that this value V_calc does indeed correspond to the actual volume of the space, notably to within 20%. If it does not, then it is necessary to modify the way in which the measurements are processed in order to obtain a corrected value for the air change rate ACH of the space.

Specifically, it has been found that the method according to the invention may lead to a calculated value V_calc for the effective volume of the space that is different from the actual volume of the space. In particular, when the gas used is water vapor injected into the space, it has been found that, when the duration of each time period D_k is too short, the calculated value V_calc is lower than the actual volume, whereas when the duration of each time period D_k is too long, the calculated value V_calc is greater than the actual volume. That may be explained by the fact that the calculated value V_calc for the effective volume V of the space does not correspond to the actual volume of the space, but rather to the volume effectively acted upon by the gas used in the context of the method. A calculated value V_calc that is underestimated with respect to the actual volume of the space may indicate that the gas has not had time to probe all of the volume of the space, whereas a calculated value V_calc that is overestimated with respect to the actual volume of the space may indicate an effect connected with the gas being absorbed by the materials present in the space.

It is therefore appropriate, for the processing of the measurements obtained according to the method of the invention, to use durations that are long enough for the gas to have time to act upon the entire volume of the space, but that are short enough that they avoid any effect connected with the gas being absorbed by the building materials and/or furnishings of the space, so that it is only the changing of air responsible for the variation in the concentration of the gas in the air that is measured. If the gas used is water vapor injected into the space, it has been found that a favorable duration for processing the measurements over each time period D_k is in the order of 10 minutes to 1 hour.

Highly advantageously, comparing the calculated value V_calc of the effective volume of the space against the actual volume thus makes it possible to validate whether the air change rate ACH of the space has been determined correctly, to help with defining favorable durations for processing the measurements over each time period D_k according to the materials present in the space, and even to make post-measurement corrections to the calculated value ACH_calc for the air change rate of the space if an excessively long duration was applied when processing the measurements. In particular, such post-measurement correction may be made to the value ACH_calc by shifting the time intervals Δt_k within each time period D_k so as to reduce the measurement processing duration, until a value for the effective volume V_calc is obtained that is substantially equal to the actual interior volume of the space.

According to one embodiment, the method comprises steps in which:

• • the following are performed, over two successive time periods D₁ and D₂:
    i. over the first time period D₁, a first gas flow rate {dot over (q)}₁ is applied in the space, and a campaign of measurements is carried out to determine the concentration of the gas inside the space c_i1 at closely-spaced time intervals, and the concentration of the gas outside the space c_e1 is determined at closely-spaced time intervals, the first gas flow rate {dot over (q)}₁ being such that the parameter

$\alpha =1-\frac{{\mathrm{ACH}}_{\mathrm{ref}}\Delta c_1\left(0\right)}{{\stackrel{.}{q}}_1}$

is less than or equal to 0.8, with Δc₁(0)=c_i1(0)−c_em, where t=0 is the starting point for the first time period D₁, c_em is the mean concentration of the gas outside the space over all the time periods D₁ and D₂, and ACH_ref is a reference value for the air change rate of the space, then
ii. over the second time period D₂, a substantially zero second gas flow rate {dot over (q)}₂ is applied in the space, and a campaign of measurements is carried out to determine the concentration of the gas inside the space c_i2 at closely-spaced time intervals, and the concentration of the gas outside the space c_e2 is determined at closely-spaced time intervals;

• • the value of the air change rate ACH of the space is determined by causing the convergence of: on the one hand, a diffusive model expressing the temporal variation of the concentration of the gas inside the space c_ik as a function of the concentration of the gas outside the space c_ek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and on the other hand, the measured change c_ik(t) in the concentration of the gas inside the space c_ik as a function of time.

In this embodiment, a specific action on the space is selected that gives access to the air change rate ACH of the space with good precision and over a short time, this specific action being the application of a first gas flow rate {dot over (q)}₁ that is strictly positive or strictly negative able to generate a forced change in the concentration of the gas inside the space c_i1, followed by the application of a second gas flow rate {dot over (q)}₂ that is substantially zero giving rise to a free change in the concentration of the gas inside the space c_i1.

For preference, the first gas flow rate {dot over (q)}₁ is such that the parameter

$\alpha =1-\frac{{\mathrm{ACH}}_{\mathrm{ref}}\Delta c_1\left(0\right)}{{\stackrel{.}{q}}_1}$

is greater than or equal to 0.3, preferably greater than or equal to 0.4. Specifically, for environments exhibiting little by way of infiltration, when the parameter α is less than 0.3 or 0.4, the sensitivity of conventional measurement sensors does not allow satisfactory data to be obtained regarding the change in the concentration of the gas inside the space c_i1 over the first time period D₁, hence an increase in the uncertainty on the value of the air change rate ACH of the space as determined according to the invention.

Determining the value of the first gas flow rate {dot over (q)}₁ to be applied over the first time period D₁ in order to meet the criteria regarding the parameter α entails knowing a reference value ACH_ref for the air change rate ACH of the space.

One way of accessing a reference value ACH_ref for the air change rate ACH of the space is to use a quantity derived from a test of the “blower door” type on the space. Other methods for accessing a reference value ACH_ref are also conceivable, and in particular, the reference value may be the air change value indicated in the thermal study submitted with the planning application.

In one advantageous embodiment, for each time period D₁ and D₂, there is a time interval Δt₁ or Δt₂ for which the measured change (c_ik(t))_{k=1 or 2} in the concentration of the gas inside the space as a function of time is substantially linear, and a diffusive R-C model and the measured change (c_ik(t))_{k=1 or 2} are made to converge as follows: for each time period D_k the gradient a_k of the tangent to the change c_ik(t) is determined over the time interval Δt_k, and the value of the air change rate ACH of the space is determined from the gradients a_k and from the gas flow rates {dot over (q)}_k applied in the space.

For preference, the time intervals Δt₁ and Δt₂ over which the measurements are processed exhibit “symmetry” where what is meant by “symmetry” of the time intervals Δt₁ and Δt₂ is that the two intervals have, on the one hand, a same duration and, on the other hand, a starting point situated at a same distance in time away from the start of the period D₁ or D₂ (notably, x minutes after the start of each period D₁ or D₂).

As described previously, the invention proposes imposing distinct gas flow rates {dot over (q)}_k in the space over at least two successive time periods D_k, and measuring, for each time period D_k, the temporal change in the concentration of the gas inside the space c_ik(t).

As an alternative, it is also possible to impose distinct gas concentrations c_ik inside the space over at least two successive time periods D_k and to measure, for each time period D_k, the temporal change in the gas flow rate inside the space {dot over (q)}_k(t).

According to this alternative form, one subject of the invention is a method for determining the air change rate ACH of a space, characterized in that it comprises steps in which:

• • over at least two successive time periods D_k corresponding to distinct given-gas concentrations c_ik applied in the space, a campaign of measurements is carried out to make it possible to determine the flow rate of the gas inside the space {dot over (q)}_k at closely-spaced time intervals, and the concentration of the gas outside the space c_ek is determined at closely-spaced time intervals;
  • the value of the air change rate ACH of the space is determined by causing the convergence of:
    on the one hand, a diffusive model expressing the temporal variation of the flow rate of the gas inside the space {dot over (q)}_k as a function of the concentration of the gas outside the space c_ek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and
    on the other hand, the measured change {dot over (q)}_k(t) in the flow rate of the gas inside the space {dot over (q)}_k as a function of time.

For preference, the method is implemented with two successive time periods D₁ and D₂ corresponding to two distinct gas concentration setpoints c_i1 and c_i2 applied in the space.

In one embodiment, at least some of the steps of the method of determining the air change rate ACH of the space are determined by computer program instructions.

In consequence, another subject of the invention is a computer program on a recording medium, this program being able to be implemented in a terminal or, more generally, in a computer, this program comprising instructions suited to implementing all or some of the steps of a method as described hereinabove.

This program may use any programming language, and be in the form of source code, object code, or a code somewhere between source code and object code, such as in a partially compiled form.

Another subject of the invention is a computer-readable recording medium, comprising instructions for a computer program as mentioned hereinabove.

The recording medium may be any entity or device capable of storing the program. For example, the medium may comprise a storage means, such as a read-only memory, a rewritable nonvolatile memory, for example a USB stick, an SD card, an EEPROM, or even a magnetic recording means, for example a hard disk.

The recording medium may also be an integrated circuit into which the program is incorporated, the circuit being designed to execute or to be used in the execution of the method.

The recording medium may be a transmissible medium such as an electrical or optical signal, which can be carried by an electrical or optical cable, by radio or by other means. The program according to the invention may in particular be downloaded on a network of the internet type.

Another subject of the invention is a device for determining the air change rate ACH of a space, this device comprising:

• • at least one apparatus configured to apply, over at least two successive time periods D_k, distinct given-gas flow rates {dot over (q)}_k in the space;
  • at least one sensor configured to measure a concentration of the gas inside the space c_ik at closely-spaced time intervals;
  • a terminal comprising a processing module configured to cause convergence of, on the one hand, a diffusive model expressing the temporal variation of the concentration of the gas inside the space c_ik as a function of the concentration of the gas outside the space c_ek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and on the other hand, the measured change c_ik(t) in the concentration of the gas inside the space c_ik as a function of time, so as to obtain the value of the air change rate of the space.

Each gas flow rate {dot over (q)}_k applied in the space over a time period D_k using the apparatus or apparatuses for applying a gas flow rate may be a positive flow rate, corresponding to an injection of the gas into the space, a negative flow rate, corresponding to an extraction of the gas from the space, or a zero flow rate.

According to one aspect of the invention, when the gas used is water vapor, the device may comprise, for applying each water vapor flow rate in the space, one or more humidifiers, notably of the ultrasound humidifier type, and, for measuring the water vapor concentration in the air inside the space, one or more humidity sensors intended to be positioned in the volume of air inside the space.

According to one feature, the device also comprises at least one sensor configured to measure a concentration of the gas outside the space c_ek at closely-spaced time intervals.

According to another feature, the device further comprises at least one temperature sensor configured to measure the temperature of the air inside the space T_ik.

Another subject of the invention is a terminal comprising a processing module configured to cause convergence of on the one hand, a diffusive model expressing the temporal variation of the concentration of a given gas inside a space c_ik as a function of the concentration of the gas outside a space c_ek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and on the other hand, a measured change c_ik(t) in the concentration of the gas inside the space c_ik as a function of time, so as to obtain the value of the air change rate of the space.

According to one aspect, the processing module of the terminal according to the invention comprises a computer program as mentioned hereinabove, this program being recorded on a recording medium according to the invention and consisting of a rewritable nonvolatile memory of the terminal, the instructions of said program being interpretable by a processor of the terminal.

The terminal, the computer program and the recording medium according to the invention have the same features as the method according to the invention. The invention may be implemented with any type of terminal, such as a laptop or non-portable computer, a tablet, or a smartphone.

In the context of the invention, the or each sensor for measuring a concentration of the gas inside the space c_ik may be a sensor independent of the terminal. As an alternative, the or each sensor for measuring a concentration of the gas inside the space c_ik may be a sensor incorporated into the terminal. In particular, it is possible according to the invention to take the measurements using gas sensors and possibly temperature sensors which are incorporated into a tablet or a smartphone, and to have an application installed on the tablet or the smartphone for acquiring measurements and implementing steps of the method.

In one embodiment, the device according to the invention comprises means, notably wireless means such as Bluetooth, WiFi, etc., of connection between the or each sensor for measuring a concentration of the gas, and the terminal.

Advantageously, the terminal comprises means of controlling the or each apparatus for applying a flow rate of said gas in the space.

The features and advantages of the invention will become apparent in the description that follows of two exemplary embodiments of a method and of a device according to the invention, which description is given solely by way of example and with reference to the attached figures in which:

FIG. 1 is a schematic view of a space of which the air change rate ACH is to be determined according to the method of the invention, using a device according to the invention comprising at least a controlled-flow rate humidifier for injecting water vapor into the space, at least one humidity sensor and a terminal;

FIG. 2 is a graph showing the change in absolute humidity c_ik inside a bungalow as a function of time, during implementation of the method of the invention comprising a first time period D₁ over which a positive first water vapor flow rate {dot over (q)}₁ is applied in the bungalow, followed by a second time period D₂ over which a substantially zero second water vapor flow rate {dot over (q)}₂ is applied in the bungalow so as to allow the absolute humidity c_ik inside the bungalow to change freely, the change in the absolute humidity c_ek outside the bungalow as a function of time also being shown in this figure;

FIG. 3 is a graph showing the change in absolute humidity c_ik inside an apartment as a function of time, during the implementation of the method of the invention comprising a first time period D₁ over which a positive first water vapor flow rate {dot over (q)}₁ is applied in the apartment, followed by a second time period D₂ over which a substantially zero second water vapor flow rate {dot over (q)}₂ is applied in the apartment so as to allow the absolute humidity c_ik inside the apartment to change freely, the change in the absolute humidity c_ek outside the apartment as a function of time also being shown in this figure;

FIG. 4 is a graph illustrating the adjusting (fitting) of an ARX model to the change shown in figure in absolute humidity c_ik inside the bungalow as a function of time, which is obtained by making the ARX model and the measured change c_ik (t) in the concentration of the gas over the set of two time periods D₁ and D₂ converge;

FIG. 5 is a graph illustrating the adjusting (fitting) of an ARX model to the change shown in figure in absolute humidity c_ik inside the apartment as a function of time, which is obtained by making the ARX model and the measured change c_ik (t) in the concentration of the gas over the set of two time periods D₁ and D₂ converge;

FIG. 6 is a diagram of a so-called “3R2C” model of a space, with three resistors and two capacitors.

EXPERIMENTAL PROTOCOL

The method according to the invention is implemented to determine the air change rate ACH of a bungalow (example 1) and of an apartment (example 2), each of which constitute a space within the meaning of the invention, referenced 1 in FIG. 1. The experimental protocol is similar for both examples, as described hereinbelow.

For each example, the method comprises a first phase of humidification over a first time period D₁ having a duration of one hour for the bungalow, from midnight to 01:00 in the morning, and of two hours for the apartment, from midnight to 02:00 in the morning, during which a strictly positive first water vapor flow rate {dot over (q)}₁ is applied to the space 1, which corresponds to an injection of water vapor into the space. The first phase is followed by a “natural dehumidification” second phase over a second time period D₂, having a duration of one hour for the bungalow, from 01:00 to 02:00 in the morning, and of two hours for the apartment, from 02:00 to 04:00 in the morning, and during which a zero second water vapor flow rate {dot over (q)}₂ is applied in the space 1, giving rise to a free reduction in the concentration of water vapor inside the space. In each example, the phase of natural dehumidification has the same duration as the humidification phase.

The application of the water vapor flow rates {dot over (q)}₁ and {dot over (q)}₂ to the space 1 is performed via one or more humidifiers 20 of “GOTA” type, marketed by the company Air Naturel, placed inside the space. Each humidifier 20 is an ultrasound humidifier with a 3 l reservoir, capable of humidifying at a rate of up to 300 g·h⁻¹. Each humidifier 20 is plugged into a programmable socket so that it can be switched on/off automatically. The sockets are programmed in such a way as to start the or each humidifier 20 at the start of the first time period D₁ and to switch the or each humidifier 20 off at the end of the first time period D₁. In order to know the water vapor flow rate {dot over (q)}₁ applied to the space during the first time period D₁, each humidifier 20 is weighed at the start and at the end of the period D₁. Knowing the duration for which each humidifier 20 is on, it is possible to determine the mean water vapor flow rate applied during the period D₁.

During the two time periods D₁ and D₂, the change in the humidity and temperature inside and outside the space 1 is measured using humidity and temperature sensors 40 of SHT15 type, marketed by the company Sensirion. For the bungalow (example 1) the number of sensors 40 used is one sensor 40 placed in the air inside the bungalow and one sensor 40 placed in the air outside the bungalow. For the apartment (example 2), the number of sensors 40 used is five sensors 40 distributed by being placed in the air inside the apartment and one sensor placed in the air outside the apartment. The positioning of the sensors 40 inside the space 1 is adjusted such as to obtain a representative measurement of the mean humidity and of the mean temperature of the air inside the space.

For each example, the method is implemented while the space 1 is unoccupied and all the water vapor producing sources other than the humidifiers 20 in the space are switched off. No mechanical ventilation or heat or cold source is active in the space 1 during the course of the method. In addition, in the case of the apartment (example 2), all the internal communicating doors are open. In each example, domestic fans are installed in the space 1, in order to agitate the air inside the space slightly.

The raw measurement data obtained in the space 1 are then acquired by an acquisition system of a terminal 10 which processes them by executing the instructions of a computer program PG according to the invention installed in the terminal 10, so as to determine the air change rate of the space 1.

As shown schematically in FIG. 1, the terminal 10 in this example consists of a tablet or smartphone offering the user, in addition to communication functions, access to various applications once these have been installed on the terminal.

From a hardware point of view, the terminal 10 notably comprises a processor 11, a read-only memory of ROM type 12 in which system functions, particularly the software drivers and the terminal operating system are recorded, a screen 15, one or more communication modules (3G, 4G, Bluetooth, WiFi, etc.) 17 and a rewritable nonvolatile memory 18 containing applications APP and user data which have not been depicted in the figure, these elements being connected to one another by a bus system.

In the known way, the screen 15 constitutes a touch-sensitive man-machine interface depicting icons I1, I2, IT corresponding to the system applications and to the various applications APP installed by the user of the terminal.

Among these icons, an icon IT allows the terminal to access, remotely via a telecommunications network, a portal for downloadable applications compatible with the operating system of the terminal and to install, possibly in return for payment and/or authentication, new applications APP in the rewritable nonvolatile memory 18.

In the embodiment described here, the computer program PG according to the invention can be downloaded from this applications portal, and an associated icon presented on the touch-sensitive interface 15.

In particular, the terminal 10 on which the computer program PG is installed comprises a processing module which is configured to implement the following steps.

Calculate the Absolute Humidity c_ik Inside the Space

The change in absolute humidity (or water vapor concentration) c_ik inside the space 1 is determined from the relative humidities and temperatures measured in the interior volume of the space. A mean of the measurements from the various sensors 40 distributed through the space 1 is calculated, weighted by the volume of air representative of each measurement point. The absolute humidity c_ik inside the space 1 is then determined by calculating first of all the saturation vapor pressure, notably by using the equation:

ln

$\begin{array}{cc}\frac{P_{\mathrm{ws}}}{P_c}=\frac{T_c}{T}\left(C\vartheta +C{\vartheta }^{1.5}+C_3{\vartheta }^3+C_4{\vartheta }^{3.5}+C_5{\vartheta }^4+C_6{\vartheta }^{7.5}\right)& \left(3\right)\end{array}$

with

$\vartheta =1-\frac{T}{T_c},$

where T is the temperature in K, P_ws is the saturation vapor pressure in hPa, T_c=647.096 K, the critical temperature, P_c=220640 hPa, the critical pressure, and C_i are dimensionless coefficients given in table 1 below. This relationship gives good precision for temperatures ranging from 0° C. to 373° C. Of course, equations other than equation (3) above can also be used for calculating the absolute humidity.

TABLE 1
C1 −7.85951783
C2 1.84408259
C3 −11.7866497
C4 22.6807411
C5 −15.9618719
C6 1.80122502

The vapor pressure is then calculated as being P_w=P_ws·RH, where RH is the relative humidity of the air, and the absolute humidity is calculated as being

$c_{\mathrm{ik}}=\frac{C.P_w}{T}$

where C=2.16679 g·K/J is a constant.

Calculate the Water Vapor Flow Rate {dot over (q)}₁ During the Period D₁

The water vapor flow rate {dot over (q)}₁ applied in the space 1 during the first time period D₁ is calculated as the difference between the total mass of the humidifiers 20 at the start and at the end of the period D₁ and by knowing the duration for which water vapor is injected:

${\stackrel{.}{q}}_1=\frac{m_{\mathrm{tot}.\mathrm{end}}-m_{\mathrm{tot}.\mathrm{start}}}{t_{\mathrm{inj}}}$

where m_tot.end and m_tot.start are respectively the total masses of the humidifiers in the space at the start and at the end of the period D₁ in grammes and t_inj is the duration for which water vapor is injected, in hours.

Calculate the Absolute Humidity c_ek Outside the Space

The change in absolute humidity (or water vapor concentration) c_ek outside the space 1 is determined from the relative humidities and temperatures measured outside the space, using the same equation (3) as was used for calculating the absolute humidity c_ik inside the space.

Calculate the Air Change Rate ACH and the Effective Volume V

The air change rate ACH and the effective volume V of the space 1 are calculated using equation (1) and equation (2) above, respectively.

The description which follows details the steps for calculating the air change rate ACH_calc and the effective volume V_calc of each space 1 with reference to the graph of FIG. 2 or to the graph of FIG. 3 which show the change in absolute humidity c_ik inside the space as a function of time. These graphs illustrate the values involved in equations (1) and (2), namely the gradients a₁ and a₂ of absolute humidity inside the space c_i1 and c_i2 over each time interval Δt₁ and Δt₂ selected over the period D₁ or D₂, and the differences in absolute humidity Δc_1m and Δc_2m between the inside and the outside of the space over each time interval Δt₁ or Δt₂.

Even though the calculation steps detailed hereinabove can be performed by hand, they are preferably carried out automatically by a terminal such as the terminal 10 described hereinabove which may, in particular, not need to resort to a graphical representation of the change c_ik(t).

What the terminal requires from the user are the input data, which may be the volume of the space, the gas flow rates {dot over (q)}₁, {dot over (q)}₂ applied over the periods D₁, D₂ (or, as an alternative, the value of the parameter α and a reference value for the air change rate ACH_ref).

The terminal supplies at output the calculated values of the air change rate ACH_calc and effective volume V_calc of the space, as well as potential other parameters such as those indicated in tables 2 and 3 below.

Within the context of the invention, it may be advantageous to store the measurement data obtained in the space. These data may for example be used as a history in the context of a renovation. In addition, these data may be reused to optimize the calculated values for the air change rate ACH_calc and the effective volume V_calc of the space, by modifying the processing parameters for the same set of measurements, as illustrated by the correction steps in the examples below. Storage of the measurement data may be performed in the memory of a terminal used to implement the invention or in an external memory of any type suited to this storage function.

Example 1: Bungalow

FIG. 2 shows the results obtained by implementing the method in a bungalow having a footprint of 13 m², a volume of 33 m³ and a total boundary surface area of 70 m². The external wall of the bungalow is made of insulating sandwich panels comprising a layer of polyurethane 4 cm thick inserted between two sheets of metal, a door and two triple-glazed windows.

Additional insulation was added to the boundary, which comprises the following materials:

• • membranes of the STOPVAP type, marketed by the company Saint-Gobain Isover,
  • VIPs (vacuum insulated panels) of the va-Q-vip F type, marketed by the company va-Q-tec, covering the walls;
  • 3 cm of expanded polystyrene for the floor and ceiling, the floor also being covered by a sheet of wooden oriented strand board (OSB).

The bungalow boundary has a heat transfer coefficient U_BAT of around 0.6 W/m²K.

The coefficient n₅₀ for the bungalow, obtained using a blower door test, is 8.6 h⁻¹. Using the Persily-Kronvall model, that corresponds to a reference air change rate value ACH_ref=15 m³·h⁻¹.

In the bungalow humidification phase, over the first time period D₁ from midnight to 01:00 in the morning, the humidifiers 20 present in the bungalow are used to apply the strictly positive first water vapor flow rate {dot over (q)}₁, which is chosen such that the parameter

$\alpha =1-\frac{{\mathrm{ACH}}_{\mathrm{ref}}\Delta c_1\left(0\right)}{{\stackrel{.}{q}}_1},$

is equal to 0.46. In this example, the reference value ACH_ref is 15 m³·h⁻¹ and the initial absolute humidity difference Δc₁(0) is 6.4 g·m⁻³, which corresponds to a value of the order of 180 g·h⁻¹ for the first water vapor flow rate {dot over (q)}₁.

The curve representative of the change in absolute humidity c_i1 inside the bungalow as a function of time during the first time period D₁ is shown in FIG. 2. As visible in this figure, the curve of increase in absolute humidity inside the bungalow has a part that is substantially linear over the time interval Δt₁ from 00:45 to 01:00 in the morning. Putting this linear part of the curve into an equation gives: c_i1=17.8 g·m⁻³+0.00630 t, where t is in seconds.

FIG. 2 also shows the change in absolute humidity c_e1 outside of the bungalow as a function of time during the first time period D₁. The absolute humidity c_e1 outside of the bungalow over the time interval Δt₁ is stable enough that it can be considered to be substantially constant and equal to the mean absolute humidity over the time interval Δt₁, namely, in this example, c_e1m=11.0 g·m⁻³.

During the phase of “natural dehumidification” of the bungalow, over the second time period D₂ from 01:00 to 02:00 in the morning, the humidifiers 20 present in the bungalow are switched off so as to apply the zero second water vapor flow rate {dot over (q)}₂.

FIG. 2 shows the curve representative of the change in absolute humidity c_i2 inside the bungalow as a function of time during the second time period D₂. As is visible in this figure, the curve of decrease in absolute humidity inside the bungalow has a part that is substantially linear over the time interval Δt₂ from 01:45 to 02:00 in the morning. The measurement processing time interval Δt₂ in the second period D₂ is chosen so that it exhibits “symmetry” with the measurement processing interval Δt₁ in the first period D₁, namely so that the two time intervals Δt₁ and Δt₂ have, on the one hand, a same duration of 15 minutes and, on the other hand, a starting point situated, for each interval Δt_k, 45 minutes after the start of the period D_k. Putting the linear part of the curve over the time interval Δt₂ into an equation gives: c_i2=19 g·m⁻³−0.00311 t, where t is in seconds.

The change in absolute humidity c_e2 outside the bungalow as a function of time during the second time period D₂ is also shown in FIG. 2. As in the first step, the absolute humidity c_e2 outside the bungalow over the time interval Δt₂ is sufficiently stable that it may be considered to be substantially constant and equal to the mean absolute humidity over the time interval Δt₂, namely in this example c_e2m=11.0 g·m⁻³.

Since

$\mathrm{ACH}=\frac{{\alpha }_1\times {\stackrel{.}{q}}_2-{\alpha }_2\times {\stackrel{.}{q}}_1}{{\alpha }_1\times \Delta c_{2m}-{\alpha }_2\times \Delta c_{1m}}$

from equation (1) above, by taking α₁=22.7 g·m⁻³·h⁻¹, α₂=−11.2 g·m⁻³·h⁻¹, Δc_1m=7.7 g·m⁻³, Δc_2m=7.0 g·m⁻³, {dot over (q)}₁=180 g·h⁻¹, {dot over (q)}₂=0 g·h⁻¹, the value for the air change rate ACH of the bungalow is obtained:

ACH_calc=8.2 m³·h⁻¹.

This value ACH_calc for the air change rate obtained according to the invention differs significantly from the estimate derived from the blower door test ACH_ref=15 m³·h⁻¹, but is in a coherent order of magnitude. Specifically, during the “blower door” type measurement, the air change occurs by force with a highly significant pressure difference, something which is not encountered naturally, and it is necessary to use a low-pressure extrapolation model, in this instance the Persily-Kronvall model, in order to return to the realistic physical parameter.

Since

$V=\frac{{\stackrel{.}{q}}_1\times \Delta c_{2m}-{\stackrel{.}{q}}_2\times \Delta c_{1m}}{{\alpha }_1\times \Delta c_{2m}-{\alpha }_2\times \Delta c_{1m}}$

according to above equation (2), the value of the effective volume of the bungalow is also obtained:

V_calc=122.9 m³.

It may be seen that the effective volume determined V_calc=122.9 m³ is far greater than the actual interior volume of the bungalow V_actual=33 m³. As explained above, that may be connected with the absorption of water vapor by the materials present in the bungalow and the fact that the duration applied for processing the measurements has been excessively long.

When such an excessively high value is obtained for the effective volume V_calc, the invention proposes making a post-measurement correction to the calculated value ACH_calc of the air change rate, by reducing the duration applied for the processing of the measurements. In practice, this correction is performed by shifting the time intervals Δt₁ and Δt₂ in each time period D₁ and D₂ while at the same time maintaining the “symmetry” of the time intervals Δt₁ and Δt₂ as defined hereinabove, namely by choosing, for the two time intervals Δt₁ and Δt₂, on the one hand, the same duration and, on the other hand, a starting point situated at a same distance in time from the start of the period D₁ or D₂ (notably, x minutes after the start of each period D₁ or D₂), until a value obtained for the effective volume V_calc is substantially equal to the actual interior volume.

Using such an approach there is obtained for the bungalow “corrected” time intervals Δt₁′ from midnight to 00:15 in the morning and Δt₂′ from 01:00 to 01:15 in the morning as shown in FIG. 2, which correspond to a reduced duration for the processing of the measurements, giving the following corrected results:

ACH_calc′=9.6 m³·h⁻¹;

V_calc′=56.6 m³.

In the case of the bungalow, the corrected effective volume V_calc′=56.6 m³ is still higher than the actual interior volume of the bungalow V_actual=33 m³. That is due to the fact that the interior coverings of the bungalow are unfinished, leading to a very rapid absorption of water vapor by the building materials of the bungalow. For such a bungalow, it would be preferable to implement the invention with a gas other than water vapor in order to gain precision on the value of the effective volume and of the air change rate.

It is evident from the above corrected results that the air change in the bungalow is around 0.29 volumes per hour, which is not high enough to ensure good interior-air quality.

The heat loss of the bungalow associated with infiltration is such that K_inf=ρ·c_p·V·ACH, where ρ is the density of dry air at 20° C. and C_p is the specific heat capacity of dry air at 20° C. From the value for the air change rate ACH_calc′=9.6 m³·h⁻¹, a value is therefore obtained for the heat loss associated with infiltration K_inf=3.3 W·K⁻¹.

The total heat loss coefficient for the bungalow has also been evaluated, giving a value K_tot=29 W·K⁻¹. Thus, the heat loss of the bungalow associated with infiltration represents around 11% of the total heat loss of the bungalow, for an annual balance of the order of 13 kWh·m⁻²·year⁻¹.

The infiltration and heat loss data for the bungalow are summarized in table 2 below.

TABLE 2
(bungalow)
		ACHcalc			K	E/Footprint
	V	(m3 ·	Vcalc	ACH	(W ·	(kWh ·
	(m3)	h−1)	(m3)	(h−1)	K−1)	m−2 · year−1)
Air changes-	33	9.6	56.6	0.29	3.3	13
Method of the
invention
Air changes-		15		0.43	4.9	20
Blower door
Heat loss					29	118

Example 2: Apartment

FIG. 3 shows the results obtained by implementing the method in an apartment situated in an old apartment block (year of construction: 1879) situated at Levallois-Perret, France. The apartment is uninsulated, is fitted with recent double glazing but has poor airtightness. The footprint is 54 m², the interior volume is 151 m³, and the apartment has two heat-losing faces of around 47 m².

The apartment boundary has a heat transfer coefficient U_BAT of around 1.9 W/m²K.

The coefficient n₅₀ of the apartment, obtained by a blower door test, is 7.3 h⁻¹. Using the Persily-Kronvall model, that corresponds to a reference value for the air change rate ACH_ref=55 m³·h⁻¹.

In the apartment humidification phase, over the first time period D₁ from midnight to 02:00 in the morning, humidifiers 20 distributed throughout the apartment are used to apply the strictly positive first water vapor flow rate {dot over (q)}₁ which is chosen such that the parameter

$\alpha =1-\frac{{\mathrm{ACH}}_{\mathrm{ref}}\Delta c_1\left(0\right)}{{\stackrel{.}{q}}_1}$

is equal to 0.78. In this example, the reference value ACH_ref is 55 m³·h⁻¹ and the initial absolute humidity difference Δc₁(0) is 2.2 g·m⁻³, which corresponds to a value of the order of 550 g·h⁻¹ for the first water vapor flow rate {dot over (q)}₁.

The curve representative of the change in absolute humidity c_i1 inside the apartment as a function of time during the first time period D₁ is shown in FIG. 3. As can be seen in this figure, the curve of increase in absolute humidity inside the apartment has a part that is substantially linear over the time interval Δt₁ from 01:30 to 02:00 in the morning. Putting this linear part of the curve into an equation gives: c_i1=7.4 g·m⁻³+0.00578 t, where t is in seconds.

FIG. 3 also shows the change in absolute humidity c_e1 outside the apartment as a function of time during the first time period D₁. The absolute humidity c_e1 outside the apartment over the time interval Δt₁ is stable enough that it can be considered to be substantially constant and equal to the mean absolute humidity over the time interval Δt₁, namely in this example c_e1m=4.3 g·m⁻³.

In the phase of “natural dehumidification” of the apartment, over the second time period D₂ from 02:00 to 04:00 in the morning, the humidifiers 20 present in the apartment are switched off so as to apply the zero second water vapor flow rate {dot over (q)}₂.

FIG. 3 shows the curve representative of the change in absolute humidity c_i2 inside the apartment as a function of time during the second time period D₂. As can be seen in this figure, the curve of decrease in absolute humidity inside the apartment has a part that is substantially linear over the time interval Δt₂ from 03:30 to 04:00 in the morning. As in the previous example, the time interval Δt₂ for which the measurements in processed over the second period D₂ is chosen to exhibit “symmetry” with the time interval Δt₁ for the processing of the measurements the first period D₁, that is to say so that the two time intervals Δt₁ and Δt₂ have, on the one hand, a same duration of 30 minutes and, on the other hand, a starting point situated, for each interval Δt_k, 1 h 30 after the start of the period D_k. Putting the linear part of the curve over the time interval Δt₂ into an equation gives: c_i2=9.0 g·m⁻³−0.00334 t, where t is in seconds.

The change in absolute humidity c_e2 outside the apartment as a function of time during the second time period D₂ is also shown in FIG. 3. As in the first step, the absolute humidity c_e1 outside the apartment over the time interval Δt₂ is stable enough that it can be considered to be substantially constant and equal to the mean absolute humidity over the time interval Δt₂, namely in this example c_e2m=4.2 g·m⁻³.

$\mathrm{ACH}=\frac{{\alpha }_1\times {\stackrel{.}{q}}_2-{\alpha }_2\times {\stackrel{.}{q}}_1}{{\alpha }_1\times \Delta c_{2m}-{\alpha }_2\times \Delta c_{1m}}$

Since according to the above equation (1), by taking α₁=20.8 g·m⁻³·h⁻¹, α₂=−12.0 g·m⁻³·h⁻¹, Δc_1m=4.8 g·m⁻³, Δc_2m, =2.9 g·m⁻³, {dot over (q)}₁=550 g·h⁻¹, {dot over (q)}₂=0 g·h⁻¹, the value for the air change rate ACH of the apartment is obtained:

ACH_calc=56.1 m³·h⁻¹.

This value ACH_calc for the air change rate which is obtained according to the invention is consistent with the estimate derived from the blower door test ACH_ref=55 m³·h⁻¹.

Since

$V=\frac{{\stackrel{.}{q}}_1\times \Delta c_{2m}-{\stackrel{.}{q}}_2\times \Delta c_{1m}}{{\alpha }_1\times \Delta c_{2m}-{\alpha }_2\times \Delta c_{1m}}$

according to the above equation (2), the value for the effective volume of the apartment is also obtained:

V_calc=321.7 m³.

It may be seen that the determined effective volume V_calc=321.7 m³ is far higher than the actual interior volume of the apartment V_actual=151 m³, something that may be associated with the absorption of water vapor by the materials present in the apartment and the fact that too long a duration was applied for the processing of the measurements.

As in the example of the bungalow, a post-measurement correction can then be made to the calculated value ACH_calc of the air change rate of the apartment, by shifting the time intervals Δt₁ and Δt₂ in each time period D₁ and D₂, maintaining the “symmetry” of these time intervals Δt₁ and Δt₂, so as to reduce the measurement processing time until a value is obtained for the effective volume V_calc that is substantially equal to the actual interior volume of the apartment.

Using such an approach, there is obtained for the apartment “corrected” time intervals Δt₁′ from midnight to 0:30 in the morning and Δt₂′ from 02:00 to 02:30 in the morning, as shown in FIG. 3, which correspond to a reduced duration for the processing of the measurements, giving rise to the following corrected results:

ACH_calc′=73.3 m³·h⁻¹;

V_calc′=159.1 m³.

The corrected value for the effective volume V_calc′=159.1 m³ is indeed consistent with the actual interior volume of the apartment V_actual=151 m³, which tends to demonstrate that the corrected value for the air change rate ACH_calc′=73.3 m³·h⁻¹ is a better estimate than the first value ACH_calc=56.1 m³·h⁻¹.

It is evident from the above results that the air changes in the apartment are around 0.48 volumes per hour, which is almost enough to ensure good interior air quality.

The heat loss of the apartment associated with infiltration is such that K_inf=ρ·C_p·V·ACH, where ρ is the density of the air and C_p is the specific heat capacity of dry air at 20° C. From the value for the air change rate ACH_calc=73.3 m³·h⁻¹, a value is therefore obtained for the thermal loss associated with infiltration K_inf=24.4 W·K⁻¹.

The total heat loss coefficient for the apartment has also been evaluated, giving a value K_tot=81 W·K⁻¹. Thus, the heat loss of the apartment associated with infiltration represents around 30% of the total heat loss of the apartment, for an annual balance of the order of 25 kWh·m⁻²·year⁻¹.

The infiltration and heat loss data for the apartment are summarized in table 3 below.

TABLE 3
(apartment)
		ACHcalc			K	E/Footprint
	V	(m3 ·	Vcalc	ACH	(W ·	(kWh ·
	(m3)	h−1)	(m3)	(h−1)	K−1)	m−2 · year−1)
Air changes-	151	73.3	159.1	0.48	24.4	25
Method of the
invention
Air changes-		55		0.36	19	19
Blower door
Heat loss					81	83

Advantageously, in the above examples, the steps of selecting the time intervals Δt_k for the processing of the data, of linearizing, and of calculating the air change rate ACH and the effective volume V of the space, are performed by means of a terminal such as the terminal 10 described above comprising the program PG.

According to another embodiment, the measurement data obtained in the context of examples 1 and 2 have been processed using an ARX model, instead of a simple R-C model as before. Thus, for each space of the bungalow and the apartment, an ARX model has been adjusted (fitted) to the change in absolute humidity c_ik inside the space as a function of time, over the totality of the two time periods D₁ and D₂, as illustrated in FIG. 4 for the bungalow and FIG. 5 for the apartment, and the air change rate ACH for the space has been obtained from the coefficients α_i, b_i, d_i of the ARX model.

The air change rate ACH value obtained by causing the first-order ARX model and the measured change c_ik(t) to converge is:

• • for the bungalow: ACH_ARX=7.84±0.89 m³·h⁻¹,
  • for the apartment: ACH_ARX=64.8±2.7 m³·h⁻¹,
    which is indeed consistent with the results of the above tables in terms of orders of magnitude. It may be noted that the order of the ARX model corresponds to the number of time constants in the diffusive model. An order-1 ARX model is thus equivalent to a simple R-C model with one resistor and one capacitor. In practice, an ARX model with an order strictly greater than 1 could have also been used for processing the data from examples 1 and 2, but it has become apparent that order gives good results while at the same time avoiding overparametrizing.

As illustrated in the preceding examples, the method of the invention proposes actions on the space in at least two phases having different flow rates for the gas (which in the examples is water vapor). This dynamic experiment in at least two phases makes it possible to reduce measurement times while at the same time maintaining good precision on the result.

Applications of the method and of the device according to the invention notably comprise:

• • prescription when renovating old dwellings, making it possible to evaluate the quantity of energy lost as a result of natural infiltration and thus to prescribe a suitable solution for improving the boundary of the space;
  • validation of the permeability of the boundary on receipt of a newbuild;
  • evaluation of the air change rate created by mechanical ventilation, so as to check that the flow rate is sufficient to ensure good interior air quality.

The invention is not restricted to the examples described and depicted.

In particular, the method according to the invention may be implemented using any suitable gas other than water vapor, notably CO₂, He, SF₆, H₂, N₂ or other refrigerant tracer gases.

In addition, over at least one time period D_k, the gas flow rate applied in the space may be negative rather than positive, corresponding to an extraction of the gas from the space rather than to an injection of gas into the space.

Moreover, in the above examples, the data processing method corresponds to the case where the diffusive model used is a simple R-C model with one resistor and one capacitor, or a first-order ARX model. As an alternative, the data regarding the change in concentration of the gas inside the space c_ik as a function of time may be processed differently, for example using an R-C model other than a simple R-C model, such as a “3R2C” model of the space with three resistors and two capacitors; or with an ARX model of order n strictly greater than 1 or any other suitable parametric identification model; or alternatively with a discrete-time recursive model of given sampling period describing the way in which the space behaves under transient conditions.

FIG. 6 shows a diagram of a “3R2C” model of a space with three resistors and two capacitors. This “3R2C” model considers a network having three nodes which are the air inside the space (I), the air outside the space (E) and the walls of the space (W). The external environment is considered to be at an imposed constant gas concentration C. Two nodes C_W and C_I schematically represent the gas concentration in the walls and in the interior air, each having an associated inertia C_W, C_I representing the gas storage capacity of the walls and of the interior air. The resistor R_FW, placed between the external environment and the walls node, and the resistor R_IW, placed between the interval environment and the walls node, represent the resistance to the diffusion of gas through the walls. The third resistor R_IE, placed between the internal environment and the external environment, represents the resistance to the diffusion of gas through infiltration. The air change rate ACH of the space is then the inverse of the resistance R_IE.

The total resistance R_T is such that:

$R_T=\frac{R_{\mathrm{IE}}\left(R_{\mathrm{IW}}+R_{\mathrm{EW}}\right)}{R_{\mathrm{IE}}+R_{\mathrm{IW}}+R_{\mathrm{EW}}}$

In practice, the resistance R_IE is very much smaller than the sum of the resistances R_EW and R_IW because the transfer of gas via infiltration is very rapid, whereas the diffusion through the opaque walls is a slow process, which explains why the simple R-C model is a good approximation.

According to an alternative form, it is also possible, in the context of the invention, to take the measurements using gas (notably humidity) sensors and temperature sensors which are incorporated into the terminal used for the acquisition of the measurements and the implementation of the data processing steps. Advantageously, such humidity and temperature sensors are commonly incorporated into tablets and smartphones.

According to another alternative form, the terminal may also comprise means of controlling the apparatus or apparatuses that apply a gas flow rate in the space, and may communicate with same via wireless means of connection such as Bluetooth or WiFi.

Claims

1. A method for determining an air change rate ACH of a space, comprising:

carrying out, over at least two successive time periods Dk corresponding to distinct given-gas flow rates {dot over (q)}k applied in the space, a campaign of measurements is carried out to make it possible to determine a concentration of the gas inside the space cik at closely-spaced time intervals, and a concentration of the gas outside the space cek is determined at closely-spaced time intervals; and

determining a value of the air change rate ACH of the space by causing a convergence of: a diffusive model expressing a temporal variation of the concentration of the gas inside the space cik as a function of the concentration of the gas outside the space cek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and the measured change cik(t) in the concentration of the gas inside the space cik as a function of time.

2. The method as claimed in claim 1, wherein: Ln  [ ( θ k  ( t ) - q. k ACH ) / ( θ k  ( 0 ) - q. k ACH ) ]

for each time period Dk starting from the measured change cik(t) in the concentration of the gas inside the space cik as a function of time: either, if there is a time interval Δtk for which the change cik(t) is substantially linear, the gradient ak of the tangent at the change cik(t) is determined over this time interval Δtk and the value of the air change rate ACH of the space is deduced from the gradients ak; or, if there is no time interval for which the change cik(t) is substantially linear, a time interval Δtk′ in which the change cik(t) is substantially exponential of the type exp(−t/τ) is selected, where τ is the time at the end of which the volume of air inside the space has been changed, and the value of the air change rate ACH of the space is deduced, this being the value such that the change

 is a straight line, where θk(t)=cik(t)−cekm′, where cekm′ is the mean of the concentration of the gas outside the space eek over the time interval Δtk′.

3. The method as claimed in claim 1, wherein the method is implemented with two successive time periods D1 and D2 corresponding to two distinct gas flow rate setpoints {dot over (q)}1 and {dot over (q)}2 applied in the space.

4. The method as claimed in claim 1, wherein the gas is H2O, CO2, He, SF6, H2, N2 or a refrigerant gas.

5. The method as claimed in claim 1, wherein, for each time period Dk, the gas flow rate {dot over (q)}k applied in the space comprises a flow rate {dot over (q)}impk imposed by means of at least one controlled-flow rate apparatus.

6. The method as claimed in claim 1, wherein the measurements making it possible to determine the concentration of the gas inside the space cik are taken using one or more sensors of said gas which are placed in the interior volume of the space.

7. The method as claimed in claim 1, wherein, over each time period Dk, the temperature inside the space Tik is stable.

8. The method as claimed in claim 1, wherein, over each time period Dk, the concentration of the gas outside the space cek is stable.

9. The method as claimed in claim 1, wherein, over each time period Dk, the solar radiation is low.

10. The method as claimed in claim 1, wherein the method is implemented while the space is unoccupied.

11. The method as claimed in claim 1, further comprising verifying that a value Vcalc of an effective volume of the space, calculated from the diffusive model and from the measured change cik(t), corresponds to an actual volume of the space.

12. The method as claimed in claim 1, wherein: α = 1 - ACH ref  Δ   c 1  ( 0 ) q. 1

the carrying out includes, over two successive time periods D1 and D2: i. over the first time period D1, a first gas flow rate {dot over (q)}1 is applied in the space, and a campaign of measurements is carried out to determine the concentration of the gas inside the space ci1 at closely-spaced time intervals, and the concentration of the gas outside the space ce1 is determined at closely-spaced time intervals, the first gas flow rate {dot over (q)}1 being such that the parameter

 is less than or equal to 0.8, with Δc1(0)=ci1(0)−cem, where t=0 is the starting point for the first time period D1, cem is the mean concentration of the gas outside the space over all the time periods D1 and D2, and ACHref is a reference value for the air change rate of the space, then ii. over the second time period D2, a substantially zero second gas flow rate {dot over (q)}2 is applied in the space, and a campaign of measurements is carried out to determine the concentration of the gas inside the space ci2 at closely-spaced time intervals, and the concentration of the gas outside the space ce2 is determined at closely-spaced time intervals.

13. The method as claimed in claim 1, wherein the diffusive model is an R-C model.

14. The method as claimed in claim 1, wherein the diffusive model is a parametric identification model.

15. (canceled)

16. A non-transitory computer-readable recording medium on which is recorded a computer program that, when executed by a computer, causes the computer to execute the method as claimed in claim 1.

17. A device for determining an air change rate ACH of a space, comprising:

at least one apparatus configured to apply, over at least two successive time periods Dk, distinct given-gas flow rates {dot over (q)}k in the space;

at least one sensor configured to measure a concentration of the gas inside the space cik at closely-spaced time intervals; and

a terminal comprising a processing module configured to cause convergence of, a diffusive model expressing a temporal variation of the concentration of the gas inside the space cik as a function of a concentration of the gas outside the space cek and of physical parameters of the space from which parameters the air change rate ACH of the space can be calculated, and the measured change cik(t) in the concentration of the gas inside the space cik as a function of time, so as to obtain a value of the air change rate of the space.

18. The device as claimed in claim 17, further comprising at least one sensor configured to measure the concentration of the gas outside the space cek at closely-spaced time intervals.

19. The device as claimed in claim 17, further comprising at least one temperature sensor configured to measure a temperature inside the space Tik.

20. The device as claimed in claim 17, further comprising means of connection between the at least one sensor and the terminal.

21. The device as claimed in claim 17, wherein the terminal comprises means of controlling the at least one apparatus configured to apply distinct given-gas flow rates {dot over (q)}k in the space.

22. A terminal, comprising:

a processing module configured to cause convergence of a diffusive model expressing a temporal variation of a concentration of a given gas inside a space cik as a function of a concentration of the gas outside the space cek and of physical parameters of the space from which parameters an air change rate ACH of the space can be calculated, and on the other hand, a measured change cik(t) in the concentration of the gas inside the space cik as a function of time, so as to obtain a value of the air change rate of the space.

23. The terminal as claimed in claim 22, wherein the processing module comprises a computer program recorded on a recording medium comprising a rewritable nonvolatile memory of the terminal, instructions of said program being interpretable by a processor of the terminal.

24. The method as claimed in claim 9, wherein the solar radiation is zero.