The technical domain of the invention is the exploitation of hydrocarbon fields. More particularly the invention concerns a method of building a reliable simulator able to forecast quantities produced vs. production parameters, in the particular case of mature fields.
BACKGROUND -
Mature hydrocarbon fields represent a special challenge both in terms of investment and allocation of human resources, because the net present value of any new investment diminishes with the degree of maturity. Therefore, less and less time and effort can be invested in reservoir studies to support field exploitation. Still, there remain opportunities to improve the production over a so-called "baseline" or "business as usual" behavior of an entire mature field, even with little investment. Past strategic choices in the way to operate the hydrocarbon field have created some heterogeneity in pressure and saturation. These can be drastically revisited and production parameters reshuffled accordingly. With respect to a mature hydrocarbon field, many production avenues have been explored in the past, and a learning process can be applied: reshuffled parameters can be implemented with low risk.
Two prior art approaches are currently known to model the behavior of a hydrocarbon field and to forecast an expected quantity produced in response to a given set of applied production parameters.

A first approach, called "meshed model" or "finite element modeling" parts a reservoir into more than 100,000s of elements (cells, flowlines...), each cell carrying several parameters (permeability, porosity, initial saturation...), and applies physical laws over each of said cells in order to model the behavior of fluids in the hydrocarbon field. In that case the so-called Vapnik-Chervonenkis, VC-dimension h of the space of solutions S, from which the simulator is selected, is very large. Therefore, the available number m of measured data in history data
remains comparatively small, even for mature fields, and the ratio ^ appears to
be very large compared to 1. As a result of the Vapnik learning theory, which is further mentioned later, the forecast expected risk R is not properly bounded (due to the Φ term), and such a simulator can not be considered to be reliable, even if it presents a very good match with history data. In practice, it is widely recognized that for such meshed models, a good history match does not guarantee a good forecast: there are billions of ways to match the past, leaving large uncertainty on which one provides a good forecast.
A second approach, by contrast, uses over-simplified models, such as, for instance, decline curves or material balance. However, this is too simplified to properly take into account the relevant physics and geology of the reservoir, in particular complex interaction and phenomena. In such case, the forecast expected risk R is not minimized, because no good match can be reached (the empirical Risk Remp term remains large).
SUMMARY -
In summary, the invention represents a proper compromise between too complex and too simplistic modeling approaches. It is valid only for mature fields, which deliver enough past information, in the form of history data HD, to allow building a space S of candidates for becoming a field production simulator, large enough to take into account all key phenomena at stake in the field, without becoming too complex and hence requiring too many history data to be calibrated.
The Vapnik statistical learning theory defines under which conditions such a simulator can be devised. Such a simulator may be designed in such a way it complies with the conditions for a reliable forecasting capacity.

The object of the Invention is a production simulator, for simulating a mature hydrocarbon field, providing quantity produced per phase, per well, per layer (or group of layers) and per time as a function of production parameters, wherein said production simulator matches sufficiently well history data of said mature hydrocarbon field and verifies a Vapnik condition. This said Vapnik condition ensures that the quantities calculated to be produced per phase, per well, per layer (or group of layers) and per time to be accurate. This will allow the users of this simulator to play different production scenarios, according to different production parameters, each of them delivering reliable quantities, so that such scenarios can be properly compared to each other and an appropriate one can be selected according to specific criteria. As all production scenarios will deliver reliable quantities, the selected one will also deliver a reliable forecast of the production, and therefore it will become a low risk and preferred path for producing the field.
DETAILED DESCRIPTION -
According to another feature of the invention, a match with history data is obtained when:
\p2yktb ~>C(fklbHD%T _x T l
■■■■ ' 'J- is a positive function defined by:

^2 em
hlog
, where

+ %
\S))
±,8
\m j
h is the Vapnik-Chervonenkis dimension of the space of solutions, and m is the number of independent measures available in history data, e is equal to exp(l).

Calibrating the production simulator among the candidates of the space of solutions means making the "empirical risk" R (a) as small as possible, while choosing the appropriate parameters a that completely defines a solution within the space of solutions. This empirical risk Ranp(a) measures a (positive) distance between actual past data and the corresponding data calculated by the simulator.

This upscaling process is a way to reach a trade-off between <& —,8

and

Remp(a) values, which need to be together as small as possible, as the objective is

' h *s
with a given probability 1-8.
to minimize their sum R.( a) + m —,8
p \m
In minimizing the above-mentioned sum, this minimizes the expected risk of the forecast, R(a), according to the Vapnik inequality:

R(a) —,8
m J
(as starting models are complex) and

small empirical risksRemp(a) (as such complex models can properly picture past

while
data) and gradually decrease the complexity, and therefore $ —,8
Km j
empx
keeping a good match of past data, therefore keeping the empirical risk RemJ a) small,
According to another feature of the invention, said reservoir partition is upscaled following the steps of:
- partitioning a reservoir G into elementary parts Gab, such that
,4 B
& = (JUG,,,, with Gab r\Ga,b, =0 for (a,b) # (a',b'), where a€{l..A} describes a
x-y area, and bC{ 1..B} describes one or several z layers,
- grouping adjacent elementary parts exhibiting homogeneous rock
properties, into sub-geologies Gc where c€{ 1..C}.
Such feature gives a practical way of upscaling the field geology in identifying a reasonably small number of sub-geologies Ge,

According to another feature of the invention, rocks properties are upscaled by following a step of averaging out rock properties over each sub-geology, according to formula:
RPC =7T J J J RP(x,y,z)dxdydz, where Vc is the volume of sub-geology Gc,
This feature explains a way to practically define the properties to be used in a given sub-geology Gc.
According to another feature of the invention, laws of reservoir physics are upscaled in such a way they apply with functioning parameters of the sub-geology and wherein space and times scales associated with the sub-geology are determined in such a way that the associated space of solutions is consistent with the complexity of history data at the well level.
Such feature gives the rales to look for upscaled reservoir physics laws, in focusing on their behavior measured at well level.
According to another feature of the invention, the production simulator is built following the steps of:
- defining initial coarse reservoir partition, rock properties, laws of reservoir physics and laws of well physics,
- downscaling said reservoir partition, rock properties, laws of reservoir physics and laws of well physics while keeping said Vapnik condition verified, until the production simulator matches history data and
- calibrating said production simulator by choosing among the production simulator candidate solutions, the candidate solution minimizing a forecast expected risk.
Downscaling means increasing complexity, starting from a simplistic description of the field, and adding relevant reservoir and/or well phenomena, which will properly picture the behavior of the entire field, well by well. Downscaling is carried out in such a way that the space of solutions candidates for

8 is a positive number close to zero, 1-8 defining a probability and <1> is a positive function defined by:

«5

(, ^
h 2
— ,d
xm j ym

hlog

lem

+ log

^^
VC/yy

, where

A is the Vapnik-Chervonenkis dimension of the space of solutions, and m is the number of independent measures available in history data, e is equal to exp(l),
Calibrating the production simulator among the candidates of the space of solutions means making the "empirical risk" R (a) as small as possible, while
choosing the appropriate parameters "a" that completely defines a solution within the space of solutions. This empirical risk measures a distance between actual past data and the corresponding data calculated by the simulator,
This downscaling process is a way to reach a trade-off between

oS0yv-(poUoyo,

<3 (Es + Ef y V.pf - MT)VT)=0, where
T = T(x,y,z) is the temperature and can vary over the reservoir, Q> is the rock porosity, S is the saturation of phase (p, pv is the density of phase u^ ) where:
Q at well k in sub-geology c at time 5 t,
Tkc is a transfer function of well k, in sub-geoiogy c
PPktc are the production parameters applied to well k in sub-geology c at time t,
u^ is the velocity of phase

C.
The first term Remr(a)is an empirical risk associated with parameters a,
indicative of the quality of the matching to history data HD provided by said parameters a. The second term is characteristic of the model and can be

/
2em (2
(h ^
expressed by —,S =2 — hlog + log — , wherein 5 is a positive
\,m ) \m\ \ h J \SJ)
number close to zero, 1-8 defining a probability of said forecast expected risk R(a) is indeed bounded by Remp(a) + ^>, where h is the aforementioned VC-
dimension of the space S of solutions, also named Vapnik-Chervonenkis or VC dimension, and m is the aforementioned number of independent measures available in history data HD.
According to said result, prior art oversimplified models all suffer form a high Remp(a)duc to the over simplification of the model. Instead, prior art
complex meshed models may provide a small R (a), but suffer from a high (D
h value, due to an high — ratio, since the VC-dimension h of the space of solutions m
is too large with respect to the number m of independent measures available in
history data HD.
A trade-off has then to be reached, m value is constant and given by history data HD available for a given hydrocarbon field. The size h of the space of
h
solutions has then to be adapted so that the — ratio remains small. With an
m
average objective of a five years forecast with a reliability of around +/-5%, a
h
value — < 0,1 has been found to be compatible with both the objective reliability
m
and the possibility of scaling, as- will be detailed further, to obtain a model.

Another way to express and check said Vaprtik condition is by realizing a blind test. A blind test over N years may be realized by parting history data into two time intervals. A first "past" interval runs from an initial time T0 for which history data are available, to a time T-Ny preceding the final time T by N years. A second "blind" interval runs from T-Ny to time T corresponding to the last time for which history data is available. T is generally the actual time. The data of "past" interval are considered as known, and are used to build a matching production simulator 2, by learning on said data. The data of "blind" interval are considered unknown or at least are concealed during the building of production simulator. They are then compared to data forecast by production simulator 2 over said "blind" interval given production parameters over the "blind" interval. A blind test is considered satisfactory when the forecast data reproduce with enough accuracy the history data over said concealed interval.
A blind test then comprises the following steps:
- determining a production simulator 2 matching history data HD over a time interval preceding T-Ny,
- forecasting quantities produced over a time interval [T-Ny, T],
- the blind test being satisfactory when:
\fxiqktb ~ >2^ktbHD\\rT_N Ti
'-LJ— n these nominal data PP and g#,wro, a nominal production simulator 2 is built.
fhese data are then slightly varied to obtain corresponding data PP' and Q^ibHD . iased on these slightly varied input data another production simulator is built that s expected to be close enough to nominal production simulator 2.
Output data, that is quantities produced Q(fktb and Q(fktb are forecast
espectively by nominal production simulator 2 and by other production imulator, over a future time interval [T, T+My], and are then compared.
\PP-PP\L n
The forecast stability property is verified when —r IJ^J- < e ancj
\PP r
I pyr]

bldctbHD ><■
>Caktb y,
gktbHD >C, and gradually merging adjacent ones together when they exhibit homogeneous rock properties RP. The result is a new coarser partition, comprising sub-geologies Gc where c€{l...C}. In figure 1, three such sub-geologies are shown. Gi gathers Gn, G12, Go, G14 and G15, exhibiting a homogenous behavior. G2 gathers G21, G22, G23, G24, G25, G3], G32, G33, G34 and
5 G35. G3 gathers G31, G32, G33, G34 and G35. In real cases a sub-geology typically includes from 3 to 50 wells. Said upscaling of the geology partition is a first way to reduce the dimension h of the space of solutions S. The size of the space of solutions then depends on the number of geologies which is of an order of few units instead of over 100 000s cells as in a meshed prior art model.
0
When using a downscaling approach, the process starts from a coarse partition, e.g. composed of a single part corresponding to the whole reservoir G. Said coarse partition s then parte into sub-geologies Gc where c€{l...C} where and every time a substantial change of properties is present around the boundary
5 between said sub-geologies. So doing, a homogeneous behavior may be expected in every sub-geology, while keeping the number of such sub-geologies as reduced as possible.

Rock properties RP comprises mainly the rock porosity, permeability k and relative permeability krifc, used to determine the dynamic of fluid through rock, but also other property such as net pay, heat capacity or conductivity, as relevant. Since the sub-geology becomes the new elementary volume unit, all of these rock properties RP, are considered to be fairly constant over a given sub-geology Gc.
When using a upscaling approach rock properties RP are homogenized over each sub-geology Gc, according to averaging formula;
RPC = —• JJJ RP(x/if,z)dxdydz. where Vc is the volume of sub-geology Gc.
When instead using a downscaling approach, rocks properties (RP) are downscaled by defining new separate rock properties RPC over each new sub-geology (Gc) obtained by parting along a discontinuity.
With respect to figure 3, is now described in more details the content of production simulator 2. Said production simulator 2 module may be parted into two main modules 6, 7. A first module implements laws of reservoir physics 6. Given a set of production parameters PP, said module provides dynamic characteristics of the fluids across the reservoir, at least at the entrance of each well 11 and at each sub-geology b. Said dynamic characteristics are e.g. expressed as a velocity field.
Said laws of reservoir physics 6 are either upscaled or downscaled in such a way they apply with functioning parameters of the sub-geology Gc. Also, space and times scales associated with the sub-geology Gc are determined in such a way that the associated space of solutions is consistent with the complexity of history data HD at the well level. For instance, if insufficient data richness is available on layer-related production (m too small), well production will be summed up, partially (some layers are grouped) or totally (all layers are grouped):
>Cf/kt ~ Z-d>£ saturation and Jip
diffusion flux. Of course, one has:
5X = 1 and Z/^=0

is the
porosity. This gives the velocity in terms of pressure gradient
which gives Darcy's law. In the case of anisotropic porous media, one ends up with
", =-^IX(fy>-/#,•)

where K denotes the symmetric permeability tensor. The resulting equation of mass conservation of fluid is given by
Actually, the fluid is generally made of gas (g), oil (o) and water (w), whose composition might be complex, depending for instance on their salinity and hydrocarbon chains. Mass conservation of phase

T^ the relative permeability coefficient of phase

and the R(a) values. The forecast expected risk R(a) is minimized and the forecast provided by the production simulator 2 may be considered reliable.
For each candidate solution, the forecast expected risk R(a) is bounded from above using the Vapnik formula:

R(a)

h x

R(a) is the forecast expected risk associated with parameters a,
Remp(a) is an empirical risk associated with parameters a, determined by a matching process with history data HD,
8 is a positive number close to zero, 1-5 defining a probability that the inequality holds, and
is a function defined by:

4>

h _ — ,5

hlog

2 em

+ log

2
\oj)

, where

h is the Vapnik-Chervonenkis dimension of the space of solutions, and m is the number of independent measures available in history data HD, e is equal toexp(l).
The best retained production simulator 2 is determined and defined by a set of optimal parameters aopt that minimizes the forecast expected risk R(a).

Once a production simulator 2 is thus determined and optimized so as to respect the matching condition, the Vapnik condition and to minimize the forecast expected risk R(a), it can be used inside an optimizer 1. The optimizer 1 generates scenarios of production parameters PP and applies the production simulator 2 over these scenarios. Many such runs are then iterated over different sets of production parameters PP. At each iteration, a gain value 5 is calculated derived from the quantity produced Q!pktc forecast by production simulator 2. The resulting gain value 5 may be used to select the next scenario. So doing an optimal set of production parameters PP can be obtained that optimize said gain value 5.
Said optimized gain value 5 can be a net present value NPV or reserves RES of the hydrocarbon field,
Any gain values 5 can be determined by module 4 from quantities produced Q(fktc output by optimizer 1, by taking into account the necessary economic parameters or indexes, as is well known by the one skilled in the art.
Said net present value NPV may e.g. be determined using the formula:

w^=ZSZi,fc*^r7Tf^-ZE4-Socft-iZ(roi*pfc+7it*Lfc)
i v k c J Cl + rf/ , v k k k c

(1 + df

where:
Pkc is oil production (in barrels) for well k and sub-geology c,
i?ik is tax and royalties for well k and year i,
Si is the oil sale price (per barrel) for year i,
d is the percentage discount rate,
/ik is investment made on well k during year i,
OCik is operating costs for well k during year i,
Lkc is the liquid production (in barrels) for well k and sub-geology c,
TO\ is treatment cost (per barrel of oil), for year i.
TL\ is treatment cost (per barrel of liquid), for year i

An alternate choice is reserves RES value of the hydrocarbon field, defined as the cumulative oil produced over a given time period. Others choices are possible,