FR2775095A1 - Fluid composition simulation method - Google Patents

Abstract

The operation of delumping is based on the fact that the oil reservoir has only two non aqueous phases (liquid and gas) , allowing fluid regrouping and detailed decomposition calculations to be carried out. The oil reservoir is split into a grid system and aggregate fluid compositional simulation using components and pseudo components carried out. For each grid section, modeling is carried out on the vaporized fraction with the regrouped fluid under constant equilibrium. For each grid step, a molar quantity is produced and evaluation of the detailed fluid composition carried out.

Description

Simulation method to predict over time
a detailed composition of a fluid produced by a reservoir
The present invention relates to a simulation method for predicting, as a function of time, a detailed composition of a fluid produced by a reservoir and more particularly a detailed composition of a fluid contained in and produced by a petroleum deposit in which are implanted a or several production wells.

 The compositional simulation of a reservoir is commonly used to provide the deposit's production profiles, which in particular make it possible to determine the production scheme best suited to this deposit.

 The compositional simulation of a petroleum deposit is implemented not by using a real description of the fluid but by using a fluid modeled by a smaller number of components than the number of components of the real fluid. Indeed, the number of components of the reservoir fluid being relatively large, the modeling with all the components would lead to too much computation time. This prohibitive calculation time has led the specialists to group the pure components into pseudo-components, for example a pseudo-component comprising nitrogen and methane, a pseudo-component comprising the C3 and C4 hydrocarbons, and the like. perform reservoir simulation on a reduced number N of pure components and pseudo-components. Such a reduced composition is referred to as "pooled fluid composition" or "pooled fluid". Generally N represents 5 to 10 components and pseudo-components, which is considered to be sufficient to properly represent the behavior of the reservoir fluid under background conditions.

The pooled fluid is described by one of the state equations well known to those skilled in the art and adapted to said pooled fluid.

 Before conducting the compositional reservoir simulation, we represent the reservoir or reservoir in the form of a mesh network, each of which constitutes an elementary volume of said reservoir. The number of meshes can reach several thousands and each mesh has its own properties, such as geometry, porosity, permeability, etc. Moreover, at certain meshes can correspond to at least one injection well or production which is implanted in said reservoir.

 The reservoir simulation makes it possible to calculate for each mesh a certain number of principal variables of the reservoir fluid, said variables possibly being the quantity (number of moles) of fluid, the composition or mole fraction of each component and pseudo-component of the grouped fluid. and the pressure prevailing in each mesh. These variables are known at time t = O (start of exploitation of the deposit) and are then calculated by the simulation of deposit at each moment t or no time m. For each cell, it is possible, from these principal variables, to calculate any other property of the fluid present in the mesh, such as the number of phases, the composition of each phase, etc.

For each mesh with which a production well is associated, it is possible, from these main variables and imposed production constraints, to also calculate the production rate and the composition of the fluid produced by said well.

 The thermodynamic properties of the pooled fluid can be calculated using the equation of state associated with it.

 The N-component model, if it is sufficient to represent the behavior of the reservoir fluid under background conditions, is no longer appropriate for simulating the behavior of the fluid in the facilities for its surface exploitation, which operation requires knowing a composition. more detailed component Q and / or pseudo-components of the fluid produced by the deposit, Q being greater than N and for example of the order of 16 to 30.

 Heretofore, this detailed component and / or pseudo-component composition was obtained from the pooled composition N assuming that the composition of the pseudo-components remained constant over time.

 Such a procedure is a source of errors because the composition of the pseudo-components varies over time. in particular depending on the pressure of the deposit or following the injection of a gas into the deposit.

 As a result, the detailed composition obtained remains very approximate and does not make it possible to satisfactorily predict the behavior of the fluid in the surface operating conditions for many years after the start of production.

 The object of the present invention is to propose a simulation method for predicting a detailed composition of the fluid produced by a reservoir taking into account the parameters of the reservoir and which is much more precise, such a prediction being termed "delumping" by the specialists. The "delumping" consists in predicting what would have been the results of a reservoir simulation if the detailed modeling of the fluid had been used and this, from the results of a simulation carried out using the grouped modeling of said fluid.

The subject of the invention is a method of the type consisting of:
a) representing the reservoir in the form of a network of meshes (j) each of which constitutes an elementary volume filled with fluid,
b) defining the fluid by N component and pseudo-component (i) grouped modeling and determining a state equation describing the fluid in this grouped modeling,
c) also defining the fluid by detailed modeling with Q components and / or pseudo-components, Q being greater than N, and determining another state equation describing the fluid in this detailed modeling,
d) producing, in a manner known per se, a compositional simulation of the fluid grouped with N components and pseudo-components (i), said compositional simulation making it possible to calculate at least for each cell (j) and at consecutive time steps (m , m + 1, ...) the vaporized fraction (OJ), the liquid-vapor equilibrium constants (km) of each component (i), the injection or production flow rates (s, J) and for each pair of meshes (j, h) the flow rates of the liquid (Uogh) and vapor (ugmssh) phases of the N-component fluid and pseudo-components, and is characterized in that it further comprises:
e) determining, at each time step (m) and for each cell (j), the composition of the liquid and vapor phases of the fluid for detailed modeling with Q components and / or pseudo-components, from the values of the vaporized fraction (or) and equilibrium constants (km) of the grouped fluid,
f) evaluating for each mesh, at the time step (m + 1), the molar amount of each of the Q components and / or pseudo-components of the detailed fluid from the values corresponding to the time step (m) of the flow rates of the phases of the fluid combined and detailed liquid and vapor phase fluid compositions determined in step e), and
g) evaluating, for each production well, the detailed composition of the fluid produced between times t and t 'corresponding to time steps m and m + 1, from the flows of the phases of the grouped fluid and the compositions of the liquid phase and detailed fluid vapor determined in step e).

 According to another characteristic of the present invention, the steps e, f and g are implemented at the same time as performing the compositional simulation of the grouped fluid.

 According to another characteristic of the present invention, the results of step d are stored and subsequently used for the implementation of steps e, f and g.

 The method according to the present invention is implemented for a reservoir constituted, for example, by a petroleum deposit. In known manner, a reservoir simulation is performed. For this purpose, the deposit is represented in the form of a mesh network, some of the meshes or a group of meshes being associated with one of the production wells implanted in the oil field to be exploited.

 To reduce the calculation time, the compositional simulation of the deposit is performed on a limited number N of components and pseudo-components, for example from 5 to 10, defined in the manner indicated above, these components and pseudo-components being selected according to the nature of the deposit.

 As indicated above, the fluid grouped with N components and pseudo-components is described by a state equation which could be for example that of PENG-ROBfNSON adapted to said grouped composition.

 The compositional simulation of the deposit makes it possible to calculate, at each time step and for each cell, a certain number of principal variables of the grouped fluid, which variables, in this case, are: the quantity of fluid: fm the molar fraction of the component i : 7m with i <i <N the pressure: prn.

 By prior measurements, the value of said principal variables is known at the beginning of the exploitation of the deposit, that is to say at the inset t = 0 or at the time step m = 0.

 To go from the time step m to the time step m + 1, the compositional simulation comprises several steps detailed below.

 In a first step and for the time step m, a liquid-vapor equilibrium calculation (flash) is performed on the pooled fluid, for each mesh j to determine the vaporized fraction #jm the molar fraction of each component i in the liquid phase (x Jm with i = 1.N) and the molar fraction of said component i in the vapor or gas phase (y "with i = 1 ... N).

dans lesquelles
'Pi est la fugacité du composant i. These various fractions are determined with the following system of equations:

in which
'Pi is the fugacity of component i.

We memorize the vaporized fraction #jm and the constants
equilibrium yijm kijm = with i varying between 1 and N, in order to use them in a
xijm another step called "delumping" which will be explained later.

 In a second step and for each mesh j, some of the properties of each liquid and gas phase are evaluated, namely density (## EQU1 ##), viscosity, saturation and relative permeability.

 In a third step, for each mesh j and at time step m, the coefficients of the equation for the pressure are calculated.

The equations for the pressure of a mesh j at time t + At or at the time step m + 1, are

- le terme source

To solve these equations, the coefficients to calculate are - the total compressibility CTjm (fluid + rock), - the generalized transmissivities

- the source term

 In these equations: h are the meshes close to the mesh j, h EJ (j), where ijm is the partial molar volume of the component i in the mesh j at the time step m, m and #gjm are the mobilities of the phases liquid (o) and gas (g), t, h is the transmissivity between the centers of meshes j and h, 1 being the upstream mesh.

 In a fourth step, the equations for the pressure at time t + At, that is to say at the time step m + 1, are solved for all meshes.

These equations form a linear system of the type
A. where p = (p1m + 1, .pjm + 1) T, where J is the number of meshes of the network.

 These equations are solved by a standard iterative process.

In a fifth step, the flow rates of the phases between each pair of adjacent meshes and for each well associated with, for example, the law of DARCY, are calculated at the time step m + 1.
uojhm = - # ojm # olm.tjh (phm + 1-pjm + 1) ugjhm = - # gjm # glm.tjh (phm + 1-pjm + 1) p being the density and 1 being the upstream mesh with l = j or h.

 According to one characteristic of the invention, the flow rates of the phases which will be used in the delumping are stored or stored.

In a sixth step, the quantity f and the composition z of the grouped fluid are evaluated, in each mesh j and at the time step m + 1, from the values at the time step m, the flow rates of the phases evaluated at the fifth step and the compositions of the phases calculated in the first step. To do this, we apply the conservation laws defined by the following equations:

By an iterative process, the above steps are repeated to calculate the principal variables at times t + At, t + 2At, t + 3At, etc ... or at the corresponding time steps m + 1, m + 2, m + 3, etc ..., increment
At that can be constant or variable.

 Since the flow can take place in any direction between the neighboring meshes, it is necessary to treat all the meshes with each step of time.

 According to the present invention, a detailed modeling is defined with Q components and / or pseudo-components as well as another state equation describing the fluid thus modeled.

 For this purpose, the components and / or pseudo-components whose characteristics are to be known and which are necessary to represent the production fluid in the surface conditions are chosen beforehand. The number Q which is greater than the number N of the grouped composition is generally of the order of 16 to 30. The composition of the detailed fluid with Q components and / or pseudo-components is known at the time step m = 0.

 The data stored in the first and fifth steps are used to extend them to the Q components and / or pseudo-components of the detailed composition, so as to perform the "delumping" operation.

For the "delumping" operation, it is assumed that the reservoir fluid has only two non-aqueous phases (liquid and gas) and that the water plays no role in the liquid-gas equilibrium and that none of the other components of the fluid does not dissolve in the water.

 In the following, uppercase letters are used to represent the detailed fluid and lowercase letters are used to represent the grouped fluid.

To carry out the "delumping", it is furthermore assumed that at each time step m, the molar fraction of the vaporized phase in each mesh is
independent of the number of constituents chosen to model the fluid, # jm = # jm - the number of moles of liquid and vapor flowing between the meshes
(U, u) and in or out of the wells (S, s) is independent of the number of
constituents chosen to model the fluid.

Uogh UOJ; 1 and Ugh UgXh
Sn; = Sn; and = = rn
To perform the "delumping", it is necessary to know the equilibrium constants K for the detailed fluid in addition to the molar fraction O- already determined by the equality # = #.

comme indiqué par C. LEIBOVICI dans son article "A Consistent
Procedure for Pseudo-Component Delumping" paru dans FLUID PHASE
EQUILIBRIA, 117 (1996), 225-232.The calculation of equilibrium constants can be done from the general equation

as indicated by C. LEIBOVICI in his article "A Consistent
Procedure for Pseudo-Component Delumping "published in FLUID PHASE
EQUILIBRIA, 117 (1996), 225-232.

où aI et bI sont les paramètres de l'équation d'état pour le composant I et où les paramètres #jm,ssjm et &gamma;jm sont des paramètres calculés à partir des constantes d'équilibre (kjj) pour le fluide regroupé en minimisant la fonction:

Les paramètres rljn,ssjm et &gamma;jm ainsi obtenus seront approximativement les mêmes pour les deux modélisations détaillée et regroupée du fluide, lesdits paramètres dépendant seulement des paramètres de phase de la pression et de la température.For a two-parameter state equation, such as
PENG ROBINSON, the generalized equation of LEIBOVICI can be written for the detailed fluid in the following way, as long as there is no binary interaction coefficient

where aI and bI are the parameters of the state equation for component I and where the parameters # jm, ssjm and &gamma; jm are parameters calculated from the equilibrium constants (kjj) for the grouped fluid by minimizing function:

The parameters rljn, ssjm and &gamma; jm thus obtained will be approximately the same for the two detailed and regrouped modelizations of the fluid, said parameters being dependent only on the phase parameters of the pressure and the temperature.

 In the presence of a binary interaction coefficient, the parameters rl, ss and y can be determined by regression.

Therefore, when the detailed composition ZIjm is known in the mesh j at the time step m, it is possible to estimate the detailed compositions of the liquid and vapor phases in the same mesh j and for the same time step m.

 I being the component and / or pseudo-component of the detailed composition These compositions can be standardized so that their sum is equal to 1 if necessary.

avecl=1 Q

dans lesquelles j'=j pour un débit de la maille j vers la maille h ou dans le puits et j'=h pour un débit de la maille h vers la maille j, et j' correspondant au fluide injecté dans le cas des puits d'injection, S étant alors négatif, et F est la quantité molaire de fluide dans chaque maille avec F = f.When the compositions of the detailed phases for all the meshes of the network are known at the time step m, it is possible to estimate the detailed compositions Z1m + I at the consecutive time step m + I from the following equations.

withl = 1 Q

in which j '= j for a flow rate from the mesh j to the mesh h or in the well and j' = h for a flow rate from the mesh h to the mesh j, and j 'corresponding to the fluid injected in the case of the wells injection, S being negative, and F is the molar amount of fluid in each mesh with F = f.

et la composition détaillée du fluide produit par le puits est obtenu en normalisant les débits ci-dessus

The molar flow rate of the detailed component I produced by the well W at the time step m is given by:

and the detailed composition of the fluid produced by the well is obtained by normalizing the flow rates above

 Thanks to the present invention, a detailed composition with Q components and / or pseudo-components is obtained which makes it possible to better define the predicted production profiles, with greater precision compared with the previous methods. This greater precision of the projected production profiles allows a more reliable choice of development scheme (type and size of surface installations, number of wells, etc.), resulting in an increase in profitability and a decrease in economic risk.

 In the foregoing, certain values obtained during the simulation of the deposit are stored or stored for later use in the delumping. It goes without saying that these same values could be used directly if one decides to carry out the delumping at the same time as said simulation of deposit.

 Another advantage of the present invention is that the method can be used to calculate the concentration of trace hydrocarbons in the fluid produced without having to perform a reservoir simulation incorporating these hydrocarbons, provided that their equation of state are known.

 It should be noted that the cases in which the initial composition of the fluid varies with the depth or laterally inside the tank, may be treated provided that the initial composition detailed at any point in the tank is known.

 Two examples are given below to demonstrate the speed and accuracy of the method according to the invention, the tests having been carried out on a parallelepipedal reservoir model comprising four layers of different permeabilities, with a dip in the x direction.

 Predictions were calculated to determine the behavior of the fluid under surface conditions over a 30-year period from the start of operation, the fluid being a volatile oil.

 In the first example, the tank has a water oil contact, while in the second example, the tank is free of water and contains only oil and gas.

 In the detailed fluid modeling, the fluid is defined by 16 components and / or pseudo-components, as shown in Table 1, and it is considered that the binary interaction coefficients are equal to zero.

 In the modeling of the grouped fluid, the fluid is defined by 7 pseudo-components, as indicated in Table 2.

 At the reservoir temperature, the bubble point pressure of the volatile oil is 338.5 bar for the detailed fluid and 336.6 bar for the grouped fluid.

Example I
The initial pressure of the tank is 400 bar and the tank is exhausted through a single well which is drilled near the top of the tank. The production of oil from the well is 300 m3 per day and the maximum production of gas is 106 normal m3 per day.

 A first compositional simulation of the reservoir was first performed using detailed modeling of the 16-component fluid and / or pseudo-components using the state equations adapted to each of the components. At the beginning, the well produces oil at the aforementioned flow rate. After about 1250 days, the bubble point pressure is reached.

The gas flow rate increases continuously up to the maximum value of 106 N m3 / day which is reached after about 5000 days. The well discharges to this maximum while the oil flow decreases until the pressure limit at the bottom of the well is reached at about 6500th day. After that, the two oil and gas flows decrease, the simulation ending at the end of 10950 days (30 years). At this time, the average pressure of the tank is just above 50 bars. The production of water appears after 5000 days.

 A second compositional simulation of the reservoir is then repeated with the modeling of the fluid grouped with 7 pseudocomponents. The production profiles produced are essentially the same as those of the simulation with the detailed fluid. This suggests that pseudo-component modeling is adequate to model the fluid phase behavior under reservoir conditions, at least for reservoir study purposes.

 When the "delumping" is applied to the results obtained with the second simulation carried out on the grouped fluid, it is found that there is a concordance between the results obtained after "delumping" according to the invention and those obtained with the first simulation which is performed using state equations adapted to each of the 16 components and / or pseudo-components. The difference lies in the fact that the first detailed fluid simulation requires a computation time of 730 seconds while the overall computation time to perform the second simulation (232 s) and the delumping (27 s) is only 259. seconds, that is to say that the calculation time is reduced by 65% while having excellent results.

Example 2
In this example, the tank is initially completely filled with oil. The oil is produced by a well opening at the bottom of the tank, with a flow rate of 1000 m3 / day.

 Gas is injected through a well in the upper part of the tank, said injection gas not being constituted by a mixture of grouped components, but comprising, in molar percentage, 80% C1, 15% C2 and 5% C3, this composition being used for the simulation with the detailed fluid as well as for the "delumping". For the reservoir simulation with the grouped fluid, the composition of the injected gas is represented in molar percentage by 80% N 2 Cl 2, 15% C 2 O 2 and 5% C 3 C 4; gas injection is carried out at a rate of 500 m3 / day during the first 15 years and 900 m3 / day for the next 15 years.

 As in Example 1, a first simulation with a detailed 16-component fluid model is performed. In the beginning. the flow rate of the injection gas is insufficient to maintain the pressure of the tank, therefore, the bubble point pressure is quickly reached and the gas-oil ratio increases. After 15 years, when the tank pressure is 120 bar, the injection gas flow is increased so that after 30 years, at the end of the simulation, the tank pressure is about 100 bar. .

 A second simulation with the grouped fluid model is performed.

 The same effects are observed as in Example 1, that is to say that the 7-component model is still adequate for modeling the phase behavior of the fluid under the conditions of the reservoir.

 When the "delumping" according to the invention is applied to the results of the second simulation, it can be seen that, thanks to the invention, the calculation time for performing the second simulation (173 s) and the "delumping" (18 s ) is 191 seconds, which represents about 15% of the calculation time required to perform the first simulation with the detailed fluid model, the results being excellent, as in Example 1.

When binary interaction coefficients are introduced, it is found that the concordance is still satisfactory, even if it is not of the same order as that of Examples 1 and 2. For the heavier components, the concordance is almost complete. . Only pseudo-components
CO2-C2 of the pooled fluid gave a relatively low agreement.

On the other hand, the gain on the computation time is still very appreciable since it represents only 35% of the computation time of the simulation carried out on the fluid model detailed with equations of state.

TABLE I

<tb> Component <SEP> Composition <SEP> oil <SEP> initial <SEP> (frac. <SEP> mol.) <SEP>
<tb> N2 <SEP> 0.00080
<tb> CO2 <SEP> 0.02929
<tb> C1 <SEP> 0.64641
<tb> C2 <SEP> 0.04165
<tb> C3 <SEP> 0.04649
<tb> 1C4 <SEP> 0.01569
<tb> NC4 <SEP> 0.02690
<tb> IC5 <SEP> 0.01024
<tb> NC5 <SEP> 0.00948
<tb> C8 <SEP> 0.01915
<tb> C7 <SEP> 0.02003
<tb> C8 <SEP>0; 01995 <SEP>
<tb> Cg <SEP> 0.01391
<tb> C10 <SEP> 0.01120
<tb> CNG1 * <SEP> 0.06644
<tb> CNH? * <SEP> 0.02309
<Tb>
TABLE 2

<tb> Component <SEP> Composition <SEP> oil <SEP> initial <SEP> (frac. <SEP> mol.)
<tb> N2C1 <SEP> 0.64721
<tb> C 2 C 2 <SEP> 0.07094
<tb> C3C4 <SEP> 0.08908
<tb> C5C7 <SEP> 0.05890
<tb> C8C10 <SEP> 0.04435
<tb> CNG1 * <SEP> 0.06644
<tb> CNH? * <SEP> 0.02309
<tb> * CNG1 and CNH2 represent the heavy part of the fluid (C1 1+) divided into two pseudo-components, one (CNG1) found mainly in the gas and the other (CNH2) in the oil.

Claims (1)

1. Simulation method for predicting, as a function of time, a detailed composition of a fluid produced by a reservoir, of the type consisting in: a) representing the reservoir in the form of a mesh network (j) each of which constitutes an elementary volume filled with fluid, b) defining the fluid by modeling grouped with N components and pseudo-components (i) and determining a state equation describing the fluid in this grouped modeling,  c) also defining the fluid by detailed modeling with Q components and / or pseudo-components, Q being greater than N, and determining another state equation describing the fluid in this detailed modeling,  d) realizing, in a manner known per se, a compositional simulation of the fluid grouped with N components and pseudo-components (i), said compositional simulation making it possible to calculate for each cell (j) and at consecutive time steps (m, m + l, ...) at least the vaporized fraction (OJ), the liquid-vapor equilibrium constants (kijm) of each component (i), the injection or production flow rates (sjm) and for each pair of meshes (j, h) the flow rates of the liquid phase (UOJh) and vapor (Um i of the fluid with N components and pseudo-components, and it is characterized in that it further comprises  e) determine, at each step, the time (m) and for each cell (j) the composition of the liquid and vapor phases of the fluid for the detailed modelization with Q components and pseudo-components, from the values of the vaporized fraction (OJ ) and equilibrium constants (km) of the grouped fluid,  f) evaluating for each mesh, at the time step (m + 1), the molar amount of each of the Q components and / or pseudo-components of the detailed fluid from the values corresponding to the time step (m), the flow rates of the phases of the grouped fluid and the compositions of the liquid and vapor phases of the detailed fluid determined in step e), and  g) evaluating, for each production well, the detailed composition of the fluid produced between times t and t 'corresponding to time steps m and m + 1, from the flows of the phases of the grouped fluid and the compositions of the liquid phase and detailed fluid vapor determined in step e). 2. Method according to claim 1, characterized in that the steps e, f and g are implemented at the same time as performing the compositional simulation of the grouped fluid. 3. Method according to claim 1, characterized in that the results of step d are stored and subsequently used for the implementation of steps e, f and g.