MX2008004460A - Method, system and apparatus for numerical black oil delumping - Google Patents

Method, system and apparatus for numerical black oil delumping

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Publication number
MX2008004460A
MX2008004460A MX/A/2008/004460A MX2008004460A MX2008004460A MX 2008004460 A MX2008004460 A MX 2008004460A MX 2008004460 A MX2008004460 A MX 2008004460A MX 2008004460 A MX2008004460 A MX 2008004460A
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Mexico
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calculation
vapor
molar
liquid
oil
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MX/A/2008/004460A
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Spanish (es)
Inventor
Holmes Jonathan
Ghorayeb Kassem
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Schlumberger Technology Corporation
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Publication of MX2008004460A publication Critical patent/MX2008004460A/en

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Abstract

A method for black oil delumping is disclosed which comprises:converting a black oil wellstream into a compositional wellstream thereby enabling the composition and component molar rates of a production well in a black oil reservoir simulation to be reconstituted.

Description

METHOD, SYSTEM AND APPARATUS FOR THE NUMERICAL DEACTION OF BLACK OIL BACKGROUND OF THE INVENTION The subject matter of this specification is concerned with a method, in which an associated system or apparatus and computer programs and storage devices of programs for deconcentration are included. of black oil that is used to convert well flows from a black oil simulation into its constituent components when a compositional representation of the well currents is required. The simulation of black oil deposits still has wide application in the oil industry because it is, from the point of view of calculation, much less demanding than the compositional simulation. However, a main limitation of the simulation of black oil deposits is that it does not provide detailed compositional information necessary for the modeling of processes on the surface. Deconcentration of black oil overcomes this limitation by converting a black oil well stream to a compositional well stream, thereby allowing the composition and molar proportions of components of a production well in a simulation of black oil fields to be reconstituted . This specification reveals an extensive method of deconcentration of black oil based mainly in the compositional information generated in a depletion process that is initially used to provide data for the simulation of black oil in a typical workflow. Examples disclosed in this specification show the accuracy of this method in different depletion processes which include: natural depletion, water injection and gas injection. The specification also presents a technique to exactly apply the method of deconcentration of black oil to wells that find cross flow.
BRIEF DESCRIPTION OF THE INVENTION One aspect of the present invention involves a method for black oil deconcentration comprising: converting a blackwell stream to a compositional well stream, thereby allowing a set of compositional proportions and molar proportions of components from a production well in a simulation of a black oil field are reconstituted. Another aspect of the invention involves a program storage device that can be read by a machine that tangibly implements a set of instructions executable by the machine to perform method steps for the deconcentration of black oil, the steps of the method comprising: convert a well current from black oil to a compositional well stream, thereby allowing a set of compositional proportions and molar proportions of components of a production well in a simulation of black oil fields to be reconstituted. Another aspect of the present invention involves a system adapted for black oil deconcentration comprising: a first apparatus adapted to convert a black oil well stream to a compositional well stream, thereby enabling a set of compositional proportions and molar proportions of components of a production well in a simulation of black oil deposits are reconstituted. Another aspect of the present invention involves a computer program adapted to be executed by a processor, the computer program, when executed by the processor, carries out a process for the deconcentration of black oil, the process comprises: converting a current from a black oil well to a compositional well stream, thereby allowing a set of composition ratio and molar proportions of components of a production well in a simulation of black oil fields to be reconstituted. Additional scope of application will be evident from the detailed description presented later in to present. However, it should be understood that the detailed description and specific examples summarized later herein are given by way of illustration only, since various changes and modifications within the spirit and scope of the "black oil deconcentration" method, as describes and claims in this specification, will be obvious to the experienced in the art from a reading of the following detailed description.
BRIEF DESCRIPTION OF THE FIGURES A full understanding will be obtained from the detailed description presented later herein and the attached figures which are given by way of illustration only and are not intended to be limiting in any way and in which: Figure 1 illustrates a multipurpose multi-platform reservoir and network coupling controller in a reservoir / coupled network system adapted to perform a pressure interaction between a reservoir and a restricted surface equipment network or to predict the behavior of several fields, which may have different fluid compositions, which share a common surface equipment; Figure 2 illustrates the reservoir and network coupling control of Figure 1, wherein the controller includes elements of oil deconcentration formation black adapted to carry out the deconcentration method of black oil that is used to convert well flows from a black oil simulation into its constituent components when a compositional representation of the well currents is required; Figures 3, 4 and 5 illustrate an integrated system representing the reservoir / coupled network system of Figures 1 and 2, where, for example, the coupling controller converts a description of black oil fluid from a reservoir simulator. to a description of compositional fluid for use by a surface network model, such as the surface network model of Figure 1; Figure 6 including Figures 6a and 6b illustrate a phase graph for the fluids used in the examples; Figure 7 including Figures 7a and 7b illustrate Example 1; Figure 8 including Figures 8a and 8b illustrate the deconcentrated composition of Example 1; Figure 9 including 9a and 9b illustrate example 2; Figure 10 including 10a and 10b illustrates example 2; deconcentrated composition; Figure 11 illustrates example 3, the production of field gas against time; Figure 12 including figures 12a and 12b illustrates example 3, deconcentrated composition; Figure 13 illustrates example 3, gas production velocity versus time for well PA4 and gas injection velocity of the three well consumations PA4; Figure 14 including Figure 14a and 14b illustrates Example 3, Well PA4; Figures 15 and 16 including Figures 15a, 15b, 15c, 16a and 16b illustrate Example 4; Figure 17 illustrates Example 4, total and gas-free production speeds against time, well PA1; Figure 18 illustrates Example 4, the molar fraction of methane from the field against time and Figure 19 illustrates Example 4, the molar fraction of methane from well PA1 against time.
DETAILED DESCRIPTION Referring to Figure 1, a multiplatform reservoir coupling controller and general purpose network 10 in a coupled reservoir / network system 12, which represents an integrated surface and subsurface modeling system is illustrated. The coupling controller 10 is adapted to analyze a pressure interaction between a reservoir simulator 16 and a restricted surface equipment network 14 or to predict the behavior of several reservoir fields that may have different fluid compositions and share a common surface equipment. The reservoir and network coupling controller 10 in the coupled reservoir / network system 12 of Figure 1 is fully described and summarized in the international publication number WO 2004/049216 Al, published on June 10, 2004, based on the international application number PCT / US / 2002/037658 filed on November 23, 2002, the disclosure of which is incorporated by reference to this specification of this application. The "controller" 10 is a "field management" system and its objective is to apply time-dependent controls and operations in the production and injection wells in one or more reservoir simulation models. In addition to reservoir simulation models, the controller 10 can also communicate with one or more surface equipment models 14 (such as a pipe network model), since the conditions of this integrated system part can feed back as well constraints in reservoir simulation models 16. One way in which controller 10 communicates with the other applications of programming elements is detailed in the international application number WO 2004/049216 Al referenced previously. In Figure 1, the coupling controller 10 (a field management tool) communicates with a selection of reservoir simulators 16 and surface network simulators 14 via a communication interface 18. Controller 10 manages the balance of reservoirs and surface networks and synchronizes their progress to through time The controller 10 also applies the global production and injection constraints and converts the hydrocarbon fluid streams between the different sets of pseudo-components used in the simulation models. In Figure 1, the integrated surface and subsurface modeling system 12 of Figure 1 includes a reservoir coupling controller and multiplatform network 10 that is adapted to affect the development and field optimization of the reservoir by analyzing a pressure interaction. between a reservoir 16 and a restricted surface equipment network 14 or by predicting the behavior of several reservoir fields that may have different fluid compositions that share a common surface equipment. The controller 10 implements a method for integrated reservoir and surface equipment simulations that includes: communication between the multiplatform and network reservoir or coupling controller 10 and at least one reservoir simulator 16 and controller 10 and at least one surface network simulator 14 (hereinafter referred to as the "communication stage"). He surface and subsurface modeling system 12 includes a communication interface 18 which is associated with the reservoir simulator 16 and the controller 10 and the surface network simulator 14, the communication interface 18 is adapted to handle an equilibrium of the simulator of reservoir 16 and the surface network simulator 14 by synchronizing the advance of the reservoir simulator 16 and the surface network simulator 14 over time. The communication stage referred to above includes communicating, via the controller 10, with the reservoir simulator 16 and the surface network simulator 14 via the communication interface 18, the interface 18 enables the application of the reservoir simulator. 16 and the application of surface network simulator 14 for exchanging data. When the communication interface 18 is enabled, the controller 10 is adapted to interact in a defined dialogue with the reservoir simulator 16 and the surface network simulator 14, the dialog includes execution commands, setting or adjustment commands and commands for question. In addition, the communication stage includes coupling the reservoir simulator 16 to the surface network simulator 14. The coupling step includes coupling, via the controller 10, a single reservoir simulator model 16 to the application of the network simulator 14. ' surface. When the controller 10 couples the individual reservoir simulator model 16 to the application of surface network simulator 14, a hermetic delayed coupling scheme is applied, the hermetic scheme balances the application of network simulator 14 with reservoir simulator application 16 in each Newton interaction of the time stage calculation of the reservoir simulator. The coupling step further includes coupling, via the controller 10, two or more reservoir simulator models 16 to the surface network simulator application 14. The two or more reservoir simulator models 16 are subject to common global reductions and when the controller 10 couples the two or more reservoir simulator models 16 that are subject to global constraints common to the surface network simulator application 14, a loosely coupled scheme is applied where, during the loose coupling scheme, reservoir simulator models 16 are balanced with respect to their global constraints at the start of each synchronization step in controller 10 and after that, each model Reservoir simulator progresses independently at the start of a next synchronization stage. Referring to Figure 2, controller 10 of Figure 1 includes "black petroleum deconcentration programming elements" 20 adapted to implement a "black oil deconcentration method" which is used to convert water well currents from ablack oil simulation (F) the "black oil well stream") to its constituent components (ie, a "compositional well stream") when a compositional representation of the well currents is required. Once the "black oil well stream" is deconcentrated to a "compositional well stream", that is, when the "molar proportions of components" are calculated, the "compositional well streams" can be used for different purposes which include: (1) feeding, as input, a simulator of process equipment since the compositional information is in general a requirement for these simulators and / or (2) in the case where a black oil simulator, such as the reservoir simulator 16 of Figure 1 is coupled to a compositional network simulator, such as the surface network simulator 14 of Figure 1, the deconcentrated compositional stream is used to provide the network simulator 14"data input "(for example with" compositional border compositions "). In Figures 1 and 2 the need for "black oil deconcentration" would arise in the following context: one or more reservoir simulation models 16 may have a "description of black oil fluid" for computational efficiency. However, the controller 10 may require a "compositional fluid description" of this fluid in order to be consistent with the "fluid descriptions" in the other models to which it is coupled, such as the "surface network model" 14. Otherwise the container 10 may be required to issue a "description of compositional fluid", where the "description of compositional fluid" is provided. as input data to a "process equipment model". Referring to Figure 3, by way of example, the controller 10 converts the "black oil model" of the reservoir simulator 16 to a "compositional model" (having M hydrocarbon components) for the surface network 14. The conversion mentioned above is carried out by means of the "black oil concentration method" 22 as shown in Figure 3 which is carried out by means of the "black oil concentration programming elements" 20 of Figure 2. Referring to Figure 4, by way of example, the controller 10 also "converts" the "black oil model" of the "black oil simulator" 16b represented by the reservoir simulator (2) 16b to a "compositional model"; however, this "conversion" takes place in such a way that the fluid of the "black oil simulator" 16b is converted to the same set of components as the compositional reservoir simulator 16a represented by the reservoir simulator (1) 16a. Then the controller 10 uses a unified fluid model for the co-mixed production of both reservoirs. This "conversion" is carried by the "black oil concentration method" 22 of Figure 4 which is carried out by the "black oil concentration programming elements 20 of Figure 2. Referring to Figure 5, by way of example, the controller 10 converts the "black oil model" of the black oil simulator 16d represented by the reservoir simulator (2) 16d to a "compositional model", however, this "conversion" takes place in such a way that the fluid of the "black oil simulator" 16d is converted to the same set of components as the compositional reservoir simulator 16c, then the controller 10 uses a unified fluid model for the co-distilled production of both reservoirs and communicates the molar proportions of the resulting component to the Surface network simulator 14. The conversions mentioned above are carried out using the "black petroleum deconcentration method" 22 as shown in Figure 5, which is carried out by means of the "black petroleum deconcentration programming elements" 20 of Figure 2.
"Black petroleum deconcentration programming elements" of Figure 2. As indicated above, controller 10 of Figures 1 and 2 includes "programming elements of deconcentration of black oil "20 that are adapted to carry out a" black oil deconcentration method "that is used to convert well flows from a black oil simulation (ie, a" black oil well stream ") ) to its constituent components (ie, a "compositional well stream") when a compositional representation of the well currents is required The "black oil well stream" is deconcentrated to the "compositional well stream" where the calculate the "molar proportions of components." In the following paragraphs of this specification, the "black petroleum deconcentration programming elements" 20 of figure 2 that carry out the "black oil deconcentration method" will be discussed in more detail with reference to Figures 6 to 19. A "black petroleum deconcentration method" converts a black oil "to a" compositional well stream ", thus allowing the composition and molar proportions of a production well in a simulation of a black oil field to be reconstituted. The "black petroleum deconcentration method" is based primarily on compositional information generated in a pooling process that is initially used to provide data for a simulation of black oil in a typical workflow. Examples show the accuracy of this deconcentration method of black oil in different depletion processes, such as natural depletion, water injection and gas injection. In addition, a method to exactly apply the method of deconcentration of black oil to wells that cross flow is also revealed. With advances in computational speed, it is becoming more common to employ a description of complete compositional fluid in the stimulation of hydrocarbon reservoirs. However, the faster computers become, the stronger the tendency of simulation designers to integrate more challenging and thus more CPU-intensive models. Compositional simulation in multimillion-cell models of today is still practically not feasible. The representation of black oil fluid is a proven technique that continues to find wide application in reservoir simulation. However, an important limitation of the simulation of black oil deposits is the lack of detailed compositional information necessary for the modeling of the surface process. The technique of "black oil deconcentration" described in this specification provides the necessary compositional information, still adds negligible calculation time to the simulation.
Deconcentration of a black oil well stream consists of recovering the detailed molar proportions of the components to convert the "black oil well stream" to a "compositional well stream". Reconstitutes the molar compositions and proportions of components of the production stream. The deconcentration of black oil can be obtained with different degrees of accuracy by using fluctuating options to establish the composition of constant gas quantity for the run to use the results of a depletion process (CVD, CCD, DL, ...) . The simplest method is to assign a fixed composition (molar fraction of component) to oil and gas inventory-tank. This could be applied throughout the reservoir or if the properties of the hydrocarbon mixture vary across the reservoir, different oil and gas compositions can be related at any time during the run. Some black oil simulators have an API traffic element that allows oils of different properties to mix within the reservoir. The PVT properties of the petroleum mixture are parameterized using the density on the oil surface. To provide a deconcentration option compatible with API traffic, tank-inventory oil and gas compositions can be tabulated against the density of the oil to surface conditions. The third option, which offers the greatest accuracy, is to provide tables of molar fractions of reservoir liquid and vapor components against saturation pressure. These can be obtained from a depletion process, ideally the same process that was initially used to generate the PVT tables of black oil. This technique, as shown in this specification, provides very accurate results in the natural depletion process and production process that involve reservoir network-pressurization by water injection. Weisenborn u Schulte1 (see references later in this) reported a similar deconcentration technique. However, they used block-grid pressure instead of saturation pressure (or saturation pressure averaged in the case of multiple grid-cell connections that cover well conservation) in the deconcentration scheme. The latter, as will be shown, provides better results in the case of production processes that involve reservoir re-pressurization by water injection. Deconcentration of black oil based on the composition tables against saturation pressure may not provide an accurate well current composition in the production process involving gas injection. This is the case when the exhaustion experiment and consequently the resulting vapor and liquid composition against the saturation pressure may not properly account for the pressure and gas composition injected into the well stream. In this situation, using tables of liquid and vapor composition against the gas / oil ratio of the liquid phase (Rs) and / or the proportion of oil and / or gas from the vapor phase (Rv) for the deconcentration process improve accuracy, as will be illustrated. Another important aspect of the deconcentration of black oil is the level at which deconcentration takes place: at the well level or the level of consumption. Deconcentration at the level of completion may be necessary in the case of deposits with multiple regions of PVT description, because different consumptions at the same point may be located in different regions of PVT. This will be discussed later in this specification. Finally, special care must be taken in the case of production wells that undergo cross flow, where some of the fluid mixture in the borehole is reinjected into low pressure layers. The speed of "injection" in these consummations must be appropriately taken into account as described hereinafter.
Formulation The following formulation applies to the deconcentration of black oil both at the well level and at the well completion level. Here deconcentration methods using one of the following tables are described: - Liquid / vapor composition against saturation pressure averaged at liquid / vapor mass velocity; that is, the average of the saturation pressure with respect to the well (or consummation), grid-cell connections, weighted by the mass velocity of the liquid / vapor of the connection. This is mainly appropriate for production harvests of natural depletion and processes that involve water injection. Note that when the consummation covers only one grid cell, the average saturation pressure of the completion is reduced to the saturation pressure of the fluid in the grid cell. - Oil / gas composition against density on the oil surface. This is mainly suitable for black oil tracking API models (which allows blends of different types of oil with different densities on the surface and properties of PVT). Liquid / vapor composition against Rs and / or Rv. This is mainly appropriate for production processes involving gas injection. The formulation considers the general context of a live oil black oil / gas humidification model.
The deconcentration of black oil for simpler oil models (that is, models of live oil / dry gas and dead oil / dry gas) is a particular case of this general population. The purpose of the deconcentration process is to recover the mole fraction of components (total composition) Zi, i = 1, ..., JV, where N ° is the number of components. The molar proportion of components n ±, i = 1, ..., if is then simply the product of the total molar ratio multiplied by the mole fraction of the component. In the following calculations, liquid and vapor refer to the existing hydrocarbon phases at the reservoir conditions, while oil and gas refer to the hydrocarbon phases to tank-inventory conditions. The deconcentration process comprises the following three stages: Stage 1. Calculation of phase mass velocity From mass conservation, the mass velocities of the vapor and liquid phases are definitely given by: Q: = QÍ + Q °, (i) v a -er + Gf. (2) ? Cm? '> t \? mt- In Equations (1) and (2), the symbols and denote the mass velocities of free gas, vaporized oil, liquid petroleum and dissolved gas, respectively. These amounts can be obtained from: QJ0 = p? ", (4) Qm ° L = pYL > (5) and Qt = PeqsL (6) In the above, qs ", qoV, q ° L. and denote the volumetric velocities of free gas, vaporized oil, liquid petroleum and dissolved surface gas respectively and p9 and p ° are the densities of gas and oil, respectively.
Stage 2. Calculation of phase composition The molar fraction of phase components (molar fractions of vapor and liquid components x ±, i = 1, ..., N °) the calculation takes place through a look-up table. First, the amount on which the table is based is calculated (if required) : - The saturation pressure averaged in mass velocity of liquid (vapor). - The gas / oil ratio of liquid phase (Ri = qgi / qoi) and / or the oil-vapor / gas ratio (RV = qgV / qoV). Once this is done, the table query is performed to obtain the vapor and liquid compositions.
Step 3. Calculation of total composition and molar proportions of components The total composition z of component i (i = -l, ..., lf) is related to the molar fractions of vapor and lyauid components and, - and Xi, respectively by: where a is the vapor fraction defined by: nv and nL are the total number of moles in the vapor and liquid phases respectively. Equation (8) can be written as: a = mv¡Mv mylMv + mLlML "(9) mV, Mv, mL and M1, are the mass and molar weight of the vapor and liquid phases respectively. In terms of molar proportions, a can be written as: where Q ?, and Q are calculated as described above. The molar weights of vapor and liquid Mv and? ^, Respectively, are given by: N 'Mv =? YtMl (11) ¡= \ v,, ML = ?? t.M. { (12) Knowing the total composition, the mass vapor velocity (liquid) of the component i = 1, ..., N ° is the product of the mass velocity of total vapor (liquid) multiplied by the mole fraction vapor of the component (liquid) and ? (i) Having calculated the molar fractions of the component z ±, i = 1, ..., -Vo, the molar proportions of components n ±, i = 1, ..., N ° are calculated directly: n ^ = (nv + nL ) z ±, i = 1, ..., N °.
Deconcentration of black oil at the completion level A well connects to the simulation grid by means of a set of grid-cell connections. For the purpose of regulated work operations, the simulator can concentrate connections together in consummations; all connections in the same consummation are opened or closed together. In the case where there is a cross flow in a production well, some of the connections could be injected instead of produced. Even within the same consummation, some connections could be producing and others could be injecting (especially if connections in layers of sites that communicate poorly are concentrated in the same consumption). A consummation in a production well could therefore have a production speed as well as a production speed. Thus, the rate of completion must be taken into account when calculating the molar proportions of the production well component based on those obtained by deconcentrating each black oil stream from completion to a compositional stream. Consider that a well has n consummations. In general, some (or rodas) connections at a completion may be injecting due to cross flow. Both oil and gas injection can take place at the injection connections. In a model of black oil wet gas / live oil is denote the gas free, vaporized oil, liquid petroleum and speeds volumetric surfaces of dissolved gas production respectively, for consumption k. These are the flow velocities of the production speeds at the given consummation. Be ? and n ° denoting the "speeds of production" of gas and oil of "coarse" surface volume of the production well respectively defined as: S ° In the following, it is assumed that 9p * "p SOn both> 0 (for a production well.) Let #ft and <? # Denote the gas and oil injection velocities of surface volume of the consummation k respectively.
These are the flow rates of the injection connections at the given consummation. Be 9? Qr denote the "injection rates" of gas and oil of surface volume of the production well, respectively: ? =? to 06) Let q and q denote the gas and oil production velocities of the surface volume "targets" of the well of production, of and qf are both > 0 (for a production well). «* = ?? -? / =? for + ró -? i) (17) ? '-? J-í /' -? Te +? Í-? I) (18) In a process of deconcentration of black oil at the consummation level, the production speeds of the completion must be adjusted to take into account the injection connections of the well. The injection speeds of the well ^ I J ^ I are distributed among all production consumptions according to their global production speeds.
Be 4Ík > > ? £ and qlí denote the adjusted values of < jpk > Vn s In and Qn, respectively. These adjusted values must satisfy: This is how the following applies: * - (- $ * -: - (21) 9 «i -MI 1n > (2. 3) Note that since in a pOZo e production, (l -? //? l) is always < 1. The same applies for (i - ?, 0 / ??) This implies that q, q%, q ^ "and q% are all > 0 Deconcentration procedure The ECLIPSE black oil and compositional reservoir simulator is used in this specification. The "Eclipse" simulator belongs to and is put into operation by Schlimberger Tevhnology Corporation of Houston, Texas. The deconcentration of black oil in this specification is done using the reservoir-to-surface link programming elements, R2SL®, which is linked to ECLIPSE through an open interface.2,3 (see references later in this). The following is a brief description of the procedure used to implement deconcentration of black oil well run at the well level. The black oil deconcentration method uses the liquid composition (vapor) tables against saturation pressure. Similar processes are used for the other deconcentration methods. - It interrogates the well information specifically needed for the deconcentration of the black oil well current (as described in the previous equations). This information includes: - Free and solution gas and oil speeds.
- Gas and oil densities on the surface. - Average saturation pressure in the connected grid blocks of the well weighted by the liquid mass influence velocity. - Average saturation pressure in the connected grid blocks of the well weighted by the mass flow rate of steam. - It uses the steam composition table (liquid) against the dew point (bubble point) of the well to calculate molar fractions of the vapor (liquid) component (composition). Having only one row in the table implies a vapor composition against constant saturation (liquid). Calculate the molar weights of liquid vapor based on the vapor and liquid compositions calculated using equations 11 and 12. - Calculate the mass velocities of liquid and vapor using Equations 1 through 6. - Calculate the vapor fraction based on the Equation 10. - Calculate the molar proportions of components and total composition used in Equation 7.
Exemplary applications A set of examples is presented in which the accuracy of the deconcentration technique is investigated. a variety of production processes and reservoir behavior: reservoir re-pressurization by means of water injection (Example 1). - Deposits with multiple fluid regions (Example 2). - Wells that find cross flow (Example 3). - Gas injection (Example 4). The validation process involves mainly comparing the composition of the well with respect to the time of a compositional reservoir model with the deconcentrated black oil well current of an equivalent black oil model. In all the examples (unless indicated otherwise), the following descriptions apply: - The deposit has three layers. The deposit has seven producers (with different extractions) and injectors and three water injectors. - The reservoir temperature is fixed at 140 ° (284 ° F). - The same set of components / pseudo components is present. - The Peng-Robinson equation of two state parameters is used in the compositional models also as in the depletion processes used to generate the PVT properties of the black oil models. A constant volume depletion (CVD) scheme is used to construct the black oil model. - The oil production speed of the deposit is set at 5000 STB / D. The wells are adjusted to produce, when possible, equal compartments of field oil production limits. - The fluid in the reservoir is initially liquid (the pressure is higher than the bubble point pressure in each layer of the reservoir). The following economic limits apply to production wells: - Minimum oil production speed of 250 STB / D. - Maximum water cuts of 0.7. - Maximum gas / oil ratio (GOR) of 5.0.
Referring now to Figure 6. Also refer to "Table 1" which is summarized below at the end of this specification. Table 1 shows the set of components / pseudo-components and the fluid compositions used in the following examples. In Figure 6, the pressure / temperature diagrams corresponding to these compositions are illustrated in Figure 6. Examples 1, 3 and 4 use Fluid 1 where different layers are initialized with different fluids in Example 2.
Example 1 - Water Injection This example shows that deconcentration using composition tables against saturation pressure provides highly accurate results in natural depletion processes and production processes involving reservoir re-pressurization using injection water. Deconcentration in this example takes place at the well level. These results were compared with those obtained in deconcentration at the consummation level and no significant difference was observed. Note that each consummation consists of a single grid-cell pressure in this example (as is also the case in all other examples). The initial composition for this example is that of Fluid 1 (see Table 1). The initial pressure in the reservoir is 500 pounds force / inch2. The entire deposit is initially in the liquid phase (subsaturated). The oil is produced at a constant total speed of 2500 STB / D through seven wells. A CVD depletion process was used to integrate the oil / gas black oil model damp . An attempt was also made to use a black oil model that contains dry gas (instead of wet gas), but this gave a significant discrepancy in the time of gas burst and the composition of the deconcentrated black oil well stream. This is expected, since the quality of the deconcentrated results are directly related to the quality of the black oil model. A natural depletion process is applied for the first three years. The re-preselection by water injection, injection twice the volume of the deposit of the produced fluids is applied in the remaining production time (5 years). Refer to Figure 7 (a). The average reservoir pressure decreases to approximately 4200 pounds / inch2 at the end of the third year and increases back to around 4500 pounds / inch2 (which is greater than the bubble point pressure) at the end of the seventh year, as shown in Figure 7 (a). Note that reservoir repressurization by water injection is taken into account in the deconcentration process when using the hydrocarbon vapor-liquid composition against averaged liquid / vapor phase saturation pressures instead of using "average pressure" "of the well (see Appendix A summarized later in this). When the pressure increases in a grid due to water injection, the saturation pressure does not increase correspondingly; therefore, using the pressure in place of the saturation pressure can result in a substantially erroneous deconcentrated black oil stream. Refer to Figure 7 (b) and Figure 8. Figure 7 (b) shows gas production over a period of eight years. There is an excellent correspondence between the compositional model and the deconcentrated black oil model. Figure 8 shows the composition of methane (a) and the composition of the pseudo-components (C7-C? 2) (b) against time. As with the speed of gas production, the composition of the deconcentrated black oil well run is in very good agreement due to the run of the well of the compositional model.
Example 2- Regions of multiple fluids This example illustrates the accuracy of deconcentration schemes in the case of reservoirs with multiple fluid regions. Referring to Table 1 summarized later in this, in the compositional model, fluids 1 are used, 2 and 3 (shown in Table 1) to initialize the bottom, middle and upper layers of the deposit, respectively. Note that the methane content decreases by depth in so much that the molar fractions of the heavy components and pseudocomponents increases with depth. The initial reservoir pressure is 5000 pound / inch2, which is slightly higher than the liquid bubble time pressure at the top of the reservoir. The black oil model has three PVT regions corresponding to the fluid regions in the equivalent compositional models. Referring to Figures 7 (a) and 9 (a), referring initially to Figure 9 (a), the black oil model is in agreement with the compositional model in terms of gas velocity versus production time. An agreement, between the compositional model and the equivalent black oil model in the example, however, is not as much in agreement as that observed in Example I, with reference to Figure 7 (a). The black oil model was not refined to obtain a better agreement. The deconcentration of black oil takes place at the consummation level in this example. Consequently, three different sets of tables are used to deconcentrate the black oil stream from well consumations belonging to the three reservoir layers. Then the composition of the deconcentrated well stream is calculated as described in the Formulation section. Referring to Figure 9 (b), a process of Natural depletion is applied during the first three years. A replacement water injection scheme of 100% emptying is applied for the remaining production time (5 years). The average reservoir pressure decreases to usually 281 kg / cm2 (4000 pounds force / inch2) at the end of the third year and increases back to around 299 kg / cm2 (4250 pounds / inch2) at the end of the eighth year as shown in Figure 9 (b). Referring to Figure 10, the methane composition and the composition of the pseudo-component of C7-C? 2 against the time illustrated in Figure 10 shows a good correspondence between the compositional model and the deconcentrated black petroleum model.
Example 3 - Well with cross flow This example is similar to Example 1 with one main difference: the three layers of the reservoir are initialized with different pressures, causing the wells to have cross flow. A natural depletion process is applied during the first three years. A replacement water injection scheme of 100% emptying is applied for the remaining production time (5 years). The initial pressures of the three layers are as follows: 387 kg / cm2 (5500 pounds force / inch2) (top), 377 kg / cm2 (4800 pounds force / inch2) (average) and 457 kg / cm2 (6500 pounds force / inch2) (background). However, all three layers use the same PVT model: that of Fluid 1 (see Figure 6). The initial pressure in these three layers is greater than the bubble point pressures, that are of 348 Kg / cm2 (4958 pounds force / inch2) (superior), 332 Kg / cm2 (4722 pounds force / inch2) (average) and 318 Kg / cm2 (4522 pounds force / inch2) (depth). Referring to Figure 11, Figure 11 illustrates the gas velocity over time of both the compositional model and its equivalent black oil model. The results of these Figures show a very good agreement between the two models. Referring to Figure 12, the composition against time of the two models in Figure 12 is presented. Referring to Figures 13 and 14, referring initially to Figure 13, the cross flow occurs mainly during the first few months of production and later during the first part of water injection. Figure 13 shows the gas production rate of a producer and the gas injection velocity due to the cross flow of the three well consumptions. The consummation 3 in the Figure corresponds to the bottom layer. Due to the higher initial pressure in this layer, consummation 3 is the only one that produces in the first few months while consumations belonging to the low pressure layers injected due to cross flow. The gas production rate against time and the mol fraction of methane against the time for the PA4 well of both the compositional model and its equivalent black oil model are shown in Figure 14, which shows a very good correspondence in terms of deconcentrated black oil stream despite the substantial cross-flow that takes place.
Example 4 - Gas Injection The objective of this example is to discuss issues related to the deconcentration of black oil in the presence of gas injection. The initial composition of the reservoir corresponding to this example is that of Fluid 1 (see Table 1). The initial pressure in the deposit is 387 Kg / cm2 (5500 pounds / inch2) and the entire deposit is initially in the liquid phase (subsaturated). No water injection takes place in this example. A replacement gas injection scheme with 80% emptying is applied from the beginning of the production process. Field production is limited to 10,000 RB / D.
This speed is equally distributed among the producers (when it is possible) . Unlike the three previous examples, no economic limits apply.
Referring to Figures 15, 16 and 17, Figure 15 shows the field gas velocity, the field GOR and the reservoir average pressure of the compositional model as well as its equivalent black oil model. Since the majority of the deposit is mainly in the subsaturated region during production, a good correspondence between these two models is obtained. Figure 16 shows the gas velocity and the GOR for the PA1 well of both models. PA1 is the first well that experiences gas inrush, which occurs in the fifth year of production, as shown in Figure 17, which shows both the total gas production velocity and the velocity of free gas production. As you can see from these figures, there is a better match in terms of GOR before the injection takes place. The deconcentration of black oil in this Example is effected using tabulated liquid and vapor composition against Rs. Appendix B details the process through which these tables are obtained. Deconcentration takes place at the well completion level. Referring to Figures 18 and 19, these figures (18 and 19) present the mole fraction of methane against the time of both the compositional model and its equivalent black oil model. Excellent correspondence is obtained in the production period before the gas emission. The deconcentrated compositional current coincides less barely after the gas emission, however, the results are acceptable. Note that this correspondence is obtained although the vapor composition table against Rs assumes that the entire gas cap is in equilibrium with the gas phase. A general conclusion can be drawn from the previous examples: the level of agreement between the black oil model and its equivalent compositional model, in terms of composition (molar proportions of component or molar fractions) against the production time is proportional to the agreement between the two models in terms of gas production (or petroleum9 versus time.) The higher the quality of the black oil model (compared to the compositional model), the better the agreement between the two models in terms of composition against The deconcentration method presented in this specification uses tables of composition of liquid and vapor against saturation pressure, systems usually obtained from a depletion process.This method allows to recover the greatest detailed compositional information possible in a process of deconcentration of black oil , provided that the pressure intervals of s Attainment in those tables are the same as those in the black oil PVT tables (obtained, basically, using the same exhaustion simulation). Having finer pressure intervals than those of the PVT tables of black oil do not necessarily result in a better description of compositional fluid. More research is necessary in the case of production processes that involve gas injection in the saturated region. It should be mentioned that black oil modeling could basically fail to stimulate the process exactly in such configurations.
Nomenclature B ° = oil formation factor, L3 / L3, RB / STB CC = constant composition depletion D CV = constant volume depletion D DE = differential release GO = gas / oil ratio L3 / L3, Mscf / STB R Hw = bore head pressure, m / Lt2, pound force / inch2 m = mass, m, lbm M = molecular weight, m, lbm / mol Mf = mobile phase n = number of moles PV = pressure / volume / temperature T p = pressure, m / Lt2, pound force / inch2 pw = bottom hole pressure, m / Lt2, pound force / inch2 q = surface volumetric velocity q = gas surface volumetric velocity, m3 / t, Mscf / D g ° = volumetric velocity of oil surface, m3 / t, STB / D Q = mass velocity, m / t, lbm / D Rs = gas / oil ratio of liquid phase, L3 / L3, Mscf / STB Rv = proportion of oil / gas in the aqueous phase Tw = transmissibility factor t = time, t, years x = liquid composition (molar fractions of component) and = vapor composition (molar fractions of component) z = total composition (molar fractions) of component) p & = surface gas density, m / L3, lbm / Mscf p ° = surface oil density, m / L3, lbm / Mscf Subscripts 0 = initial state a = adjusted bu = bubble point b 1 = injection I = injection i = components j = well connection k = well completion m = mass P = production s = surface v = volume Superscripts f = phase g = gas L = liquid or = oil V = vapor References "References" that are incorporated by reference to this specification. 1. Weisenborn, A. J., and Schulte, A.M. : "Compositional Integrated Sub-Surface-Surface Modeling," document SPE 65158 presented at the European Petroleum Conference SPE, Paris, France (October 24-25, 2000). 2. Ghorayeb, K. et al: "A General Purpose Controller for Multiple Coupling Reservoir Simulations and Surface Facility Networks," document SPE 79702 presented at the SPE 2003 Reservoir Simulation Symposium, Houston, Texas, United States of America (February 3-5, 2003). 3. Ghorayeb, K., Holmes, J.A. , and Torrens R.: "Field Planning Using Integrated Surface / Subsurface Modeling," document SPE 92381 presented at the 14th Middle East Oil and Gas Show and Conference, Bahrain (March 12-15, 2005). 4. Barroux, CC. et al: "Linking Reservoir and Surface Simulators: How to Improve Coupled Solutions," document SPE 65159 presented at the European Petroleum Conference SPE, Paris, France (October 24-25, 2000).
Appendix A - Average well pressure The following is a summary of the calculation of average well pressure (pressure4 equivalent grid-block). The inflow performance ratio can be described in terms of the volumetric production speed in each phase at inventory tank conditions such as: where: q is the volumetric flow velocity of phase f in connection j to tank-inventory conditions. The flow is taken as positive from the formation to the well and negative from the well to the formation.
T is the connection transmissibility factor, ME is the phase mobility in the connection PJ is the pressure in the grid block that contains the connection. PJ is the hole pressure from the bottom of the well and A. is the head of the hole pressure between the connection and the data depth of the bottom hole By adding all grid cells Ng you get: (26 > The average pressure of ~? Zo is defined by: P ° = tWjPjltWj (27) The phase against the highest mass velocity is selected in Equation 27.
Appendix B - Query Tables for Example 4 Black petroleum deconcentration tables for Examples 1, 2 and 3 were generated automatically by the programming elements package used to simulate the black oil model (CVD) friction process. This is not the case for the tables used for deconcentration of black oil in Example 4 (involves gas injection). In Example 4, an experimental swelling-test simulation is carried out to investigate the effect of the injected gas on the behavior of the fluid. This consists of adding prescribed volumes of gas to G0R1 given (volume of gas injection at standard conditions per volume of original reservoir fluid at its saturation pressure). Among other information, the experiment provides tabulated liquid composition against GOR1. The experiment also provides tables for vapor composition (in equilibrium with the liquid) against GOR1.
Let R50 denote the proportion of gas-oil in the initial mixture (corresponding to zero injected gas). The proportion of gas-liquid oil that corresponds to a given aggregate volume of gas can be approximated by the following: Rs = - ^ r- - (28) where v - V5L denote the volumes of gas and oil resulting from the instantaneous vaporization of a volume of liquid (without injected gas) to surface conditions; ? F is the volume on the surface of the gas injected. In Equation 28, the following is assumed: • The volume of the gas in the total surface is equal to the sum of the volume of the gas in the injected surface and the volume of the gas in the surface in liquid phase. • The injected gas does not affect the surface oil volume of the liquid phase. Equation 28 implies: Rs = RS0 + GOR, xB ° (29) where B "is the oil formation volume factor (of the order of 2.1 Rb / STB in Example 4). The liquid and vapor composition tabulated against Rs are thus used in the deconcentration of black oil in Example 4.
Conversion factors of the international metric system "F (° F + 459.67) /1.8 = K Mscf x 3.048 * E + 02 = m3 STB x 1,589 873 E-01 = m3 psi x 6,894 757 E + 00 = pa * E1 factor of conversion is accurate Table 1 Molar fractions of components for the three fluids used in the examples.
The above description of the method of "deconcentration of black oil" is thus provided, it will be obvious that in the same way it can be varied in many ways. Such variations will not be considered as deviation from the spirit or scope of the method or apparatus or storage device of claimed programs and that all of such claims would be obvious to one skilled in the art which is intended to be included within the scope of the following claims:

Claims (26)

  1. CLAIMS 1. A method for the deconcentration of black oil, characterized in that it comprises: converting a black oil well current to a compositional well current, thereby allowing a set of molar proportions of composition and components of a production well in A simulation of a black oil deposit is reconstituted.
  2. 2. The method according to claim 1, characterized in that the deconcentration method is adapted to recover molar proportions of components ni, i = l, ..., lf, where N ° is the number of components and where the molar proportion of components is the product of the total molar ratio multiplied by the mole fraction of the component and wherein the conversion step comprises: (a) performing a phase mass velocity calculation; (b) carry out a calculation of phase composition and (c) perform a calculation of the molar velocities of total components 3. The method according to claim 2, characterized in that the execution of step (a) to carry out the Phase mass velocity calculation comprises: performing the phase mass velocity calculation where the mass velocities of the vapor and liquid phases are given respectively by: oV Qm * = Q? "v + Q m, > Y They denote mass velocities of free gas, vaporized oil, liquid petroleum and dissolved gas respectively. 4. The method according to claim 3, characterized in that the symbols Q t? And *) Q ° t- and g * are obtained from the following expressions: Q ° = p ° qoy, ß ° L -? Or "oL. = P? " Y and where qfv, q ° v, q ° L and c denote volumetric velocities at the surface of the free gas, vaporized oil, liquid petroleum and dissolved gas respectively; and p9 and p ° are the gas and oil densities at the surface, respectively. 5. The method according to claim 2, characterized in that the execution of step (b) to perform the calculation of compositions per phase comprises: (bl) performing a molar fraction calculation of the phase component, stage (bl) of execution includes, calculate an amount, the quantity is selected from the group consisting of: a saturation pressure averaged of liquid mass velocity (steam), a petroleum gas / oil ratio in liquid phase R > ~ 1 '9 -', and a ratio of oil / gas in the vapor phase and using the amount to obtain representative values of the vapor and liquid compositions. 6. The method according to claim 2, characterized in that the execution of step (b) to perform the calculation of molar velocities of the total composition and components comprises: performing the calculation of total composition wherein the molar fraction z ± of the component i (i = l, ..., l) is related to the molar fractions of the liquid vapor component yiyx, respectively by: z, = < * > > , + (l-a) x /, where a is the vapor fraction defined by: nv and - ny + nL ' nv and nL are the total number of moles in the vapor and liquid phases, respectively. The method according to claim 4, characterized in that the execution of step (b) to carry out the phase composition calculation comprises: (bl) performing the calculation of the molar fraction of the phase component, the execution step (bl) includes, calculate an amount, the amount is selected of the group consisting of: a saturation pressure averaged in mass velocity of liquid (vapor), a gas / oil ratio in the liquid phase and a ratio of oil / gas in the vapor phase and using the amount to obtain values representative of the compositions of vapor and liquid. 8. The method according to claim 7, characterized in that the execution of step (c) to perform a calculation of speeds or molar proportions of the total composition and components comprises: performing the calculation of the total composition wherein the molar fraction i (i = l, ..., lf) of component z is related to the molar fractions of the vapor and liquid component yi and Xi, respectively by: where a is the vapor fraction defined by: nv and a - nr + nL nv and nL are the total number of moles in the vapor and liquid phases, respectively. 9. A program storage device that can be read by a machine that tangibly implements a set of instructions executable by the machine to perform method steps for the deconcentration of black oil, the steps of the method are characterized because comprises: converting a black oil well stream to a compositional well stream, thereby enabling a set of proportions of the composition and molar proportions of the component of a production well of a black oil reservoir simulation to be reconstituted. 10. The program storage device according to claim 9, characterized in that the steps of the method for the deconcentration of black oil are adapted to recover molar proportions of the component ni, i = l, ..., l, where N ° is the number of components and where the molar proportion of components is the product of the total molar ratio multiplied by the mole fraction of the component, the conversion stage comprises: (a) performing the phase mass velocity calculation; (b) carry out the calculation of phase composition and (c) perform the calculation of the molar velocities of total components. 11. The program storage device according to claim 10, characterized in that the execution step (a) for performing the phase mass velocity calculation comprises: performing the mass velocity calculation in where the mass velocities of the vapor and liquid phases are given respectively by: Qmy = Q¿ V m8 ++ Q¡ or Q, m 'and where the symbols ^ »> Qm > Qm and fí denote mass velocities of free gas, vaporized oil, liquid petroleum and dissolved gas respectively. The program storage device according to claim 11, characterized in that the symbols Q «> Qm »Qm ° and Qm are obtained from the following expressions: Q = PgqgV, Q L = P ° q ° L, and and where qfv, q ° v, q ° L and q ^ L denote the volumetric velocities at the surface of the free gas, vaporized oil, liquid petroleum and dissolved gas, respectively; and p9 and p ° are the gas and oil densities at the surface, respectively. The program storage device according to claim 10, characterized in that the execution of step (b) to perform the calculation of the phase composition comprises: (bl) perform the calculation of the mole fraction of phase components, the execution stage (bl) inclye, calculate an amount, the quantity is selected from the group consisting of: a saturation pressure averaged speed mass of liquid (vapor), a petroleum gas / oil ratio in liquid phase v s9 g - "and a proportion of oil / gas in vapor phase and use the amount to obtain representative values of the vapor and liquid compositions. program storage device according to claim 10, characterized in that the execution of step (c) to perform the calculation of the total proportion and calculation of molar proportions of components comprises: performing the calculation of total composition wherein the molar fraction z ± of component i (i = 1, ..., N °) is related to the molar fractions of the vapor and liquid component and ± and x, respectively, by: z (= ay (+ (l-a) x (, where a is the vapor fraction defined by: a = y nr + nL nv and nL are the total number of moles in the vapor and liquid phases, respectively. 15. The program storage device according to claim 12, characterized in that the execution of step (b) to perform the phase composition calculation comprises: (bl) performing the molar fraction calculation of the phase component, the execution step (bl) includes, calculating an amount, the quantity is selected from the group consisting of: an average saturation pressure of liquid mass velocity (vapor), a gas oil / oil ratio in liquid phase R '~ Q IQ and a ratio of oil / gas in vapor phase and use the amount to obtain representative values of the vapor and liquid compositions. 16. The program storage device according to claim 15, characterized in that the execution of step (c) to perform the calculation of the total composition of the molar proportions of the component comprises: performing the total composition calculation where the mole fraction z¿ of component i (i = l, ...,! ^) is related to the molar fractions of the liquid vapor component yiyx ±, respectively by: z, = oyt + (la) x "where a is the vapor fraction defined by: and a = nv + nL ¡nv and nL are the total number of moles in the vapor and liquid phases, respectively. 17. A system adapted for the decompression of black oil, characterized in that it comprises: a first apparatus adapted to convert a black oil well current to a compositional well current, thereby allowing a set of composition proportions and molar proportions of components of a production well in a simulation of a black oil field are reconstituted. 18. The system according to claim 17, characterized in that the first apparatus is adapted to perform a deconcentration function that is further adapted to recover molar proportions of components ni, i = 1, ..., N, where N ° is the number of components and wherein the molar proportion of components is a product of the total molar ratio multiplied by the mole fraction of the component and wherein the first apparatus comprises: an apparatus adapted to perform a mass velocity calculation of phase; an apparatus adapted to perform a phase composition calculation and an apparatus adapted to perform a calculation of total composition and calculation of molar proportions of components. 19. A computer program adapted to be executed by a processor, characterized in that the computer program, when executed by the processor, carries out a process for the deconcentration of black oil, the process is characterized because it comprises: converting a current from a black oil well to a compositional well stream, thereby causing a set of molar proportions of the composition of molar proportions of components of a production well in a simulation of a black oil field to be reconstituted. 20. The computer program according to claim 19, characterized in that the process for the deconcentration of black oil is based on recovering molar proportions of components ni, i = l, ..., lf, where N is the number of components and wherein the molar proportion of components is the product of the total molar ratio multiplied by the mole fraction of the component and wherein the conversion step comprises: (a) performing a phase mass velocity calculation; (b) perform a phase composition calculation and (c) calculate the molar velocities of total components. 21. The computer program according to claim 20, characterized in that the execution step (a) for carrying out the phase mass velocity calculation comprises: performing the phase mass velocity calculation, wherein the phase mass velocities Liquid vapor are given respectively by: Y , _. * _.-.-- _.., -_, _....., ^ - »'« »' Um and ^ m denote mass velocities of free gas, vaporized oil, liquid petroleum and gas dissolved respectively. 22. The computer program according to claim 21, characterized in that the symbols QsV, Q ° r, Q ° L and Q * L are obtained from the following expressions: Q? = P * < ? "r, QJ ° = P ° q ° V, Qm ° L = p ° q ° L> and QmsL = p8qeL and where qfv, q ° v, q ° L and qf denote volumetric velocities at the surface of the free gas, vaporized oil, liquid petroleum and dissolved gas respectively; and p9 and p ° are the gas and oil densities at the surface, respectively. 23. The computer program according to claim 20, characterized in that the execution of step (b) to perform the phase composition calculation comprises: (bl) performing a molar fraction calculation of the phase component, step (bl) of execution includes, calculating an amount, the quantity is selected from the group consisting of: an average saturation pressure of liquid mass velocity (steam), a petroleum gas / oil ratio in liquid phase ^, s "9 -" and a ratio of oil / gas in vapor phase and use the amount to obtain representative values of the vapor and liquid compositions 24. The computer program according to claim 20, characterized in that the execution of step (c) to perform a calculation of total composition and calculation of molar proportions of components comprises: performing the calculation of total composition in which the molar fraction z of component i (i = 1, ..., N °) is related to the molar fractions of the liquid vapor component yiyx ±, respectively by: z, = ayt + ^ - a) x " where a is the vapor fraction defined by: nv and a = - n - + n t > nv and nL are the total number of moles in the vapor and liquid phases, respectively. 25. The computer program according to claim 22, characterized in that the execution of step (b) to perform the phase composition calculation comprises: (bl) performing a molar fraction calculation of the phase component, the step ( bl) of execution includes, calculating an amount, the quantity is selected from the group consisting of: an average saturation pressure of liquid mass velocity (steam), a petroleum gas / oil ratio in liquid phase R '~ 9 lq »and a ratio of oil / gas in vapor phase and use the amount to obtain representative values of the vapor and liquid compositions. 26. The computer program according to claim 25, characterized in that the execution of step (c) to perform the calculation of total composition and the calculation of molar proportions of components comprises: performing the calculation of total composition wherein the fraction molar z? of the component i (i = l, ..., jT) is related to the molar fractions of the liquid vapor component y¿ and xl t respectively by: z, = a, + (l-) x "where a is the vapor fraction defined by: a = nr + ní nv and nL are the total number of moles in the vapor and liquid phases, respectively.
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