Patent Application
20180163515
The invention relates to the field of oil exploration, and more particularly the field of exploitation of a deposit of hydrocarbons containing organosulfur compounds, by a thermal process such as a steam injection process.
During the exploitation of reservoirs of heavy crudes by a steam injection process, a phenomenon of aquathermolysis occurs, which may generate hydrogen sulfide (H2S). In fact, this type of reservoir may often have high sulfur contents. The thermal processes make it possible, by supplying calories and raising the temperature, to reduce the viscosity of the heavy crudes and thus make them producible.
Aquathermolysis is defined in the present description as a set of physicochemical reactions between rock impregnated with crude oil (or with bitumen) and steam, at temperatures between 200° C. and 300° C.
Hydrogen sulfide is a gas that is both extremely corrosive and highly toxic, or even lethal above a certain concentration. Thus, predicting the concentration of H2S in the gas produced during recovery assisted by steam injection helps, on the one hand, to reduce the costs of production by adapting the completion materials and the gas treatment devices, optimizing the operating conditions, and on the other hand to avoid emissions that are dangerous to people and the environment.
One technical problem is prediction of the amount of H2S generated in relation to the nature of the crude, the reservoir conditions and the conditions of steam injection. If we wish to predict the risk of production of H2S based on a reservoir model (used by flow simulators), a kinetic model of hydrogen sulfide generation is required.
Moreover, the physicochemical reactions associated with the phenomenon of aquathermolysis produce a change in the composition of heavy oil. It may therefore be advantageous if the kinetic model used for predicting hydrogen sulfide generation could also predict the variations in the composition of the oil in the reservoir. This capacity would in fact make it possible to predict the effects of the steam injection process on the quality of the oil produced.
The following documents will be cited in the description:
Barroux, C., Lamoureux-Var, V., Flauraud, E., 2013. Forecasting of H2S Production due to Aquathermolysis Reactions, Paper SPE 164317, presented at the SPE Middle East Oil and Gas Show and Conference, Manam, Bahrain.
Belgrave J. D. M., Moore R. G., Ursenbach R. G, (1997), “Comprehensive kinetic models for the aquathermolysis of heavy oils”, Journal of Canadian Petroleum Technology, v 36, n 4, p 38-44.
Boduszynski, M. M. 1987. Composition of Heavy Petroleums. 1. Molecular Weight, Hydrogen Deficiency, and Heteroatom Concentration as a Function of Atmospheric Equivalent Boiling Point up to 1400° F. (760° C.). Energy & Fuels, 1, 2-11.
Coats, K. H. 1980. In-Situ Combustion Model. SPE Journal, December, 533-554.
Merdrignac, I. and Espinat D. 2007. Physicochemical Characterization of Petroleum Fractions: the State of the Art. Oil & Gas Science and Technology—Rev. IFP, 62, 1, 7-32.
Crookston, R. B., Culham, W. E., Chen, W. H. 1979. A Numerical Simulation Model Recovery Processes for Thermal Recovery Processes. SPE 6724, SPE J., February, 37-58.
Fan T. and Buckley, J., Rapid and Accurate SARA Analysis of Medium Gravity Crude Oils, Energy Fuels, 2002, 16 (6), pp 1571-1575.
Lamoureux-Var, V. and Lorant, F. (2005a). Barroux, C., (2013), Using Geochemistry to Address H2S Artificial Formation as a Result of Production Risk due to Steam Injection for EOR: a Compositional Kinetic Approach. In Oil Sands. Paper 13HOCC-P-412-SPE 97810, SPE/PS-CIM/CHOA International Thermal Operations and Heavy Oil Symposium, 1-3 November Conference, Calgary, Alberta, Canada, 11-14 June.
Lamoureux-Var, V. and Lorant, F. (2005b). Experimental evaluation of H2S yields in reservoir rocks submitted to steam injection. Paper D08, 13th European Symposium on Improved Oil Recovery, EAGE, Budapest, Hungary, 25-27 April.
Peng, D. Y., and Robinson, D. B. 1976. A New Two-Constant Equation of State. Industrial and Engineering Chemistry Fundamentals, 15, 59-64.
Søreide, I. and Whitson, C. H. 1992. Peng-Robinson Predictions for Hydrocarbons CO2, N2, and H2S with Pure Water and NaCl Brine. Fluid Phase Equilibria, 77, 217-240.
A method is known from patent application FR 2892817 (U.S. Ser. No. 11/588,365) for constructing a kinetic model for estimating the mass of hydrogen sulfide produced by aquathermolysis of a rock containing crude oil. This method uses a mass-based compositional representation of the crude oil by classes of chemical compounds of the SARA type (description of hydrocarbons in four mass fractions or pseudo-constituents: Saturates, Aromatics, Resins and Asphaltenes; see for example (Fan and Buckley, 2002)) and describes the variation of the distribution of sulfur in said mass fractions of the oil and a so-called insoluble fraction (which represents the solid receiving a part of the sulfur initially held in the oil during the aquathermolysis reactions). The method proposed is based on an elementary reaction scheme for the element sulfur, obtained by mass balances for the element sulfur distributed in the various fractions (SARA and solid). However, this scheme cannot be used in a reservoir simulation. In fact, reservoir simulation requires information on pseudo-constituents, each described by a molecule, and not only by a mass as in patent application FR 2892817 (U.S. Ser. No. 11/588,365).
Application FR 3002969 (U.S. Ser. No. 14/200,682) is also known, which aims to transform the kinetic model based on the distribution of sulfur of application FR 2892817 (U.S. Ser. No. 11/588,365) into a molecular compositional kinetic model. This model was developed with the aim of predicting the production of H2S resulting from the aquathermolysis reactions in the context of reservoir simulation. However, this model has a number of drawbacks. Firstly, the atomic balance for sulfur, assumed to be respected by this method (since the compositional kinetic model is constructed around the reaction scheme for the element sulfur developed in application FR 2892817 (U.S. Ser. No. 11/588,365)), is not so in practice. In fact, application of this method shows that the stoichiometric coefficients derived on the basis of the reaction scheme for sulfur are unable to reproduce the results observed in the laboratory, notably the variations in mass of the SARA fractions and H2S over time. The stoichiometric coefficients must therefore be modified in order to match the observations in aquathermolysis experiments. The atomic balance for sulfur, which after all forms the basis of this compositional kinetic model, is then no longer respected once the kinetic model is calibrated. Moreover, the kinetic model developed in this application, based solely on the element sulfur, cannot respect the average atomic balances of the atomic elements, other than sulfur, making up the pseudo-molecules representing the various SARA fractions, namely carbon (C), hydrogen (H) and oxygen (O). These limitations have the result that the reaction scheme described in application FR 3002969 (U.S. Ser. No. 14/200,682) does not allow experimental data to be incorporated, such as the results of elemental analyses performed in the laboratory, which might, however, act as constraints to be respected by linking the number of atoms of the constituent elements of each of the pseudo-constituents to its number of carbon atoms. Moreover, the kinetic model of application FR 3002969 (U.S. Ser. No. 14/200,682) does not allow the element oxygen to be taken into account, which prevents prediction of the evolution of water (H2O) and carbon dioxide (CO2) during the aquathermolysis reactions. However, H2O is an essential reactant of the aquathermolysis reactions, without which the reactions cannot take place. The possibility of taking water into account in the compositional reaction scheme of the aquathermolysis model therefore seems to be important when enhanced accuracy of the results of reservoir simulation is desired, and in order to reinforce the predictive aspect of the model. Finally, the mass balance between reactants and products of each of the reactions on which application FR 3002969 (U.S. Ser. No. 14/200,682) is based is indeed respected during calibration of the model, but this constraint is only satisfied by adjusting the stoichiometric coefficients of the saturates fraction. In fact, the method described in patent application FR 3002969 (U.S. Ser. No. 14/200,682), which is based on the reaction scheme for sulfur in patent FR 2892817 (U.S. Ser. No. 11/588,365), deduces the stoichiometric coefficient associated with the saturates by effecting a simple mass balance between reactants and products for each reaction. Now, as water is not incorporated in the compositional reaction scheme, like numerous chemical species, a simple mass balance for the reactions of the model cannot allow a stoichiometric coefficient suitable for the saturates to be determined. Therefore, within the model in application FR 3002969 (U.S. Ser. No. 14/200,682), the saturates perform the role of adjustment variable in order to respect the mass balance of each of the reactions of the aquathermolysis reaction scheme.
The invention relates to a method for exploiting a hydrocarbon deposit containing organosulfur compounds by means of a thermokinetic model and a compositional reservoir simulation. The kinetic model constructed by the method according to the invention adheres more closely to the theory of the physical and chemical phenomena involved in an aquathermolysis reaction (notably respecting the atomic balances), but can also take into account certain experimental measurements that are available (such as elemental analyses), and thus contribute to more accurate quantification of the hydrogen sulfide emissions.
Thus, the present invention relates to a method for exploiting an underground deposit of hydrocarbons containing organosulfur compounds. The method according to the invention comprises the following steps:
Advantageously, said compositional representation of the hydrocarbons may consist of the following pseudo-constituents: saturated hydrocarbons, aromatic hydrocarbons, resins and asphaltenes.
Preferably, said experimental measurements may consist of aquathermolysis experiments simulated in the laboratory.
According to one embodiment of the invention, step ii) may be carried out according to the following steps:
Preferably, a third system of equations may be defined, linking the number of sulfur, carbon and oxygen atoms as a function of the number of carbon atoms for each of said pseudo-constituents and constituents.
Advantageously, said number of sulfur, carbon and oxygen atoms may be linked as a function of said number of carbon atoms for each of said pseudo-constituents via ratios determined by elemental analyses carried out on products of aquathermolysis simulated in the laboratory.
The method as claimed in one of the preceding claims, in which, in step iii), at least kinetic parameters of said thermokinetic model are calibrated.
The method as claimed in one of claims 1 to 6, in which, in step iii), kinetic parameters of said thermokinetic model and said pseudo-stoichiometric coefficients of said reaction scheme are calibrated.
According to one embodiment of the invention, variation over time of the amount of each of said pseudo-constituents of said compositional representation may additionally be determined in step A).
According to one embodiment of the invention, said conditions of exploitation may be determined by adapting completion materials and/or gas treatment devices as a function of said amount of hydrogen sulfide.
According to one embodiment of the invention, said conditions of exploitation may consist of modifying steam injection conditions so as to minimize said amount of hydrogen sulfide.
According to one embodiment of the invention, said conditions of exploitation may be determined so as to keep production of hydrogen sulfide below a legal maximum content.
The invention further relates to a computer program product downloadable from a communication network and/or recorded on a computer-readable medium and/or executable by a processor, comprising program code instructions for implementing the method according to the above description, when said program is executed on a computer.
Other features and advantages of the method according to the invention will become clear on reading the following description of nonlimiting embodiment examples, referring to the appended figures that are described below.
The following definitions are used in the description of the invention:
The present invention relates to a method, and the use thereof, for modeling the production of hydrogen sulfide (H2S) induced by reactions taking place in an underground deposit of hydrocarbons when said deposit is submitted to a thermal recovery process, in particular to a steam injection process, the reactions then being due to a phenomenon of aquathermolysis.
The method according to the invention comprises at least the following steps:
1. Determination of an amount of hydrogen sulfide (H2S) produced
The following are required for carrying out the present invention:
The main steps of the present invention are detailed below.
The objective of this step is to estimate, by compositional reservoir simulation, the amount of hydrogen sulfide (H2S) that would be produced if a thermal process were used for exploiting an underground reservoir impregnated with oil or bitumen containing organosulfur compounds (i.e. impregnated with hydrocarbons in the broad sense).
In this step, an elementary reaction scheme is constructed that is representative of a material balance for the element sulfur, also called a reaction scheme for sulfur. The reaction scheme for sulfur according to the invention requires definition of a compositional representation of the hydrocarbons.
According to a preferred embodiment of the present invention, as in patent application FR 2892817 (U.S. Ser. No. 11/588,365), a compositional representation by classes of chemical compounds of the SARA type, described for example in (Fan and Buckley, 2002), is used. This representation, used conventionally in industry, consists of describing the hydrocarbons in four fractions: saturated hydrocarbons (Saturates), aromatic hydrocarbons (Aromatics), Resins and Asphaltenes, and supplying the mass fraction of each of these fractions. More precisely, the SARA representation consists of:
Moreover, the reaction scheme for sulfur according to the invention also takes into account at least:
Moreover, the reaction scheme for sulfur according to the invention is a function of pseudo-stoichiometric coefficients relating to the pseudo-constituents and constituents involved in said reaction scheme.
According to a preferred embodiment of the present invention, we use the elementary reaction scheme representative of a material balance for the element sulfur employed in patent application FR2892817, which describes the distribution of all the sulfur in the various pseudo-constituents mentioned above on the basis of the following assumptions:
According to a preferred embodiment of the invention, the elementary reaction scheme representative of a material balance for the element sulfur described in patent application FR 289281 is used, only considering two pseudo-constituents representing the resins class (designated RES1 and RES2), two pseudo-constituents representing the asphaltenes class (designated ASP1 and ASP2), and a single solid pseudo-constituent (designated SLD). Moreover, for each class of reactants (RESi and ASPi, with i=1, 2), it is assumed that the two associated pseudo-constituents each generate a reaction with its own reaction kinetics. This leads to the construction of a reaction scheme for sulfur with four reactions as described by a system of reactions of the form:
S
RES1
→a
S1H2S
S
H2S
+a
S1ARO
S
ARO
+a
S1SLD
S
SLD
S
RES2
→a
S2H2S
S
H2S
+a
S2ARO
S
ARO
+a
S2SLD
S
SLD
S
ASP1
→a
S3H2S
S
H2S
+a
S3ARO
S
ARO
+a
S3SLD
S
SLD
S
ASP1
→a
S4H2S
S
H2S
+a
S4ARO
S
ARO
+a
S4SLD
S
SLD
where SH2S, SRES1 and SRES2, SASP1 and SASP2, SARO, SSLD, denote respectively the sulfur retained by the H2S, by the pseudo-constituents RES1 and RES2 representing the resins class, by the pseudo-constituents ASP1 and ASP2 representing the asphaltenes class, by the pseudo-constituent ARO representing the aromatics class, and by the pseudo-constituent SLD of the solid type, the coefficients aSrConstk (with 1≤r≤4 and Const1≤k≤3={H2S, ARO, SLD}) being pseudo-stoichiometric coefficients defined in such a way that the reactions defined above are balanced with respect to mass. According to one embodiment of the present invention, the coefficients aSrConstk (with 1<r≤4 and 1<k S 3) are estimated by taking mass balances for the distribution of sulfur using the Geokin Compo software (IFPEN, Energies nouvelles).
In this step, a kinetic model is constructed for estimating the evolution of the mass of hydrogen sulfide produced by a phenomenon of aquathermolysis. According to one embodiment of the invention, the kinetic model may in addition be used for estimating the evolution over time of the composition of the hydrocarbons of the deposit under investigation, i.e. the variation over time of the amount of each of the pseudo-constituents of the compositional representation selected in the preceding step 1.1.
The kinetic model according to the invention is defined on the basis of at least one system of reactions simulating the phenomenon of aquathermolysis, the elementary reaction scheme representative of a material balance for the element sulfur as defined in step 1.1, atomic balances relating to each of the reactions of the system of reactions thus defined, the balances relating at least to the sulfur, carbon and hydrogen atoms. Moreover, according to the invention, the system of reactions simulating said phenomenon of aquathermolysis is a function of stoichiometric coefficients relating at least to the pseudo-constituents defined in step 1.1 and at least to the constituent H2S.
The kinetic model according to the invention may be obtained by the nonlimiting sequence of the following steps:
In this substep, it is a matter of defining a system of reactions describing said phenomenon of aquathermolysis in said deposit. According to the invention, the system of reactions simulating aquathermolysis is a function of at least the pseudo-constituents defined in step 1.1 and at least the constituent H2S. Moreover, this system of reactions is expressed as a function of stoichiometric coefficients relating to each of the pseudo-constituents and constituents involved in the reactions.
According to a preferred embodiment of the present invention, each of the pseudo-constituents defined in step 1.1 is represented by a pseudo-molecule of the type CnCHnHSnSOnO, where nC, nH, nS, and nO are respectively the number of atoms of carbon, hydrogen, sulfur and oxygen in said pseudo-molecule. By taking oxygen into account in the kinetic model it is notably possible to incorporate water (H2O) and carbon dioxide (CO2) in the system of reactions simulating aquathermolysis. In particular, by taking water into account in the kinetic model it is possible to improve the accuracy of the prediction of the mass balances, but also ensure that the aquathermolysis reactions are only simulated when water molecules are indeed present. Moreover, the pseudo-molecules allow the appropriate average thermodynamic characteristics of the pseudo-constituents of the compositional representation selected and or of the solid pseudo-constituents to be incorporated in the kinetic model. In order to determine the pseudo-molecule associated with each pseudo-constituent, it is assumed that the elemental analysis of each pseudo-constituent is constant throughout the aquathermolysis reactions. This leads to a system of reactions (designated (2) hereinafter) of the form:
RES1+a1H20H2O→a1SATSAT+a1AROARO+a1H2SH2S+a1SLDSLD+a1CO2C02 (r1)
RES2+a2H20H2O→a2SATSAT+a2AROARO+a2H2SH2S+a2SLDSLD+a2CO2C02 (r2)
ASP1+a3H20H2O→a3SATSAT+a3AROARO+a3H2SH2S+a3SLDSLD+a3CO2C02 (r3)
ASP1+a4H20H2O→a4SATSAT+a4AROARO+a4H2SH2S+a4SLDSLD+a4CO2C02 (r4)
SAT+a
5H20
H
2
O→a
5CO2
C02+a5CH4CH4 (r5)
where ai Const j are the stoichiometric coefficients associated with each pseudo-constituent/constituent Constj={1:7}={H2O, SAT, ARO, H2S, SLD, CO2, CH4} involved in the system of reactions thus defined, with have ai Const j≤0 for the reactants (to the left of the arrow in a reaction) and ai Const j≥0 for the products (to the right of the arrow in a reaction) of this system of reactions. Note that the fifth reaction (designated r5) models cracking of the saturates in the presence of steam, which makes it possible (in contrast to patent application FR 3002969 (U.S. Ser. No. 14/200,682) that does not have a reaction involving the saturates) to take into account the variation of mass of the saturates class, said variation being observed during aquathermolysis experiments performed in the laboratory.
Moreover, each chemical reaction of the system of reactions according to the invention is characterized by its own reaction rate Ki={1:5} that depends on parameters called kinetic parameters. According to one embodiment of the present invention, each reaction rate is expressed by an Arrhenius law, familiar to a person skilled in the art, of the form: Ki=Aie−Ei/RT, where Ai is the frequency factor, Ei is the activation energy, R is the ideal gas constant and T is the temperature of the system.
1.2.2. Definition of Atomic Balances for Each of the Reactions
In this substep, it is a matter of defining atomic balances at least for carbon (C), sulfur (S) and hydrogen (H) for each of the reactions of the system of reactions established in step 1.2.1.
According to a preferred embodiment of the present invention, an atomic balance for carbon (C), sulfur (S), hydrogen (H) and oxygen (O) is defined for each of the reactions of the system of reactions established in (2). We then arrive at a system of equations of the form:
n
C
=Σj=1j=Nal Product jnC
n
S
=Σj=1j=Nal Product jnS
n
H
+2ai H20=Σj=1j=Nal Product jnH
n
O
+2ai H20=Σj=1j=Nal Product jnO
with the index i corresponding to the number of reactions (from i=1 to i=5) of system (2) and Reactanti={1:5}={RES1, RES2, ASP1, ASP2, SAT}, index j corresponding to the products of the reaction and Productj={1:6}={SAT, ARO, H2S, SLD, CO2, CH4}, and n{C, S, H, O} {Reactant i, Product j} corresponding respectively to the number of carbon, sulfur, hydrogen and oxygen atoms present in the constituent or pseudo-constituent considered.
According to a preferred embodiment of the present invention, and for the purpose of solving the systems of equations involved in the present invention, in addition the number of sulfur, hydrogen and oxygen atoms is expressed as a function of the number of carbon atoms for each of the pseudo-constituents and constituents considered in system of reactions (2). For this purpose, we may use the ratios S/C, H/C and O/C of the SARA pseudo-constituents and SLD (designated Rx/c with x={S,H,O}), which is information accessible from experimental measurements performed in the laboratory, notably by elemental analysis of the products of aquathermolysis simulated in the laboratory. Note that these ratios change slightly over time, but these changes can be neglected to a first approximation. Based on this assumption, a new set of equations can be written in the form:
n
S
1
=R
S
n
C
1
n
H
=R
H
n
C
n
O
=R
O
n
C
, (4)
with
Componentl={1:11}={RES1, RES2, ASP1, ASP2, ARO, SAT, SLD, H2O, CO2, H2S, CH4}, n{S,H,O}Component 1 being the number of atoms of sulfur, hydrogen, and oxygen, respectively, in a pseudo-constituent/constituent Componentl={1:11}, and nCComponent 1 being the number of carbon atoms in a pseudo-constituent/constituent Componentl={1:11}. Note that the elementary ratios H/C and O/C of the constituents (H2O, CO2, H2S, CH4) involved in system of reactions (2) are immediate and do not have to be determined by elemental analysis.
1.2.3. Establishment of a Link Between the Pseudo-Stoichiometric Coefficients of the Reaction Scheme and the Stoichiometric Coefficients of the System of Reactions
In this substep, a link is established between the pseudo-stoichiometric coefficients of the reaction scheme for sulfur established in step 1.1 and the stoichiometric coefficients of the system of reactions simulating aquathermolysis established in step 1.2.1 This link can be expressed in the form of the following system of equations:
a
i H2S
=a
S
n
S
a
i ARO
=a
S
n
S
/n
S
a
i SLD
=a
S
n
S
/n
S
a
S
+a
S
+a
S
=1 (5)
1.2.4. Determination of the Stoichiometric Coefficients of the System of Reactions
In this step, it is a matter of determining an expression for the stoichiometric coefficients of system of reactions (2) by jointly solving the systems of equations (3), (4), and (5).
According to one embodiment of the present invention, it is possible to use a formal program, such as Maple (Maplesoft, Canada), in order to obtain an expression for the stoichiometric coefficients of system of reactions (2) as a function of the set of variables involved in the systems of equations (3), (4), and (5).
Thus, the kinetic model constructed by the method according to the invention allows better account to be taken of the theory of the physical and chemical phenomena involved in an aquathermolysis reaction (notably respecting the atomic balances for sulfur, but also for carbon, hydrogen and possibly oxygen, as well as the possibility of including water or carbon dioxide in the system of reactions), but also take into account certain experimental measurements available (such as elemental analyses).
By describing the pseudo-constituents by molecular formulas (of the pseudo-molecules), it is possible to deduce directly the thermodynamic properties that depend on these molecular formulas, notably by correlations based on the molecular weight. As the molecular description of the pseudo-constituents is also consistent with the system of reactions adopted for describing the aquathermolysis reactions, notably with its stoichiometric coefficients, a consistent set is obtained between the molecular pseudo-formulas of these pseudo-constituents, the system of reactions that describes aquathermolysis by causing these pseudo-constituents to interact, and finally the thermodynamic properties of these pseudo-constituents.
1.3 Construction of a Thermodynamic Model
In this step, it is a matter of constructing a thermodynamic model for estimating the properties or behavior of the liquid and/or vapor phases of mixtures of multiple constituents and pseudo-constituents, such as those encountered in situ in reservoirs of petroleum, bitumen or gas, or on the surface during exploitation of these same deposits, and offering the possibility of predicting the detailed composition of fluids produced during production, as a function of time.
In the reaction context of the invention, we need a compositional thermodynamic model where the compositions of nonaqueous and nonsolid phases are detailed using the same constituents and pseudo-constituents as those involved in construction of the reaction scheme for sulfur. According to one embodiment of the present invention, the molecular weight of each of the pseudo-constituents is selected as identical to that used for constructing the system of reactions, and the other thermodynamic parameters of each of the constituents are selected by correlation with their molecular weight, deduced in its turn from their pseudo-molecular formula. As for the solid or solids, they are characterized solely by their molecular weight and are not considered in the calculation of the properties of the oil, gas and water phases.
If we choose to use thermodynamics by correlation, the parameters of the constituents/pseudo-constituents in the correlations can be adjusted on the basis of calculations performed with an equation of state, where the parameters per constituent/pseudo-constituent are typically obtained from databases when it is a question of “pure substances”, such as H2S, or when it is a question of pseudo-constituents, from correlations based at least partly on the molecular weight.
1.4 Calibration of the Thermokinetic Model
Thus, at the end of the preceding steps, we obtain a thermokinetic model, i.e. a model resulting from combining the kinetic model constructed in step 1.2 described above and the thermodynamic model constructed in step 1.3 described above. According to one embodiment of the present invention, the thermokinetic model according to the invention can be implemented in a reservoir simulator, with a view to calibration of the thermokinetic model.
In the present step, it is a matter of calibrating the previously constructed thermokinetic model, i.e. of adjusting the parameters of the thermokinetic model in question so that the results of numerical simulation of the phenomenon of aquathermolysis by the thermokinetic model are in agreement with the experimental measurements.
According to one embodiment of the present invention, the parameters to be adjusted are the pseudo-stoichiometric coefficients of the reaction scheme for sulfur (described in step 1.1) as well as the kinetic parameters (i.e. the frequency factors and the activation energies described in step 1.2) of the system of reactions of the kinetic model. Preferably, calibration of the thermokinetic model consists of adjustment of the kinetic parameters of the five reactions of the system of reactions defined by equation (2) and pseudo-stoichiometric coefficients of the reaction scheme for sulfur defined by equation (1).
According to another embodiment of the invention, if the pseudo-stoichiometric coefficients of the reaction scheme for sulfur were determined beforehand on the basis of aquathermolysis experiments, calibration of the numerical results with the experimental measurements is obtained by adjusting only the kinetic parameters of the reactions, i.e. the frequency factors and the activation energies.
According to one embodiment of the present invention, calibration of the kinetic parameters of the five reactions of the system of reactions defined by system (2) and the pseudo-stoichiometric coefficients of the reaction scheme for sulfur defined in equation (1) is carried out by means of an iterative inversion technique. More precisely, based on initial values for the parameters to be determined, an objective function is constructed, measuring the difference between the normed quantities predicted by systems (1) and (2) for H2S and the pseudo-constituents of the compositional representation selected and their respective experimental measurements, then the values of these parameters are modified, iteration after iteration, until a minimum of the objective function is found. During calibration, reproduction of the normed experimental data for H2S is preferred, as the quality of the predictions of H2S production at the surface, in reservoir simulations involving aquathermolysis reactions, mainly depends on good prediction of this quantity. A great many algorithms for objective function minimization are known by a person skilled in the art, such as the Gauss-Newton method, the Newton-Raphson method or the conjugated gradient. According to a preferred embodiment of the present invention, the Gauss-Newton method is used as the algorithm for minimizing the objective function described above. An example of software using an inversion technique is the CougarFlow software (IFP Energies nouvelles, France), which can be coupled with the PumaFlow reservoir simulation software (IFP Energies nouvelles, France), in which the thermokinetic model defined above will have been implemented, for estimating the various terms of the objective function.
1.5 Application of the Simulation Reservoir
In this step, it is a matter of determining the amount of hydrogen sulfide (H2S) produced over time by a phenomenon of aquathermolysis by performing a reservoir simulation, applied to the grid representation of the deposit under investigation, and by means of a compositional and reactive thermal simulator, said simulator using the previously defined and calibrated thermokinetic model.
Reservoir simulation involves performing calculations of phase equilibrium and calculations of phase properties, which will be detailed below.
1.5.1 Phase Equilibria
In compositional reservoir simulation with presence of steam as in the case under investigation, the phase equilibria between the “aqueous liquid” phase (called “water”), the “liquid hydrocarbon” phase (called oil), and the gas phase, are calculated using typically the following assumptions:
According to one embodiment of the invention, the equilibria between phases are calculated on the basis of equilibrium constants per constituent/pseudo-constituent calculated in the course of simulation (or precalculated before the simulation) from fugacities per constituent/pseudo-constituent per phase, obtained in their turn from an equation of state. Preferably, a cubic equation of state is used:
Industrial reservoir simulation programs also offer the possibility of calculating the equilibria between phases starting from tabulated equilibrium constants, as a function of pressure and temperature and possibly as a function of a compositional index, which are introduced by the engineer as input data for the simulation.
Another possibility offered for gas-oil equilibria is for the equilibrium constants to be calculated from analytical correlations, the engineer then having to introduce the parameters of each constituent/pseudo-constituent into the correlations. These two possibilities, tabulated equilibrium constants or those obtained by analytical correlation, are the ones that are offered primarily by industrial software in a reaction and thermal context; a description of these options can be found in (Coats, 1980).
Since the inputs for calculating the equilibria are equilibrium constants per constituent, tabulated or by correlation, a methodology used by a person skilled in the art is to generate the tables or the parameters of the constituents/pseudo-constituents based on a reference equation of state. The tables must be generated for pressures and temperatures that may be encountered in the course of numerical reservoir simulation.
The parameters of the constituents/pseudo-constituents in the reference equation of state are typically the critical parameters (temperature, pressure, volume or compressibility factor), the acentric factor, and parameters of binary interactions between constituents/pseudo-constituents.
The thermodynamic parameters of pure substances such as H2S are known and are listed by various organizations such as N.I.S.T. (National Institute of Standards and Technology, http://www.nist.gov). In contrast, the parameters of pseudo-constituents, critical parameters, acentric factor, and parameters of binary interactions must be estimated. A great many correlations are available, including correlations based on the molecular weight of the pseudo-constituent, its density and its boiling point, and these last two properties may in their turn be estimated by correlations based on the molecular weight of the pseudo-constituent. As a guide for choosing the correlations to use, it is possible to employ certain data relating to the nature of the pseudo-constituent (such as elemental analysis, which gives the mass distribution of different atomic elements), and/or its structure, taking inspiration for example from (Boduszynski, 1987).
Finally, it is should be added that the measured value of the molecular weight of heavy compounds is known to depend on the experimental technique used, for example as reported in (Merdrignac and Espinat, 2007).
Regardless of the degree of sophistication of the method used for determining them, the molecular weights of the heavy pseudo-constituents are still just estimates, which may be used as initial estimates in a process of optimization of parameters, notably of the number of carbon atoms of the pseudo-constituents, or not to be modified if they are considered to be sufficiently representative, or if it is found a posteriori that the values adopted a priori were a judicious choice.
1.5.2 Phase Properties
The phase properties for use in the calculations performed in numerical compositional reservoir simulation are, per phase: viscosity, enthalpy, molecular weight, molar density (inverse of molar volume), the product of these last two properties being equal to the density, estimation of which is indispensable for calculations of the gravitational effects, the latter in fact being linked to the differences in densities between phases. The molecular weights of the phases can be calculated directly from results of the calculations of equilibrium, which give the compositions of each phase.
Various possibilities are offered for calculating the molar volumes of the oil and gas phases:
For calculating the viscosities, it is possible to use a single correlation for the calculations of viscosity of the oil and gas phases or, more frequently for simulation of reservoirs of heavy oil, one correlation for the viscosity of the oil and a different correlation for the viscosity of the gas. These correlations use specific parameters defined per constituent/pseudo-constituent.
The enthalpies of the phases are usually calculated from specific heats defined per constituent/pseudo-constituent and per phase, and the specific heat per constituent/pseudo-constituent in the gas phase may alternatively be calculated from a specific heat per constituent/pseudo-constituent in the oil phase and a latent heat per constituent/pseudo-constituent. Further details may be found in Coats' work cited above, in the work of (Crookston, 1979), and in the reference manuals of industrial software for reservoir simulation such as PumaFlow.
The method according to the invention therefore makes it possible to model hydrocarbon-containing fluids in a mixture of constituents/pseudo-constituents, each of these constituents/pseudo-constituents being characterized by thermodynamic parameters for modeling the physical properties of the fluid, and moreover this thermodynamic modeling is consistent with a multi-reaction kinetic model, where one of the products of the reactions modeled is hydrogen sulfide (H2S).
At the end of this step, through so-called “reservoir” simulation, we obtain the amounts of H2S that may be generated during exploitation of oil deposits by steam injection, as well as the variations in the composition of the oil at the surface and in the reservoir, i.e. the variation over time of the amount of each of said pseudo-constituents of the compositional representation of the hydrocarbons selected in step 1.1.
These amounts of hydrogen sulfide may be compared with an amount measured in the past (production history). We may then adjust parameters of the kinetic model and/or of the thermal model, so that the estimates are more accurate for the deposit under investigation. With these adjusted models it is possible to predict the production of H2S from the deposit, for given exploitation conditions.
It is also possible to determine the conditions of exploitation on adapting the completion materials and/or the gas treatment devices, so as to limit the damage caused by acid attack.
It is also possible to modify the steam injection conditions in an attempt to reduce the amounts of H2S produced.
It is also possible to compare the amount of hydrogen sulfide against a legal maximum content (from 10 to 50 ppm by volume, according to the following organization: Agency for Toxic Substances & Disease Registry of the United States), and then we determine the exploitation conditions so as to keep the production of hydrogen sulfide below this legal maximum content.
By applying the exploitation conditions determined in step 2, for example the amount, flow rate, temperature of the steam injected, or type of material, the hydrocarbons are produced observing the legal norms and minimizing the effects on the equipment.
Moreover, the invention relates to a computer program product downloadable from a communication network and/or recorded on a computer-readable medium and/or executable by a processor, comprising program code instructions for carrying out the method as described above, when said program is executed on a computer.
The features and advantages of the method according to the invention are illustrated in the context of the exploitation of bituminous sands of the Fisher Field (Foster Creek project) in Alberta, a province in the west of Canada, by a so-called SAGD technique (“Steam-assisted gravity drainage”).
For this example of application, the method according to the invention is applied with the following assumptions:
For this application of the method according to the invention, experimental measurements were performed beforehand and are presented in Table 1. Table 1 summarizes the results from elemental analyses performed in the laboratory on samples of bituminous sands from the field under investigation (Lamoureux-Var and Barroux, 2013). More precisely, this table gives the values of the ratios S/C, H/C obtained at the end of aquathermolysis (after 203 h), and O/C at the start of aquathermolysis for the pseudo-constituents SAT, ARO, RES, ASP and SLD.
Table 2 shows the number of carbon atoms adopted for the pseudo-constituents SAT, ARO, RES1, RES2, ASP1, and ASP2. This number of atoms was selected from a database of molecular weights (see Barroux et al. 2013). To simplify the equations, the numbers of carbon atoms adopted for the two pseudo-constituents describing the resins fraction were selected as equal (i.e. nCRES1=nCRES2).
Substituting these experimental values for the variables in the equations of system (2) governing the model of the aquathermolysis reactions allows the resultant system of equations to be solved as a function of the stoichiometric coefficients of the kinetic model. This solution is performed using the formal program Maple. By construction, the stoichiometric coefficients of the first 4 reactions of system (2) depend only on the pseudo-stoichiometric coefficients of the reaction scheme for sulfur.
For the first 2 kinetic reactions (i.e. ri with i={1.2}), we get:
a
i H2S
=f(aS
a
i SAT
=f(aS
a
i ARO
=f(aS
a
i SLD
=f(aS
a
i H20
=f(aS
a
i CO2
=f(aS
For reaction r3, we get:
a
3 H2S
=f(aS
a
3 SAT
=f(aS
a
3 ARO
=f(aS
a
3 SLD
=f(aS3SLD)=76.3120aS3 SLD
a
3 H20
=f(aS
a
3 CO2
=f(aS
For reaction r4, we get:
a
4 H2S
=f(aS
a
4 SAT
=f(aS
a
4 ARO
=f(aS
a
4 SLD
=f(aS
a
4 H2O
=f(aS
a
4 CO2
=f(aS
As the saturates do not contain any sulfur, the stoichiometric coefficients associated with the last reaction (reaction r5) do not depend on the matrix of the coefficients [aSij] and are fully constrained by the atomic balance of reaction 5. We then get:
a
5 H2O=−7.3118
a
5 CO2=3.6559
a
5 CH4=10.3441 (7d)
The compositional kinetic model thus obtained is then coupled to the PumaFlow reservoir simulator (IFP Energies nouvelles, France) in order to carry out reservoir simulations involving aquathermolysis reactions. The same thermodynamic properties were selected for the 2 pseudo-constituents RES1 and RES2 associated with the resins fraction, i.e. MWRES1/2=1320 g/mol. This assumption makes it possible to simplify the compositional kinetic model derived from equations (3), (4), and (5).
To calibrate the kinetic model, aquathermolysis experiments on a sample of oil sand from the Fisher Field in Canada (see for example Lamoureux-Var and Lorant (2005a, 2005b)) are simulated in the laboratory. In parallel, a model is set up for numerical simulation of these aquathermolysis experiments. This model (called “0D” as there is no flow) consists of a grid that models the reactor surrounded by several grids representing the furnace used in the experiments. The central grid of the reactor represents the experimental gold tube in which the aquathermolysis reactions take place. The Peng-Robinson equation of state is used for the reservoir simulations of the aquathermolysis experiments in the laboratory. The numerical results are compared with the variations by mass of the SARA fractions and H2S observed experimentally. The results for the SARA fractions are expressed as instantaneous mass of the component per initial mass of the component (gram by gram) whereas the production of H2S is evaluated as mass of H2S per total initial mass of the SARA components (gram by gram). This scaling makes it possible to compare the numerical results with the experimental results, limited to reproduction of the experiment in terms of mass fraction of the different components.
Calibration of the parameters of the thermokinetic model, namely the kinetic parameters (frequency factor and activation energy) of the five reactions of system (2) and the pseudo-stoichiometric coefficients of the reaction scheme for sulfur defined in (1), was performed by means of an inversion loop (using the CougarFlow inversion software (IFP Energies nouvelles)) directly coupled to the PumaFlow reservoir simulator (IFP Energies nouvelles), without an intermediate step. The convergence is evaluated using an objective function that calculates the differences between the normed mass predictions of the simulator and the respective experimental data for H2S, Saturates, Aromatics, Resins and Asphaltenes. For optimal reproduction of the emissions of H2S relative to the mass of oil, the weighting of the term for H2S is increased relative to the other terms. The Gauss-Newton algorithm is then used for optimization of the object function. Note that if the experiments in the laboratory supply the whole of the reaction scheme for sulfur, calibration of the compositional kinetic model for reservoir simulation may be limited to calibration of the kinetic parameters (frequency factors and activation energies).
The values of the kinetic parameters (frequency factors and activation energies) and the values of the pseudo-stoichiometric coefficients obtained after calibration with the experimental data are summarized in Table 3. The associated stoichiometric coefficients, obtained using system of equations (7), for each of the reactions r1 to r5 and for each pseudo-constituent and constituent involved in system of equations (7), are presented in Table 4.
The characteristics of the reservoir model used for modeling the field under investigation are presented in Table 5. The region of the reservoir is rectangular with the respective dimensions 420, 150 and 18 meters in directions X, Y and Z. The grid used for simulation is a Cartesian grid of 3375 grid cells (1×75×25). The two horizontal wells are located at the center of the Y axis and are a distance of 6 meters apart along the Z axis. The length of the wells along the X axis is equal to the width of the reservoir, i.e. 420 meters. The reservoir simulation is performed in a vertical section perpendicular to the Y axis, characterized by permeability and homogeneous porosity. In the reservoir simulations simulating the SAGD method, the oil-gas system is described using tables of equilibrium constants.
The initial pressure is 29 bar at the top of the reservoir, which is located at a depth of 300 meters. The initial composition of the fluid is summarized in Table 5 and is derived from experimental measurements on the field under investigation. Further details concerning characterization of the oil and the relative permeabilities used are available in (Barroux et al., 2013). Before starting steam injection, the wells are preheated for a period of 4 months to mobilize the oil in the vicinity.
Thus, the present invention adheres more closely to the theory representing the physical and chemical phenomena involved in an aquathermolysis reaction (notably respecting the atomic balances of sulfur, but also of carbon, hydrogen and possibly oxygen; possibility of including water in the system of reactions), but also takes into account certain experimental measurements that are available (such as elemental analyses) in the elaboration of the reaction mechanism. For this purpose, the stoichiometric coefficients associated with the reactions are expressed in terms of molar fraction. This kinetic model also ensures consistency between the thermodynamic parameters of the constituents, their pseudo-molecular formula and the reaction scheme.
