CN115584952A - Method and system for judging gas channeling of carbon dioxide flooding reservoir - Google Patents
Method and system for judging gas channeling of carbon dioxide flooding reservoir Download PDFInfo
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- 230000005465 channeling Effects 0.000 title claims abstract description 167
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- 238000000034 method Methods 0.000 title claims abstract description 27
- 229910002092 carbon dioxide Inorganic materials 0.000 title claims abstract description 23
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Abstract
The invention discloses a method and a system for judging gas channeling of a carbon dioxide flooding oil reservoir, wherein the type of the oil reservoir and the gravity load of the reservoir are determined by collecting geological samples of an oil field; acquiring oil field well parameters, constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters, predicting a suspicious gas channeling occurrence area according to the first gas channeling model, and collecting CO marked in the suspicious gas channeling occurrence area 2 Concentration value distribution of (D), if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; according to the method, the gas channeling judgment effect and the calculation accuracy of the calculation influence range are improved through the correction fitting of the gas channeling judgment model and the gas channeling inversion model, and the early recognition of the gas channeling can be effectively reduced through the establishment of the numerical model.
Description
The technical field is as follows:
the invention belongs to the field of computer prediction, and particularly relates to a method and a system for judging gas channeling of a carbon dioxide flooding reservoir.
Background art:
CO 2 flooding is a core technology for tertiary oil recovery based on enhanced recovery ratio, and has low costHigh oil displacement efficiency and wide application range. By introducing CO 2 The residual oil gas can be pushed out by injecting the oil gas into the oil gas field in the later period of exploitation, so that the purpose of improving the recovery ratio is achieved, and the service life of the oil field is prolonged.
However, CO 2 In the process of driving, CO 2 The production of flooding gas channeling will reduce CO 2 The effect of flooding, the effect of formation heterogeneity, can lead to CO 2 Most of the CO preferentially flows along the high permeability layer, and a cross flow channel, CO, is quickly formed in the high permeability layer 2 Will be greatly reduced, accompanied by CO 2 The oil displacement effect of the oil displacement agent can be greatly reduced, and the stronger the heterogeneity of the stratum is, the CO is 2 The more severe the gas channeling will be, and eventually CO 2 The lower the recovery of the flood will be.
Currently, oil deposits are in CO 2 In the oil displacement process, the more serious influence on the recovery ratio is CO 2 Gas channeling is driven, so how to effectively identify, judge and inhibit the delay of gas channeling and guarantee the oil recovery rate becomes a technical problem to be solved urgently.
Disclosure of Invention
Aiming at the existing CO 2 The invention provides a method for determining the reservoir type and the reservoir gravity load of an oil field by collecting oil field geological samples; acquiring oil field well parameters including quantity, mark number and distribution coordinates, acquiring inclination and perforation information of the coordinate well, and acquiring oil production, water injection, water production and CO injection in a first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 The purity is obtained by constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters, predicting a suspicious gas channeling occurrence area according to the first gas channeling model, and collecting marked CO in the suspicious gas channeling occurrence area 2 Concentration value distribution of (D), if CO 2 Determining a scheme of gas channeling in the area if the maximum concentration of the concentration value exceeds a first threshold; according to the method, the gas channeling judgment effect and the calculation accuracy of the calculation influence range are improved through the correction fitting of the gas channeling judgment model and the gas channeling inversion model, and the gas channeling can be effectively reduced through the establishment of the numerical modelEarly identification of fleeing; by the aid of the multi-granularity model numerical model, the application range of the model is effectively widened, the model can be used for prediction and judgment, can be used for gas channeling analysis, and improves the gas channeling simulation efficiency; the offset calculation of the volume of the gas channeling can be further improved according to the offset of the radius in the gas channeling inversion model, so that the plugging effect is improved, and the oil yield of an oil field is improved; the model accuracy is further optimized through iteration of model optimization and actual measurement verification and multi-granularity calculation.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for judging the gas channeling of the carbon dioxide flooding reservoir comprises the following steps of;
s1, collecting an oil field geological sample, and determining the type of an oil field reservoir and the gravity load of the reservoir;
s2, obtaining oil field well parameters including the number, the labels and the distribution coordinates, obtaining the inclination and the perforation information of the coordinate well, and obtaining the oil production, the water injection, the water production and the CO injection in the first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 The purity of the product is high,
s3, constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters,
s4, predicting a suspicious gas channeling occurrence area according to the first gas channeling model, and collecting marked CO in the suspicious gas channeling occurrence area 2 The distribution of the concentration values of (a),
s5, if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; if CO is present 2 If the maximum concentration of the concentration value exceeds a second threshold value, reducing the first granularity of the first time period, and optimizing a first gas channeling model by using the oil field well parameters under the first granularity; if CO is present 2 Amplifying a second granularity of the first time period if the maximum concentration of the concentration value of (a) is less than a second threshold value, constructing a second gas channeling model by using the oilfield well parameters under the second granularity,
wherein the second threshold is less than the first threshold.
Further, the S1 further includes: and if the oil field reservoir type is heterogeneous, determining the thickness, permeability, heterogeneity and oil saturation of a small reservoir layer.
Further, the perforation information comprises the diameter of the perforation and the distribution density of the perforation.
Further, the predicting the suspicious gas channeling occurrence area according to the first gas channeling model comprises the steps of marking the area as the suspicious gas channeling occurrence area and sending alarm information if the area prediction value exceeds a third threshold value.
Further, according to the collection of the CO in the suspected gas channeling occurrence area 2 Determining a first radius according to the coordinate of the maximum value and the minimum value of the concentration value, determining a second radius according to the injection well and the production well, determining the offset of the first radius and the second radius, and determining the volume of a gas channeling channel according to a gas channeling model with the second radius.
And further S6, determining a plugging type according to the volume of the gas channeling channel, wherein the plugging type comprises gel and foam.
Further, the first time period comprises, a year or a month; the first particle size is any one of 12 hours, 6 hours, and 4 hours, and the second particle size is weeks.
Further, the gas channeling inversion model includes:
wherein R is according to noteA second radius determined for the well entering and producing wells, theta being the gas channeling angle, L being the horizontal gas channeling length, f g For gas production rate, M is the gas-oil fluidity ratio, K rg Is CO 2 Relative permeability, K ro Relative permeability of petroleum phase, mu g Is CO 2 Viscosity, μ o Is the viscosity of petroleum, Q g For ground gas production, Q o For ground oil production, B g Is the underground volume coefficient of gas, B o Is the underground volume coefficient of petroleum;
wherein S is the gas channeling area, V is the gas channeling volume, k is the thermal expansion coefficient, h is the gas channeling geological rock thickness, phi is the reservoir porosity, A or Is the residual oil saturation of the reservoir, A wc Is the irreducible water saturation of the reservoir;
further, the CO is 2 The gas channeling determination model is as follows:
ε＝ε 0 e Ct
wherein R is a second radius determined according to the injection well and the production well, theta is a gas channeling angle, L is a horizontal gas channeling length, f g For gas production rate, M is the gas-oil fluidity ratio, K rg Is CO 2 Relative penetrationTransmittance, K ro Relative permeability of petroleum phase, mu g Is CO 2 Viscosity, μ o Is the viscosity of the oil; Δ p is the differential pressure between the well entry and production well legs; phi is the reservoir porosity; epsilon is the initial value of gas channeling 0 And alpha is the included angle between the reservoir stratum and the horizontal plane.
If C >0, gas channeling occurs;
if C <0, the reservoir is stable.
A system for determining carbon dioxide flooding reservoir gas breakthrough, the system comprising:
the acquisition module is used for acquiring oil field geological samples and determining the type of an oil field reservoir and the gravity load of the reservoir; acquiring oil field well parameters including quantity, mark number and distribution coordinates, acquiring inclination and perforation information of the coordinate well, and acquiring oil production, water injection, water production and CO injection in a first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 Purity, if the type of the oil field reservoir is heterogeneous, determining the thickness, permeability, heterogeneity and oil saturation of a small layer of the reservoir;
a gas channeling model module for constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters,
the gas channeling judgment module is used for predicting a suspicious gas channeling occurrence area according to the first gas channeling model and collecting marked CO in the suspicious gas channeling occurrence area 2 Concentration value distribution of (1), if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; if CO is present 2 If the maximum concentration of the concentration value exceeds a second threshold value, reducing the first granularity of a first time period, and optimizing a first gas channeling model by using the oilfield well parameters under the first granularity; if CO is present 2 Amplifying a second granularity of the first time period if the maximum concentration of the concentration value is smaller than a second threshold value, and constructing a second gas channeling model according to the oilfield well parameters under the second granularity, wherein the second threshold value is smaller than the first threshold value;
a gas channeling inversion module for collecting CO in the suspected gas channeling region 2 The coordinates of the maximum value and the minimum value of the density value of (1) are determinedA radius, a second radius is determined according to the injection well and the oil production well, the offset between the first radius and the second radius is determined, and the volume of a gas channeling channel is determined according to a gas channeling model with the second radius
And the gas channeling blocking module is used for determining the blocking type according to the volume and the permeability of the gas channeling channel.
A computer-readable storage medium having a computer program stored thereon, wherein execution of the computer program by the processor implements a method for determining carbon dioxide flooding reservoir gas breakthrough.
The terminal equipment comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, and is characterized in that the processor executes the computer program to implement the method for judging the carbon dioxide flooding reservoir gas channeling.
The invention has the following beneficial effects:
1. according to the method, the gas channeling judgment effect and the calculation accuracy of the calculation influence range are improved through the correction fitting of the gas channeling judgment model and the gas channeling inversion model, and the early recognition of the gas channeling can be effectively reduced through the establishment of the numerical model;
2. by the aid of the multi-granularity model numerical model, the application range of the model is effectively widened, the model can be used for prediction and judgment, can be used for gas channeling analysis, and improves the gas channeling simulation efficiency;
3. the offset calculation of the volume of the gas channeling can be further improved according to the offset of the radius in the gas channeling inversion model, so that the plugging effect is improved, and the oil yield of an oil field is improved;
4. the model accuracy is further optimized through iteration of model optimization and actual measurement verification and multi-granularity calculation.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above description and other objects, features, and advantages of the present invention more clearly understandable, the preferred embodiments are specifically described below.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 is an architecture diagram of a system for determining carbon dioxide flooding reservoir gas channeling
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
In the description of the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be connected or detachably connected or integrated; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
Example 1
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for judging the gas channeling of the carbon dioxide flooding reservoir comprises the following steps of;
s1, collecting an oil field geological sample, and determining the type of an oil field reservoir and the gravity load of the reservoir;
s2, obtaining oilfield well parameters, wherein the oilfield well parameters comprise the number, the labels and the distribution coordinates, and obtaining the inclination of the coordinate wellPerforation information and oil production, water injection, water production and CO injection in the first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 The purity of the product is high,
s3, constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters,
s4, predicting a suspicious gas channeling occurrence area according to the first gas channeling model, and collecting marked CO in the suspicious gas channeling occurrence area 2 The distribution of the concentration values of (a),
s5, if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; if CO is present 2 If the maximum concentration of the concentration value exceeds a second threshold value, reducing the first granularity of a first time period, and optimizing a first gas channeling model by using the oilfield well parameters under the first granularity; if CO is present 2 Amplifying a second granularity of the first time period if the maximum concentration of the concentration value of (a) is less than a second threshold value, constructing a second gas channeling model by using the oilfield well parameters under the second granularity,
wherein the second threshold is less than the first threshold.
Further, the S1 further includes: and if the oil field reservoir type is heterogeneous, determining the thickness, permeability, heterogeneity and oil saturation of a small reservoir layer.
Further, the perforation information comprises the diameter of the perforation and the distribution density of the perforation.
Further, the predicting of the suspicious gas channeling occurrence area according to the first gas channeling model comprises marking the area mark as the suspicious gas channeling occurrence area and sending alarm information if the area prediction value exceeds a third threshold value.
Further, according to the collection of the CO in the suspected gas channeling occurrence area 2 Determining a first radius according to the coordinate of the maximum value and the minimum value of the concentration value, determining a second radius according to the injection well and the production well, determining the offset of the first radius and the second radius, and determining the volume of a gas channeling channel according to a gas channeling model with the second radius.
And further S6, determining a plugging type according to the volume of the gas channeling channel, wherein the plugging type comprises gel and foam.
Further, the first time period comprises, a year or a month; the first particle size is any one of 12 hours, 6 hours, and 4 hours, and the second particle size is weeks.
Further, the gas channeling inverse model comprises:
wherein R is a second radius determined according to the injection well and the production well, theta is a gas channeling angle, L is a horizontal gas channeling length, f g For gas production rate, M is the gas-oil fluidity ratio, K rg Is CO 2 Relative permeability, K ro Relative permeability of petroleum phase, mu g Is CO 2 Viscosity, μ o Is the viscosity of petroleum, Q g For ground gas production, Q o For ground oil production, B g Is the gas subsurface volume coefficient, B o Is the underground volume coefficient of petroleum;
wherein S is the gas channeling area, V is the gas channeling volume, and k isCoefficient of thermal expansion, h is gas channeling geological formation thickness, phi is reservoir porosity, A or Is the residual oil saturation of the reservoir, A wc Irreducible water saturation for the reservoir;
further, the CO is 2 The gas channeling determination model comprises the following steps:
ε＝ε 0 e Ct
wherein R is a second radius determined according to the injection well and the production well, theta is a gas channeling angle, L is a horizontal gas channeling length, f g For gas yield, M is the gas-oil fluidity ratio, K rg Is CO 2 Relative permeability, K ro Relative permeability of petroleum phase, mu g Is CO 2 Viscosity, μ o Is the viscosity of the oil; Δ p is the differential pressure between the well entry and production well legs; phi is reservoir porosity; epsilon is the initial value of gas channeling 0 And alpha is the included angle between the reservoir stratum and the horizontal plane.
If C >0, gas channeling occurs;
if C <0, the reservoir is stable.
Example 2
A system for determining carbon dioxide flooding reservoir gas breakthrough, the system comprising:
the acquisition module is used for acquiring oil field geological samples and determining the type of an oil field reservoir and the gravity load of the reservoir; acquiring oil field well parameters including quantity, mark number and distribution coordinates, acquiring inclination and perforation information of the coordinate well, and acquiring oil production, water injection, water production and CO injection in a first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 Purity, if the type of the oil field reservoir is heterogeneous, determining the thickness, permeability, heterogeneity and oil saturation of a small layer of the reservoir;
a gas channeling model module for constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters,
the judgment module is used for predicting the suspicious gas channeling occurrence area according to the first gas channeling model and collecting the marked CO in the suspicious gas channeling occurrence area 2 Concentration value distribution of (1), if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; if CO is present 2 If the maximum concentration of the concentration value exceeds a second threshold value, reducing the first granularity of a first time period, and optimizing a first gas channeling model by using the oilfield well parameters under the first granularity; if CO is present 2 Amplifying a second granularity of the first time period if the maximum concentration of the concentration value is smaller than a second threshold value, and constructing a second gas channeling model according to the oilfield well parameters under the second granularity, wherein the second threshold value is smaller than the first threshold value;
a gas channeling inversion module for collecting CO in the suspected gas channeling region 2 Determining a first radius according to the coordinates of the maximum value and the minimum value of the concentration value, determining a second radius according to the injection well and the production well, determining the offset of the first radius and the second radius, and determining the volume of a gas channeling channel according to a gas channeling model with the second radius
And the gas channeling blocking module is used for determining the blocking type according to the volume and the permeability of the gas channeling channel.
A computer-readable storage medium having a computer program stored thereon, wherein execution of the computer program by the processor implements a method for determining carbon dioxide flooding reservoir gas breakthrough.
The terminal equipment comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, and is characterized in that the processor executes the computer program to implement the method for judging the carbon dioxide flooding reservoir gas channeling.
The invention has the advantages that:
1) According to the method, the gas channeling judgment effect and the calculation accuracy of the calculation influence range are improved through the correction fitting of the gas channeling judgment model and the gas channeling inversion model, and the early recognition of the gas channeling can be effectively reduced through the establishment of the numerical model;
2) By the aid of the multi-granularity model numerical model, the application range of the model is effectively widened, the model can be used for prediction and judgment, can be used for gas channeling analysis, and improves the gas channeling simulation efficiency;
3) The offset calculation of the volume of the gas channeling can be further improved according to the offset of the radius in the gas channeling inversion model, so that the plugging effect is improved, and the oil yield of an oil field is improved;
4) The model accuracy is further optimized through iteration of model optimization and actual measurement verification and multi-granularity calculation.
According to the method and the system, parameter adjustment is carried out at the cloud server, so that the problem of dizziness caused by focusing conflict in vision is solved, the picture setting operation is simplified, the interaction experience efficiency is improved through an improved gesture recognition mode, and the virtual reality environment interaction mode recognition efficiency is improved.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (10)
1. A method for judging gas channeling of a carbon dioxide flooding reservoir is characterized by comprising the following steps:
s1, collecting oil field geological samples, and determining the type of an oil field reservoir and the gravity load of the reservoir;
s2, obtaining oil field well parameters including the number, the labels and the distribution coordinates, obtaining the inclination and the perforation information of the coordinate well, and obtaining the oil production, the water injection, the water production and the CO injection in the first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 The purity of the product is high,
s3, constructing a first gas channeling model according to the reservoir type parameters of the oil field and the well parameters of the oil field,
s4, predicting a suspicious gas channeling occurrence area according to the first gas channeling model, and collecting marked CO in the suspicious gas channeling occurrence area 2 The distribution of the concentration values of (a),
s5, if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; if CO is present 2 If the maximum concentration of the concentration value exceeds a second threshold value, reducing the first granularity of a first time period, and optimizing a first gas channeling model by using the oilfield well parameters under the first granularity; if CO is present 2 Amplifying a second granularity of the first time period if the maximum concentration of the concentration value of (a) is less than a second threshold value, constructing a second gas channeling model by using the oilfield well parameters under the second granularity,
wherein the second threshold is less than the first threshold.
2. The method for judging the gas channeling of the carbon dioxide flooding reservoir according to claim 1, characterized by: the S1 further comprises: and if the oil field reservoir type is heterogeneous, determining the thickness, permeability, heterogeneity and oil saturation of a small reservoir layer.
3. The method for judging the gas channeling of the carbon dioxide flooding reservoir according to claim 1, characterized by comprising the following steps: the perforation information comprises the diameter of the perforation and the distribution density of the perforation.
4. The method for judging the gas channeling of the carbon dioxide flooding reservoir according to claim 1, characterized by: the predicting of the suspicious gas channeling occurrence area according to the first gas channeling model comprises the steps of marking the area mark as the suspicious gas channeling occurrence area and sending alarm information if the area prediction value exceeds a third threshold value.
5. The method for judging the gas channeling of the carbon dioxide flooding reservoir according to claim 1, characterized by comprising the following steps: according to miningGathering suspected CO in gas channeling areas 2 Determining a first radius according to the coordinate of the maximum value and the minimum value of the concentration value, determining a second radius according to the injection well and the production well, determining the offset of the first radius and the second radius, and determining the volume of a gas channeling channel according to a gas channeling model with the second radius.
6. The method for judging the gas channeling of the carbon dioxide flooding reservoir according to claim 1, characterized by comprising the following steps: and S6, determining a plugging type according to the volume of the gas channeling channel, wherein the plugging type comprises gel and foam.
7. The method for judging the gas channeling of the carbon dioxide flooding reservoir according to claim 1, characterized by comprising the following steps: the first time period comprises a year or a month; the first particle size is any one of 12 hours, 6 hours, and 4 hours, and the second particle size is weeks.
8. A system for determining carbon dioxide flooding reservoir blow-by, the system comprising:
the acquisition module is used for acquiring oil field geological samples and determining the type of an oil field reservoir and the gravity load of the reservoir; acquiring oil field well parameters including quantity, mark number and distribution coordinates, acquiring inclination and perforation information of the coordinate well, and acquiring oil production, water injection, water production and CO injection in a first time period of the coordinate well 2 Mass, injection of CO 2 Velocity, CO 2 Purity, if the type of the oil field reservoir is heterogeneous, determining the thickness, permeability, heterogeneity and oil saturation of a small layer of the reservoir;
a gas channeling model module for constructing a first gas channeling model according to the oil field reservoir type parameters and the oil field well parameters,
the judgment module is used for predicting the suspicious gas channeling occurrence area according to the first gas channeling model and collecting the marked CO in the suspicious gas channeling occurrence area 2 Concentration value distribution of (1), if CO 2 Determining that the area has gas channeling if the maximum concentration of the concentration value exceeds a first threshold value; if CO is present 2 Maximum of concentration value of (2)If the large concentration exceeds a second threshold value, reducing the first granularity of the first time period, and optimizing a first gas channeling model by using the oilfield well parameters under the first granularity; if CO is present 2 Amplifying a second granularity of the first time period if the maximum concentration of the concentration value is smaller than a second threshold value, and constructing a second gas channeling model according to the oilfield well parameters under the second granularity, wherein the second threshold value is smaller than the first threshold value;
a gas channeling inversion module for collecting CO in the suspected gas channeling area 2 Determining a first radius according to the coordinate of the maximum value of the concentration value and the minimum value, determining a second radius according to the injection well and the oil production well, determining the offset of the first radius and the second radius, and determining a volume gas channeling plugging module of the gas channeling channel according to the gas channeling model with the second radius, wherein the volume gas channeling plugging module is used for determining the plugging type according to the volume of the gas channeling channel and the permeability.
9. A computer-readable storage medium storing a computer program, wherein the computer program is executed by a processor to perform the method for determining carbon dioxide flooding reservoir gas channeling according to any one of claims 1-7.
10. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform the method for determining carbon dioxide flooding reservoir gas breakthrough of any of claims 1-77.
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