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The invention relates to the Oil and Gas Industry.
The invention is an equation that describes in unambiguous terms the relation between the rate of oil production from a well completion and the rate of gas-lift applied to the well completion.
Many hydrocarbon well completions do not have sufficient reservoir energy (pressure) to lift the column of hydrocarbon fluid (oil) entirely to the surface. This reservoir energy may be insufficient in the initial stages or in the later stages during the life of the producing well completion. When the reservoir energy is insufficient to lift the oil to the surface or when the desired rate of oil production is greater than the rate of oil production that can be achieved purely through the reservoir energy, then it becomes necessary to install artificial lift systems to maximize recovery and profitability. One such lift system, is the gas lift system, which uses high pressure gas as the source of the lifting energy. The industry currently relies on complex software modeling tools that take into account a number of well completion and hydrocarbon fluid characteristics in predicting the relation between the rate of oil production and the rate of gas-lift. Not only are these modeling tools expensive but also it is expensive to capture the well completion and hydrocarbon characteristics usually required by these tools. This invention provides an equation that relates the rate of oil production to the rate of gas-lift and can be used in lieu of other complex methodologies.
The invention is an equation that describes the non-linear relation between the rate of oil production from a well completion and rate of gas-lift applied to the well completion. This equation is defined as,
Q_{oil}=A*(1−e^{−B*(gl−C)})−D*gl (Equation 1)
Where,
Furthermore,
From a standpoint of dimensional consistency, it needs to be emphasized that non-linear regression parameters A, B, C and D can take on any dimension (unit of measure) as long as both the left hand and right hand sides of Equation 1 are dimensionally consistent. Since gas-lift and oil production rates can be represented in a number of different units of measure, Equation 1 does not restrict itself to any particular combination of units of measure. The equation can be used for any set of units, as long as, Q_{oil }is representative of the rate of oil production and gl is representative of the rate of gas-lift.
Improvements to Process as a Result of Invention
The non-linear regression parameters listed in Equation 1 can be derived using non-linear regression numerical methods, provided that there are sufficient empirical data points. In other words, a minimum of 5 empirical datasets of oil production rate and gas-lift rate would be required to solve for the 4 non-linear regression parameters. Once the 4 parameters have been determined it is possible to predict the oil production rate at any desired gas-lift rate. There is therefore no need to obtain costly information about the well completion and hydrocarbon characteristics. Moreover, an equation can easily be integrated into the software engineering systems deployed by the oil and gas industry. It can potentially be far more cumbersome to integrate third party software results. Furthermore, it is possible to determine the optimal gas-lift rate using Equation 1. The optimal gas-lift rate is the gas-lift rate beyond which any further increase to the gas-lift rate would result in a decrease in the oil production rate. This can be obtained by differentiating Equation 1 with respect to the gas-lift rate and setting the resultant equation to zero in order to obtain the maxima. Thus, the optimal gas-lift rate (gl_{optimal}) can be defined as,
gl_{optimal}=C−1/B* log_{e}(D/AB) (Equation 2)
Thus, to summarize the improvements to process are as follows:
(1)There are cost, time, and human resource savings resulting from the use of a simple equation as opposed to costly and complex modeling tools.
(2)There are cost, time, and human resource savings resulting from not needing to capture costly well completion and hydrocarbon information.
(3) One is able to accurately determine the relation between rate of oil production and rate of gas-lift.
(4) One is able to accurately determine the optimal gas-lift rate that would result in maximum oil production rate.
Non Obviousness of Invention
The process of creating a single equation that describes the relationship between oil production rate and gas-lift rate involved the following steps:
(1) A detailed study of empirical data involving gas-lift rate and oil production rate.
(2) Creating a number of equations that attempted to relate oil production rate to gas-lift rate and subsequently studying their nature.
(3) Selecting a few equations that would best fit the empirical data.
(4) Performing a series of non-linear regression analyses that resulted in the computation of regression parameters.
(5) Analyzing the Goodness-of-Fit of the different equations by examining the Goodness-of-Fit indicator i.e. R^{2}.
(6) Finally selecting the one equation that best fit the empirical data.
(7) In summary, developing Equation 1, involved a thorough understanding of basic reservoir engineering concepts, an understanding of statistical modeling concepts, and finally corroboration of the equation developed through analysis of empirical data.
Validity of Invention
Equation 1 has been validated through a rigorous study of empirical data. FIGS. 1 through 7 clearly show that it is possible to fit the equation through a wide variety of data points. What is truly remarkable about the equation is its ability to take on a wide range of shapes. This ability is very critical because different well completion and hydrocarbon combinations exhibit different behaviors. The curve fits exhibited in all the diagrams showed a very high degree of Goodness-of-Fit (R^{2}) because the Goodness-of-Fit was always found to be close to 1.
In order to provide the visual appearance of Equation 1, as well as, to prove the validity and versatility of Equation 1, 7 diagrams have been presented. Each diagram shows the curve fit results for different hydrocarbon well completions having different characteristics. Due to the proprietary and confidential nature of the oil production data, the actual source of the information has not been disclosed. In each of these diagrams the abscissa is the rate of gas-lift (gl) and has been measured in millions of cubic feet per day and has been denoted by MMCF. The ordinate is the rate of oil production (Q_{oil}) and has been measured in standard stock tank barrels per day and has been denoted by STB. The regression parameters A, B, C, and D are displayed in each diagram. The Goodness-Of-Fit indicator R^{2 }has also been displayed. The range for R^{2 }is between 0 and 1.0 implying a poor fit and 1 implying a perfect fit. In cases where a minimum of 5 empirical datasets have not been available, the dataset having the maximum value for Q_{oil }has been repeated as many times as needed in order to create a total of 5 datasets. For clarification, a dataset is an abscissa-ordinate pair.
FIG. 1: Equation 1 has a perfect fit (R^{2}=1) for data obtained for Well-1. We observe that the oil production rate increases with gas-lift rate, reaches maxima, and subsequently oil production rate decreases with gas-lift rate.
FIG. 2: Equation 1 has a near perfect fit (R^{2}=0.9997) for data obtained for Well-2. We observe that the oil production rate increases with gas-lift rate, reaches maxima, and subsequently oil production rate does not reduce significantly with increase in gas-lift rate.
FIG. 3: Equation 1 has a near perfect fit (R^{2}=0.9998) for data obtained for Well-3. We observe that the oil production rate increases with gas-lift rate, reaches maxima, and subsequently oil production rate reduces gradually with increase in gas-lift rate.
FIG. 4: Equation 1 has a near perfect fit (R^{2}=0.9921) for data obtained for Well-4. We observe that the oil production rate increases substantially with gas-lift rate, reaches maxima, and subsequently oil production rate reduces with increase in gas-lift rate.
FIG. 5: Equation 1 has a perfect fit (R^{2}=1) for data obtained for Well-5. We observe that the oil production rate increases substantially with gas-lift rate, reaches maxima, and subsequently oil production rate reduces substantially with increase in gas-lift rate.
FIG. 6: Equation 1 has a perfect fit (R^{2}=1) for data obtained for Well-6. We observe that the oil production rate increases dramatically with gas-lift rate, reaches maxima, and subsequently oil production rate almost remains constant with increase in gas-lift rate.
FIG. 7: Equation 1 has a perfect fit (R^{2}=1) for data obtained for Well-7. We observe that the oil production rate increases substantially with gas-lift rate, reaches maxima, and subsequently oil production rate reduces dramatically with increase in gas-lift rate.
Definition List 1 | ||
Term | Definition | |
Well | The hole made into the formation of the | |
earth by a drilling bit. A well may be | ||
open, cased, or both. | ||
Open Hole | The portion of a well that has no casing. | |
Casing | Steel pipe placed in an oil or gas well to | |
prevent the wall of the hole from caving | ||
in, to prevent movement of fluids from | ||
one formation to another, and to | ||
improve the efficiency of extracting | ||
petroleum if the well is productive. | ||
Cased Hole | The portion of the well which has casing. | |
Well Completion | The system of tubulars, packers, and | |
other tools installed in the well | ||
production casing. The tool assembly | ||
that provides the hydrocarbon flow path | ||
or paths. | ||
Tubular | Any kind of pipe such as tubing, casing, | |
drill pipe, and line pipe. | ||
Packer | A piece of downhole equipment that | |
consists of a sealing device, a holding or | ||
setting device, and an inside passage for | ||
fluids. It is used to block the flow of | ||
fluids through the annular space | ||
between the pipe and the wall of the | ||
wellbore by sealing off the space | ||
between them. | ||
Oil Production Rate | The amount of oil (simple or complex | |
mixture of liquid hydrocarbons) | ||
produced from a well completion in a | ||
given period of time. | ||
Gas-Lift Rate | Amount of high pressure gas injected | |
into the well completion in a given | ||
period of time. | ||
Reservoir Energy | Natural energy within the reservoir. | |
Typically, used in conjunction with the | ||
term reservoir pressure. This is the | ||
average pressure within the reservoir at | ||
any given time. | ||
Reservoir | A subsurface, porous, permeable rock | |
body in which oil and/or gas has been | ||
accumulated. | ||
Goodness-of-Fit | A measure of how well observed data | |
conform to a specified model. | ||
Hydrocarbon | Organic compounds of hydrogen and | |
carbon. Petroleum is a mixture of many | ||
different hydrocarbons. | ||