Air drilling is low cost and effectively improves the penetration rate and causes minimal damage to liquid-sensitive pay zones. However, there is a potential downhole explosion when combustible gas mixed with drilling fluid reaches the combustible condition. In this paper, based on the underground combustion mechanism, an explosive range calculation model is established. This model couples the state equation and the empirical formula method, which considers the inert gas content, pressure, mixed gas component, and temperature. The result shows that increase of the inert gas content narrows the explosive range, while increase of the gas temperature and pressure improves the explosive range. A case in Chongqing, China, is used to validate the explosive range calculation model.
Air drilling technology takes the compressed air as the flow medium and uses this continuous air flow to cool the bit and take the rock debris out of the well [
The lower limit of explosion refers to the lowest concentration of combustible gas mixed air for the flame to spread, represented by
Working principle of the calculation of explosive range.
This program mainly considers the influence of gas pressure, temperature, and inert gas on the explosive range. The basic assumptions are as follows: The reaction proceeds in a closed container, and the temperature remains the same during the reaction. The temperature and concentration of the reactant in the entire container are isotropic (the speed of the reaction is the same everywhere). The temperature of the reactant remains the same as the surface of the container at the beginning of the reaction. The combined heat exchanger system through which the air exchanges to the surface does not change with the temperature, gas pressure, and physical properties.
The model considers the effect of the temperature and gas pressure on the explosive range, and the explosive range is calculated by the empirical formula and state equation.
During drilling, the underground temperature is usually higher than the ground temperature. Once the ground temperature exceeds 100°C, the influence of temperature on the explosion is obvious. The limits can be calculated from [
In addition, increase of the gas pressure also affects the range of the explosion. Equation (
For each individual gas, the lower and upper limit of the explosion can be calculated using the carbon number. The calculation formula is as follows [
Empirical coefficients used in explosive range calculation of single gas.
Empirical coefficient |
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Values | 0.1314–0.1448 | 0.0103–0.0193 | 0.0418–0.0686 | 0.0472–0.0563 |
The ideal gas law ignores the force acting between the molecules and the volume of the molecule, which has a relatively obvious error for air drilling. Thus, the compressibility factor
With
The actual volume of each gas can be calculated by (
Virtual critical parameters are as follows:
Substituting the gas pressure and temperature obtained by using the above approach into (
State equation of the ground is as follows:
State equation of any point in the well is as follows:
The total volume of the gas mixture is as follows:
Volume of individual gas is as follows:
Percentage of individual gas in the well is as follows:
Substituting (
An inert gas exists in the combustible gas, meaning that the inert gas molecules participate in the collision but that there is no reaction in the gas mixture. The gas molecules reduce the valid molecule collision in the entire system and consume the kinetic energy of a large amount of activated molecules, which decreases the chemical reaction rate and affects the explosive range of the gas mixture in the well [
It should be pointed out that (
The programming of the explosive range model in the well is carried out in the Visual Basic Microsoft 6.0 environment of the Windows system. Visual Basic is a graphical user interface (GUI) programming language, which also fully supports object-oriented programming. In addition, with the aid of visibility programming, Visual Basic provides users with a quick and simple way to develop Windows applications [
The calculation model of the explosive range in the well realizes the functions of the input of logging data and automatically chooses the compression factor component values
Software interface based on calculation model of explosive range in well.
A case in Chongqing, China, is used to validate the calculation model of explosion. The tectonic map is shown in Figure
Gas content and explosive range of DM001.
Depth (m) | Gas content from gas logging (%) |
Explosive range calculated |
Measured total hydrocarbon |
Carbon dioxide (%) | |||
---|---|---|---|---|---|---|---|
Methane | Ethane | Propane | Butane | ||||
2024.06 | 27.21 | 1.05 | 0.31 | 0.16 | 22.83–64.70 | 4.78 | 2.31 |
2025.23 | 31.78 | 1.23 | 0.87 | 0.58 | 18.80–54.16 | 5.90 | 1.33 |
2026.52 | 48.43 | 2.85 | 0.95 | 0.88 | 12.17–35.11 | 7.82 | 2.54 |
2027.11 | 59.39 | 4.62 | 1.75 | 1.28 | 9.44–27.70 | 11.21 | 2.20 |
2028.90 | 69.41 | 5.05 | 2.87 | 1.53 | 7.94–23.48 | 14.32 | 2.94 |
2029.39 | 87.61 | 6.74 | 3.04 | 2.10 | 6.34–18.67 | 14.04 | 5.34 |
2030.43 | 82.98 | 6.41 | 2.91 | 1.93 | 6.68–19.69 | 15.88 | 3.12 |
2030.98 | 85.01 | 6.51 | 2.82 | 1.95 | 6.56–19.28 | 16.74 | 4.85 |
2032.16 | 86.48 | 6.52 | 2.80 | 1.90 | 6.47–19.00 | 16.19 | 7.36 |
2033.15 | 84.25 | 6.48 | 2.75 | 1.82 | 6.62–19.47 | 17.86 | 8.74 |
2034.35 | 84.49 | 6.40 | 2.70 | 1.79 | 6.62–19.45 | 17.45 | 9.34 |
2034.71 | 87.70 | 6.91 | 3.20 | 2.18 | 6.29–18.57 | 13.47 | 7.40 |
2036.34 | 93.40 | 6.90 | 2.67 | 1.64 | 6.05–17.71 | 20.97 | 11.45 |
2038.31 | 87.93 | 6.72 | 3.09 | 2.11 | 6.31–18.60 | 13.79 | 11.37 |
2039.36 | 88.42 | 7.02 | 3.22 | 2.21 | 6.23–18.41 | 12.34 | 12.48 |
2039.86 | 88.95 | 6.66 | 3.03 | 2.05 | 6.27–18.44 | 13.62 | 13.70 |
2041.01 | 87.66 | 5.98 | 2.47 | 1.64 | 6.51–18.99 | 19.24 | 15.78 |
2042.83 | 87.03 | 5.91 | 2.48 | 1.71 | 6.55–19.13 | 17.82 | 14.59 |
2043.62 | 81.31 | 5.08 | 1.94 | 1.23 | 7.15–20.73 | 20.07 | 16.58 |
Tectonic map of the real case.
In Table
Figure
Analysis of results of calculation model and measurement.
(a) Drill; (b) carbide material with drill after explosion.
In order to investigate the relations between the calculated explosive range and the inert gas content, temperature, and borehole gas pressure, we assumed the formation temperature (75°C (348.15 K)), pressure (30 MPa), surface temperature (7°C (280.15 K)), borehole gas pressure (10 MPa), and the content of methane, ethane, propane, butane, and inert gas as, respectively, 95, 3, 1.5, 0.3, and 0.2%.
According to the calculation model, when the content of inert gas is, respectively, 0.1, 0.5, 1.5, 2, 2.5, and 3%, the explosive range is as shown in Figure
Relation between the explosive range and the content of inert gas: (a) upper explosive limit; (b) lower explosive limit; (c) explosive limit.
With the increment of temperature, the explosive range predicted by the calculation model is as shown in Figure
Relation between the explosive range and the temperature: (a) upper explosive limit; (b) lower explosive limit; (c) explosive limit.
With the increment of gas pressure, the explosive range predicted by the calculation model is as shown in Figure
Relation between the explosive range and the pressure: (a) upper explosive limit; (b) lower explosive limit; (c) explosive limit.
All the results above remain the same as the theoretical law. (1) A higher content of inert gas induces a smaller possibility of explosion in the well. (2) A higher temperature means a bigger internal energy of the molecules. Thus, between molecules a higher speed of chemical reaction leads to a greater possibility of explosion. (3) A higher gas pressure shortens the distance between the molecules of the combustible gas, meaning a greater probability of bigger collisions between the molecules.
Considering the influence of temperature and pressure, our straightforward method is established to determine the explosive range of air drilling downhole by combining the state equation and the empirical formula method. The empirical formula method is convenient and effective but has a limited range of application; the state equation is a strict theoretical method but is time-consuming because of the complex calculation involved. The model can realize the calculation of the maximum range based on the two methods (the union of two ranges), which is more reliable for the prediction of explosive range. A case in Chongqing, China, validates the explosive range calculation model.
For the empirical formula method, (
Some valuable conclusions are as follows.
Lower explosive limit of the single component, %
Upper explosive limit of the single component, %
Carbon number in the chain hydrocarbon molecule, 1
Empirical coefficient, 1
Empirical coefficient, 1
Empirical coefficient, 1
Empirical coefficient, 1
Upper limit of the gas mixture under normal pressure and temperature, %
Lower limit of the gas mixture under normal pressure and temperature, %
Concentration of individual gas in the gas mixture, %
Upper limit of individual gas, %
Lower limit of individual gas, %
The number of the single gas contained in the gas mixture, 1
Lower explosive limit of the gas mixture when considering the inert gas, %
Upper explosive limit of the gas mixture when considering the inert gas, %
Lower explosive limit of the gas mixture when not considering the inert gas, %
Upper explosive limit of the gas mixture when not considering the inert gas, %
Volume fraction of the inert gas, %
8.31 J/K·mol
Compressibility factor, 1
Value of subentry of compressibility factor, 1
Value of subentry of compressibility factor, 1
Reduced temperature, °C
Reduced gas pressure, MPa
Critical temperature of the air, °C
Critical pressure of the air, MPa
Acentric factor, 1
Cirtual critical temperature of the mixture, °C
Virtual critical pressure of the mixture, MPa
Virtual reduced temperature, °C
Virtual reduced gas pressure, MPa
Critical temperature of individual gas, °C
Critical pressure of individual gas, MPa
The critical acentric factor of every single gas, 1
Mole fraction of every single gas, 1
Ground gas pressure, MPa
Gas pressure in the shaft, MPa
Ground volume, g/cm3
Ground volume, volume in the shaft, g/cm3
Compressibility factor of the ground, 1
Compressibility factor in the shaft, 1
Temperature of the ground, °C
Temperature in the shaft, °C
Lower explosive limit at
Upper explosive limit at
Upper explosive limit at normal temperature (25°C), %
Lower explosive limit at normal temperature (25°C), %
Temperature of the combustible gas, °C
Lower explosive limit of the combustible gas under high pressure, %
Upper explosive limit of the combustible gas under high pressure, %
Gas pressure at the bottom of well, MPa.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The research is supported by the National Natural Science Foundation of China (Grant no. 51474185), the National Key Basic Research and Development Program, (973 Program) China (Grant no. 2013CB228003), and the China Postdoctoral Science Foundation (Grant no. 2014M560728).