Dynamic behavior of coalbed methane flow along the annulus of single-phase production
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Dynamic behavior of coalbed methane (CBM) flow will provide the theoretical basis to optimize production performance for a given well. A mathematical model is developed to simulate flowing pressures and pressure drops of CBM column from well head to bottom hole. The measured parameters and independent variables of flow rates, flowing pressures and temperatures are involved in CBM producing process along the annulus. The developed relationships are validated against full-scale measured data in single-phase CBM wellbores. The proposed methodology can analyze the dynamic behavior in CBM reservoir and process of CBM flow with an overall accuracy of 2%. The calculating process of flowing pressures involves friction factor with variable Reynolds number and CBM temperature and compressibility factor with gravitational gradients. The results showed that the effect of flowing pressure on CBM column was more obvious than that on CBM and water column accompanied by an increase of dynamic water level. The ratios of flowing pressure on increment of CBM column to the whole column increased with the declined flow rates of water column. Bottom-hole pressure declined with the decreased flowing pressure of CBM column along the annulus. It will lead to the results of the increased pressure drop of CBM column and CBM flow rate in single-phase CBM wellbores.
KeywordsDynamic characteristic Single-phase CBM wellbore Flowing pressure of CBM column Flow rate of CBM column
Periodic analysis of flowing pressures can forecast the dynamic behavior in coal reservoirs and solve the common problems of matching the CBM reservoir behavior with wellbore conditions in single-phase CBM wellbores (Mitchell 2011; Mohammed and Enty 2013; Towler et al. 2016). A reliable and accurate approach to predict flowing pressures is essential to design artificial lifting systems and to optimize production performance for the given CBM well. An alternative is to propose a reliable and accurate approach and estimate the flowing pressures and pressure drops in single-phase CBM wellbores with respect to the well liquids and well datum (Osman et al. 2005; Bello and Asafa 2014). In order to calculate the flowing pressures, Rendeiro and Obeida (Rendeiro and Kelso 1988; Obeida and Mosallam 2007) developed the Average Temperature and Pressure method. And Z-factor could be computed by assuming the whole wellbore to be at an average temperature and pressure along the annulus. This methodology does not perform well for most deep CBM wells and is even less reliable for such CBM wells at low gas/liquid ratios. Cullender et al. (Cullender and Smith 1956; Peffer et al. 1988; Guzman et al. 2014) proposed Cullender and Smith methodology for the single-phase well with gas occupying the wellbore. This methodology took the variations in temperature and gas compressibility with depth into account. And the absolute roughness of rough-turbulent flow was 6.0 × 10−4 inches in dry-gas wells. Wang et al. (2014) calculated the flowing pressures and pressure distributions using experimental and numerical simulations. The distributions of temperature and pressure on the bottom of the hole during the SC-CO2 jet drilling were simulated experimentally and numerically, and the impacts of the nozzle diameter, the jet length, and the inlet pressure of the SC-CO2 jet were analyzed. Artificial neural networks (ANN) (Osman and Aggour 2002; Mohammadpoor et al. 2010; Li et al. 2017) create models that can recognize highly complex and non-straight-forward problems. ANN provides an integrated approach for the prediction of bottom-hole pressures in multiphase flow. Ashena and Menad (Ashena and Moghadasi 2011; Menad et al. 2018) estimated the flowing pressures using evolved neural networks and grey wolves optimization. ANN with 7 neurons in its hidden layer was utilized to solve the non-straightforward problem of two-phase flow in annulus. Much more promising results were obtained when the highly efficacious tool of ant colony optimization (ACO) was utilized as the next method to optimize the weights and thresholds of the neural networks. The models were developed and tested using 100 field data collected from Algerian fields and covering a wide range of variables. The main problem that ANN models suffer from, is the presence of some inaccuracies caused by the defaulted training algorithms that trap in local minima.
The above relationships generally conducted various theoretical analytic approaches of conventional oil fields and dry-gas wells to calculate the flowing pressures and pressure drops. Therefore, these modeling procedures do not give the desired results to predict the flowing performance along the annulus. The main reason is that there exists the differences between coal geology and gas formations (Yao and Ge 2011; Liu 2013; Liu et al. 2018; Underschultz et al. 2018), including low water production, high dynamic water level, short stroke and rapid dropping down of pumping speed. Another aspect to consider is that the flowing pressures in CBM wellbores have not been further developed and the available models cannot satisfy the accuracy requirements in engineering design.
A mathematical model is developed to simulate flowing pressures and pressure drops of CBM column from well head to bottom hole. The measured parameters and independent variables of flow rates, flowing pressures and temperatures were involved in CBM producing process along the annulus. The flowing pressures were predicted on the basis of single-phase CBM wellbore conditions along the annulus stretching over a wider range in order to predict the dynamic characteristics of CBM flow in single-phase CBM wells and provide the theoretical basis to design artificial lifting systems.
2 Model development of CBM flow
Calculate the integrand Ihf and the product of γc and hc in single-phase CBM wellbores.
Complete the initial computation with the help of the integrand Imf equal to Ihf.
Determine the flowing pressure, pmf, and the integrand, Imf, for the middle part of the whole CBM column in single-phase CBM wells.
Iterate by returning to Step 3 until the accurate result of pmf is obtained.
Complete the initial computation with the help of the integrand Ibf equal to Imf.
Determine the flowing pressure, ptcf, and the integrand, Itcf, on dynamic water level in wellbores.
Iterate by returning to Step 2.
The flowing pressure on dynamic water level in single-phase CBM wellbores, ptcf, can be iterated as the sum of pressure of well head and CBM column. Repeat the above procedure until the desired accuracy of ptcf is obtained.
3 Flowing pressures in single-phase CBM wellbores
The complete CBM producing process can be divided into several phases including single-phase water flow, two-phase (CBM and water) flow and single-phase CBM flow (Okuszko et al. 2008; Liu et al. 2011, 2019; Sugiarto et al. 2015). Undersaturated coal reservoirs may produce water mainly for a substantial period of time until desorption pressure is reached (Lyubarskii and Ivanov 1989; Boltenko 2013; Smith et al. 2019). And then the coal reservoirs produce water mostly and little CBM and exhibit single-phase water flowing performances (Vicki and Paul 2002; Clarkson et al. 2007; Liu et al. 2017; Fan et al. 2019). Therefore, the bottom-hole pressures are affected by well-head pressure, pressure drops of CBM column and water column in producing wellbores for single-phase water flow. The CBM column flows upward while the water column flows downward along the annulus between tubing and casing. And hence the flowing pressures can be found by the CBM and water flow formulae.
The coal reservoirs may produce CBM mostly during the phase of single-phase CBM flow (Borowsky and Wei 2006; White and Smith 2012; Tang et al. 2016). And hence the CBM wellbores exhibit single-phase flowing performances for at least a portion of their producing process. The bottom-hole pressures are affected by well-head pressure and pressure drop of CBM column in producing wellbores for single-phase CBM flow. The value of well-head pressure can be recorded by the pressure gauges. The CBM column flows upward in the wellbore, and hence the pressure can be found by the CBM flow formulae. Knowing the values of these pressures, bottom-hole pressures of single-phase CBM wellbores, pbf, can be determined as the sum of well-head pressure, phf, and pressure of CBM column, Δpc, in single-phase CBM wellbores.
4 Application and interpretation
4.1 Field application
The dynamic characteristics of CBM column flow are clarified by the examples of Hancheng coalfield in Ordos Basin, China. The CBM wells in Hancheng coalfield make continuous production and accumulate a lot of pumping data. The producing characteristics that might influence flowing performances in the wellbores were determined upon the single-phase flow properties.
The operational parameters were selected from the CBM wells in Hancheng coalfield, including: well depth of the whole CBM column, 430 m; CBM langmuir pressure in coal reservoirs, 3.50 MPa; tubing diameter, 2 7/8 in.; casing diameter, 7.0 in.; specific gravity of CBM column, 0.58; density of water column, 1015 kg/m3; and flowing viscosity of CBM column and water column, 1.70 × 10−2 mPa s and 7.85 × 10−4 Pa s, respectively.
Measured parameters and selected variables in single-phase CBM wellbores
Dynamic water level hc (m)
Flow rate of CBM qsc (m3/d)
Flow rate of water qw (m3/d)
Well-head pressre phf(MPa)
Flowing pressure on dynamic level ptch (MPa)
Measured bottom-hole pressure pbf (MPa)
Well-head temperature Th (K)
4.2 Results and interpretations
Predicted variables of flowing pressures and pressure drops using the developed algorithm
Upper pressure of CBM column Δpuf (MPa)
Pressure of CBM column at midpoint Δpmf (MPa)
Lower pressure of CBM column Δplf (MPa)
Pressure of CBM column Δpc (MPa)
Flowing pressure on dynamic level ptch (MPa)
Column pressure of CBM and water Δpt (MPa)
Predicted variables of bottom-hole pressure and relative error for single-phase CBM wellbores
Average temperature and pressure method
Cullender and Smith methodology
The proposed methodology
Predicted bottom-hole pressure pbf (MPa)
Error E (%)
Predicted bottom-hole pressure pbf (MPa)
Error E (%)
Predicted bottom-hole pressure pbf (MPa)
Error E (%)
Table 3 shows the flowing pressures and errors for single-phase CBM wellbores using Average Temperature and Pressure methodology. And the errors are calculated between − 11.2% and 4.3%. Z-factor could be computed by assuming the whole wellbore to be at an average temperature and pressure along the annulus. This methodology does not perform well for most deep and low gas/liquid ratio CBM wells.
Table 3 shows the flowing pressures and errors for single-phase CBM wellbores using Cullender and Smith methodology. And the errors are evaluated between − 10.4% and 4.8%. The calculation of flowing pressures took the variations in gas compressibility and temperature with depth into account. However, this methodology was proposed for the single-phase well with gas occupying the wellbore. And the absolute roughness of rough-turbulent flow is 6.0 × 10−4 inches in dry-gas wells.
The calculating process of flowing pressures involves friction factor with variable Reynolds number and CBM temperature and compressibility factor with gravitational gradients. The developed relationships are validated against full-scale measured data in single-phase CBM wellbores.
Well-head pressure, pressure drop of CBM column and CBM and water column, and bottom-hole pressure along the annulus can fully reflect dynamic characteristics of CBM producing process because of the combination of dynamic water level and flow rates of CBM column and water column.
The effect of flowing pressure on CBM column is more obvious than that on CBM and water column accompanied by an increase of dynamic water level. The ratios of flowing pressure on increment of CBM column to the whole column increase from 0.6% to 24% and then up to 67% while dynamic water levels along the annulus increase from 160 to 439 m.
The decreased pressures of CBM column from 69.7 to 5.2 kPa will lead to the results of the decreased bottom-hole pressures from 2.3 to 1.3 MPa and the increased flow rates of CBM column from 3327 up to 6721 m3/d.
This work was financially supported by National Science and Technology Major Project of the Ministry of Science and Technology of China (2016ZX05065-001), Key Research Project of Shandong Province (2019GHY112029 and 2019GSF109090) and Higher Education Research and Development Project of Shandong Province (J17KA033).
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