Productivity equation of low-permeability condensate gas well considering the influence of multiple factors
- 274 Downloads
Establishment of productivity equation is an important premise for rational and efficient development of low-permeability condensate gas reservoir and accurate analysis of production performance. Based on two-phase seepage mechanism of gas and condensate oil in formation, the productivity equation is established considering threshold pressure, stress sensitivity, slippage effect, retrograde condensate effect and high-velocity non-Darcy effect. The integrals of pseudo-pressure, turbulence factor and pseudo-threshold pressure are calculated with numerical method to resolve the productivity equation. Example calculation results indicate that with the decrease in bottom hole pressure, the increase in condensate gas well production rate is near linear first and then the increase is getting slower and slower. Slippage effect increases apparent permeability and condensate gas well productivity. Retrograde condensate effect, stress sensitivity and threshold pressure decrease apparent permeability and condensate gas well productivity. Based on orthogonal experiment design, the sensitive parameters influencing the productivity of low-permeability condensate gas well are analyzed. Various factors have different influence degrees on gas well productivity in different ranges of bottom hole pressure. Research results lay a theoretical foundation for taking measures to improve gas well productivity in the gas field.
KeywordsLow permeability Condensate gas reservoir Threshold pressure Stress sensitivity Productivity equation
Most of the condensate gas reservoirs are discovered in deep and tight formations with low permeability (Mohammadi et al. 2013). Complex physical and chemical phenomena in low-permeability condensate gas reservoir result in the change in gas well productivity (Zhang et al. 2014). When reservoir pressure is lower than dew point pressure, generation of condensate oil will decrease the gas relative permeability and well productivity (Li and Firoozabadi 2000; Rahimzadeh et al. 2016). In low-permeability reservoir, the absolute permeability is often sensitive to the stress and pore pressure (Sun et al. 2009; Shar et al. 2017). As effective stress increases, the absolute permeability will obviously decrease (Moghadam and Chalaturnyk 2016). Because of the influence of slippage effect, the apparent permeability of low-permeability reservoir will increase (Li et al. 2014; Wang et al. 2018). Furthermore, many experiments found that threshold pressure gradient existed in low-permeability reservoir (Guo and Wu 2007; Gao et al. 2008; Dou et al. 2014). Condensate blockage and relative permeability are research focuses in condensate gas reservoir (Farhoodi et al. 2019; Gholampour and Mahdiyar 2019). Slippage effect, stress sensitivity and threshold pressure gradient are usually considered in low-permeability and tight gas reservoir. However, all these phenomena including retrograde condensation, slippage effect, stress sensitivity and threshold pressure gradient which can influence gas well productivity are rarely considered simultaneously in low-permeability condensate gas reservoir.
Productivity analysis of condensate gas well is mainly based on the method of conventional dry gas well, including binomial and exponential productivity equation as well as empirical modified productivity equation based on them (Yan et al. 2006, 2007; Yuan et al. 2009; Xue et al. 2014). In recent years, productivity equation considering multiphase seepage has been paid more and more attention by scholars (Mokhtari et al. 2013; Huang et al. 2018; Li et al. 2018). With the further study of seepage mechanism of condensate gas reservoir, productivity analysis of condensate gas wells began to take into account the effects of many factors, such as phase change based on experiment and flash calculation, and adsorption effect of porous media (Shi et al. 2006, 2015; Qi et al. 2011; Lu et al. 2014; Jia et al. 2017). Seepage mechanism of low-permeability condensate gas reservoir is complicated because of its characteristics of low porosity, low permeability and phase change. Productivity analysis of low-permeability condensate gas well is not only different from conventional dry gas reservoirs but also different from conventional condensate gas reservoirs.
Combining the phase change characteristics of condensate gas reservoirs with the results of productivity studies of conventional dry gas reservoirs (Wu et al. 2008; Liao et al. 2012), according to steady seepage theory of condensate gas reservoir, the productivity equation of gas well in low-permeability condensate gas reservoir is established, which considers threshold pressure, stress sensitivity, slippage effect, high-speed non-Darcy effect and retrograde condensate effect. Because of nonlinear characteristics of the productivity equation, pseudo-pressure m(p), turbulence coefficient B and pseudo-threshold pressure coefficient C are calculated with numerical method to resolve the productivity equation. There are many factors influencing productivity of gas well in low-permeability condensate gas reservoir. Various factors have different influence degrees on gas well productivity. Orthogonal experiment design method is used to analyze the sensitivity, and the order of productivity influencing factors in low-permeability condensate gas well under different bottom hole pressures is known; thus, the corresponding measures can be taken to improve the productivity of gas well.
Establishment of productivity equation of low-permeability condensate gas well considering the influence of multiple factors
In the process of depletion development of condensate gas reservoir, once formation pressure is lower than dew point pressure of condensate gas, the change in phase behavior will happen and condensate oil will appear, which will result in the change in seepage rule in formation. Based on steady seepage theory of condensate gas, the following assumptions are made. ① Seepage of gas and condensate oil in formation abides by non-Darcy rule. For the gas, high-velocity turbulence effect near the well, threshold pressure gradient effect, stress sensitivity and slippage effect are considered. For the condensate oil, threshold pressure gradient and stress sensitivity are considered. ② The stress-sensitive relationship between reservoir permeability and effective stress is exponential. ③ The threshold pressure gradient of gas phase and condensate oil phase is the same. ④ The influence of capillary pressure is ignored. ⑤ Formation temperature is constant in the process of seepage. According to these assumptions, productivity equation of low-permeability condensate gas well considering the influence of multiple factors is established.
Solution of productivity equation of low-permeability condensate gas well considering the influence of multiple factors
To calculate gas well productivity by Eq. (19), the key is to solve three integral terms including pseudo-pressure m(p), turbulence coefficient B and pseudo-threshold pressure coefficient C.
Solution of pseudo-pressure m(p)
Solution of coefficients B and C in the productivity equation
Analysis of single factor impact
Tested components and compositions of condensate gas
Molar composition (%)
Molar composition (%)
Statistical table of gas–liquid parameters under different pressures of fluid in a condensate gas reservoir
Condensate oil viscosity (mPa s)
Gas viscosity (mPa s)
Condensate oil density (kg/m3)
Gas density (kg/m3)
Condensate oil saturation (%)
Comparison table of productivity calculation results of a condensate gas well considering different factors
Calculated production rate (104 m3/day)
Phase change + slippage
Phase change + stress sensitivity
Phase change + stress sensitivity + slippage
Phase change + stress sensitivity + slippage + threshold pressure
Multifactor sensitivity analysis based on orthogonal design
Level table of influencing factors for productivity of a low-permeability condensate gas well
Threshold pressure gradient λ (MPa/m)
Stress sensitivity coefficient α (1/MPa)
Slippage factor b (MPa)
Condensate oil saturation So (%)
Orthogonal experiment result table L9(34) with 4 factors influencing productivity of a low-permeability condensate gas well (Pwf = 12 MPa)
Production rate (104 m3/day)
Orthogonal experiment result table L9(34) with 4 factors influencing productivity of a low-permeability condensate gas well (Pwf = 20 MPa)
Production rate (104 m3/day)
In Tables 5 and 6, k1, k2, k3 are average values of production rate at the same level for each factor. R is the difference between the maximum and the minimum of k1–k3. The bigger the R is, the more obvious the influence of this factor is. Results indicate that in the range of threshold pressure gradient λ = 0–0.004 MPa/m, stress sensitivity coefficient α = 0–0.06/MPa, slippage factor b = 0–0.6 MPa, condensate oil saturation So = 0–6%, when bottom hole pressure is 10–17.5 MPa, the order of productivity influencing factors in low-permeability condensate gas wells is stress sensitivity > retrograde condensate phase change > threshold pressure gradient > slippage effect. When bottom hole pressure is 17.6–24.7 MPa, the order of productivity influencing factors in low-permeability condensate gas wells is stress sensitivity > threshold pressure gradient > retrograde condensate phase change > slippage effect. When bottom hole pressure is 24.8–33.8 MPa MPa, the order of productivity influencing factors in low-permeability condensate gas wells is threshold pressure gradient > stress sensitivity > retrograde condensate phase change > slippage effect. Within different ranges of bottom hole pressure, corresponding measures can be taken to improve the productivity of gas well according to the key sensitive factors affecting the productivity of low-permeability condensate gas well.
In low-permeability condensate gas reservoir, because of condensate banking or blockages near the well bore area, two-phase flow of gas and condensate oil arises in the reservoir. The relative permeability and mobility of each fluid are different, and they compete for flow toward the well. Compared to conventional dry gas reservoir, seepage mechanism is more complicated in low-permeability condensate gas reservoir, where two-phase flow with various non-Darcy effects of gas and condensate oil should be considered simultaneously.
The binomial productivity equation with the form of pseudo-pressure in low-permeability condensate gas well is established considering the comprehensive effect of multiple factors including threshold pressure gradient, stress sensitivity, slippage effect, retrograde condensate effect, high-speed non-Darcy effect. The integrals of pseudo-pressure, turbulence factor and pseudo-threshold pressure are calculated with numerical method to resolve the productivity equation.
The productivity of an example well is calculated by considering different factors. Results indicate that slippage effect increases apparent permeability; thus, the pseudo-pressure and gas well production rate increase. Retrograde condensate effect decreases gas relative permeability and gas well production. The apparent permeability decreases with the increase in effective stress, so pseudo-pressure and gas well production rate decreases. Threshold pressure gradient reduces the production pressure difference; therefore, the productivity of gas well decreases.
Based on orthogonal experiment design, the sensitivity factors affecting productivity of low-permeability condensate gas well are analyzed in different ranges of bottom hole pressure. The research lays a theoretical foundation for taking measures to improve gas well productivity in the gas field.
The authors wishes to acknowledge the assistance of the National Natural Science Foundation of China (51574052), the Chongqing Basic Science and Advanced Technology Research Project (cstc2016jcyjA0293), the Science and Technology Research Project of Chongqing Municipal Education Committee (KJ1601319), the University Innovation Team Project of Chongqing Municipal (CXTDX201601033) and the Internal research fund of Chongqing University of Science and Technology (ck2017zkyb006).
- Farhoodi S, Sadeghnejad S, Dehaghani AHS (2019) Simultaneous effect of geological heterogeneity and condensate blockage on well test response of gas condensate reservoirs. J Nat Gas Sci Eng 66:192–206Google Scholar
- Gao H, Cheng L, Feng R (2008) Productivity calculation of horizontal wells in low-permeability gas reservoirs considering starting pressure gradient. Nat Gas Ind 28(7):75–77Google Scholar
- Guo X, Wu Y (2007) Influence of start-up pressure gradient and stress sensitivity on productivity of low-permeability gas reservoirs. Oil Gas Geol 289(4):539–543Google Scholar
- He J, Hu Y, He D et al (2013) Productivity prediction methods for tight gas reservoir with low permeability. Fault-Block Oil Gas Field 20(3):334–336Google Scholar
- Liao F, Miao J, Chen W et al (2012) The new calculation method of condensate gas well production and reservoirs. J Southwest Pet Univ (Sci Technol Ed) 34(4):100–104Google Scholar
- Lu D, He P, Niu C et al (2014) Dynamic productivity calculation of condensate gas wells considering flash evaporation. Nat Gas Ind 34(10):47–53Google Scholar
- Luo R, Cheng L, Zhu H et al (2007) Problems on the study of slippage effect in low-permeability gas reservoirs. Nat Gas Ind 27(4):92–94Google Scholar
- Qi Z, Li Z, Lei D et al (2011) The productivity calculation model of abnormal high pressure and low permeability condensate gas well. Oil-Gas Field Surf Eng 30(8):8–9Google Scholar
- Shar AM, Mahesar AA, Chandio AD et al (2017) Impact of confining stress on permeability of tight gas sands: an experimental study. J Pet Explor Prod Technol 7(3):1–10Google Scholar
- Shi P, Li X, Liu Y (2006) Deliverability equation study of gas condensate well considering phase change. Oil Drill Prod Technol 28(4):68–70Google Scholar
- Sun L, Li C, Li C et al (2009) Stress sensitivity effect of low-permeability gas reservoirs and production analysis of gas wells. Nat Gas Ind 29(4):74–76Google Scholar
- Wang D, Wang X, Yan J et al (2012) Study on the influence of non-Darcy effects on the gas well productivity in low-permeability gas reservoirs. Spec Oil Gas Reserv 19(5):97–99Google Scholar
- Wu X, An Y, Li F (2008) Productivity of horizontal gas wells considering reservoir damage effects. Nat Gas Ind 28(97):78–80Google Scholar
- Xue Z, Liu P, Xia J et al (2014) A new method of correction of gas condensate well productivity considering capillary number. J Chongqing Univ Sci Technol (Nat Sci Ed) 16(2):78–81Google Scholar
- Yan W, Guo X, Sun L (2006) A new equation for estimating gas well productivity in low-permeability gas reservoirs. Nat Gas Ind 26(1):88–89Google Scholar
- Yan W, Sun L, Cheng X et al (2007) Appraisal and analysis of deliverability by special flow mechanism in low-permeability gas reservoir. Nat Gas Ind 27(11):76–78Google Scholar
- Yuan Y, Zhang L, Wang J et al (2009) A binomial deliverability equation for horizontal gas wells in formations with nonlinear seepage flow features. Oil Gas Geol 30(1):122–126Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.