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ABSTRACT
The accurate determination of reservoir heat efficiency of steam injection in heavy oil reservoirs is very important for heating radius calculation and production dynamic prediction. In conventional calculation methods of reservoir heat efficiency, the steam-injection wellbore is assumed as taking steam over the entire height. In fact, a liquid level in steam-injection wellbore is a very significant observation with respect to the steam override. Aiming at the actual situation that the steam-injection wellbore always has a liquid level, combined with the formation temperature distribution, the new mathematical model for reservoir heat efficiency with the consideration of liquid in steam-injection wellbore was established based on the Van Lookeren steam override theory and the energy conservation principle. The established mathematical model was used to calculate and analyze the reservoir heat efficiency of steam injection in heavy oil reservoirs. The results show that because the new mathematical model considers the liquid in the steam-injection wellbore, the predicted results are more reasonable, thus verifying the correctness of the new model. According to the influential factors analysis based on the new model, it is observed that although increasing the steam quality can effectively increase the steam-taking degree of the steam-injection wellbore, it has limited impact on reservoir heat efficiency. Moreover, the larger the steam-injection rate, the higher the steam-taking degree and reservoir heat efficiency. The reservoir heat efficiency decreases with the pay-zone thickness when the steam-injection wellbore has liquid.
Acknowledgments
This work was supported by the Major Projects of China (2017ZX05030).
Nomenclature
| Ah = | = | area of the hot-fluid zone, m2 |
| As = | = | area of the steam zone, m2 |
| Ahe = | = | area of hot-fluid-zone top, m2 |
| Ahb = | = | area of hot-fluid-zone bottom, m2 |
| ARD = | = | shape factor, dimensionless |
| g = | = | gravitational acceleration |
| hst = | = | thickness of the steam zone, m |
| hD = | = | ratio of the latent heat of steam to the sensible heat, dimensionless |
| hws = | = | specific enthalpy of water at the steam temperature, J/kg |
| hwr = | = | specific enthalpy of water at the reservoir temperature, J/kg |
| hst = | = | thickness of the steam zone at r, m |
| H = | = | thickness of the reservoir, m |
| Hst = | = | steam-taking thickness of the steam-injection wellbore, m |
| is = | = | injection rate of steam, kg/s |
| kst = | = | effective permeability of steam, mD |
| Lv = | = | latent heat of vaporization of steam, J/kg |
| L(·) = | = | Laplace transformation function |
| M* = | = | mobility ratio at reservoir temperature, dimensionless |
| MR = | = | heat capacity of the reservoir, J/(m3·°C) |
| Qs = | = | heat loss rate to the overburden of the steam zone, J/s |
| Qis = | = | heat injection rate of the steam zone, J/s |
| Qih = | = | heat injection rate of the hot-fluid zone, J/s |
| Qos = | = | heat growth of the steam zone, J/s |
| Qoh = | = | heat growth of the hot-fluid zone, J/s |
| r = | = | radial distance into the reservoir, m |
| res = | = | radius of the steam-zone top, m |
| S = | = | variable in Laplace space |
| t = | = | injection time, s |
| tD = | = | dimensionless time |
| Ts = | = | injected steam temperature, °C |
| Ti = | = | initial reservoir temperature, °C |
| Th = | = | temperature of the hot-fluid zone, °C |
| wsti = | = | steam mass flow rate at the injection end, kg/s |
| Vbst = | = | steam zone volume, m3 |
| Vb = | = | total reservoir volume, m3 |
| xi = | = | steam quality, dimensionless |
| Greek letters | = | |
| αs = | = | thermal diffusivity of the overburden and underburden, m2/d |
| λs = | = | thermal conduction coefficient of overburden and underburden, W/(m·°C) |
| μst = | = | steam viscosity, mPa·s |
| ρst = | = | steam density, kg/m3 |
| ρo = | = | oil density, kg/m3 |
| φ = | = | reservoir porosity, dimensionless |
| δ = | = | the instant at which the cold boundary becomes exposed to the hot fluid |
| η = | = | reservoir heat efficiency, dimensionless |