A New Mathematical Model For Heat Radius of Cyclic Superheated Steam Stimulation with Horizontal Wellbore

He, Congge; Xu, Aiguo; Fan, Zifei; Zhao, Lun; Bo, Bing

doi:10.1155/2018/7601702

Cited by 3 publications

(6 citation statements)

References 13 publications

(11 reference statements)

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“… The formation thickness is relatively small, and therefore, the steam override effect is not taken into account, as shown in Figure A.

Heating process (A) and temperature distribution (B) of formation The hemispheric heating zones at the heel position and the toe position of the horizontal wellbore are ignored. The formation is divided into three zones: steam zone, hot fluid zone, and unheated zone. The temperature in the steam zone equals to the injected steam temperature, while the temperature in the hot fluid zone equals to the arithmetic mean value of the steam temperature and the initial reservoir temperature (as shown in Figure B). Heat transfers radially at the first stage; accordingly, the heated zone of each horizontal wellbore segment has the shape of cylinder.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Based on Equations and , the time that the hot fluid zone frontier is just reaching the boundary and the time that the steam zone frontier is just reaching the boundary can be expressed as

t_{1 i} = π M_{normalR} Δ l d^{2} {()(, \frac{H_{s i}}{T_{normals i} - T_{r}} + \frac{H_{w i}}{T_{normalh i} - T_{r}})}^{- 1}

t_{2 i} = π M_{normalR} Δ l d^{2} \frac{T_{s i} - T_{normalr}}{H_{normals i}},

where t 1 i is the time that the hot fluid zone frontier of the i ‐th segment reaches the boundary; t 2 i is the time that the steam zone frontier of the i ‐th segment reaches the boundary; d is the half thickness of the formation.…”

Section: Model Descriptionmentioning

confidence: 99%

“…When the hot fluid zone frontier reached the boundary but the steam zone frontier did not, that is, t 1 i ≤ t < t 2 i , the steam zone radius still can be obtained by Equation . Based on the energy conservation principle, a heat balance of hot fluid zone yields

\begin{matrix} H_{w i} = & \frac{4 Δ l}{\sqrt{π α_{s}}} {false\int}_{0}^{t - t_{1 i}} \frac{λ_{normals} (T_{h i} - T_{normalr})}{\sqrt{t - t_{1 i} - δ}} \frac{d (r_{h i} - d)}{d δ} d δ \\ + 2 π d M_{normalR} Δ l (T_{h i} - T_{normalr}) \frac{d (r_{h i} - d)}{dt}, \end{matrix}

where λ s is the thermal conduction coefficient of boundary; α s is the thermal diffusivity of boundary; δ is the instant at which the boundary becomes exposed to the hot fluid.…”

Section: Model Descriptionmentioning

confidence: 99%

“…For instance, for vertical wells, a part of heat loses to the boundary and the remaining part is used for heating the formation when the steam reaches the bottomhole. However, for the horizontal wells, the heating process is divided into several processes based on whether the frontier of heat area reaches boundary or not . More importantly, as the steam flows along the horizontal wellbore, the steam temperature, pressure, and quality always change with horizontal well length .…”

Section: Introductionmentioning

confidence: 99%

“…Hamid et al established a two‐dimensional transient heat conduction model to address the formation heating process by CSSHW with consideration of the effect of partial penetration of the horizontal well in radial coordinate. He et al built a mathematical model for heat radius of cyclic superheated steam stimulation with horizontal wellbore, and this method is adopted to calculate the heating radius of CSSHW in this paper. As for the production prediction of CSS and CSSHW, numerical thermal simulation method is usually adopted.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An integrated model for productivity prediction of cyclic steam stimulation with horizontal well

Fan

et al. 2019

Energy Science & Engineering

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As the accurate productivity prediction of cyclic steam stimulation with horizontal well (CSSHW) is essential for its effective utilization in heavy oil reservoirs, a novel integrated model for predicting productivity of CSSHW was proposed in this paper. Firstly, governing equations to predict thermophysical parameters of injected steam in the horizontal well were established. On the basis, the heating model for radius of hot fluid zone and steam zone were derived respectively according to a more realistic temperature distribution of formation. Then, coupled with heating model, the productivity prediction model was established according to the principle of equivalent percolation resistance. Then, comparisons have been made among the new model results, CMG STARS results, and measured data to verify its accuracy. Finally, after the new proposed model is validated, the effects of steam quality and injection rate on heating radius and oil production were analyzed in detail. The results indicate that the result of new model is in good agreement with that of CMG STARS and measured data, verifying the correctness of the model. In addition, the radius of hot fluid zone and steam zone both decreases with horizontal well length because of the heat losses as the steam flows along the horizontal wellbore. Influential factor analysis shows that high steam quality and steam injection rate can improve heating radius and cumulative oil production.

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“… The formation thickness is relatively small, and therefore, the steam override effect is not taken into account, as shown in Figure A.

Section: Model Descriptionmentioning

confidence: 99%

“…Based on Equations and , the time that the hot fluid zone frontier is just reaching the boundary and the time that the steam zone frontier is just reaching the boundary can be expressed as

t_{1 i} = π M_{normalR} Δ l d^{2} {()(, \frac{H_{s i}}{T_{normals i} - T_{r}} + \frac{H_{w i}}{T_{normalh i} - T_{r}})}^{- 1}

t_{2 i} = π M_{normalR} Δ l d^{2} \frac{T_{s i} - T_{normalr}}{H_{normals i}},

Section: Model Descriptionmentioning

confidence: 99%

\begin{matrix} H_{w i} = & \frac{4 Δ l}{\sqrt{π α_{s}}} {false\int}_{0}^{t - t_{1 i}} \frac{λ_{normals} (T_{h i} - T_{normalr})}{\sqrt{t - t_{1 i} - δ}} \frac{d (r_{h i} - d)}{d δ} d δ \\ + 2 π d M_{normalR} Δ l (T_{h i} - T_{normalr}) \frac{d (r_{h i} - d)}{dt}, \end{matrix}

where λ s is the thermal conduction coefficient of boundary; α s is the thermal diffusivity of boundary; δ is the instant at which the boundary becomes exposed to the hot fluid.…”

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An integrated model for productivity prediction of cyclic steam stimulation with horizontal well

Fan

et al. 2019

Energy Science & Engineering

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Mechanistic simulation study of air injection assisted cyclic steam stimulation through horizontal wells for ultra heavy oil reservoirs

Wang

Ren

Zhang

2019

Journal of Petroleum Science and Engineering

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An integrated heat efficiency model for superheated steam injection in heavy oil reservoirs

Fan

et al. 2019

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Accurate calculation of heat efficiency in the process of superheated steam injection is important for the efficient development of heavy oil reservoirs. In this paper, an integrated analytical model for wellbore heat efficiency, reservoir heat efficiency and total heat efficiency was proposed based on energy conservation principle. Comparisons have been made between the new model results, measured data and Computer Modelling Group (CMG) results for a specific heavy oil reservoir developed by superheated steam injection, and similarity is observed, which verifies the correctness of the new model. After the new model is validated, the effect of injection rate and reservoir thickness on wellbore heat efficiency and reservoir heat efficiency are analyzed. The results show that the wellbore heat efficiency increases with injection time. The larger the injection rate is, the higher the wellbore heat efficiency. However, the reservoir heat efficiency decreases with injection time and the injection rate has little impact on it. The reservoir thickness has no effect on wellbore heat efficiency, but the reservoir heat efficiency and total heat efficiency increase with the reservoir thickness rising.

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A New Mathematical Model For Heat Radius of Cyclic Superheated Steam Stimulation with Horizontal Wellbore

Cited by 3 publications

References 13 publications

An integrated model for productivity prediction of cyclic steam stimulation with horizontal well

An integrated model for productivity prediction of cyclic steam stimulation with horizontal well

Mechanistic simulation study of air injection assisted cyclic steam stimulation through horizontal wells for ultra heavy oil reservoirs

An integrated heat efficiency model for superheated steam injection in heavy oil reservoirs

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