﻿ 稠油油藏水平井热采吞吐产能预测新模型
 西南石油大学学报(自然科学版)  2018, Vol. 40 Issue (1): 114-121

Model for Capacity Forecasting of Thermal Soaking Recovery in Horizontal Wells in Heavy Oil Reservoirs
MA Kuiqian , LIU Dong
Tianjin Branch of CNOOC Co. Ltd., Binghai New Area, Tianjin 300459, China
Abstract: To address the lack of a suitable calculation model for productivity prediction of thermal soaking recovery in horizontal wells in conventional heavy oil reservoirs, by establishing composite geological model including heating zone and unheated zone and considering the difference of crude oil viscosity between the heating and unheated zones, an analytical model describing the production capacity of thermal soaking recovery in a single horizontal well was determined. Further, an equation for calculating the productivity increase of thermal soaking recovery with respect to cold recovery was proposed. The results show that the productivity multiple is mainly affected by factors such as the heating radius, oil layer thickness, and horizontal section length. Based on typical thermal recovery data in horizontal wells in the Bohai N oilfield, a mechanistic model was established. The heating radius of different soaking cycles was obtained by numerical simulation. On this basis, the increase of production capacity in different soaking cycles was calculated by the new model. It is predicted that the productivity increase of the first soaking cycle was 1.6 times, which was in good agreement with the evaluation results of the first thermal soaking cycle in the ten thermal soaking recovery horizontal wells at the Bohai N Oilfield.
Key words: heavy oil reservoir     horizontal well     steam soaking     heating radius     productivity prediction

1 热采吞吐水平井复合流动模型

 图1 水平井热采复合流动模型示意图 Fig. 1 Diagram for the horizontal well of cycle steam stimulation

2 吞吐产能增产倍数计算模型推导

(1) 单相、稳态流；

(2) 流体微可压缩；

(3) 各向同性、均质油藏，不考虑地层伤害；

(4) 外边界和井筒压力为常数；

(5) 水平井段与上边界距离一定。

2.1 常规水平井产能模型

Joshi利用电场流理论，假定水平井的泄油体是以水平井两端点为焦点的椭圆体，将三维渗流问题简化为垂直及水平面内的二维问题，利用势能理论推导了均质各向同性油藏水平井产能公式，得到了广泛的应用。Joshi导出的具有偏心距的水平井产能公式可表示为[13]

 $\left\{ \begin{array}{l} {{Q}_{\delta }}=\dfrac{2{π} {{K}_{{\rm o}}}h\Delta p}{{{\mu }_{{\rm o}}}{{B}_{{\rm o}}}\left[\ln \dfrac{a+\sqrt{{{a}^{2}}-{{\left( 0.5L \right)}^{2}}}}{0.5L}+\dfrac{h}{L}\ln \dfrac{{{\left( 0.5h \right)}^{2}}+{{\delta }^{2}}}{0.5h{{r}_{{\rm w}}}} \right]}\\ a=\dfrac{L}{2}{{\left[0.5+\sqrt{0.25+\dfrac{1}{{{\left( 0.5{L}/{{{r}_{{\rm e}}}}\; \right)}^{4}}}} \;\right]}^{0.5}} {, \kern 15pt}\left( L > \beta { h}{, \kern 10pt}\dfrac{{L}}{{\rm 2}}<0.9{{r}_{{\rm e}}} \right) \end{array} \right.$ (1)

${{K}_{{\rm o}}}$ —油相渗透率，mD；

$h$ —油层厚度， ${\rm m}$

$\Delta p$ —生产压差， ${\rm MPa}$

${{\mu }_{{\rm o}}}$ —原油黏度， ${\rm mPa}\cdot {\rm s}$

${{B}_{{\rm o}}}$ —原油体积系数，无因次；

$L$ —水平井水平段长度，m；

$\delta$ —水平井的偏心距，m；

${{r}_{{\rm w}}}$ —井筒半径，m；

${{r}_{{\rm e}}}$ —供油半径，m；

$\beta$ —水平渗透率与垂直渗透率之比的平方根，无因次。

 ${{Q}_{\delta }}\!=\!\dfrac{2{π} {{K}_{{\rm o}}}h\Delta p}{\mu {{B}_{{\rm o}}}\left[\ln \dfrac{a\!+\!\sqrt{{{a}^{2}}\!-\!{{\left( 0.5L \right)}^{2}}}}{0.5L}\!+\!\dfrac{h}{L}\ln \dfrac{0.5h\pm \delta }{{{r}_{{\rm w}}}} \right]}$ (2)

2.2 热采吞吐水平井产能模型

 ${{p}_{{\rm e}}}-{{p}_{{\rm wf}}}=\dfrac{{{q}_{{\rm l}}}{{\mu }_{{\rm l}}}}{2{π} K{{K}_{{\rm roc}}}h}\left[\ln \dfrac{{{a}_{{\rm l}}}+\sqrt{a_{{\rm l}}^{2}-{{\left( 0.5L \right)}^{2}}}}{0.5L}+\dfrac{h}{L}\ln \dfrac{0.5h+\delta }{{{r}_{{\rm w}}}} \right]$ (3)

${{q}_{{\rm l}}}$ —油井泄油量， ${{{{\rm m}}^{{\rm 3}}}}/{{\rm d}}\;$

${{\mu }_{{\rm l}}}$ —原始地层原油黏度， ${\rm mPa}\cdot {\rm s}$

$K$ —地层绝对渗透率，mD；

${{K}_{{\rm roc}}}$ —冷采时的油相相对渗透率，无因次。

 ${{A}_{\rm l}}=\left[\ln \dfrac{{{a}_{\rm l}}+\sqrt{a_{\rm l}^{2}-{{\left( {L}/{2}\; \right)}^{2}}}}{0.5L}+\dfrac{h}{L}\ln \dfrac{0.5h+\delta }{{{r}_{\rm w}}} \right]$ (4)
 ${{a}_{{\rm l}}}=\dfrac{L}{2}{{\left[0.5+\sqrt{0.25+{\left({\dfrac{r_{\rm e}}{0.5L}}\right)^{4}}} \;\right]}^{0.5}}%, \\{\kern 40pt}\left( L > \beta { h, }\dfrac{{ L}}{{\rm 2}}<0.9{{r}_{{\rm e}}} \right)$ (5)

 ${{p}_{{\rm h}}}-{{p}_{{\rm wf}}}=\dfrac{{{q}_{{\rm h}}}{{\mu }_{\operatorname{h}}}}{2{π} K{{K}_{{\rm roh}}}h}{\cdot}\\[6pt]{\kern 40pt}\left[\ln \dfrac{{{a}_{{\rm h}}}+\sqrt{a_{{\rm h}}^{2}-{{\left( 0.5L \right)}^{2}}}}{0.5L}+\dfrac{h}{L}\ln \dfrac{0.5h+\delta }{{{r}_{\rm w}}} \right]$ (6)
 ${{a}_{{\rm h}}}=\dfrac{L}{2}{{\left[0.5+\sqrt{0.25+\dfrac{1}{{{\left( 0.5{L}/{{{r}_{{\rm h}}}}\; \right)}^{4}}}} \;\right]}^{0.5}}, \\{\kern 40pt}\left( L > \beta { h}{, \kern 15pt}\dfrac{{ L}}{{\rm 2}}<0.9{{r}_{{\rm e}}} \right)$ (7)

${{q}_{{\rm h}}}$ —加热区的泄油量， ${{{{\rm m}}^{{\rm 3}}}}/{{\rm d}}\;$

${{\mu }_{{\rm h}}}$ —加热区的地层原油黏度， ${\rm mPa}\cdot {\rm s}$

${{K}_{{\rm roh}}}$ —加热区域的油相相对渗透率，无因次。

 ${{p}_{{\rm e}}}-{{p}_{{\rm h}}}=\dfrac{{{q}_{{\rm c}}}{{\mu }_{{\rm c}}}}{2{π} K{{K}_{{\rm roc}}}h}{\cdot}\\[8pt]{\kern 40pt}\left[\ln \dfrac{{{a}_{{\rm c}}}\!+\!\sqrt{a_{{\rm c}}^{2}\!-\!{{\left( 0.5L \right)}^{2}}}}{0.5L}\!+\!\dfrac{h}{L}\ln \dfrac{ 0.5h +\delta }{{{r}_{{\rm h}}}} \right]$ (8)
 ${{a}_{\rm c}}=\dfrac{L}{2}{{\left[0.5+\sqrt{0.25+\dfrac{1}{{{\left( 0.5{L}/{{{r}_{\rm e}}}\; \right)}^{4}}}} \right]}^{0.5}}, \\{\kern 40pt}\left( L > \beta { h}{, \kern 15pt}\dfrac{{ L}}{{\rm 2}}<0.9{{r}_{{\rm e}}} \right)$ (9)

${{q}_{{\rm c}}}$ —冷区的泄油量， ${{{{\rm m}}^{3}}}/{{\rm d}}\;$

${{\mu }_{{\rm c}}}$ —冷区的地层原油黏度， ${\rm mPa}\cdot {\rm s}$

 ${{q}_{{\rm h}}}={{q}_{{\rm c}}}={{q}_{{\rm s}}}$ (10)

$q_{\rm s}$ —井底处的泄油量，m3/d。

 ${{p}_{{\rm e}}}-{{p}_{{\rm wf}}}=\dfrac{{{q}_{{\rm s}}}}{2{π} Kh}\left( \dfrac{{{\mu }_{{\rm h}}}}{{{K}_{{\rm roh}}}}{{A}_{{\rm h}}}+\dfrac{{{\mu }_{{\rm c}}}}{{{K}_{{\rm roc}}}}{{A}_{{\rm c}}} \right)$ (11)
 ${{A}_{{\rm h}}}=\left[\ln \dfrac{{{a}_{\rm h}}\!+\!\sqrt{a_{\rm h}^{2}\!-\!{{\left( 0.5L \right)}^{2}}}}{0.5L}\!+\!\dfrac{h}{L}\ln \dfrac{0.5h\!+\!\delta }{{{r}_{{\rm w}}}} \right]$ (12)
 ${{A}_{{\rm c}}}=\left[\ln \dfrac{{{a}_{{\rm c}}}\!+\!\sqrt{a_{\rm c}^{2}\!-\!{{\left( 0.5L \right)}^{2}}}}{0.5L}\!+\!\dfrac{h}{L}\ln \dfrac{0.5h\!+\!\delta }{{{r}_{{\rm h}}}} \right]$ (13)

 ${{J}_{{\rm h}}}=\dfrac{{{q}_{{\rm s}}}}{{{p}_{{\rm e}}}-{{p}_{{\rm wf}}}}=\dfrac{2{π} Kh}{\left( \dfrac{{{\mu }_{{\rm h}}}}{{{K}_{{\rm roh}}}}{{A}_{{\rm h}}}+\dfrac{{{\mu }_{{\rm c}}}}{{{K}_{{\rm roc}}}}{{A}_{{\rm c}}} \right)}$ (14)

 $\overline{J}=\dfrac{{{J}_{{\rm h}}}}{{{J}_{{\rm l}}}}=\dfrac{{{A}_{{\rm l}}}}{\dfrac{{{\mu }_{{\rm h}}}}{{{\mu }_{{\rm l}}}}{{A}_{{\rm h}}}+{{A}_{{\rm c}}}}$ (15)

$\overline{J}$ —增产倍数，无因次。

 ${{\overline{J}}_{\mbox{ 简化} }}=\dfrac{{{J}_{{\rm h}}}}{{{J}_{{\rm l}}}}=\dfrac{{{A}_{{\rm l}}}}{{{A}_{{\rm c}}}}=\dfrac{\ln \dfrac{{{a}_{\rm l}}+\sqrt{a_{\rm l}^{2}-{{\left( 0.5L \right)}^{2}}}}{0.5L}+\dfrac{h}{L}\ln \dfrac{0.5h+\delta }{{{r}_{{\rm w}}}}}{\ln \dfrac{{{a}_{\rm c}}+\sqrt{a_{\rm c}^{2}-{{\left( 0.5L \right)}^{2}}}}{0.5L}+\dfrac{h}{L}\ln \dfrac{0.5h+\delta }{{{r}_{{\rm h}}}}}$ (16)
3 增产倍数影响因素分析

3.1 无因次加热半径的影响

 图2 增产倍数随无因次加热半径的变化 Fig. 2 Influence of dimensionless heated radius

3.2 原油黏度降低程度的影响

 图3 增产倍数随原油黏度降低程度的变化( $r_{\rm h}/r_{\rm e}=0.2$ ) Fig. 3 Influence of oil viscosity reduction( $r_{\rm h}/r_{\rm e}=0.2$ )

4 矿场应用实例 4.1 新模型的理论预测

 图4 N油田水平井注多元热流体后的温度场（数值模拟结果） Fig. 4 Temperature field after steam injection for N Oilfield(numerical model result)

 图5 水平井加热半径随吞吐周期的变化（数值模拟） Fig. 5 Heated radius of horizontal well(numerical model result)

 图6 热采增产倍数随吞吐周期的变化 Fig. 6 ROPI calculated by analytical model

4.2 矿场效果评价

 图7 N油田热采水平井井位图 Fig. 7 Thermal wells of N Oilfield

5 结语

(1) 以常规冷采水平井产能计算模型为基础，通过建立加热区和冷区的复合流动模型，考虑加热区和冷区原油黏度随温度变化的差异，研究了水平井单井热采吞吐产能预测解析模型，推导了水平井热采增产倍数的预测模型，可方便地预测热采水平井吞吐产能，有助于新油田热采方案设计。

(2) 热采吞吐水平井产能的增产倍数，取决于油层被加热的范围和加热区内原油的黏度降低程度。相同井距时，无因次加热半径越大，增产倍数越大；相同无因次加热半径时，井距越小，增产倍数越大。

(3) 以渤海N油田热采水平井典型模型为基础，用新模型计算了不同吞吐轮次的产能增产倍数，预测第一轮吞吐的增产倍数为1.6倍，该预测值与渤海N油田10口热采吞吐水平井第一轮吞吐效果评价的结果吻合程度较高。本文方法工程计算简单，计算精度满足海上实际要求，对于渤海油田普通稠油油藏后续热采方案研究具有指导意义。

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