利用Duhamel褶积方法确定气藏动态储量

Determination of the dynamic reserves by Duhamel method

赵文琪1 李 季 安颜颜3 王晓冬1 王平平

中国地质大学能源学院，北京 100083 中国地质大学工程技术学院，北京 100083 北京科技大学土木与环境工程学院，北京 100083 4．长庆油田分公司第六采油厂，陕西 定边 718606

1．Faculty of Energy Resources, China University of Geosciences, Beijing 100083, China School of Engineering and Technology, China University of Geosciences, Beijing 100083, China School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China 6 Oil Production Plant, Changqing Oilfield Company, CNPC, Dingbian 718606, China

针对目前利用物质平衡方法确定气藏储量仅局限于关井或定产的情况，文中以圆形封闭气藏为例提出了确定气藏动态储量的Duhamel褶积方法。首先利用Duhamel褶积方法解决油气井变产量生产问题的原理，推导得出油气井变产量不稳定渗流井底压力解，然后结合气藏拟稳态阶段的渗流特征，确立平均地层压力和累计产量之间的关系，再利用传统的物质平衡方法达到最终确定气藏动态储量的目的。通过一口实际生产的气井进行计算验证，该方法对于确定气藏的动态储量是十分有效和可行的。文章给出利用Duhamel褶积方法确定气藏动态储量的基本步骤，应用起来简单明了，所需参数少，气井在生产条件下就可确定其地质储量；适用于常流量和变流量2种情形。该方法可推广到其他情形的储层中。

Currently the material balance method is usually used to determine the gas-in-place. Since it can only be used in the case of well off or single rate well, Duhamel method is introduced to determine the dynamic gas-in-place in this paper and circular closed gas reservoir is taken as an example. Firstly it gives the derivation of the bottom-hole pressure of variable rate fluid flow in pseudo-steady-state by the Duhamel′s principle which is used to solve the problem of variable rate fluid flow.  Then combined with the fluid flow characteristic of pseudo-steady-state in gas reservoirs, we can fetch the relationship equations between cumulative production and average reservoir pressure. Finally, classical material balance method is used to determine the dynamic gas-in-place. A real gas production well is used to illustrate efficiency of this method. The results show that the method is efficient and workable in determining the dynamic reserve. Basic procedures of the new method are presented in this paper to determine the dynamic reserve of gas reservoir. The method has characteristics of simple and clear and can be used with fewer parameters. And the gas-in-place can be determined with well flowing. The method can be used both in stabilized rate and variable rate and can be extended to the application of other types of gas reservoirs.