New method for analysis of oil and gas well production decline

  • Nu-tao WANG , 1 ,
  • Ling-yun DU 1 ,
  • Hai-bo HE 2 ,
  • Huo-yang LIN 2 ,
  • Ming-qian ZHU 1
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  • 1. Oil and Gas Engineering Institute of Southwest Petroleum University, Chengdu 610500, China
  • 2. Research Institute of Petroleum Exploration & Development, Dagang Oilfield Company, CNPC, Tianjin 300280, China

Received date: 2019-07-10

  Revised date: 2019-11-19

  Online published: 2020-03-26

Supported by

The China National Science & Technology Major Project during the 13th Five Year Plan(2016ZX05048-004-005)

Highlights

According to the study of production decline law of oil and gas fields, many researchers have proposed a variety of production decline models, such as Arps model, SEPD model, Duong model and combination model. In practical production, due to the variety of declining models and different use conditions, it is difficult to choose the optimal decline model because of the complexity of decline models and different conditions. The usual practice is to fit the actual production data by linear fitting or nonlinear fitting method, and determine the selected model by the correlation coefficient. When use those methods, you will waste time on fitting each model. Based on this, a new production decline model is proposed in this paper. Through theoretical verification, it is determined that the model includes not only Arps decline law, but also SEPD model and Duong model. Through the analysis of actual production data, the method has high fitting accuracy and wide application range, which can effectively avoid the problem of model selection and provide a basis for the selection of decline analysis method.

Cite this article

Nu-tao WANG , Ling-yun DU , Hai-bo HE , Huo-yang LIN , Ming-qian ZHU . New method for analysis of oil and gas well production decline[J]. Natural Gas Geoscience, 2020 , 31(3) : 335 -339 . DOI: 10.11764/j.issn.1672-1926.2019.11.007

0 引言

研究大量现场实际生产经历可以发现,50%左右的油气可采地质储量都是在产量递减过程中产出,递减期内产出油气数量大,持续时间长,递减规律复杂[1]。因此,研究产量递减规律对油气田生产动态预测、油气生产规划工作具有重要意义[2]。基于此,国内外研究者[3]提出了大量产量递减模型,其中的Arps模型递减应用最为广泛,但是利用该模型分析常规油气井产量递减时,很多情况下出现递减指数可能出现n<-1或n>1的情况,造成累计产量无限大的不合理性[4]。主要原因在于Arps递减模型适合于达到拟稳定状态的流动,而致密低渗透油气井生产很难达到拟稳定状态。因此,在此模型基础上,国内外学者[5,6]提出了通过对Arps模型中的递减指数加以修正的方法,还有学者提出了一些新模型,如SEPD模型[7,8]、Duong模型[9,10]和组合模型[11,12,13]。SEPD模型与Arps模型中指数递减类似,区别在于:Arps指数递减的递减率为常数,而SEPD模型递减率是变化的[14];Duong模型基本原理是当流体处于裂缝线性流时,流量与时间存在一定关系,当气井产量递减处于缓慢递减的稳定阶段时,该方法预测结果较为准确,但是受生产前期液体反排或工作制度影响,会导致生产数据离散波动,造成多解问题。与此同时,这些模型在实际应用时,具体选择哪种模型进行产量递减分析往往难以确定[15]。针对以上问题,本文提出一种新的产量递减模型。

1 产量递减新模型推导

油气井产量递减模型主要有Arps模型、SEPD模型、Duong模型等,这3种方法具体产量预测公式如下:
Arps模型[3]
q = q i 1 + D i n t 1 / n
SEPD模型[7,8]
q = q i 1 + D i n t 1 / n q = q i e - t τ n
Duong模型[9,10]:
q = q i t - m
式中:q i为最大或初始产量, m3/d;q为某时刻的产量, m3/d;D i为递减率;t为生产时间, d;τ为时间常数;mn为指数系数。
将Arps递减公式(1)按泰勒展开式展开为:
q = q i 1 + D i n t 1 n = q i 1 + 1 n D i n t + 1 n 1 n - 1 ( D i n t ) 2 2 ! +
将公式(2)按泰勒展开式展开为:
q = q i e - t τ n = q i e t τ n = q i 1 + t τ n + 1 2 ! t τ 2 n +
公式(3)可以写成:
q = q i t m
从式(4)、式(5)、式(6)可以看出,这些递减公式的分母都是关于时间t的多项式或多次幂,因此将式(4)—式(6)的通式可以写成(取前面3项即可):
q = q i 1 + a t + b t 2
从式(7)可以看出,产量递减预测是以初始产量为基础,上式分子为初始递减产量,是一个常数,分母是关于t 的二次函数。因此作出q/q it关系曲线,见图1,图中红色横线即为初始产量,选取不同初始点,该值不同。同时,若旋转该直线,即可得到不同产量递减模型,现在将图1沿顺时针和逆时针分别旋转得到图2,从图2可以看出原来递减常数旋转后就变成不同的直线,此时直线方程可以写成的形式,因此新的递减模型可以写成:
q = q i + c t 1 + a t + b t 2
图1 各种递减模型示意

Fig.1 Schematic diagram of various decreasing models

图2 新的递减模型组合图

Fig.2 New descending model combination chart

利用该递减模型产量递减分析时,将ab作为拟合参数,对实际生产数据进行非线性拟合即可。

2 产量递减新模型理论验证

先用最基本的Arps递减方法验证,假设n=0.6,D i=0.1,q i=1.0,Arps模型计算与新模型计算结果如图3所示,从图中可以看出,新模型完全可以包含Arps递减模型。
图3 Arps递减模型与新模型对比

Fig.3 Comparison of Arps declining model and new model

用SEPD递减模型验证,假设n=0.6,τ=1.0,q i=1.0,SEPD模型计算与新模型计算结果如图4所示,从图中可以看出,新模型完全可以包含SEPD递减模型。
图4 SEPD递减模型与新模型对比

Fig.4 Comparison of SEPD declining model and new model

用Duong递减模型验证,假设n=1.0,q i=1.0,Duong模型计算与新模型计算结果如图5所示,从图中可以看出,新模型完全可以包含Duong递减模型。
图5 Duong递减模型与新模型对比

Fig.5 Comparison of Duong declining model and new model

由此可以看出新的递减模型完全包含了Arps、SEPD和Duong递减模型,新模型适应范围更广泛,在进行递减规律分析时,不需要对递减模型做选择,直接进行生产递减拟合即可。

3 实例分析

利用文献[12]的生产数据,用各种递减模型分别对某低渗透气井生产历史进行拟合,该井基础数据见表1,其拟合效果如图6所示,这种新递减模型拟合曲线相关系数达到0.844,与Duong模型接近,是所有模型中相关系数最高的,见表2所示,说明该井递减模型主要以Duong模型为主。
表1 基础参数

Table 1 Basic parameter

参数 数值 参数 数值
气藏初始压力/MPa 16.7 压裂裂缝条数 9
气藏厚度/m 12 基质渗透率/(10-3 μm2) 0.05
基质孔隙度/% 8 水平井水平段长度/m 1 086
图6 各种递减模型拟合曲线对比

Fig.6 Comparison graph of various decreasing model fitting curves

表2 各种递减模型计算对比

Table 2 Various decreasing models calculation comparison

模型 Arps模型 SEPD模型 Duong模型 新模型
拟合相关系数 0.722 0.616 0.817 0.844

4 结论

(1)各递减模型对比发现,Arps递减模型适用于晚期递减,而Duong模型和SEPD模型适用于早期递减,从各个模型计算结果来看,Duong模型预测结果偏高,而SEPD模型则偏低。
(2)通过将Arps递减模型及SEPD模型公式进行泰勒展开,发现Arps、SEPD、Duong共3种模型递减公式的分母都是关于时间t的多项式或多次幂,取前3项可得到其通式。
(3)新递减模型综合3种模型适用范围,且拟合效果较原3种模型有所提高,能避免模型选择,减少工作量。
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