超深层高压油气藏天然气偏差系数计算新模型

杨鹏程; 薛浩楠; 李升; 陈科杉

doi:10.11911/syztjs.2023112

超深层高压油气藏天然气偏差系数计算新模型

1.
中国石油集团西部钻探工程有限公司井下作业公司，新疆克拉玛依 834000
2.
中国石油大学（华东）石油工程学院，山东青岛 266580

详细信息

作者简介:
杨鹏程（1980—），男，辽宁海城人，2006年毕业于中国石油大学（华东）石油工程专业，工程师，主要从事储层改造工作。E-mail：38850115@qq.com

中图分类号: TE311⁺.1
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出版历程
- 收稿日期: 2023-03-10
- 修回日期: 2023-10-31
- 网络出版日期: 2023-12-06
- 刊出日期: 2023-11-24

A New Model for Calculating Deviation Factor of Natural Gas in Ultra-Deep Oil and Gas Reservoirs under High Pressure

1.
Downhole Operation Company, CNPC Xibu Drilling Engineering Company Limited, Karamay, Xinjiang, 834000, China
2.
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, Shandong, 266580, China

摘要

摘要:
为适应我国深层、超深层高压油气藏钻采需要，利用高温高压PVT特性测量系统，开展了高压条件下不同组分天然气样品的PVT特性测量试验，试验结果表明，高压下天然气偏差系数随压力升高大致呈线性增大，随温度升高而减小，但总体差别较小。基于1443组Standing-Katz图版拟合数据、试验测量数据和公共试验数据，建立了大温度压力范围的天然气偏差系数试验数据库。采用多元非线性拟合数值方法，对现有模型进行改进，建立了计算超深层高压油气藏天然气偏差系数的新模型。将该模型与常用的HY法、DPR法、LXF法等方法进行了对比，误差分析表明，该模型在高压段的相对误差在2%以内，计算精度高于HY法、DPR法、LXF法等方法，满足工程要求，可以为超深层高压油气藏安全高效钻采提供指导与帮助。
- 超深层高压油气藏 /
- 天然气偏差系数 /
- 数据库 /
- 计算模型 /
- Standing-Katz图版 /
- 误差
Abstract:
In order to meet the drilling and production requirements of deep and ultra-deep oil and gas reservoirs under high pressure in China, PVT characteristic measurement experiments of natural gas samples with different components under high-pressure conditions were carried out by using high-temperature and high-pressure PVT characteristic measurement system. The experiments show that the deviation factor of natural gas under high pressure increases linearly with the increase in pressure and decreases with the increase in temperature, but the overall difference is small. At the same time, an experimental database of the deviation factor of natural gas in a large temperature and pressure range is established based on 1443 sets of data including Standing-Katz chart fitting data, experimental measurement data, and public experimental data. Through the numerical method of multivariate nonlinear fitting, the existing models are improved, and a new model for calculating the deviation factor of natural gas of ultra-deep oil and gas reservoirs under high pressure is established. The predicted results of the model are compared with those of HY, DPR, LXF, and other common methods. The error analysis shows that the relative error of the model is less than 2% in the high-pressure section, and its calculation accuracy is higher than that of HY, DPR, LXF, and other methods, which meets the practical needs of engineering and can provide guidance and support for safe and efficient drilling and production of ultra-deep oil and gas reservoirs under high pressure.
- ultra-deep reservoirs under high pressure /
- deviation factor of natural gas /
- database /
- calculation model /
- Standing-Katz chart /
- error

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图 1 超高压全可视PVT测试系统结构示意

Figure 1. Structure of ultra-high pressure and fully visual PVT test system

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图 2 试验条件下天然气样品1和样品2偏差系数的分布规律

Figure 2. Distribution law of deviation factor of natural gas of sample 1 and sample 2 under experimental conditions

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图 3 S-K图版和外推得到的高压段偏差系数图版

Figure 3. S-K chart and extrapolated deviation factor relationship chart of high-pressure section

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图 4 高压下天然气偏差系数试验数据库

Figure 4. Experimental database of deviation factor of natural gas under high pressure

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图 5 A(T_pr)和B(T_pr)分别与拟对比温度T_pr的关系

Figure 5. Relationship of A(T_pr) and B(T_pr) with temperature T_pr respectively

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图 6 新模型以及不同计算方法与实测天然气偏差系数对比

Figure 6. Comparison of deviation factor of natural gas of new model and different calculation methods with measured data

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表 1 样品1和样品2天然气组分分析结果

Table 1 Analysis of natural gas components of sample 1 and sample 2

组分	含量，%
组分	样品1	样品2
二氧化碳	1.782	0.53
氮气	0.302	0.66
甲烷	81.493	95.04
乙烷	12.042	2.46
丙烷	2.606	0.44
异丁烷	0.445	0.11
正丁烷	0.518	0.12
异戊烷	0.162	0.06
正戊烷	0.132	0.05
己烷	0.150	0.10
庚烷	0.096	0.10
辛烷	0.071	0.12
壬烷	0.029	0.06
癸烷	0.028	0.03
十一烷及以上	0.145	0.11

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表 2 常用天然气偏差系数计算方法

Table 2 Commonly used calculation method for deviation factor of natural gas

计算方法	模型形式	适用范围
Beggs-Brill法^[26]	$Z = A\left( {1 - A} \right)\exp \left( { - B} \right) + Cp_{ {\text{pr} } }^D$	0≤p_pr≤10.0； 1.2≤T_pr≤2.4
HY法^[19]	$Z = \left[ {\dfrac{ {0.061\;25{p_{ {\text{pr} } } }t} }{ { {\rho _{ {\text{pr} } } } } } } \right]\exp \left[ { - 1.2{ {(1 - t)}^2} } \right]$	0.1≤p_pr≤24.0； 1.2≤T_pr≤3.0
DPR法^[20]	${\begin{gathered} Z = 1 + \left( { {A_1} + {A_2}/{T_{ {\text{pr} } } } + {A_3}/T_{ {\text{pr} } }^3} \right){\rho _{ {\text{pr} } } } +\\ \left( { {A_4} + {A_5}/{T_{ {\text{pr} } } } } \right)\rho _{ {\text{pr} } }^2 + {A_5}{A_6}\rho _{ {\text{pr} } }^5/{T_{ {\text{pr} } } }+ \\ {A_7}\left( {1 + {A_8}\rho _{ {\text{pr} } }^2} \right)\rho _{ {\text{pr} } }^2\exp \left( { - {A_8}\rho _{ {\text{pr} } }^2} \right)/T_{ {\text{pr} } }^3 \end{gathered} }$	0.2≤p_pr≤30.0； 1.05≤T_pr≤3.00
DAK法^[21]	$\begin{gathered} Z = 1 + \left( { {A_1} + {A_2}/{T_{ {\text{pr} } } } + {A_3}/T_{ {\text{pr} } }^3 + {A_4}/T_{ {\text{pr} } }^4 + {A_5}/T_{ {\text{pr} } }^5} \right){\rho _{ {\text{pr} } } } + \\ \left( { {A_6} + {A_7}/{T_{ {\text{pr} } } } + {A_8}/T_{ {\text{pr} } }^2} \right)\rho _{ {\text{pr} } }^2 - {A_9}\left( { {A_7}/{T_{ {\text{pr} } } } + {A_8}/T_{ {\text{pr} } }^2} \right)\rho _{ {\text{pr} } }^5 +\\ {A_{10} }\left( {1 + {A_{11} }\rho _{ {\text{pr} } }^2} \right)\left( {\rho _{ {\text{pr} } }^2/T_{ {\text{pr} } }^3} \right)\exp \left( { - {A_{11} }\rho _{ {\text{pr} } }^2} \right) \end{gathered}$	0.2≤p_pr＜30.0； 1＜T_pr≤3
E.Heidaryan等的方法^[27]	$Z = \dfrac{{{A_1} + {A_2}\ln \left( {{p_{{\text{pr}}}}} \right) + {A_3}{{\left( {\ln {p_{{\text{pr}}}}} \right)}^2} + {A_4}{{\left( {\ln {p_{{\text{pr}}}}} \right)}^3} + \dfrac{{{A_5}}}{{{T_{{\text{pr}}}}}} + \dfrac{{{A_6}}}{{T_{{\text{pr}}}^2}}}}{{1 + {A_7}\ln \left( {{p_{{\text{pr}}}}} \right) + {A_8}{{\left( {\ln {p_{{\text{pr}}}}} \right)}^2} + \dfrac{{{A_9}}}{{{T_{{\text{pr}}}}}} + \dfrac{{{A_{10}}}}{{T_{{\text{pr}}}^2}}}}$	0.2≤p_pr≤15.0； 1.2≤T_pr≤3.0
LXF法^[11]	$Z = {x_{ {\text{F1} } } }{p_{ {\text{pr} } } } + {x_{ {\text{F2} } } }$	0≤p_pr≤30.0； 1.05≤T_pr≤3.00
ZGD法^[12]	$\begin{gathered} Z = \left( { {A_1}T_{{\rm{pr}}}^4 + {A_2}T_{{\rm{pr}}}^3 + {A_3}T_{{\rm{pr}}}^2} \right.\left. { + {A_4}{T_{{\rm{pr}}} } + {A_5} } \right){p_{{\rm{pr}}} }+ \\ \left( { {A_6}T_{{\rm{pr}}}^4 + {A_7}T_{{\rm{pr}}}^3} \right.{A_8}{T_{{\rm{pr}}} }^2\left. { + {A_9}{T_{{\rm{pr}}} } + {A_{10} } } \right) \end{gathered}$	8.0≤p_pr＜30.0； 1.05≤T_pr＜3.00
W-Z-G法^[23]	$Z = ap_{ {\text{pr} } }^2 + b{p_{ {\text{pr} } } } + c$	15.0≤p_pr≤30.0； 1.6≤T_pr≤2.4

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表 3 高压下天然气偏差系数试验数据库

Table 3 Experimental database of deviation factor of natural gas under high pressure

数据来源	p/MPa	T/K	数据点数
文献[33]	70.00～100.00	323.15～413.15	60
文献[34]	70.00～110.00	359.79～384.85	20
文献[7]	70.00～122.88	409.85～429.85	33
文献[35]	70.00～118.89	313.20～407.20	320
文献[36]	70.00～110.00	313.15～404.55	60
文献[37]	70.00～114.68	399.25～437.65	26
本文试验数据	0～120.00	383.15～423.15	284
总计			803

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表 4 新模型计算值与实测值相对误差

Table 4 Relative error between calculated and experimental results of new model

本文试验数据						文献[39]试验数据
T_pr=1.71		T_pr=1.90		T_pr=2.18		T_pr=2.13
p_pr	相对误差，%	p_pr	相对误差，%	p_pr	相对误差，%	p_pr	相对误差，%
22.13	1.66	23.42	0.77	26.28	0.15	22.49	1.03
21.57	1.77	22.95	0.37	25.97	0.06	21.96	0.87
21.28	1.75	22.36	0.50	24.89	0.06	21.32	0.65
20.71	1.74	21.68	0.55	23.81	0.12	20.90	0.51
20.15	1.79	21.05	0.57	22.73	0.02	20.58	0.38
19.57	1.80	20.37	0.37	21.64	0.21	20.26	0.27
19.02	1.91	19.74	0.20	20.56	0.02	19.83	0.08
18.45	1.90	19.11	0.46	19.48	0.11	19.30	0.08
17.88	1.97	18.43	0.48	18.40	0.07	18.83	0.23
17.32	1.69	17.79	0.61	17.31	0.08	18.51	0.37
16.75	1.86	17.12	0.45	16.23	0.12	18.12	0.53
16.19	1.84	16.48	0.46	15.15	0.11
15.62	1.96	15.81	0.30			15.54	1.69
15.03	1.61					15.20	1.90
平均	1.80		0.47		0.09		0.78

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表 5 不同计算方法平均相对误差对比

Table 5 Comparison of average relative errors of different calculation methods

拟对比温度	平均相对误差，%
拟对比温度	HY法	DPR法	LXF法	ZGD法	W-Z-G法	新模型
T_pr=1.71	22.23	22.02	2.89	3.39	19.46	1.80
T_pr=1.90	23.38	23.73	0.67	0.51	8.38	0.47
T_pr=2.13^[39]	17.00	17.47	0.80	0.83	1.33	0.78
T_pr=2.18	21.86	22.04	0.99	1.09	3.22	0.09

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