原位技术在超高静压食品加工中的应用研究进展

林颖凤; 付超; 张司南; 姚雪霜; 郑镇洪; 杨嘉欣; 蒋卓

doi:10.11858/gywlxb.20230815

原位技术在超高静压食品加工中的应用研究进展

doi: 10.11858/gywlxb.20230815

林颖凤^1,,
付超²,
张司南¹,
姚雪霜¹,
郑镇洪¹,
杨嘉欣¹,
蒋卓^1,*, ,

1.
华南农业大学食品学院, 广东广州　510642
2.
塔里木大学食品科学与工程学院, 新疆阿拉尔　843300

基金项目: 国家自然科学基金（22078117）

详细信息

作者简介:
林颖凤（1998－），女，硕士研究生，主要从事超高压灭菌研究. E-mail：1014137257@qq.com

通讯作者:
蒋　卓（1986－），男，博士，副教授，主要从事超高静压食品加工技术、高压原位技术研究.E-mail：jiangzhuo@scau.edu.cn

中图分类号: O521.9; Q518.4
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- 文章访问数: 185
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出版历程
- 收稿日期: 2023-12-15
- 修回日期: 2024-03-03
- 刊出日期: 2024-07-25

Research Progress of In-Situ Technology in Ultra-High Static Pressure Food Processing

1.
College of Food Science, South China Agricultural University, Guangzhou 510642, Guangdong, China
2.
School of Food Science and Engineering, Tarim University, Aral 843300, Xinjiang, China

摘要

摘要: 超高静压加工技术可应用于食品灭菌、改良食品品质以及活性成分提取等。传统研究中，高静压下的有机物结构及功能分析均是在压力释放后进行的，只有在压力施加过程中发生了不可逆变化才能在卸压后被测量出来，鲜少进行压力施加过程中的原位监测。原位测量可提供样品动态信息并了解其变化过程。基于此，近年来发展了许多高压下的原位研究工作。本文综述了高压原位分析技术的发展及其在高静压食品加工中的应用，主要包括高压下的蛋白质折叠与变性、淀粉糊化机理的原位研究、微生物原位监测等，并总结了原位技术在食品加工中的挑战。
- 原位技术 /
- 蛋白质 /
- 碳水化合物 /
- 微生物
Abstract: Ultra high static pressure processing technology holds promise for food sterilization, improving food quality, and extracting active ingredients. Traditional research typically assesses the analysis of the structure and function of organic matter under high static pressure after pressure release, capturing only irreversible changes occurring during compression. In-situ monitoring under pressure is rarely conducted. In-situ technology provides dynamic insights into sample behavior, offering a deeper understanding of its transformation process. Consequently, recent years have witnessed a surge in-situ studies performed under high pressure. This article reviews the advancement of high-pressure in-situ analysis technology and its application in high static pressure food processing. Key areas covered, include structural changes and phase transition intervals of protein folding and denaturation under high pressure, in-situ investigations into the mechanism of starch gelatinization, microbial in-situ monitoring and the challenges of in-situ technology in food processing.
- in-situ technology /
- protein /
- carbohydrates /
- microorganism

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我国页岩气可采资源量为2.508×10¹³ m^3[1]，四川盆地具有丰富的页岩气资源，已成为我国页岩气开发的主战场。四川盆地的页岩气储层埋深较大，其中龙马溪组的地层埋深普遍在4 000～4 500 m之间，埋深较浅处约为3 000～4 000 m^[2]。由于地下的地温梯度和静水压力梯度分别为0.03 K/m和0.01 MPa/m^[3]，所以龙马溪组的地层温度范围为378～423 K（地表温度按288 K计算）。Gensterblum等^[3]测定了甲烷在303、318、333和348 K（对应的储层深度分别为500、1 000、1 500和2 000 m）时的吸附等温线，发现甲烷的吸附能力与温度和孔隙压力有关。在不同温度（373～873 K）和不同压力（0.1～15.0 MPa）条件下，Geng等^[4]对油页岩进行了热解反应实验发现，随着温度的升高，孔隙率逐渐增大，裂隙的最大张开度也随之增大；最大孔隙率为室温下的13.52倍，裂隙总数为813条，裂隙最大孔径为0.383 mm。对于页岩储层，裂隙是气体流动的主要通道，气体解吸引起的体应变对页岩气的开采有着显著的影响。因此，建立热-流-固耦合作用下页岩的渗透率模型对准确预测深部页岩气的渗流规律尤为重要。

目前，国内外学者主要通过理论分析和室内实验相结合的方法研究温度对页岩渗透率的影响。利用岩石三轴渗流仪，赵瑜等^[5]研究了孔压和温度对页岩渗流的影响机理。利用自制的煤岩稳态实验装置，Wang等^[6]测试了我国无烟煤在不同气体压力和温度下的渗透率。吴迪等^[7]利用三轴渗流实验装置，研究了孔隙压力、体积应力和温度对页岩中CH₄气体渗流规律的影响。张道川等^[8]采用多场耦合作用下不同相态CO₂致裂驱替CH₄实验装置，研究了有效应力、孔隙压力、温度以及吸附膨胀等因素对裂隙页岩渗透特性的影响。基于典型S&D模型，李波波等^[9]建立了考虑温度和恒定外应力条件下的渗透率模型。Wang等^[10]采用高温三轴渗透率实验设备研究了现场应力条件下油页岩的各向异性渗透率。Schwartz等^[11]认为在恒定孔隙压力和温度变化下，页岩渗透率的演化规律可以用热解吸应变和页岩的热膨胀应变来描述，由此提出了热解吸渗透率增强模型。Teng等^[12]提出了变温度下煤气相互作用的热敏感性渗透率模型，该模型能够解释热膨胀、热压裂、基质吸附和裂隙表面的热挥发对煤渗透率的影响。在围压10～25 MPa、温度298～343 K、注入压力6～12 MPa作用下，Ju等^[13]测试了煤样的CO₂渗透率，建立了表征裂隙煤CO₂渗透率的力学模型。Sinha等^[14]利用稳态渗透率测试设备研究了应力、压力、温度、吸附作用和气体类型对完整页岩岩样渗透率的影响。

综上所述，国内外学者主要通过实验研究温度、围压、孔压和吸附等因素对页岩渗透率的影响，能够解释上述因素（特别是温度）对页岩渗透率影响的解析模型凤毛麟角。为此本研究将深部页岩储层简化为多孔弹性介质模型，考虑温度和吸附作用对渗透率的影响，推导页岩气开采过程中页岩储层的有效应力-渗透率模型，阐述围压、孔隙压力、有效应力、热解吸和温度对页岩渗透率的影响机理。然后，结合多孔介质弹性理论（考虑温度和解/吸附对变形的影响）建立页岩储层在单轴应变条件下的渗透率解析模型，利用实验数据验证该模型的有效性。最后，通过该模型分析不同温度下页岩渗透率的演化规律。

1. 温度作用下的有效应力-渗透率模型

页岩的孔隙率可以表示为

$\phi = \frac{{{V_{\rm{p}}}}}{{{V_{\rm{b}}}}}$

(1)

式中：V_p为页岩孔隙的体积，m³；V_b为页岩的体积，m³。对式(1)微分，获得

$\frac{{{\rm{d}}\phi }}{\phi } = - {\rm{d}}{\varepsilon _{\rm{p}}}+{\rm{d}}{\varepsilon _{\rm{b}}}$

(2)

式中：dε_p为孔隙的体应变增量，dε_b为页岩的体应变增量。

考虑有效应力、气体的解吸附和温度对页岩变形的影响，dε_b和dε_p分别为

${\rm{d}}{\varepsilon _{\rm{b}}} = - \frac{{{\rm{d}}{V_{\rm{b}}}}}{{{V_{\rm{b}}}}} = \frac{1}{K}\left( {{\rm{d}}\sigma - \alpha {\rm{d}}p} \right) - {\rm{d}}{\varepsilon _{\rm{s}}} - 3{\alpha _{\rm{T}}}{\rm{d}}T$

(3)

${\rm{d}}{\varepsilon _{\rm{p}}} = - \frac{{{\rm{d}}{V_{\rm{p}}}}}{{{V_{\rm{p}}}}} = \frac{1}{{{K_{\rm{p}}}}}{\rm{d}}\sigma - \left( {\frac{1}{{{K_{\rm{p}}}}} - \frac{1}{{{K_{\rm{s}}}}}} \right){\rm{d}}p - {\rm{d}}{\varepsilon _{\rm{s}}}$

(4)

式中：dV_b和dV_p分别为页岩的体积增量和孔隙的体积增量，m³；K、K_p和K_s分别为页岩的体积模量、孔隙体积模量和固体颗粒的体积模量，Pa；dσ为平均法向应力增量，Pa；dp为孔隙压力增量，Pa； ${\rm{d}}{\varepsilon _{\rm{s}}}$ 为吸附引起的体应变增量；α为Biot系数，α=1−K/K_s；α_T为页岩的线胀系数，K⁻¹；dT为温度增量，K。

联立式(2)、式(3)和式(4)，得到

$\frac{{{\rm{d}}\phi }}{\phi } = \left( {\frac{1}{K} - \frac{1}{{{K_{\rm{p}}}}}} \right)\left( {{\rm{d}}\sigma - {\rm{d}}p} \right) - 3{\alpha _{\rm{T}}}{\rm{d}}T$

(5)

对式(5)积分

$\frac{\phi }{{{\phi _0}}} = \exp \left\{ {\left( {\frac{1}{K} - \frac{1}{{{K_{\rm{p}}}}}} \right)\left[ {\left( {\sigma - {\sigma _0}} \right) - \left( {p - {p_0}} \right)} \right] - 3{\alpha _{\rm{T}}}\left( {T - {T_0}} \right)} \right\}$

(6)

式中： ${\phi _0}$ 为页岩的初始孔隙率；σ和σ₀分别为平均法向应力和初始平均法向应力，Pa；p和p₀分别为孔隙压力和初始孔隙压力，Pa；T和T₀分别为页岩气储层的温度和初始温度，K。

页岩气储层的渗透率和孔隙率的关系^[15]

$\frac{k}{{{k_0}}} = {\left( {\frac{\phi }{{{\phi _0}}}} \right)^3}$

(7)

式中：k和k₀分别为页岩气储层的渗透率和初始渗透率，m²。

将式(6)代入式(7)，考虑页岩的体积模量远大于其孔隙体积模量，得到考虑温度、吸附作用的有效应力-渗透率模型

$\frac{k}{{{k_0}}} = \exp \left[ { - \frac{3}{{{K_{\rm{p}}}}}\left( {{\sigma _{\rm{e}}} - {\sigma _{{\rm{e}}0}}} \right) - 9{\alpha _{\rm{T}}}\left( {T - {T_0}} \right)} \right]$

(8)

式中：σ_e和σ_e0分别为有效应力和初始有效应力，单位Pa，σ_e=σ−p，σ_e0=σ₀−p₀。

该模型第1项为有效应力变化引起的体应变增量，第2项为温度（储层深度）变化引起的体应变增量。页岩气开采过程中储层渗透率的演化本质是储层的应变演化影响孔隙体积，该渗透率模型综合考虑了有效应力、温度对储层渗透率的影响。

当不考虑温度对页岩气储层渗透率的影响时，式(8)可简化为文献[16-17]推导的煤的有效应力-渗透率模型

$\frac{k}{{{k_0}}} = \exp \left[ { - 3{C_{\rm{p}}}\left( {{\sigma _{\rm{e}}} - {\sigma _{{\rm{e}}0}}} \right)} \right]$

(9)

式中：C_p为孔隙压缩系数，单位Pa⁻¹，C_p=1/K_p。

2. 单轴应变条件下的热解吸渗透率模型

2.1 单轴应变条件下的热解吸渗透率模型

将页岩气储层简化为线弹性多孔介质，随着温度的升高，孔隙率和裂隙张开度均随之增大^[4]。因此，考虑温度作用，规定压应力和压应变为正，页岩气储层的本构关系

${\sigma _{ij}} = \lambda {\varepsilon _{\rm{kk}}}{\delta _{ij}}+2G{\varepsilon _{ij}}+\alpha p{\delta _{ij}}+K{\varepsilon _{\rm{s}}}{\delta _{ij}}+3K{\alpha _{\rm{T}}}T{\delta _{ij}}$

(10)

式中：σ_ij为应力分量，单位Pa；λ为拉梅常数，单位Pa，λ=Eμ/[(1+μ)(1−2μ)]；ε_kk为体应变；δ_ij为Kronecker符号；G为剪切模量，单位Pa，G=E/[2(1+μ)]；E为岩体的弹性模量，单位Pa；μ为泊松比；ε_ij为应变分量；α为Biot系数，α=1−K/K_s；K为体积模量，单位Pa，K=E/[3(1−2μ)]；K_s为固体颗粒体积模量，单位Pa。

当考虑温度作用时，气体吸附/解吸引起的体应变利用下式计算^[11]

${\varepsilon _{\rm{s}}} = {\varepsilon _{\rm{L}}}\frac{{{b_{\infty 0}}{{\left( {{T \mathord{\left/ {\vphantom {T {{T_0}}}} \right. } {{T_0}}}} \right)}^{ { - 1/2} }}\exp \left[ {{Q \mathord{\left/ {\vphantom {Q {RT}}} \right. } ({RT})}} \right]p}}{{1+{b_{\infty 0}}{{\left( {{T \mathord{\left/ {\vphantom {T {{T_0}}}} \right. } {{T_0}}}} \right)}^{ { - 1/2} }}\exp \left[ {{Q \mathord{\left/ {\vphantom {Q {RT}}} \right. } {(RT)}}} \right]p}}$

(11)

式中：ε_L为Langmuir体应变；b_∞0为在无限大压力下的亲和常数，单位Pa⁻¹， ${b_{\infty 0}} = \dfrac{1}{{p_{\rm{L}}}} \dfrac{1}{{\exp \left[ {{Q \mathord{\left/ {\vphantom {Q ({R{T_0}})}} \right. } ({R{T_0}})}} \right]}}$ ；p_L为Langmuir压力，单位Pa；Q为吸附热，单位J/mol；R为普适气体常数，单位J/(mol·K)。

联立式(8)、式(10)和式(11)，得到页岩气储层在单轴应变条件下的热解吸渗透率模型

$\begin{gathered} \frac{k}{{{k_0}}} = \exp \left\{ {\frac{3}{{{K_{\rm{p}}}}}\left[ {\frac{{1+\mu }}{{3\left( {1 - \mu } \right)}}\left( {p - {p_0}} \right) - \frac{{2E}}{{9\left( {1 - \mu } \right)}}\left( \begin{gathered} \frac{{{\varepsilon _{\rm{L}}}{b_{\infty 0}}{{\left( {{T \mathord{\left/ {\vphantom {T {{T_0}}}} \right. } {{T_0}}}} \right)}^{ { - 1/2} }}\exp \left( {{Q \mathord{\left/ {\vphantom {Q {RT}}} \right. } {(RT)}}} \right)p}}{{1+{b_{\infty 0}}{{\left( {{T \mathord{\left/ {\vphantom {T {{T_0}}}} \right. } {{T_0}}}} \right)}^{ { - 1/2} }}\exp \left( {{Q \mathord{\left/ {\vphantom {Q {RT}}} \right. } {(RT)}}} \right)p}} - \frac{{{\varepsilon _{\rm{L}}}{b_{\infty 0}}\exp \left( {{Q \mathord{\left/ {\vphantom {Q {R{T_0}}}} \right. } {(R{T_0})}}} \right){p_0}}}{{1+{b_{\infty 0}}\exp \left( {{Q \mathord{\left/ {\vphantom {Q {R{T_0}}}} \right. } {(R{T_0})}}} \right){p_0}}} \\ \end{gathered} \right)} \right]} \right\} \\ \quad \quad \exp \left\{ { - \frac{3}{{{K_{\rm{p}}}}}\left[ {\frac{{2E}}{{3\left( {1 - \mu } \right)}}+3{K_{\rm{p}}}} \right]{\alpha _{\rm{T}}}\left( {T - {T_0}} \right)} \right\} \\ \end{gathered}$

(12)

式中， ${K_{\rm{p}}} = {\phi _0}K$ ^[18]， ${\phi _0} = {{2{b_0}} \mathord{\left/ {\vphantom {{2{b_0}} {{a_0}}}} \right. } {{a_0}}}$ ^[19-20]。

2.2 热解吸渗透率模型的验证

文献[11]测试了Marcellus裂隙页岩和完整页岩岩样的渗透率比随温度的变化，分别见表1和表2。实验所用气体为CH₄，实验过程中保持围压（24 MPa）和孔隙压力（6 MPa）不变。

表 1 裂隙页岩的渗透率比

Table 1. Permeability ratio of fractured shale

Temperature/K	k/k₀ of fractured shale
295	1.000
303	1.044
313	1.113
323	1.211

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表 2 完整页岩的渗透率比

Table 2. Permeability ratio of intact shale

Temperature/K	k/k₀ of intact shale	Temperature/K	k/k₀ of intact shale
307.1	1.000	332.7	1.095
308.0	0.978	333.3	1.045
313.8	1.051	337.7	1.058
321.1	1.037	337.9	1.061
321.2	1.008	338.0	1.084
325.9	1.085

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| 显示表格

将式(12)热解吸渗透率模型的理论解和不同温度下Marcellus裂隙页岩的实验数据进行对比，当模型中的参数T₀=295 K^[11]、ε_L=1.7×10^−3[18]、b_∞0=1.83×10⁻⁴ MPa^−1[11]、Q=1.7×10⁴ J/mol^[11]、p=p₀=6 MPa、R=8.31 J/(mol·K)^[11]、μ=0.35、E=32.75 GPa^[21]、K_p=24.26 MPa、α_T=1.8×10⁻⁶ K⁻¹时，该模型的理论解与Marcellus裂隙页岩的实验数据对比如图1所示。

图 1 不同温度下热解吸模型解析解与裂隙页岩的实验数据对比

Figure 1. Comparison of analytical results of thermal-sorptive model and experimental data offractured shale under different temperatures

下载: 全尺寸图片幻灯片

图1中，当温度从295 K升高到323 K时，Marcellus裂隙页岩的渗透率增大了21.1%。由于黏土和有机质的解吸以及岩桥的热膨胀，裂隙页岩的渗透率比值随着温度的升高而逐渐增大。由此可见，该热解吸渗透率模型的理论解与Marcellus裂隙页岩的实验数据基本一致。

将式(12)的热解吸渗透率模型理论解与不同温度下Marcellus完整页岩（含天然裂隙）的实验数据进行对比，当模型中T₀=295 K^[11]、ε_L=1.7×10^−3[18]、b_∞0=1.83×10⁻⁴ MPa^−1[11]、Q=1.7×10⁴ J/mol^[11]、p=p₀=6 MPa、R=8.31 J/(mol·K)^[11]、μ=0.35，E=32.75 GPa^[21]、K_p=43.53 MPa、α_T=1.8×10⁻⁶ K⁻¹时，该模型的理论解与Marcellus完整页岩的实验数据对比见图2。

图 2 不同温度下热解吸模型解析解与完整页岩的实验数据对比

Figure 2. Comparison of analytical results of thermal-sorptive model and experimental data of intact shaleunder different temperatures

下载: 全尺寸图片幻灯片

由图2可知，随着温度的升高，完整页岩的渗透率比值呈反弹趋势，且整体逐渐增大，这是由于热解吸引起的孔隙膨胀量大于固体颗粒膨胀引起的孔隙闭合量。该渗透率模型的解析解能够与不同温度下Marcellus完整页岩的实验数据较好地吻合。

3. 温度作用下渗透率的演化机理

3.1 渗透率随温度和孔压变化的演化机理

由式(12)计算得到，页岩储层在单轴应变条件下的渗透率随温度和孔隙压力的演化规律如图3所示，储层初始温度为300 K，初始孔压为6 MPa。

图 3 渗透率随温度和孔压的演化规律

Figure 3. Evolution of permeability withtemperature and pore pressure

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如图3所示，当储层温度介于300～420 K范围内且保持不变时，随着孔隙压力的增大，渗透率比值先下降然后反弹，这是因为温度不变时，影响渗透率的因素主要为有效应力和气体吸附/解吸，随着孔隙压力的增大，有效应力减小，孔隙体积变大，导致渗透率增大；另一方面，孔隙压力增大，气体吸附量增大，孔隙体积减小，导致渗透率减小。孔隙压力增大前期，有效应力引起的渗透率增大量小于气体吸附引起的渗透率减小量，导致渗透率下降；孔隙压力增大后期，有效应力引起的渗透率增大量大于气体吸附引起的渗透率减小量，从而导致渗透率反弹。温度越高，渗透率比值下降越平缓，反弹越急剧。

当储层温度介于420～440 K范围内，且保持不变时，随着孔压的增大，渗透率逐渐增大。这是因为温度较高时，随着孔隙压力的增大，有效应力引起的渗透率增大量始终大于气体吸附引起的渗透率减小量，导致渗透率逐渐增大。

从图3还可以看出，当孔隙压力保持不变时，随着温度升高，渗透率比值先增大然后逐渐减小；孔隙压力越大，渗透率比值开始下降时的温度越大。这是因为当孔隙压力不变时，影响渗透率的主要因素为气体热解吸/热吸附和岩体热膨胀，随着温度升高，气体热解吸量增大，孔隙体积增大，导致渗透率增大；另一方面，随着温度升高，页岩固体颗粒膨胀，孔隙体积缩小，导致渗透率减小。温度升高前期，热解吸引起的渗透率增大量大于热膨胀引起的渗透率减小量，从而导致渗透率增大；而温度升高后期，热解吸引起的渗透率增大量小于热膨胀引起的渗透率减小量，导致渗透率减小。

3.2 不同孔压作用下渗透率随温度变化的演化机理

不同孔隙压力作用下，页岩气储层渗透率随温度变化的演化规律如图4所示。当孔隙压力保持不变（5、15 和25 MPa）时，随着温度升高，渗透率比值先增大，然后逐渐减小，孔隙压力越小，热解吸引起的渗透率增大的速率越大，导致渗透率比值开始减小时的温度越小；当渗透率比值开始减小以后，孔隙压力越小，热膨胀引起的渗透率减小的速率越大，从而导致渗透率比值减小的越急剧。

图 4 不同孔压下渗透率随温度的演化规律

Figure 4. Evolution of permeability with temperatureunder different pore pressures

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当孔隙压力保持35和45 MPa不变时，随着温度升高，渗透率比值轻微下降，然后反弹，最后逐渐下降。孔隙压力较小时，反弹现象较为明显。从图4可以看出，当温度在300～440 K范围内变化，孔隙压力为5 MPa时，渗透率比值变化范围为0.7～1.2。而孔隙压力为5和40 MPa时，渗透率比值在0.9～1.1范围内波动。由此可见，孔隙压力越大，温度对储层渗透率的影响越小。

3.3 不同温度作用下渗透率随孔压的演化机理

不同温度作用下，页岩气储层渗透率随孔压的演化规律如图5所示。当储层温度保持不变（318、348、378和408 K，对应的储层深度分别为1000、2000、3000和4000 m）时，随着孔隙压力的减小，渗透率比值先减小然后逐渐增大，其演化规律呈反弹现象。储层温度（储层深度）越大，渗透率的反弹现象越不明显，当储层深度达到3000 m时，渗透率基本不反弹。

图 5 不同温度下渗透率随孔压的演化规律

Figure 5. Evolution of permeability with porepressure under different temperatures

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当储层温度均保持不变时，影响储层渗透率的主要因素为有效应力和孔压降低引起的气体解吸。当孔隙压力下降时，一方面吸附于有机质颗粒表面和孔隙表面的气体解吸，孔隙体积和裂隙张开度增大，导致储层渗透率增大；另一方面，孔隙压力下降导致储层有效应力增大，孔隙和裂隙被压缩，导致储层渗透率减小。当气体解吸引起的基质收缩量小于有效应力增大引起的孔隙和裂隙的压缩量时，渗透率下降；当气体解吸引起的基质收缩量大于有效应力增大引起的孔隙和裂隙压缩量时，渗透率增大，这也正是恒温作用下储层渗透率随着孔隙压力的下降呈现反弹现象的原因。

4. 讨　论

在式(12)所示的热解吸渗透率模型中，泊松比、孔隙体积模量、热膨胀系数和Langmuir体应变对储层渗透率的影响较为显著，下面将分别讨论恒压、恒温作用下上述参数对储层渗透率的影响。

4.1 恒压下渗透率的敏感性分析

当孔隙压力保持10 MPa不变时，泊松比对储层渗透率的影响如图6所示。可以看出，泊松比不变时，随着温度升高，储层渗透率比值先增大然后减小，呈现“倒U形”演化规律。泊松比越大，渗透率比值的梯度越大。

图 6 恒压下泊松比对渗透率的影响

Figure 6. Effect of Poisson’s ratio on permeabilityunder constant pore pressure

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究其原因，储层孔隙压力不变，热解吸/吸附和热膨胀是影响页岩储层渗透率的主要因素。当温度升高时，页岩岩体膨胀导致储层孔隙和裂隙体积压缩，使得储层渗透率下降；另外，由于温度升高，页岩的吸附能力逐渐降低^[22]，从而导致储层孔隙体积逐渐增大，裂隙张开度随之增大^[4]，储层渗透率也随之增大。综上所述，热解吸和热膨胀对页岩储层渗透率的影响是相反的。温度升高初期，热解吸引起的渗透率变化量大于热膨胀引起的渗透率变化量；温度升高后期，热解吸引起的渗透率变化量小于热膨胀引起的渗透率变化量，从而导致恒压下渗透率随温度呈现“倒U形”变化。泊松比越大，热解吸引起的渗透率变化量越大，热膨胀引起的渗透率变化量越小，因此渗透率比值梯度随之增大。

当孔隙压力保持10 MPa不变时，孔隙体积模量对储层渗透率的影响见图7。如图7所示，当孔隙压力恒定时，储层渗透率比值随温度升高仍然呈现“倒U形”的演化规律，而且随着孔隙体积模量的增大，储层渗透率比值梯度减小。这是因为孔隙体积模量越大，热膨胀引起的渗透率变化量越大，而热解吸引起的渗透率变化量越小，从而导致渗透率比值梯度随孔隙体积模量的增大而减小。

图 7 恒压下孔隙体积模量对渗透率的影响

Figure 7. Effect of pore volume modulus onpermeability under constant pore pressure

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当储层的孔隙压力不变时，页岩的线胀系数对储层渗透率的影响见图8。如图8所示，当线胀系数小于临界值（渗透率随温度的演化规律不再呈现“倒U形”时的线胀系数）时，渗透率比值随温度的演化规律呈现“倒U形”现象，可通过式(12)计算出该临界值；当线胀系数大于该临界值时，渗透率比值随温度的升高而逐渐下降，不再呈现“倒U形”。在温升初期，线胀系数越大，渗透率比值梯度越大；在温升后期，渗透率比值梯度随线胀系数的增大而减小。这是因为孔隙压力不变时，只有气体的热解吸和岩体的热膨胀影响储层渗透率，线胀系数越大，页岩岩体因温度升高而引起的体积膨胀量越大，挤压的孔隙体积和裂隙体积越大，渗透率下降的越快。当热膨胀引起的渗透率变化量总是大于热解吸引起的渗透率变化量时，渗透率比值随温度的升高呈现逐渐下降的趋势。

图 8 恒压下线胀系数对渗透率的影响

Figure 8. Evolution of coefficient of linear expansionon permeability under constant pore pressure

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恒压作用下朗缪尔体应变对储层渗透率的影响见图9。如图9所示，当朗缪尔体应变大于临界值（渗透率随温度的演化规律不呈现“倒U形”时的朗缪尔体应变）时，储层渗透率随温度的变化曲线呈“倒U形”趋势，可以通过式(12)计算出此临界值；当朗缪尔体应变小于临界值时，渗透率随着温度的升高而逐渐降低。在温升初期，朗缪尔体应变越小，渗透率比值梯度越大；而在温升后期，朗缪尔体应变越小，渗透率比值梯度越小。这是因为朗缪尔体应变发生变化时，热解吸引起的体应变随之变化，热膨胀引起的体应变不发生变化，因此当升温过程中热解吸引起的渗透率变化量始终小于热膨胀引起的渗透率变化量时，渗透率比值随温度的升高逐渐下降。朗缪尔体应变越大，温升初期热解吸引起的渗透率变化量越大，此渗透率比值梯度越小，温升后期热解吸引起的渗透率变化量越小，渗透率梯度比值越大。

图 9 恒压下Langmuir体应变对渗透率的影响

Figure 9. Evolution of Langmuir volume strain onpermeability under constant pore pressure

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4.2 恒温下渗透率的敏感性分析

当储层温度不变时，泊松比对储层渗透率的影响见图10。如图10所示，恒温下储层渗透率随孔隙压力的下降，先逐渐降低然后反弹逐渐增大。泊松比越大，有效应力变化引起的孔隙和裂隙的体积变化越大，从而导致渗透率变化量越大；泊松比越大，气体解吸引起的孔隙和裂隙的体积变化越小，进而导致渗透率变化量越小。因此，泊松比越大，渗透率比值梯度越大。

图 10 恒温下泊松比对渗透率的影响

Figure 10. Effect of Poisson’s ratio on permeabilityunder constant temperature

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当储层温度不变时，孔隙体积模量对储层渗透率的影响见图11。如图11所示，当储层温度保持不变时，渗透率比值随孔隙压力的减小均呈现先变小再反弹增大的趋势。孔隙体积模量越大，孔隙抵抗变形的能力越强，相同的有效应力变化量引起的孔隙体积变化量越小，所以有效应力变化引起的渗透率变化量越小。另外，孔隙体积模量越大，气体解吸引起的渗透率变化量越小。因此，孔隙体积模量越大，渗透率比值梯度越小。

图 11 恒温下孔隙体积模量对渗透率的影响

Figure 11. Effect of pore volume modulus onpermeability under constant temperature

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当储层温度不变时，朗缪尔体应变对渗透率的影响见图12。如图12所示，朗缪尔体应变越大，渗透率随孔隙压力变化呈现的先变小再反弹现象越明显，随着朗缪尔体应变的减小，反弹现象逐渐消失。这是因为有效应力引起的渗透率变化量与朗缪尔体应变无关，而气体解吸引起的渗透率变化量取决于朗缪尔体应变。朗缪尔体应变越小，气体解吸引起的渗透率变化量越小，从而导致在孔隙压力的下降过程中有效应力变化引起的渗透率变化量（减小）始终大于气体解吸引起的渗透率变化量（增大）。

图 12 恒温下Langmuir体应变对渗透率的影响

Figure 12. Effect of Langmuir volume strain onpermeability under constant temperature

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5. 结　论

(1) 考虑温度、气体压力、有效应力和热解吸对储层渗透率的影响，推导了页岩气储层的有效应力-渗透率模型，该模型能解释有效应力不变时渗透率随孔隙压力的演化机制。

(2) 建立了储层在单轴应变条件下的热解吸渗透率模型，该模型能准确地阐述Marcellus裂隙页岩和完整页岩岩样的渗透率随温度的演化机制。

(3) 热解吸/吸附、热膨胀和孔隙压力是影响页岩气储层渗透率的主要因素。当孔隙压力恒定时，渗透率随温度呈“倒U形”演化规律。孔隙压力越大，温度对渗透率的影响越小；当温度恒定时，渗透率随孔压变化呈“U形”演化规律，温度（对应储层深度）越高，渗透率随孔压下降的反弹现象越不明显。

(4) 储层孔压恒定时，泊松比越大，渗透率比值梯度越大；孔隙体积模量越大，渗透率比值梯度越小；当线胀系数大于临界值时，渗透率比值随温度的演化规律不呈现“倒U形”；当朗缪尔体应变小于临界值时，渗透率比值随温度的演化规律也不呈现“倒U形”。

(5) 储层温度恒定时，泊松比越大，渗透率比值梯度越大；孔隙体积模量越大，渗透率比值梯度越小。当朗缪尔体应变小于临界值时，渗透率比值随孔压的变化不呈现“U形”演化规律。

图 1 DAC高压装置示意图（a）和实物照片（b）^[11]

Figure 1. Schematic diagram (a) and physical picture (b) of DAC high pressure device^[11]

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图 2 高压NMR装置示意图^[13]

Figure 2. Schematic diagram of high-pressure NMR equipment^[13]

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图 3 PE-cell实物照片

Figure 3. Physical picture of PE-cell

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图 4 IPMDH二聚体的内部腔和观察到的水渗透：0.1 MPa (a)和580 MPa (b)下IPMDH二聚体的内部空腔表面表征，0.1 MPa (c)和580 MPa (d)下空腔周围的放大图

Figure 4. Internal cavities of the IPMDH dimer and observed water penetration: (a) and (b) show internal cavities of the IPMDH dimer as surface representations at 0.1 and 580 MPa, respectively; (c) and (d) are magnified views around the cavity at 0.1 and 580 MPa, respectively

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图 5 SNase及其空腔突变体的展开：(a) SNase 3D结构和(b) SNase色氨酸（trp140）荧光谱，(c) I92A 空腔突变体的高压荧光平均发射波长分布，(d) SNase及其10个空腔突变体的体积

Figure 5. Unfolding of SNase and cavity-containing variants: (a) SNase 3D structure and (b) fluorescence emission from SNase tryptophan (trp140); (c) high-pressure fluorescence average emission wavelength profile for I92A variant;(d) volume measurements were performed on SNase and its 10 cavity mutants

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图 6 不同压力下HRP溶液的AFM图像

Figure 6. AFM images of HRP solution under different pressures

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图 7 高压原位和非原位方法研究土豆淀粉的高压糊化过程

Figure 7. High pressure gelatinization process of potato starch through combined high pressure in-situ and ex-situ study

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图 8 枯草芽孢杆菌的TEM图像：枯草芽孢杆菌的(a)正常营养形态和(b)正常孢子（箭头指向营养细胞壁的残余），(c)～(d)高温灭菌后枯草芽孢杆菌的营养物质和孢子

Figure 8. TEM images of Bacillus subtilis: (a) normal vegetative form and (b) normal spore of Bacillus subtilis (Arrowheads point to the remains of vegetative cell wall); (c)−(d) nutrients and spores of Bacillus subtilis after HHP

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图 9 DAC内培养液在30 ℃、25 MPa条件下培养24 h前后的拉曼光谱

Figure 9. Raman spectra of the culture medium inside the DAC at 30 ℃ and 25 MPa before and after 24 h incubation

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图 10 未标记（绿色）和完全同位素标记（红色）细菌的单细胞拉曼/SERS光谱

Figure 10. Single-cell Raman/SERS spectra of unlabeled (green) and fully isotope-labeled bacteria (red)

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图 11 (a) 在含¹³C-葡萄糖的培养基中生长的单个裂殖酵母活细胞的延时多模式拉曼成像目标细胞的亮场光学图像（31 h的箭头表示脂滴，被识别为黑点），(b) 细胞线粒体的 GFP 荧光图像，(c)～(f) 分别在1003 cm⁻¹（¹²C-蛋白质的苯环呼吸模式）、967 cm⁻¹（¹³C取代蛋白质的苯环呼吸模式）、1301 cm⁻¹（脂质的平面内CH₂ 扭曲）和1602 cm⁻¹ 处的拉曼图像，(g) (d)与(e)的关联图像

Figure 11. (a) Time-lapse multimode Raman imaging of single living S. pombe cell grown in ¹³C-glucose-containing medium bright-field optical images of the target cell. (The arrow at 31 h represents lipid droplets, which was recognized as black dots.); (b) GFP fluorescence images of the cell’s mitochondria; (c)–(f) Raman images at 1003 cm⁻¹ (Phe breathing mode of¹²C-proteins), 967 cm⁻¹ (Phe breathing mode of ¹³C-substituted proteins), 1301 cm⁻¹ (in-plane CH₂ twist of lipids), and 1602 cm⁻¹; (g) correlation images between (d) and (e)

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表 1 土豆淀粉的非原位高压糊化实验的热力学数据^[45]

Table 1. Thermodynamic data of potato starch non in-situ high-pressure gelatinization experiment^[45]

Pressure/MPa	Onset temperature/℃	Peak temperature/℃	Conclusion temperature/℃	Enthalpy of gelatinization/(J·g⁻¹)	Gelatinization degree/%
0	52.7±0.3^b	58.3±0.5^c	66.2±1.0^abc	3.163±0.043^a
200	53.3±0.2^b	59.8±0.5^b	67.0±0.2^a	2.878±0.066^b	9.01
300	52.9±0.7^b	58.8±0.9^bc	65.5±0.6^bc	2.846±0.127^b	10.02
400	53.4±0.5^b	58.7±0.8^bc	65.1±0.8^c	2.435±0.065^c	23.01
500	55.0±0.1^a	59.5±0.1^b	65.6±0.4^bc	2.188±0.037^d	30.82
600	55.9±1.6^a	62.4±1.5^a	66.5±0.5^ab	0.353±0.082^e	88.84
Note：Different letters (Superscript a, b, c, d, e) in the same column indicate significant differences (P<0.05).

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