关于溶蚀试片法计算溶蚀速率公式的一点认识

彭郭智; 蒲俊兵

doi:10.11932/karst20250108

关于溶蚀试片法计算溶蚀速率公式的一点认识

doi: 10.11932/karst20250108

彭郭智,
蒲俊兵^,

重庆师范大学地理与旅游学院/山区生态系统碳循环与碳调控重庆市重点实验室, 重庆 401331

基金项目: 国家高层次人才特殊支持计划青年拔尖人才项目（2022）；重庆市自然科学基金联合基金项目（CSTB2022NSCQ-LZX0022）；重庆师范大学博望学者计划青年拔尖人才项目（BWQB2023016）

详细信息

作者简介:
彭郭智（2000－），女，硕士研究生，主要研究方向为岩溶环境与碳循环。E-mail：guozhipeng0606@163.com

通讯作者:
蒲俊兵（1982－），男，研究员，博士，主要从事岩溶环境与全球变化及水文地球化学等方面的研究。E-mail：junbingpu@163.com。

中图分类号: P642.25
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出版历程
- 收稿日期: 2024-01-01
- 录用日期: 2024-09-04
- 修回日期: 2024-07-31
- 刊出日期: 2025-02-25

Discussion on the formulas used to calculate the dissolution rate by the rock tablet method

PENG Guozhi,
PU Junbing^,

Karst Research Team, Chongqing Key Laboratory of Carbon Cycle and Carbon Regulation of Mountain Ecosystem/School ofGeography and Tourism, Chongqing Normal University, Chongqing 401331, China

摘要

摘要: 测算碳酸盐岩的溶蚀速率对研究岩溶发育规律和提高岩溶碳汇估算精度至关重要。溶蚀试片法是得到广泛认可和使用的计算研究区碳酸盐岩溶蚀速率的方法，但目前利用其计算溶蚀速率的公式却并不统一，还存在日溶蚀量和年溶蚀量计算错误、时间尺度外推过大、单位不统一等问题。文章对溶蚀试片法的起源与方法原理进行了简要介绍，并就当前利用溶蚀试片法测算溶蚀速率的部分已发表公式进行了分析，发现相关公式存在忽略试验时间长度、日溶蚀量与年溶蚀量转换系数（方法）错误、短期试验结果进行了长时间尺度外推等问题，导致溶蚀速率测算误差较大，区域间无法进行对比。基于溶蚀试片法的基本原理，本文提出了用溶蚀试片法测算溶蚀速率的建议公式，以期进一步提高就溶蚀试片法测算溶蚀速率的规范性及结果的可对比性，从而为提高岩溶碳汇估算精度提供数据支持。
- 碳酸盐岩 /
- 溶蚀试片法 /
- 溶蚀速率 /
- 岩溶 /
- 问题讨论
Abstract: The dissolution rate of carbonate rocks is an important parameter for investigating the karst carbon cycle and evaluating the carbon sink effect; as well as a key indicator for studying karst development and karst hydrogeological problems. The rock tablet method is currently one of the main methods for quantitatively evaluating karstification and its carbon sink intensity, and has been widely recognized and used. The rock tablet method can not only analyze the factors affecting the dissolution rate of carbonate rocks (e.g., climate, lithology, soil properties), but also further explore the temporal and spatial variation characteristics of subsurface karstification by burying carbonate rock tablets at different depths. However, in current studies related to the calculation of carbonate dissolution rates using the rock tablet method, there are different versions of the dissolution rate calculation formula, and there are still some problems in its application, resulting in significant differences in the dissolution rate values calculated using different formulas for the same monitoring data, which adversely affects the accurate determination of the regional dissolution process and assessment of the karst carbon sink effect.This study firstly reviewed the origin, operational procedure, and basic principles of the carbonate rock tablet method and clarified the key links such as the preparation of the rock tablets (the standard rock tablets were uniformly made of limestone in the same stratum, usually the Rongxian formation of the upper Devonian collected from Guilin in Guangxi, or the upper Cretaceous collected from Slovenia, with a diameter of 4 cm and a thickness of 3mm to5 mm), burial layers (in the air, on the surface, and at the soil depths of 20 cm and 50 cm), burial duration (typically corresponding to one hydrological year), and weighing (using a balance with one-millionth precision). The advantages and limitations of commonly used carbonate dissolution rate calculation methods are summarized.Then, the paper analyzed some of the published formulas for calculating the carbonate dissolution rate using the rock tablet method and discovered that some of the formulas have the following issues,(1) The coefficient (method) from the daily dissolution rate to the annual dissolution rate is incorrect, further intensifying the uncertainty of the results; (2) The short-term test results were extrapolated over a long time scale, disregarding the influence of the dynamic changes in environmental conditions on the carbonate dissolution rate; (3) Unit conversion errors. These problems can result in significant calculation errors in the carbonate dissolution rate and make it difficult to conduct comparisons among regions.Finally, based on the fundamental principle of the rock tablet method, this study proposes a suggested formula for calculating the carbonate dissolution rate using the rock tablet method. The suggested formula can further enhance the standardization of the carbonate dissolution rate using the rock tablet method, providing data support for conducting global analysis and comparative research, revealing the laws of karst development, and improving the accuracy of karst carbon sink estimation. This study also proposes that methods should be selected based on the characteristics of the study area and research purpose. At the same time, it is of great necessity to strengthen the correlations between various test methods.
- carbonate rock /
- rock tablets method /
- dissolution rate /
- karst /
- problem discussion

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表 1 常用溶蚀速率测算方法的特点

Table 1. Characteristics of commonly used methods for measuring dissolution rates

方法	优点	缺点
溶蚀试片法	不需要长期监测；埋放方法成熟；接近自然状态；影响因子可控；试验成本低	难以获得历史数据；需多个代表性测试点；时间分辨率不高；动态变化不易掌握
微侵蚀计法	应用范围广；相对短时间内获得数据；限制条件少	难以获得历史数据；不适合大尺度区域研究
水化学法	可得出流域溶蚀速率；适合较大尺度区域研究	所需数据量较大
宇宙成因核素法	应用范围广；可估算长时间尺度数据	测试成本较高；精确度有待提升
灰岩基座法	原理简单；可估算长时间尺度数据	存在地域限制；误差较大

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表 2 利用溶蚀试片法计算溶蚀速率的公式

Table 2. Formulas used to calculate dissolution rates using rock tablets

公式	注释	问题	出处
$ d=\dfrac{\left ({G}_{0}-{G}_{1}\right)}{A\times 2.71} $	$ d $：溶蚀速率/mm $ {G}_{0}、{G}_{1} $：试验前后试片重量/mg $ A $：试样的表面积/mm² $ 2.71 $：石灰岩比重/mg·mm⁻³	缺少试验时间，不利于对比研究	[44]
$ W=\dfrac{wm}{mt}\times 365;v=\dfrac{w}{d}; h=\dfrac{v}{a} $	$ W $：年损失量/g $ wm $：试片重量损失/g $ mt $：代表测量的时间/d $ v $：损失体积/cm³ $ d $：密度/g.cm⁻³ $ h $：岩石剥蚀厚度/cm·yr⁻¹ $ a $：试片表面积/cm²	无误，单位面积溶蚀量可据此转换为剥蚀厚度	[47]
$ Sr=\dfrac{\left ({W}_{2}-{W}_{1}\right)}{2.7A·t} $	$ Sr $：溶蚀速率/mm·ka⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量 $ t $：试验时间 $ A $：试样的表面积/mm² $ 2.7 $：石灰岩比重/g·cm⁻³	式中$ Sr $应为mm·a⁻¹	[11]
$ ER=\left ({W}_{1}-{W}_{2}\right)\times 1000\times T/365/S $	$ ER $：溶蚀速率/mg·cm⁻²·a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ T $：埋放时间/d $ S $：试片表面积/cm⁻²	误将试片绝对溶蚀量与埋放时间相乘；日溶蚀速率转换为年溶蚀速率计算错误	[14, 67−68]
$ ER=\left ({W}_{1}-{W}_{2}\right)\times {10}^{7}/T/S $	$ ER $：溶蚀速率/mg·m⁻²·d⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ {W}_{1}-{W}_{2} $：绝对溶蚀量/mg $ T $：埋放天数/d $ S $：试片表面积/cm²	无误	[36, 54, 56−57, 69−71]
$ ER=\left ({W}_{1}-{W}_{2}\right)\times 1000\times 365/\left (T\times S\right) $	$ ER $：溶蚀速率/mg·cm⁻²·a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ {W}_{1}-{W}_{2} $：试片绝对溶蚀量/g $ T $：埋放时间 $ S $：试片表面积/cm²	无误	[58, 72]
$ ER=\left ({W}_{1}-{W}_{2}\right)\times 1000\times T\times {365}^{-1}\times {S}^{-1} $	$ ER $：溶蚀速率/mg·cm⁻²·a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ T $：埋放时间/d $ S $：试片表面积/cm²	误将试片绝对溶蚀量与埋放时间相乘；日溶蚀速率转换为年溶蚀速率计算错误	[12, 18, 20, 60, 73−74]
$ E=\left ({W}_{1}-{W}_{2}\right)/S $	$ E $：溶蚀速率/g·cm⁻²·a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ {W}_{1}-{W}_{2} $：试片绝对溶蚀量/g $ S $：溶蚀试片的表面积/cm⁻²	省略了溶蚀时间，易造成误导	[75]
$ D=\left ({W}_{1}-{W}_{2}\right)\times 1000\times {S}^{-1} $	$ D $：喀斯特溶蚀量/mg·cm⁻² $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ S $：试片表面积/cm²	省略了溶蚀时间，易造成误导	[76]
$ R=\dfrac{\left ({W}_{1}-{W}_{2}\right)\times T}{365\times S} $	$ R $：溶蚀速率/mg·cm⁻²· a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/mg $ T $：埋放时间/d $ S $：试片表面积/cm²	误将试片绝对溶蚀量与埋放时间相乘；日溶蚀速率转换为年溶蚀速率计算错误	[7, 62, 77]
$ ER=\dfrac{{W}_{1}-{W}_{2}}{T·S} $	$ ER $：溶蚀速率/mg·cm⁻²·a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/mg $ T $：溶蚀时间/a $ S $：试片表面积/cm²	无误	[21, 78−79]
$ ER=\left ({W}_{1}-{W}_{2}\right)\times 10000/\left (T\times S\right) $	$ ER $：溶蚀速率/mg·m⁻²·d⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/mg $ T $：埋放天数/d $ S $：试片表面积/cm²	无误	[38]
$ RS=3.65\times {10}^{10}n\left ({W}_{1}-{W}_{2}\right)/\left (A\times T\right) $	$ RS $：碳酸盐岩溶蚀或碳汇强度/mol·km⁻²·a⁻¹ $ n $：试片中碳酸盐的含量 $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ T $：埋放时间/d $ A $：试片表面积/cm²	日溶蚀速率转换为年溶蚀速率计算错误	[28]
$ E=365\times {10}^{4}\left ({W}_{1}-{W}_{2}\right)/\left (A\times T\right) $	$ E $：溶蚀量/g·km⁻²·a⁻¹ $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ T $：埋放时间/d $ A $：试片表面积/cm²	面积单位换算错误	[23]
$ DR=\left (W1-W2\right)\times 1000\times T/S $	$ DR $：溶蚀速率/mg·a⁻¹·cm⁻² $ {W}_{1}、{W}_{2} $：试验前后试片重量/g $ T $：埋放时间/a $ S $：试片表面积/cm²	误将试片绝对溶蚀量与埋放时间相乘	[80]

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