Figure
1.
Tectonic units of Ordos Basin and location of the Daniudi gas field (modified from Xu et al., 2011; Hao et al., 2006).
| Citation: | Longwei Qiu, Shengchao Yang, Changsheng Qu, Ningning Xu, Qingsong Gao, Xiangjin Zhang, Xugang Liu, Donghui Wang. A Comprehensive Porosity Prediction Model for the Upper Paleozoic Tight Sandstone Reservoir in the Daniudi Gas Field, Ordos Basin. Journal of Earth Science, 2017, 28(6): 1086-1096. doi: 10.1007/s12583-016-0935-2
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As an important part of unconventional natural gas, tight sandstone gas is attracting attention of more and more petroleum and geological researchers (Wei et al., 2016; Hu et al., 2015; Hu and Zhao, 2013; Fu et al., 2012; Zou et al., 2012). Tight sandstone reservoirs have typical features of tight lithology, low porosity and low permeability (Guo and Zhao, 2010; Spencer, 1989). Nowadays, controlling factors of tight sandstone reservoir properties have been studied well, and reservoir properties were jointly influenced by three major aspects, sedimentation, diagenesis and structure respectively (Zhang J Z et al., 2013; Zhang and Ding, 2010; Zhang X F et al., 2010; Liu et al., 2008; Zhou et al., 2008; Tang et al., 2007). The quality of reservoirs was largely characterized by sedimentation control, compaction dominance, cementation enhancement, and dissolution improvement (Cao et al., 2012). Pore development mechanism of tight sandstone and its influence factors vary greatly from regions and horizons (Zhang, 2008). Now that porosity is a crucial factor dictating development of high quality reservoirs or "sweet spots" in tight sandstone (Liu et al., 2013), whichever factor plays the predominant role, its impact on reservoir would eventually reflect to porosity alteration, therefore porosity is the basis for correct evaluation and effective prediction of tight sandstone reservoirs.
Regarding factors influencing Upper Paleozoic reservoir properties in Daniudi gas field, Ordos Basin, some scholars thought that sedimentary factor prevails (Yang et al., 2010; Yin and Ying, 2005), while others argued that diagenesis plays a pivotal role (Xu et al., 2011). In addition, previous studies on influencing factors of tight sandstone reservoir properties in the study area were mainly qualitative analyses, lacking quantitative studies on the influence degree of various factors on physical properties. In order to define controlling effect and influence degree of each factor on properties of tight sandstone reservoir, taking Upper Paleozoic tight sandstone reservoir in Daniudi gas field, Ordos Basin for example, the authors conducted a quantitative/semi-quantitative analysis of reservoir controlling factors including sedimentation and diagenesis. The key point of this paper is to discuss porosity evolution mechanism subjected to compaction by establishing normal compaction curves of rock as a function of lithology, grain size and sorting; and mathematical methods were used to quantify influence degree of each controlling factor on reservoir porosity, so as to build a comprehensive porosity prediction model under various key factors.
Daniudi gas field lies in the northeastern Yishan ramp in Ordos Basin, at a junction area between Yulin City, Shaanxi Province and Ordos City, Inner Mongolia Autonomous Region, cove-ring an exploration area of about 2 003 km2 (Zhang, 2014; Du et al., 2013; Jiang et al., 2012). Regionally, it is a gentle monocline high in the northeast and low in the southwest (Fig. 1). The Upper Paleozoic depositional systems of the study area are marine facies, marine-continental transition-continental facies (Qiu et al., 2013). The Upper Carboniferous Taiyuan Formation is mainly developed littoral deposit, the Lower Permian Shanxi Formation is mainly developed braided river delta deposit, and the Lower Permian Lower Shihezi Formation is dominated by braided river deposit (Hou and Liu, 2012). Main gas-bearing intervals are reservoir beds of Carboniferous Taiyuan Formation, Permian Shanxi Formation and Lower Shihezi Formation (Luo et al., 2007). In reservoir petrological characteristics, quartz is the highest content, but varies over a wide range, i.e., 74.0%-97.0% of the total clast, averaging 88.9%. Feldspar is universally low and generally not more than 20.0%. Lithic fragment is 3.5.0%-58.0%, averaging 19.6%, dominated by sedimentary rock fragments and shallow parametamorphic rock fragments, as well as minor amount of magmatic rock fragments. Cements include kaolinite, illite, calcite, quartz, siderite and dolomite (Qiu et al., 2013). Besides, minor amounts of mica chips and heavy minerals are observable, with contents generally less than 5%. Data of molded thin sections and scanning electron microscopy (SEM) indicate that reservoir space type is diverse, dominated by intergranular pores, intercrystalline pores, and intragranular dissolution pores, fewer primary pores in addition to minor microfissures (Qiu et al., 2013).
Properties of tight sandstone reservoir are influenced by many factors, and factors influencing reservoir porosity differ greatly from regions and horizons (Zhang, 2008). Understanding controlling effect of each factor is a prerequisite of effective prediction of porosity. Based on existing data, this paper primarily analyzed porosity controlling factors of the Upper Paleozoic tight sandstone reservoir in Daniudi gas field in terms of sedimentation and diagenesis.
Sedimentary facies macroscopically control sand body's origin type, thickness, scale and spatial distribution, and microscopically dictate petrological characteristics such as clastic particle size, sorting, psephicity, contact mode and components of interstitial material and their contents (Zhang et al., 2013; Zhou et al., 2008; Tang et al., 2007).
Macroscopically, reservoir properties data of different sedimentary facies in the study area indicate that, variations in reservoir properties were small within each sedimentary microfacies, only mouth bar and mid-channel bar had slightly better physical properties (Table 1), and favorable sedimentary facies features were insignificantly manifested.
| Sedimentary microfacies | Braided channel | Mouth bar | Underwater braided channel | Mid-channel bar |
| N | 877 | 121 | 687 | 594 |
| Φ (%) | 5.99 | 7.49 | 6.40 | 7.18 |
| K (×10-3 μm2) | 0.475 | 0.508 | 0.448 | 0.508 |
| Notes: N. number of data points; Φ. average porosity; K. average permeability. | ||||
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Microscopically, studies over the relationships between grain size and sorting coefficient versus reservoir properties indicate that, the coarser the grain size of rock, the better the physical properties (Fig. 2a); and reservoir porosity was the best at sorting coefficient of 1.6-2.0 and tended to get worse significantly at sorting coefficient greater than 2.0 (Fig. 2b). Given the porosity controlling effect of sedimentary microfacies is insignificant while controlling effects of rock grain size and sorting are stronger, this study focuses on reservoir porosity controlling effects of microscopical parameters including rock grain size and sorting.
Clastic reservoir researches reveal that, the availability of reservoir is a depositional problem, there is a reservoir where there is a sand body, but reservoir quality is more diagenesis-dependent (Zhang et al., 2010). Having knowledge about effect of diagenesis on reservoir porosity is important to defining for-mation of a favorable reservoir. For development of the Upper Paleozoic tight sandstone reservoir in Daniudi gas field, constr-uctive diagenesis consists of dissolution and fracturing, and dis-ruptive diagenesis is made up of compaction and cementation.
Compaction phenomenon is relatively pervasive in tight sandstone reservoirs, microscopic qualitative studies show that the reservoir particles are in an ascending order of compaction extent as compaction-deformed plastic particles, directional aligned major axes of clastic particles, skeleton particles with line contact or asperity contact (Fig. 3a), and rigid particles fractured under pressure (Fig. 3b). Quantitatively, apparent compaction rate can be used to characterize compaction strength.
Apparent compaction rate=(primary porosity-intergranular volume)/primary porosity×100%, where, intergranular volume= intergranular porosity+cement (Houseknecht, 1987), and primary porosity was calculated using Trask sorting coefficient method (Scherer, 1987), Primary porosity=20.91+(22.9/So). In which So is Trask sorting coefficient, So=(P25/P75)0.5. P25 and P75 are particle diameters corresponding to 25% and 75% at grain size probability cumulative distribution curve (Scherer, 1987), and grain size data were all obtained from microscopic inspection of rock thin sections, particle diameter statistics were aided by image analysis software.
As calculated, compaction extent of the Carboniferous-Permian tight sandstone reservoir in Daniudi gas field was quite uneven, with apparent compaction rate being 17.4%-97.0%, averaging 71.5%. And the rate of Taiyuan Formation was 25.0%-91.6%, averaging 77.9%. Shanxi Formation was 17.4%-92.6%, averaging 63.4%, and that of Lower Shihezi Formation was 26.0%-97.0%, averaging 72.8%. According to compaction extent classification (Zhang, 2014; Hu et al., 2007), the study area was regarded to have moderate-to-strong overall compaction.
Compaction is an important factor of reservoir tightness, and to find causes of such variations, it is necessary to further study compaction mechanism. Studies indicate that, a number of factors influence compaction, such as rock type, rigid particle content, particle size, sorting coefficient, cement content, abnormal fluid pressure, burial mode and acting time (Wei et al., 2016; Wilkinson and Haszeldine, 2011; Xiao et al., 2011; Shou et al., 2006; Warren and Pulham, 2001). Many scholars used normal compaction curves they built to conduct mechanical compaction correction of porosity evolution process, or utilized the compaction curves in combination with porosity envelopes to judge development of abnormal porosity zone, but most of them did not consider petrophysical properties (lithology, grain size, sortability, etc.), except that some scholars conducted such discussions (Zhang H L et al., 2014; Cao et al., 2013; Zhang R H et al., 2011; Zhang Q et al., 2004) or simulated compaction mechanism (Xi et al., 2015; Cao et al., 2011; Liu et al., 2006).
In order to take petrological characteristic variation into full account and discuss compaction mechanism more precisely, the authors established normal compaction curves in terms of three petrological parameters, namely, lithology, grain size and sorting. To eliminate the effects of cementation and dissolution as much as possible, data points corresponding to cement content less than 6% (reservoir porosity is less affected under such condition) and undeveloped dissolution were selected to calculate normal compaction curves. As can be known from particle sorting coefficient versus porosity cross plot (Fig. 2b), sorting coefficient of 1.6-2.0 is more favorable to preservation of reservoir porosity; therefore, data points at sorting coefficient of 1.6-2.0 were selected to establish normal compaction curves as a function of lithology and grain size. As can be known from pore decreasing rate (ΔΦ) of sandstone at the same depth interval under normal compaction condition (Fig. 4), compaction resistance of quartz sandstone was stronger than that of litharenite, and the coarser the grain size of rock, the stronger the compaction resistance. In addition, normal compaction curves were established for sandstones as a function of grain size and sorting coefficient, and it is found that, given the same burial depth, the coarser the grain size, the better the petrophysical properties (Fig. 5a), while sandstones of different sorting coefficients had relatively prominent difference in normal compaction curves (Fig. 5b). Therefore, if considered from perspectives of grain size and sorting coefficient only, the vibrational patterns shown are still similar, even though error increases somewhat. In light of research operability, porosity evolution could be well handled just from perspectives of grain size and sorting coefficient.
Petrofabric features have much impact on compaction, and reservoir porosity is influenced by grain size, sorting coefficient and burial depth under normal simple burial condition. Therefore, by calculating weighting factors of grain size and sorting coefficient with respect to porosity, we can obtain a calculation formula of porosity Φ1 under normal burial compaction condition (calculated through grey relational analysis, influence coefficients of grain size and sorting with respect to porosity were 0.501 42 and 0.498 58 respectively, with detailed description of the method shown below)
| Φ1=0.50142×{−14.7ln(H)+117.63(fs)−46.01ln(H)+367.89(ms)−47.47ln(H)+382.41(cs)}+0.49858×{−134.8ln(H)+1076.1(s1)−78.35ln(H)+624.71(s2)−98.08ln(H)+793.18(s3)−44ln(H)+350.65(s4)} |
Here, fs means fine sandstone; ms means medium sandstone; cs means coarse sandstone; s1, s2, s3 and s4 represent sorting value "1.3-1.6", "1.6-2.0", "2.0-2.1", "2.1-2.4" respectively.
Types of cementation presented in the study area mainly include siliceous cementation, carbonate cementation and clay mineral cementation. In quantity, siliceous and carbonate cements were the most abundant and had multiple phases (Fig. 3c), followed by clay mineral, and other authigenic minerals were of lower content. In occurrence, siliceous cement mainly occurred in the form of secondary enlargement edge (Fig. 3c), with developed authigenic quartz particles being observed too (Figs. 3d, 3f). Authigenic kaolinite had generally good crystal form, filling intergranular pores in pseudohexagonal flakes (Fig. 3e). It was common to see chlorite coating distributed over particle rims (Fig. 3d), and it was also observed that minor amount of foliated chlorite filled in the intergranular pores (Fig. 3f). Carbonate cement has double effects on reservoir properties: on one hand, cements deposited among particles directly occupy intergranular pores, enabling worse reservoir properties; and on the other hand, due to uneven distribution, cements formed in early stage can serve as skeleton particles having certain compaction resistance, which alleviate compaction effect and are likely to provide material basis for dissolution in late stage, thereby exerting certain pore-preserving effect (Lin et al., 2011; Xu et al., 2011; Zhang et al., 2008).
In the Upper Paleozoic tight sandstone reservoir of Daniudi gas field, common metasomatic processes mainly occurred among quartz, carbonate and clay minerals, such as calcite-metasomatized clastic particles (Fig. 3g) and ferrocalcite metasomatized calcite. Besides, as well as clay mineral-metasomatized quartz secondary enlargement edge, ferrocalcite-metasomatized cryptocrystalline silicalite clast, and calcite-metasomatized clay mineral (Tang et al., 2007).
Multiple dissolution occurred in tight sandstone reservoir of the study area due to diagenetic environment alteration, and the secondary pores formed could improve reservoir properties well (Xu et al., 2017). What commonly seen are secondary enlargement edge dissolution of quartz (Fig. 3h), dissolution of quartz particles and lithic fragment particles, and dissolution of carbonate particles (Fig. 3i); among which, quartz dissolution and lithic fragment dissolution were predominant in the area, while carbonate particle dissolution was less common. As occurring dissolution is mainly dissolution of quartz particles and secondary enlargement edge of quartz (Qiu et al., 2015), it's found in data points with relatively developed dissolution that secondary plane porosity of dissolution has certain positive correlation with quartz content (Fig. 6). On the other hand, alteration of aluminum silicate mineral is a process of increasing pores. For example, feldspar kaolinization and illitization is a volume-decreasing process and will form additional pore space (Huang et al., 2009; Zhang, 2007), therefore, such alterations have constructive effects on properties of tight sandstone reservoir. Various types of dissolution pores improved pore connectivity effectively, so dissolution is an important way improving reservoir properties in the context of tightening.
In summary of the above diagenesis analysis, the Upper Paleozoic reservoir of Daniudi gas field underwent intense diagenetic alteration, where compaction and cementation are main causes of porosity reduction, while dissolution and partial alteration improved reservoir properties to some extent.
Qualitative analysis of each factor's influence on physical properties is a common way discussing main controlling factors of physical properties, however, influence degree of each factor on reservoir properties is still less studied, lacking quantitative data to calculate the degree. Based on analysis of property controlling factors of the Upper Paleozoic tight sandstone reservoir in Daniudi gas field, this paper quantifies the influence degree of each parameter on reservoir porosity. Comprehensive evaluation of various influence factors yields a comprehensive calculation formula about porosity: Ф=∑niaiXi, where, Ф is the ultimately calculated porosity of the reservoir, n is the number of total reservoir parameters selected, ai is weighting factor of a selected parameter, Xi is relational expression between a selected parameter and porosity (Zhang, 2014). Weighting factor is an indicator of influence degree of a selected parameter on reservoir properties, and can be determined in a number of ways, such as factor analysis (Lü et al., 2006), analytic hierarchy process (Wang et al., 2003), and grey relational analysis (Chen et al., 2014; Liu et al., 2005). Grey relational analysis is a classical method, relatively objective and easy to operate. Thus, grey relational analysis was employed to solve for weighting factor of each property influence factor of tight sandstone reservoir as per the following computation principle (Liu et al., 2005)
| X(0)=[x(0)1(0)x(0)1(1)⋯x(0)1(m)x(0)2(0)x(0)2(1)⋯x(0)2(m)⋮⋮⋯⋮x(0)n(0)x(0)n(1)⋯x(0)n(m)] | (1) |
| X(1)t(i)=X(0)t(i)/X(0)1(i),t=1,2⋯,n;i=1,2⋯,m | (2) |
Here Xn (m) represents the nth data point, and each data point has m factor parameters. ∆max and ∆min are absolute extrema of the difference between each subfactor and the principal factor at the same observation time point.
| ξi,0=Δmin | (3) |
where, ρ is grey relational resolution factor used to adjust magnitude of numerical difference between influence factors, ranging between 0 and 1 (Liu et al., 2005), the smaller the ρ, the greater the resolving power, its value is normally set as 0.5.
| {{r}_{i, 0}}=\frac{1}{n}\sum\limits_{t=1}^{n}{{{\xi }_{i, 0}}} | (4) |
| {{a}_{i}}={{{r}_{i}}}/{\sum\limits_{i=1}^{m}{{{r}_{i, 0}}}}\; | (5) |
As factors of a system have different physical meanings and original variable series has different dimensions, all data have to be preliminarily nondimensionalized to guarantee comparability among parameters. Common nondimensionalization methods include initial value, maximum value and mean method (Liu et al., 2005). In this paper, nondimensionalization is done using initial value method. Various selected parameters (1) were initialized using Eq. (2). Then relational coefficients were calculated using Eq. (3), grey relational grades were calculated using Eq. (4), and finally, weighting factors of each parameter were calculated using Eq. (5).
Based on geological data configuration, six relatively independent major parameters were selected to reflect primary geological information and diagenetic alteration information influencing reservoir properties in a relatively comprehensive way. Specifically, we selected parameters representative of sedimentary environment-median grain size and sorting coefficient, parameters representative of reservoir lithological characteristics-quartz content and clay mineral content, parameter representative of diagenesis-cement content, and parameter representative of compaction degree-burial depth. With porosity as principal factor (principal series), median grain size, sorting coefficient, quartz content, clay mineral content, burial depth and cement content serve as subfactors. According to a porosity calculation formula under multi-factor comprehensive control, present porosity Ф was obtained.
Ф=a×(relational formula between grain size and porosity)+b×(relational formula between sorting coefficient and porosity)+c×(relational formula between depth and porosity)+d×(relational formula between quartz content and porosity)+e×(relational formula between clay mineral content and porosity)+f×(relational formula between cementation and porosity), in which, a, b, c, d, e and f are weighting factors to solve for (Table 2).
| Well No. | M value (mm) | Sorting coefficient | Clay mineral content (%) | Depth (m) | Cement content (%) | Quartz content (%) |
| Da-2 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 |
| Da-14 | 0.973 86 | 0.796 10 | 0.526 53 | 0.740 97 | 0.947 91 | 0.734 61 |
| Da-14 | 0.755 11 | 0.884 61 | 0.979 06 | 0.975 11 | 0.652 50 | 0.978 25 |
| Da-14 | 0.998 18 | 0.922 25 | 0.989 21 | 0.910 13 | 0.84751 | 0.852 76 |
| Da-14 | 0.853 03 | 0.894 94 | 0.909 43 | 0.916 54 | 0.634 24 | 0.966 97 |
| Da-3 | 0.935 00 | 0.956 85 | 0.814 97 | 0.992 42 | 0.705 28 | 0.984 05 |
| Da-3 | 0.854 39 | 0.849 15 | 0.801 54 | 0.880 65 | 0.997 77 | 0.828 65 |
| Da-3 | 0.502 46 | 0.733 36 | 0.899 50 | 0.721 06 | 0.688 46 | 0.686 31 |
| Da-3 | 0.980 14 | 0.810 76 | 0.744 47 | 0.897 21 | 0.715 43 | 0.950 17 |
| Da-3 | 0.942 88 | 0.898 50 | 0.859 42 | 0.989 27 | 0.709 75 | 0.91365 |
| Da-3 | 0.926 39 | 0.746 70 | 0.668 41 | 0.824 82 | 0.639 29 | 0.885 78 |
| Da-3 | 0.869 59 | 0.944 62 | 0.865 07 | 0.908 42 | 0.821 48 | 0.865 94 |
| Da-3 | 0.811 42 | 0.742 27 | 0.703 28 | 0.768 54 | 0.724 11 | 0.830 70 |
| Da-3 | 0.998 41 | 0.861 91 | 0.681 23 | 0.790 40 | 0.605 34 | 0.830 29 |
| Da-3 | 0.555 10 | 0.868 64 | 0.754 51 | 0.913 12 | 0.690 59 | 0.976 95 |
| Da-3 | 0.860 37 | 0.873 08 | 0.890 90 | 0.786 52 | 0.497 78 | 0.754 92 |
| Da-3 | 0.758 26 | 0.693 94 | 0.691 55 | 0.660 91 | 0.333 33 | 0.693 29 |
| Datan-1 | 0.691 59 | 0.948 61 | 0.874 88 | 0.870 07 | 0.942 11 | 0.842 72 |
| Datan-1 | 0.792 27 | 0.890 96 | 0.803 84 | 0.928 64 | 0.642 04 | 0.825 55 |
| Datan-1 | 0.778 79 | 0.771 87 | 0.602 53 | 0.819 97 | 0.735 41 | 0.803 04 |
| Datan-1 | 0.801 73 | 0.672 04 | 0.627 89 | 0.706 96 | 0.534 17 | 0.679 04 |
| Datan-1 | 0.742 49 | 0.654 52 | 0.617 50 | 0.693 86 | 0.521 02 | 0.670 14 |
| Datan-1 | 0.748 90 | 0.670 58 | 0.631 44 | 0.711 66 | 0.557 11 | 0.686 60 |
| Datan-1 | 0.965 48 | 0.893 15 | 0.764 30 | 0.979 72 | 0.692 19 | 0.939 11 |
| Datan-1 | 0.615 50 | 0.704 40 | 0.627 19 | 0.765 45 | 0.614 07 | 0.805 27 |
| Datan-1 | 0.765 76 | 0.672 09 | 0.653 57 | 0.740 25 | 0.542 42 | 0.716 56 |
| Grey relational grade | 0.826 04 | 0.821 38 | 0.768 55 | 0.842 03 | 0.691 97 | 0.834 67 |
| Weighting factor | 0.172 64 | 0.171 67 | 0.160 63 | 0.175 99 | 0.144 62 | 0.174 45 |
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Substituting weighting factors into the above formula yields porosity.
Ф=0.172 64×(relational formula between grain size and porosity)+0.171 67×(relational formula between sorting coefficient and porosity)+0.160 63×(relational formula between depth and porosity)+0.175 99×(relational formula between quartz content and porosity)+0.144 62×(relational formula between clay mineral content and porosity)+0.174 45×(relational formula between cementation and porosity)
| {\Delta _{\max }} = \mathop {\max }\limits_i {\mkern 1mu} \mathop {\max }\limits_t {\mkern 1mu} \left| {{X_t}^{(1)}(i) - {X_t}^{(1)}(0)} \right| |
| {\Delta _{\min }} = \mathop {\min }\limits_i {\mkern 1mu} \mathop {\min }\limits_t {\mkern 1mu} \left| {{X_t}^{(1)}(i) - {X_t}^{(1)}(0)} \right| |
Quantitative computation of influence degree of each factor on porosity enabled reservoir porosity solving to be operable. Nonetheless, more important objective of controlling factor study is to predict favorable reservoir. Therefore, it is necessary to establish a porosity prediction model based on controlling factor study.
During geological period, reservoir properties were subjected to extremely complex influence of various geologic factors, it is impossible to recover reservoir property evolution process in a completely precise way. During discussion in this paper, pores are regarded as superposition of two portions, one portion is pores preserved under normal compaction condition, and the other portion is pores contributed by diagenesis to the reservoir, so that a quantitative porosity prediction model was established. To make the prediction model brief and operable, following assumptions were thus set as follow.
(1) The present porosity is deemed as algebraic sum of normal compaction porosity and diagenesis contribution to porosity.
(2) In contribution to porosity, cement and authigenic clay mineral occupy pore volume leading to reduced porosity, so their contributions were negative values; dissolution is able to improve porosity, thus its contribution is positive value; sorting coefficient and grain size are parameters concerning normal co-mpaction curve, used to solve for normal compaction porosity.
(3) Dissolution is hard to quantify, and as there is certain positive correlation between quartz content and percentage of secondary dissolution pores and quartz dissolution is the main type of dissolution, the weighting factor of quartz content was used to replace dissolution weighting factor, and their relational expression was used to approximately solve for dissolution pore percent.
Under the above predetermined conditions, simply by calculating weighting factors of parameters concerning normal compaction porosity Φ1 (depth, sorting coefficient, and grain size), parameter having pore enlargement effect (dissolution) and parameters having pore decreasing effect (clay mineral content, and cement) with respect to porosity, one can obtain comprehensive calculation formula of porosity Φ.
| \begin{align} &\mathit{\Phi} =c\times {{\mathit{\Phi} }_{1}}+d\times ({{\mathit{\Phi} }_{1}}+{{\mathit{\Phi} }_{\rm{dissolution}}})+e\times ({{\mathit{\Phi} }_{1}}-{{\mathit{\Phi} }_{\rm{clay}}})+ \\ &\ \ \ \ \ \ \ ~f\times ({{\mathit{\Phi} }_{1}}-{{\mathit{\Phi} }_{\rm{cementation}}}) \\ \end{align} |
where Φdissolution is percent of dissolution enlarged pores, Φclayis percent of pores occupied by authigenic clay mineral, and Φcementation is percent of cement-occupied pores.
With the latter four parameters in Table 2 as an entirety, percent of each parameter was calculated, which was the very weighting factor of each factor, and grain size and sorting coefficient were thus calculated, too, i.e., 0.501 42 and 0.498 58, respectively.
Therefore, the porosity calculation formula for the Upper Paleozoic reservoir at Daniudi is as follows
| \begin{align} &\mathit{\Phi} =0.268\;40\times {{\mathit{\Phi} }_{1}}+0.266\;05\times ({{\mathit{\Phi} }_{1}}+{{\mathit{\Phi} }_{\rm{dissolution}}})+0.244\;98\times \\ &\ \ \ \ \ \ \ ({{\mathit{\Phi} }_{1}}-{{\mathit{\Phi} }_{\rm{clay}}})+0.220\;57\times ({{\mathit{\Phi} }_{1}}-{{\mathit{\Phi} }_{\rm{cementation}}}), \\ \end{align} |
that is, Φ=Φ1+0.266 05×Φdissolution-0.244 98×Φclay-0.220 57×Φcementation; where Φ1 is normal compaction porosity, and substituting expression of Φ1 into algebraic expression of Φ, we get
| \begin{array}{l} {\mathit{\Phi} _1} = 0.501\;42 \times \left\{ \begin{array}{l} - 14.7\ln \,(H) + 117.63\,(fs)\\ - 46.01\ln \,(H) + 367.89\,(ms)\\ - 47.47\ln \,(H) + 382.41\,(cs) \end{array} \right\} + 0.498\;58 \times \\ \;\;\;\;\;\;\;\;\left\{ \begin{array}{l} - 134.8\ln \,(H) + 1076.1\,(s1)\\ - 78.35\ln \,(H) + 624.71\,(s2)\\ - 98.08\ln \,(H) + 793.18\,(s3)\\ - 44\ln \,(H) + 350.65\,(s4) \end{array} \right\} + 0.266\;05 \times {\mathit{\Phi} _{\text{dissolution}}} - \\ \;\;\;\quad \quad 0.244\;98 \times {\mathit{\Phi} _{\text{clay}}} - 0.220\;57 \times {\mathit{\Phi} _{\text{cementation}}} \end{array} |
Here, fs means fine sandstone; ms means medium sandstone; cs means coarse sandstone; s1, s2, s3 and s4 represent sorting value "1.3-1.6", "1.6-2.0", "2.0-2.1", "2.1-2.4" respectively.
In the study area, Member 1 of the Lower Permian Shanxi Formation (Shan-1 member in short) has many data points and complete reservoir parameter data, reservoir property parameters of Shan-1 member were substituted into the calculation formula, and comparison between the calculated result and measured porosity shows that most errors were less than 15% and only about 25% of data points had error over 15%, that is, 75% of the data can be corresponded to each other (Table 3). Therefore, the porosity calculation formula eventually obtained under multi-factor comprehensive control has certain reference value.
| Well No. | Median grain size (mm) | Sorting coefficient | Clay mineral (%) |
Depth (m) |
Cement content (%) | Quartz content (%) | Description | Primary porosity (%) | Calculated porosity (%) | Error (%) |
| Da-14 | 0.480 | 1.97 | 7 | 2 791.38 | 1.0 | 88 | Coarse-grained quartz sandstone | 6.3 | 6.91 | 10.6 |
| Da-3 | 0.400 | 1.90 | 6 | 2 775.81 | 0 | 74 | Medium-grained litharenite | 6.2 | 6.88 | 11.0 |
| Da-3 | 0.480 | 2.19 | 12 | 2 776.54 | 5.0 | 85 | Coarse-grained lithic quartz sandstone | 4.6 | 5.07 | 10.3 |
| Da-3 | 0.400 | 1.72 | 14 | 2 790.70 | 0 | 89 | Coarse-grained lithic quartz sandstone | 5.1 | 5.51 | 8.1 |
| Da-3 | 0.450 | 1.97 | 12 | 2 791.96 | 0 | 89 | Coarse-grained lithic quartz sandstone | 5.6 | 5.96 | 6.4 |
| Da-3 | 0.690 | 1.80 | 5 | 2 795.55 | 3.0 | 70 | Over coarse-grained feldsparthiclitharenite | 6.3 | 5.53 | 12.2 |
| Da-3 | 0.550 | 1.75 | 9 | 2 806.09 | 3.0 | 88 | Coarse-grained lithic quartz sandstone | 4.9 | 5.50 | 12.3 |
| Da-3 | 0.320 | 1.60 | 9 | 2 819.16 | 0.5 | 73 | Medium-grained litharenite | 4.1 | 4.55 | 11.0 |
| Da-3 | 0.570 | 1.63 | 2 | 2 822.86 | 1.0 | 85 | Coarse-grained lithic quartz sandstone | 7.5 | 6.90 | 8.0 |
| Da-3 | 0.500 | 1.61 | 10 | 2 824.30 | 2.0 | 80 | Coarse-grained litharenite | 6.1 | 4.31 | 29.3 |
| Da-3 | 0.670 | 1.84 | 6 | 2 826.62 | 1.5 | 89 | Gravelly over Coarse-grained lithic quartz sandstone | 6.1 | 5.98 | 2.0 |
| Da-3 | 0.500 | 1.92 | 8 | 2 827.20 | 1.5 | 84 | Gravelly coarse-grained lithic quartz sandstone | 5.1 | 5.11 | 0.2 |
| Da-3 | 0.680 | 2.47 | 0 | 2 829.67 | 1.0 | 85 | Gravelly over coarse-grained lithic quartz sandstone | 9.2 | 7.17 | 22.1 |
| Datan-1 | 0.330 | 2.00 | 3 | 2 745.92 | 2.0 | 70 | Gravelly medium-and coarse-grained litharenite | 8.1 | 7.87 | 2.8 |
| Datan-1 | 0.325 | 2.38 | 1 | 2 739.25 | 0.5 | 66 | Gravelly medium-grained litharenite | 10.1 | 8.63 | 14.6 |
| Datan-1 | 0.400 | 2.11 | 10 | 2 741.28 | 2.0 | 58 | Coarse-grained litharenite | 4.8 | 5.45 | 13.5 |
| Datan-1 | 0.380 | 2.16 | 0 | 2 742.91 | 1.5 | 71 | Gravelly coarse-and medium-grained litharenite | 12.8 | 8.89 | 30.6 |
| Datan-1 | 0.360 | 2.20 | 0 | 2 743.30 | 2.0 | 77 | Gravelly coarse-grained litharenite | 13.4 | 9.20 | 31.4 |
| Datan-1 | 0.515 | 1.84 | 0 | 2 744.56 | 6.0 | 81 | Gravelly coarse-grained litharenite | 11.5 | 8.56 | 25.6 |
| Datan-1 | 0.285 | 1.70 | 0 | 2 746.84 | 2.0 | 66 | Medium-grained litharenite | 9.6 | 8.29 | 13.7 |
| Datan-1 | 0.400 | 1.86 | 7 | 2 786.46 | 1.0 | 57 | Gravelly coarse-grained litharenite | 6.3 | 4.84 | 23.1 |
| Datan-1 | 0.300 | 1.88 | 0 | 2 787.47 | 1.0 | 57 | Medium-grained litharenite | 7.0 | 6.53 | 6.8 |
| Datan-1 | 0.400 | 1.76 | 1 | 2 789.03 | 1.0 | 74 | Coarse-grained litharenite | 8.6 | 7.45 | 13.3 |
| Datan-1 | 0.370 | 1.81 | 0 | 2 790.02 | 2.0 | 72 | Coarse-and medium-grained litharenite | 8.4 | 7.30 | 13.1 |
| Datan-1 | 0.350 | 1.68 | 0 | 2 791.10 | 2.5 | 74 | Medium-grained litharenite | 7.7 | 7.30 | 5.2 |
| Datan-1 | 0.400 | 1.76 | 1 | 2 835.14 | 0 | 73 | Medium-grained litharenite | 5.5 | 6.11 | 11.1 |
| Datan-1 | 0.400 | 2.12 | 0 | 2 835.67 | 0 | 74 | Medium-coarse-grained litharenite | 7.9 | 6.41 | 18.9 |
| Datan-1 | 0.400 | 1.89 | 5 | 2 838.71 | 0 | 65 | Coarse-grained litharenite | 5.1 | 4.44 | 13.0 |
| Datan-1 | 0.300 | 1.82 | 0 | 2 840.41 | 0 | 61 | Medium-grained litharenite | 5.0 | 5.32 | 6.4 |
| Datan-1 | 0.250 | 1.50 | 6 | 2 841.19 | 0 | 56 | Medium-grained litharenite | 3.2 | 3.47 | 8.4 |
| Datan-1 | 0.500 | 1.64 | 10 | 2 841.54 | 0 | 57 | Coarse-grained litharenite | 3.6 | 2.55 | 29.2 |
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(1) The Upper Paleozoic tight sandstone reservoir in Daniudi gas field, Ordos Basin has many property controlling factors, in which compaction and cementation are main causes of porosity reduction, while dissolution and partial alteration improved reservoir properties to some extent. Compaction is a key factor of reservoir tightness and its variability is mainly manifested in grain size fraction and sorting. Under normal compaction condition (cement content less than 6% and with no dissolution), change of porosity with burial depth was well correlated with rock composition, grain size fraction and sorting.
(2) Influence degree of each factor on reservoir porosity was quantified by grey relational analysis, grey relational grade and weighting factor of each parameter (median grain size, sorting coefficient, clay mineral content, depth, cement content, and quartz content) with respect to reservoir porosity were calculated, and present porosity was deemed as superposition of normal compaction porosity and contribution of diagenetic alteration to porosity, so as to obtain reservoir porosity calculation formula under multi-factor control
| {{\mathit{\Phi} }_{1}}=0.501\;42\times \left\{ \begin{align} &-14.7\ln \, (H)+117.63\, (fs) \\ &-46.01\ln \, (H)+367.89\, (ms) \\ &-47.47\ln \, (H)+382.41\, (cs) \\ \end{align} \right\}+0.498\;58\times |
| \begin{array}{l} \left\{ \begin{array}{l} - 134.8\ln \,(H) + 1076.1\,(s1)\\ - 78.35\ln \,(H) + 624.71\,(s2)\\ - 98.08\ln \,(H) + 793.18\,(s3)\\ - 44\ln \,(H) + 350.65\,(s4) \end{array} \right\} + 0.266\;05 \times {\mathit{\Phi} _{\text{dissolution}}} - \\ 0.244\;98 \times {\mathit{\Phi} _{\text{dclay}}} - 0.220\;57 \times {\mathit{\Phi} _{\text{dcementation}}} \end{array} |
fs means fine sandstone; ms means medium sandstone; cs means coarse sandstone; s1, s2, s3 and s4 represent sorting value "1.3-1.6", "1.6-2.0", "2.0-2.1", "2.1-2.4" respectively.
(3) Such qualitative analysis through precise quantitative analysis helps quantify the influences of main controlling fact-ors of reservoir properties and their interaction on reservoir properties, and can provide reference for geological log interpretation model and plays a guiding role in analysis and prediction of reservoir "sweet spots".
ACKNOWLEDGMENTS: This study was supported by the China National Science and Technology Special Funds (No. 2016ZX05009-002), Sinopec Key Project (No. ZDP17008), Joint Key Petrochemical Project Funded by the National Natural Science Foundation of China (No. U1262203) and Project of Graduate Innovation Program in China University of Petroleum (East China) (No. YCX20150007). The authors thank Research Institute of Expl-oration and Development, North-China Branch Company, SINOPEC, for some data preparation. The final publication is available at Springer via https://doi.org/10.1007/s12583-016-0935-2.| Cao, Y. C., Xi, K. L., Wang, Y. Z., et al., 2013. Quantitative Research on Porosity Evolution of Reservoirs in Member 4 of Paleogene Shahejie Formation in Hexiwu Tectonic Zone of Langgu Sag, Jizhong Depression. Journal of Palaeogeograhy, 15(5): 593-604 (in Chinese with English Abstract) http://www.sciencedirect.com/journal/petroleum-exploration-and-development/vol/42/issue/4 |
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| 16. | Fei Shen, Linsong Cheng, Qiang Sun, et al. Evaluation of the Vertical Producing Degree of Commingled Production via Waterflooding for Multilayer Offshore Heavy Oil Reservoirs. Energies, 2018, 11(9): 2428. doi:10.3390/en11092428 |
Figures(6) / Tables(3)
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Longwei Qiu, Shengchao Yang, Changsheng Qu, Ningning Xu, Qingsong Gao, Xiangjin Zhang, Xugang Liu, Donghui Wang. A Comprehensive Porosity Prediction Model for the Upper Paleozoic Tight Sandstone Reservoir in the Daniudi Gas Field, Ordos Basin. Journal of Earth Science, 2017, 28(6): 1086-1096. doi: 10.1007/s12583-016-0935-2
| Sedimentary microfacies | Braided channel | Mouth bar | Underwater braided channel | Mid-channel bar |
| N | 877 | 121 | 687 | 594 |
| Φ (%) | 5.99 | 7.49 | 6.40 | 7.18 |
| K (×10-3 μm2) | 0.475 | 0.508 | 0.448 | 0.508 |
| Notes: N. number of data points; Φ. average porosity; K. average permeability. | ||||
DownLoad:
CSV
| Well No. | M value (mm) | Sorting coefficient | Clay mineral content (%) | Depth (m) | Cement content (%) | Quartz content (%) |
| Da-2 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 |
| Da-14 | 0.973 86 | 0.796 10 | 0.526 53 | 0.740 97 | 0.947 91 | 0.734 61 |
| Da-14 | 0.755 11 | 0.884 61 | 0.979 06 | 0.975 11 | 0.652 50 | 0.978 25 |
| Da-14 | 0.998 18 | 0.922 25 | 0.989 21 | 0.910 13 | 0.84751 | 0.852 76 |
| Da-14 | 0.853 03 | 0.894 94 | 0.909 43 | 0.916 54 | 0.634 24 | 0.966 97 |
| Da-3 | 0.935 00 | 0.956 85 | 0.814 97 | 0.992 42 | 0.705 28 | 0.984 05 |
| Da-3 | 0.854 39 | 0.849 15 | 0.801 54 | 0.880 65 | 0.997 77 | 0.828 65 |
| Da-3 | 0.502 46 | 0.733 36 | 0.899 50 | 0.721 06 | 0.688 46 | 0.686 31 |
| Da-3 | 0.980 14 | 0.810 76 | 0.744 47 | 0.897 21 | 0.715 43 | 0.950 17 |
| Da-3 | 0.942 88 | 0.898 50 | 0.859 42 | 0.989 27 | 0.709 75 | 0.91365 |
| Da-3 | 0.926 39 | 0.746 70 | 0.668 41 | 0.824 82 | 0.639 29 | 0.885 78 |
| Da-3 | 0.869 59 | 0.944 62 | 0.865 07 | 0.908 42 | 0.821 48 | 0.865 94 |
| Da-3 | 0.811 42 | 0.742 27 | 0.703 28 | 0.768 54 | 0.724 11 | 0.830 70 |
| Da-3 | 0.998 41 | 0.861 91 | 0.681 23 | 0.790 40 | 0.605 34 | 0.830 29 |
| Da-3 | 0.555 10 | 0.868 64 | 0.754 51 | 0.913 12 | 0.690 59 | 0.976 95 |
| Da-3 | 0.860 37 | 0.873 08 | 0.890 90 | 0.786 52 | 0.497 78 | 0.754 92 |
| Da-3 | 0.758 26 | 0.693 94 | 0.691 55 | 0.660 91 | 0.333 33 | 0.693 29 |
| Datan-1 | 0.691 59 | 0.948 61 | 0.874 88 | 0.870 07 | 0.942 11 | 0.842 72 |
| Datan-1 | 0.792 27 | 0.890 96 | 0.803 84 | 0.928 64 | 0.642 04 | 0.825 55 |
| Datan-1 | 0.778 79 | 0.771 87 | 0.602 53 | 0.819 97 | 0.735 41 | 0.803 04 |
| Datan-1 | 0.801 73 | 0.672 04 | 0.627 89 | 0.706 96 | 0.534 17 | 0.679 04 |
| Datan-1 | 0.742 49 | 0.654 52 | 0.617 50 | 0.693 86 | 0.521 02 | 0.670 14 |
| Datan-1 | 0.748 90 | 0.670 58 | 0.631 44 | 0.711 66 | 0.557 11 | 0.686 60 |
| Datan-1 | 0.965 48 | 0.893 15 | 0.764 30 | 0.979 72 | 0.692 19 | 0.939 11 |
| Datan-1 | 0.615 50 | 0.704 40 | 0.627 19 | 0.765 45 | 0.614 07 | 0.805 27 |
| Datan-1 | 0.765 76 | 0.672 09 | 0.653 57 | 0.740 25 | 0.542 42 | 0.716 56 |
| Grey relational grade | 0.826 04 | 0.821 38 | 0.768 55 | 0.842 03 | 0.691 97 | 0.834 67 |
| Weighting factor | 0.172 64 | 0.171 67 | 0.160 63 | 0.175 99 | 0.144 62 | 0.174 45 |
DownLoad:
CSV
| Well No. | Median grain size (mm) | Sorting coefficient | Clay mineral (%) |
Depth (m) |
Cement content (%) | Quartz content (%) | Description | Primary porosity (%) | Calculated porosity (%) | Error (%) |
| Da-14 | 0.480 | 1.97 | 7 | 2 791.38 | 1.0 | 88 | Coarse-grained quartz sandstone | 6.3 | 6.91 | 10.6 |
| Da-3 | 0.400 | 1.90 | 6 | 2 775.81 | 0 | 74 | Medium-grained litharenite | 6.2 | 6.88 | 11.0 |
| Da-3 | 0.480 | 2.19 | 12 | 2 776.54 | 5.0 | 85 | Coarse-grained lithic quartz sandstone | 4.6 | 5.07 | 10.3 |
| Da-3 | 0.400 | 1.72 | 14 | 2 790.70 | 0 | 89 | Coarse-grained lithic quartz sandstone | 5.1 | 5.51 | 8.1 |
| Da-3 | 0.450 | 1.97 | 12 | 2 791.96 | 0 | 89 | Coarse-grained lithic quartz sandstone | 5.6 | 5.96 | 6.4 |
| Da-3 | 0.690 | 1.80 | 5 | 2 795.55 | 3.0 | 70 | Over coarse-grained feldsparthiclitharenite | 6.3 | 5.53 | 12.2 |
| Da-3 | 0.550 | 1.75 | 9 | 2 806.09 | 3.0 | 88 | Coarse-grained lithic quartz sandstone | 4.9 | 5.50 | 12.3 |
| Da-3 | 0.320 | 1.60 | 9 | 2 819.16 | 0.5 | 73 | Medium-grained litharenite | 4.1 | 4.55 | 11.0 |
| Da-3 | 0.570 | 1.63 | 2 | 2 822.86 | 1.0 | 85 | Coarse-grained lithic quartz sandstone | 7.5 | 6.90 | 8.0 |
| Da-3 | 0.500 | 1.61 | 10 | 2 824.30 | 2.0 | 80 | Coarse-grained litharenite | 6.1 | 4.31 | 29.3 |
| Da-3 | 0.670 | 1.84 | 6 | 2 826.62 | 1.5 | 89 | Gravelly over Coarse-grained lithic quartz sandstone | 6.1 | 5.98 | 2.0 |
| Da-3 | 0.500 | 1.92 | 8 | 2 827.20 | 1.5 | 84 | Gravelly coarse-grained lithic quartz sandstone | 5.1 | 5.11 | 0.2 |
| Da-3 | 0.680 | 2.47 | 0 | 2 829.67 | 1.0 | 85 | Gravelly over coarse-grained lithic quartz sandstone | 9.2 | 7.17 | 22.1 |
| Datan-1 | 0.330 | 2.00 | 3 | 2 745.92 | 2.0 | 70 | Gravelly medium-and coarse-grained litharenite | 8.1 | 7.87 | 2.8 |
| Datan-1 | 0.325 | 2.38 | 1 | 2 739.25 | 0.5 | 66 | Gravelly medium-grained litharenite | 10.1 | 8.63 | 14.6 |
| Datan-1 | 0.400 | 2.11 | 10 | 2 741.28 | 2.0 | 58 | Coarse-grained litharenite | 4.8 | 5.45 | 13.5 |
| Datan-1 | 0.380 | 2.16 | 0 | 2 742.91 | 1.5 | 71 | Gravelly coarse-and medium-grained litharenite | 12.8 | 8.89 | 30.6 |
| Datan-1 | 0.360 | 2.20 | 0 | 2 743.30 | 2.0 | 77 | Gravelly coarse-grained litharenite | 13.4 | 9.20 | 31.4 |
| Datan-1 | 0.515 | 1.84 | 0 | 2 744.56 | 6.0 | 81 | Gravelly coarse-grained litharenite | 11.5 | 8.56 | 25.6 |
| Datan-1 | 0.285 | 1.70 | 0 | 2 746.84 | 2.0 | 66 | Medium-grained litharenite | 9.6 | 8.29 | 13.7 |
| Datan-1 | 0.400 | 1.86 | 7 | 2 786.46 | 1.0 | 57 | Gravelly coarse-grained litharenite | 6.3 | 4.84 | 23.1 |
| Datan-1 | 0.300 | 1.88 | 0 | 2 787.47 | 1.0 | 57 | Medium-grained litharenite | 7.0 | 6.53 | 6.8 |
| Datan-1 | 0.400 | 1.76 | 1 | 2 789.03 | 1.0 | 74 | Coarse-grained litharenite | 8.6 | 7.45 | 13.3 |
| Datan-1 | 0.370 | 1.81 | 0 | 2 790.02 | 2.0 | 72 | Coarse-and medium-grained litharenite | 8.4 | 7.30 | 13.1 |
| Datan-1 | 0.350 | 1.68 | 0 | 2 791.10 | 2.5 | 74 | Medium-grained litharenite | 7.7 | 7.30 | 5.2 |
| Datan-1 | 0.400 | 1.76 | 1 | 2 835.14 | 0 | 73 | Medium-grained litharenite | 5.5 | 6.11 | 11.1 |
| Datan-1 | 0.400 | 2.12 | 0 | 2 835.67 | 0 | 74 | Medium-coarse-grained litharenite | 7.9 | 6.41 | 18.9 |
| Datan-1 | 0.400 | 1.89 | 5 | 2 838.71 | 0 | 65 | Coarse-grained litharenite | 5.1 | 4.44 | 13.0 |
| Datan-1 | 0.300 | 1.82 | 0 | 2 840.41 | 0 | 61 | Medium-grained litharenite | 5.0 | 5.32 | 6.4 |
| Datan-1 | 0.250 | 1.50 | 6 | 2 841.19 | 0 | 56 | Medium-grained litharenite | 3.2 | 3.47 | 8.4 |
| Datan-1 | 0.500 | 1.64 | 10 | 2 841.54 | 0 | 57 | Coarse-grained litharenite | 3.6 | 2.55 | 29.2 |
DownLoad:
CSV
| Sedimentary microfacies | Braided channel | Mouth bar | Underwater braided channel | Mid-channel bar |
| N | 877 | 121 | 687 | 594 |
| Φ (%) | 5.99 | 7.49 | 6.40 | 7.18 |
| K (×10-3 μm2) | 0.475 | 0.508 | 0.448 | 0.508 |
| Notes: N. number of data points; Φ. average porosity; K. average permeability. | ||||
| Well No. | M value (mm) | Sorting coefficient | Clay mineral content (%) | Depth (m) | Cement content (%) | Quartz content (%) |
| Da-2 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 | 1.000 00 |
| Da-14 | 0.973 86 | 0.796 10 | 0.526 53 | 0.740 97 | 0.947 91 | 0.734 61 |
| Da-14 | 0.755 11 | 0.884 61 | 0.979 06 | 0.975 11 | 0.652 50 | 0.978 25 |
| Da-14 | 0.998 18 | 0.922 25 | 0.989 21 | 0.910 13 | 0.84751 | 0.852 76 |
| Da-14 | 0.853 03 | 0.894 94 | 0.909 43 | 0.916 54 | 0.634 24 | 0.966 97 |
| Da-3 | 0.935 00 | 0.956 85 | 0.814 97 | 0.992 42 | 0.705 28 | 0.984 05 |
| Da-3 | 0.854 39 | 0.849 15 | 0.801 54 | 0.880 65 | 0.997 77 | 0.828 65 |
| Da-3 | 0.502 46 | 0.733 36 | 0.899 50 | 0.721 06 | 0.688 46 | 0.686 31 |
| Da-3 | 0.980 14 | 0.810 76 | 0.744 47 | 0.897 21 | 0.715 43 | 0.950 17 |
| Da-3 | 0.942 88 | 0.898 50 | 0.859 42 | 0.989 27 | 0.709 75 | 0.91365 |
| Da-3 | 0.926 39 | 0.746 70 | 0.668 41 | 0.824 82 | 0.639 29 | 0.885 78 |
| Da-3 | 0.869 59 | 0.944 62 | 0.865 07 | 0.908 42 | 0.821 48 | 0.865 94 |
| Da-3 | 0.811 42 | 0.742 27 | 0.703 28 | 0.768 54 | 0.724 11 | 0.830 70 |
| Da-3 | 0.998 41 | 0.861 91 | 0.681 23 | 0.790 40 | 0.605 34 | 0.830 29 |
| Da-3 | 0.555 10 | 0.868 64 | 0.754 51 | 0.913 12 | 0.690 59 | 0.976 95 |
| Da-3 | 0.860 37 | 0.873 08 | 0.890 90 | 0.786 52 | 0.497 78 | 0.754 92 |
| Da-3 | 0.758 26 | 0.693 94 | 0.691 55 | 0.660 91 | 0.333 33 | 0.693 29 |
| Datan-1 | 0.691 59 | 0.948 61 | 0.874 88 | 0.870 07 | 0.942 11 | 0.842 72 |
| Datan-1 | 0.792 27 | 0.890 96 | 0.803 84 | 0.928 64 | 0.642 04 | 0.825 55 |
| Datan-1 | 0.778 79 | 0.771 87 | 0.602 53 | 0.819 97 | 0.735 41 | 0.803 04 |
| Datan-1 | 0.801 73 | 0.672 04 | 0.627 89 | 0.706 96 | 0.534 17 | 0.679 04 |
| Datan-1 | 0.742 49 | 0.654 52 | 0.617 50 | 0.693 86 | 0.521 02 | 0.670 14 |
| Datan-1 | 0.748 90 | 0.670 58 | 0.631 44 | 0.711 66 | 0.557 11 | 0.686 60 |
| Datan-1 | 0.965 48 | 0.893 15 | 0.764 30 | 0.979 72 | 0.692 19 | 0.939 11 |
| Datan-1 | 0.615 50 | 0.704 40 | 0.627 19 | 0.765 45 | 0.614 07 | 0.805 27 |
| Datan-1 | 0.765 76 | 0.672 09 | 0.653 57 | 0.740 25 | 0.542 42 | 0.716 56 |
| Grey relational grade | 0.826 04 | 0.821 38 | 0.768 55 | 0.842 03 | 0.691 97 | 0.834 67 |
| Weighting factor | 0.172 64 | 0.171 67 | 0.160 63 | 0.175 99 | 0.144 62 | 0.174 45 |
| Well No. | Median grain size (mm) | Sorting coefficient | Clay mineral (%) |
Depth (m) |
Cement content (%) | Quartz content (%) | Description | Primary porosity (%) | Calculated porosity (%) | Error (%) |
| Da-14 | 0.480 | 1.97 | 7 | 2 791.38 | 1.0 | 88 | Coarse-grained quartz sandstone | 6.3 | 6.91 | 10.6 |
| Da-3 | 0.400 | 1.90 | 6 | 2 775.81 | 0 | 74 | Medium-grained litharenite | 6.2 | 6.88 | 11.0 |
| Da-3 | 0.480 | 2.19 | 12 | 2 776.54 | 5.0 | 85 | Coarse-grained lithic quartz sandstone | 4.6 | 5.07 | 10.3 |
| Da-3 | 0.400 | 1.72 | 14 | 2 790.70 | 0 | 89 | Coarse-grained lithic quartz sandstone | 5.1 | 5.51 | 8.1 |
| Da-3 | 0.450 | 1.97 | 12 | 2 791.96 | 0 | 89 | Coarse-grained lithic quartz sandstone | 5.6 | 5.96 | 6.4 |
| Da-3 | 0.690 | 1.80 | 5 | 2 795.55 | 3.0 | 70 | Over coarse-grained feldsparthiclitharenite | 6.3 | 5.53 | 12.2 |
| Da-3 | 0.550 | 1.75 | 9 | 2 806.09 | 3.0 | 88 | Coarse-grained lithic quartz sandstone | 4.9 | 5.50 | 12.3 |
| Da-3 | 0.320 | 1.60 | 9 | 2 819.16 | 0.5 | 73 | Medium-grained litharenite | 4.1 | 4.55 | 11.0 |
| Da-3 | 0.570 | 1.63 | 2 | 2 822.86 | 1.0 | 85 | Coarse-grained lithic quartz sandstone | 7.5 | 6.90 | 8.0 |
| Da-3 | 0.500 | 1.61 | 10 | 2 824.30 | 2.0 | 80 | Coarse-grained litharenite | 6.1 | 4.31 | 29.3 |
| Da-3 | 0.670 | 1.84 | 6 | 2 826.62 | 1.5 | 89 | Gravelly over Coarse-grained lithic quartz sandstone | 6.1 | 5.98 | 2.0 |
| Da-3 | 0.500 | 1.92 | 8 | 2 827.20 | 1.5 | 84 | Gravelly coarse-grained lithic quartz sandstone | 5.1 | 5.11 | 0.2 |
| Da-3 | 0.680 | 2.47 | 0 | 2 829.67 | 1.0 | 85 | Gravelly over coarse-grained lithic quartz sandstone | 9.2 | 7.17 | 22.1 |
| Datan-1 | 0.330 | 2.00 | 3 | 2 745.92 | 2.0 | 70 | Gravelly medium-and coarse-grained litharenite | 8.1 | 7.87 | 2.8 |
| Datan-1 | 0.325 | 2.38 | 1 | 2 739.25 | 0.5 | 66 | Gravelly medium-grained litharenite | 10.1 | 8.63 | 14.6 |
| Datan-1 | 0.400 | 2.11 | 10 | 2 741.28 | 2.0 | 58 | Coarse-grained litharenite | 4.8 | 5.45 | 13.5 |
| Datan-1 | 0.380 | 2.16 | 0 | 2 742.91 | 1.5 | 71 | Gravelly coarse-and medium-grained litharenite | 12.8 | 8.89 | 30.6 |
| Datan-1 | 0.360 | 2.20 | 0 | 2 743.30 | 2.0 | 77 | Gravelly coarse-grained litharenite | 13.4 | 9.20 | 31.4 |
| Datan-1 | 0.515 | 1.84 | 0 | 2 744.56 | 6.0 | 81 | Gravelly coarse-grained litharenite | 11.5 | 8.56 | 25.6 |
| Datan-1 | 0.285 | 1.70 | 0 | 2 746.84 | 2.0 | 66 | Medium-grained litharenite | 9.6 | 8.29 | 13.7 |
| Datan-1 | 0.400 | 1.86 | 7 | 2 786.46 | 1.0 | 57 | Gravelly coarse-grained litharenite | 6.3 | 4.84 | 23.1 |
| Datan-1 | 0.300 | 1.88 | 0 | 2 787.47 | 1.0 | 57 | Medium-grained litharenite | 7.0 | 6.53 | 6.8 |
| Datan-1 | 0.400 | 1.76 | 1 | 2 789.03 | 1.0 | 74 | Coarse-grained litharenite | 8.6 | 7.45 | 13.3 |
| Datan-1 | 0.370 | 1.81 | 0 | 2 790.02 | 2.0 | 72 | Coarse-and medium-grained litharenite | 8.4 | 7.30 | 13.1 |
| Datan-1 | 0.350 | 1.68 | 0 | 2 791.10 | 2.5 | 74 | Medium-grained litharenite | 7.7 | 7.30 | 5.2 |
| Datan-1 | 0.400 | 1.76 | 1 | 2 835.14 | 0 | 73 | Medium-grained litharenite | 5.5 | 6.11 | 11.1 |
| Datan-1 | 0.400 | 2.12 | 0 | 2 835.67 | 0 | 74 | Medium-coarse-grained litharenite | 7.9 | 6.41 | 18.9 |
| Datan-1 | 0.400 | 1.89 | 5 | 2 838.71 | 0 | 65 | Coarse-grained litharenite | 5.1 | 4.44 | 13.0 |
| Datan-1 | 0.300 | 1.82 | 0 | 2 840.41 | 0 | 61 | Medium-grained litharenite | 5.0 | 5.32 | 6.4 |
| Datan-1 | 0.250 | 1.50 | 6 | 2 841.19 | 0 | 56 | Medium-grained litharenite | 3.2 | 3.47 | 8.4 |
| Datan-1 | 0.500 | 1.64 | 10 | 2 841.54 | 0 | 57 | Coarse-grained litharenite | 3.6 | 2.55 | 29.2 |
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