Journal of Geoscience and Environment Protection, 2014, 2, 60-65
Published Online June 2014 in SciRes. http://www.scirp.org/journal/gep
How to cite this paper: Jiang, B.-C. et al. (2014). Research on Determination of the Main Factors Influencing the Gas Well
Post-Frac Productivity Prediction for Tight Sandstone Reservoirs Based on Factors Analysis. Journal of Geoscience and
Environment Protection, 2, 60-65. http://dx.doi.org/10.4236/gep.2014.23008
Research on Determination of the Main
Factors Influencing the Gas Well Post-Frac
Productivity Prediction for Tight Sandstone
Reservoirs Based on Factors Analysis
Bi-Ci Jiang1*, Bao-Zhi Pan1, Hai-Tao Zhang2, Xiao-Ming Yang2, Gang Chen3, Wen-Bin Liu4
1Jilin University, Changchun, China
2Research Institute of Exploration and Development, Petro Changqing Oilfield Company, Xi’an, China
3China Coal Research Institute Xi’an Science and Industry Group, Xi’an, China
4China University of Petroleum (East China), Qingdao, China
Received March 2014
With the characteristics such as low porosity, low permeability and low gas saturation, tight sand-
stone reservoirs almost have no natural capacity and need to be fractured (or fracturing) for pro-
ductivity. Therefore, fracturing capacity prediction is very necessary. However there we re so
many factors, and the relations between the factor and the post-frac productivity are complex. In
this study, first of all factors are concluded from the gas well stable productivity formula, then I
used factor analysis to look for the main factors from the logging parameters and fracturing pa-
rameters in SULIGE area. This study could provide basal references for the gas post-frac produc-
tivity prediction in tight sandstone reservoirs.
Factor Analysis, Tight Sandstone, SULIGE Region, Post-Frac Produ c ti vi ty
The fracturing is needed for tight reservoirs’ productivity, and the factors influencing the gas productivity pre-
diction became complicated after fracturing. At present, there are two methods for tight sandstone gas post-frac
productivity prediction that are formula method (Chen, 1998) and mathematical statistical method (Zhang, 2011;
Zhang, 2007; Zhang, 2013; Zhang, 2008). For formula method, the accurately determined parameters involved
in the equation are needed. However, for mathematical statistical method, the main factors were needed. The
main factors come from the logging parameters and fracturing parameters. Zhang Jing (2011) used linear regres-
sion analysis and Zhang Song-yan g (2007) used method of trial and error to look for the relationship between
B.-C. Jiang et al.
the log parameters and the open-flow potential. Zhuang Hua (2013) used gray correlation method to search for
the main factors in post-frac capacity in SULIGE region. Huang, He and Zhang (2010) integrated gray correla-
tion, stepwise analysis, principal component analysis to analyze the main factors which had influence on ul-
tra-low permeability reservoir oil production capacity. Factor analysis puts all of the information involved in
original variables together, by exploring the internal structure of the correlation matrix and makes multivariate
integrated into a small number of factors, which can reproduce the original relationship between the variables
(Luo et al., 2005). Factor analysis is a good application in lithology identification (Luo et al., 2013). In this study,
first it concluded the total factors from the gas well stable productivity formula, then it used factor analysis to
analyze the main factors of tight sandstone gas Post-frac capacity forecast. This study could provide basal refer-
ences for mathematical statistical method in the gas post-frac productivity.
2. Theoretical Formulas of Gas Reservoir Fracturing Capacity
In the literature (Chen, 1998), gas well stable binomial deliverability equation is
P PAQ BQ
is reservoir static pressure, (MPa); wf
is the bottom hole flowing pressure (MPa); A and
, the gas well absolute open flow is
(4(0.101)) / 2
QABpA B=+− −
is effective thickness(m);
is terrestrial standard pressure (MPa);
is permeability (mD);
is terrestrial standard temperature (K);
is gas deviation factor;
is apparent skin factor;
is inertial re-
sistance coefficient caused turbulence;
is gas gravity;
is gas viscosity(mPa·s);
is gas control ra-
bottom radius, m;
is universal gas constant (
/( )KMPa mKmolK⋅⋅
In the formula (4), it’s very difficult to accurately determine the various parameters. For these parameters h
, R, T,
, it is easy to obtain obtained. However, for the others, exact values are difficult to be ob-
tained. K suffered many influential factors, so it is usually established by the relationship of porosity. Sa is af-
fected by many factors (Chen & Yan, 2004), so it is difficult to get an accurate value. β is related to Sa. Z is the
function of formation temperature and formation pressure (Gao & Hao, 2001), so there were some discrepancies;
is got based on the empirical formula proposed by Lee and Gonzalez (Gao & Hao, 2001), and there will be
is affected by permeability, reservoir pressure and other factors, there is some deviation too.
Therefore, there is a big difficulty and a certain deviation when using the formula method to calculate gas well
fracturing capacity, it’s necessary to predict gas well fracturing capacity by using statistical mathematical meth-
ods. However there are too many parameters to response reservoir conditions and fracturing conditions. We
need to filter out the main influencing parameters.
In the formula (4) we could see that factors influencing gas well fracturing capacity besides the gas’s property,
the thickness and the reservoir’s conditions, gas well fracturing capacity is also closely related to reservoir’s
properties (permeability K),fracturing parameters (mainly effect Sa,
and reservoir properties). In order to
avoid the impact of reservoir thickness and the various parameters referred come from unit thickness.
2. Selecting Factors Influencing the Gas Well Post-Frac Productivity for Tight
Nowadays, the forecast of productivity is building a model with an indicator which can reflect the gas produc-
tivity. The indicator is built by the well deliver ability testing, the porosity, the absolute permeability and so on
(Zhang, 2011; Zhang, 2007; Zhang, 2013; Zhang, 2008). Compared with conventional reservoir, tight gas res-
ervoir has tight lithology, poor physical property, strong aeolotropism, low trap amplitude and low natural de-
liverability. In the actual production process, fracturing has a great impact on tight gas productivity. So it is
B.-C. Jiang et al.
needed to consider the reservoir property and the fracturing parameters in the post-frac productivity predicting.
The formation P1-2sh in SULIGE area is a typical representative of tight sand stone reservoirs with the per-
meability (0.1 - 1) * 10−3∙μm2. In this study, the data came from 52 wells in west of SULIGE region, ten pa-
rameters from logging and fracturing parameters were picked up: natural gamma (GR, API), acoustic travel time
(AC, us/m), resistance (RT, Ω∙m), density (DEN, g/cm3), neutron(CNL,%), the amount of sand per meter (SD,
m3), the sand ratio (SR,%), the sand concentration (SC, kg/m3), delivery capacity per meter(VOE, m3/min) and
total amount of fluid into the well per meter (FV, m3/min).
3. Analyzing the Impact of Various Factors on Fracturing Capacity by Factor
Factor analysis method put all relevant information of the original variables together. It reduces the number of
factors by exploring the internal structure of the correlation matrix, which can reflect the relationship among the
original variables, and looks for the reason of the correlation additionally (Zhu et al., 2014). Factor analysis
method that can determine the main factors for tight sandstone post-frac predicting, it could search out the in-
ternal correlation among all of the factors, and afford a few general factors to explain the varieties of post-frac
productivities in the tight sandstone. Then we could select the main effect factors of tight sand stone fracturing
capacity forecast based on the contribution made by each factor in the common factors.
The step of factor analysis method is just as following:
First: importing the raw data Xn*p, then calculating the average values and variance of the sample, and stan-
dardizing the data. Second: evaluating the sample’s correlation matrix R = (rij) p * p. Third: finding the eigen
value of correlation coefficient matrix λi (λ1, λ2, ..., λp > 0) and the corresponding standard orthonormal eigen
vectors (li). Forth: determining the number of common factors; Fifth: calculating the common variance of com-
mon factors hi2. Last: calculating the score of the common factors component and then explaining the practical
Depending on the method factor analysis, we analyze the data with SPSS software. The detail procedure is as
Step one: Judging the parameters selected whether are suitable for factor analysis
The precondition of using factor analysis method is that there is a linear relationship between the variables.
Then the factors could be reduced and the purpose could be achieved. The result of analyzing of correlation ma-
trix shows that the correlation coefficients were greater than 0.3. So there is a strong correlation between the
factors which has an impact on tight sand gas reservoir fracturing capacity forecast. The correlation matrix of
various factors was below (Table 1):
Meanwhile calculating KMO and BaetlettSphere degree of the above table, results were as follows (Table 2):
Table 2 shows: the statistic observation of BaetlettSphericity testing was 477.417, and the corresponding
probabilities P (Sig) was close to zero. If the significance level was 0.05, due to the probability P was less than
the significance level 0.05, you could pull off the null hypothesis. So obviously there were differences between
correlation matrix and unit matrix, meanwhile KMO value was 0.715, that fit the criteria well. In short the
method of factor analysis was available in this study.
Step two: Extracting factors
According to the correlation coefficient matrix of the original variants, eigen values over1were selected by
PCA. Then calculating the explained variance of each parameters. The initial common factor variance is esti-
mators of eachvariant’s explained variance. It is always equal to 1 in PCA. Because the number of components
equals to the original parameters’ number, the common value is equal to 1. The common factor variance extract-
ed was used to predict factors’ multiple correlation square value. The low value shows that the variant is not
suitable as a factor, so it will be abandoned in the analysis. Now calculate the communality of the chosen factors.
The results are as following in Table 3:
The third column in table 3(extracted) is the final solution of common variable degree according to the factor
analysis. What can be obtained is that most of the information has been analyzed with factor analysis, just a few
information was lost. The overall effect of factor extraction is well.
The number of the analyzed factors is ten, so there are ten ingredients. Now calculating characteristic values
for each component (the total characteristic values). The proportion of each component’s explained variance in
the total variance is just the proportion of the factors’ characteristic value in the total eigen value. Now calculat-
B.-C. Jiang et al.
Table 1. Correlation coefficient matrix.
Factors SD SR SC VOE FV RT GR AC CNL DEN
SD 1 0.623 0.612 0.652 0.641 0.02 −0.04 0.107 0.074 0.104
SR 0.623 1 0.991 0.879 0.706 −0.2 0.24 0.079 0.063 0.14
SC 0.612 0.991 1 0.883 0.7 −0.1 0.246 0.075 0.083 0.135
VOE 0.652 0.879 0.883 1 0.764 −0 0.187 0.093 0.09 0.22
FV 0.641 0.706 0.7 0.764 1 0.19 −0.08 −0.08 −0.13 0.129
RT 0.022 −0.154 −0.145 −0.03 0.189 1 −0.37 −0.53 −0.44 0.249
GR −0.039 0.24 0.246 0.187 −0.076 −0.4 1 −0.08 0.339 0.472
AC 0.107 0.079 0.075 0.093 −0.08 −0.5 −0.08 1 0.557 −0.62
CNL 0.074 0.063 0.083 0.09 −0.126 −0.4 0.339 0.557 1 −0.26
DEN 0.104 0.14 0.135 0.22 0.129 0.25 0.472 −0.62 −0.26 1
Table 2. KMO and Bartlett’s test results.
Sphericity test of Bartlett
Similar chisquare 477.417
Table 3. Common factor variance table.
SR 1 0.949 GR 1 0.908
SC 1 0.94 AC 1 0.849
VOE 1 0.893 CNL 1 0.922
FV 1 0.813 DEN 1 0.872
ing the summation percentage of the proportion of each component’s explained variance in the total variance.
Then extract the components whose total variance is greater than 0.5. The results are shown in Table 4.
The section 2 (total) of Table 4, there are four values greater than 0.5 in the variant correlation matrix as
4.079, 2.402, 1.625, 0.63. These four factors integrated 87.368 percentage information of the ten variants. In
other words, the four factors which are in front reflect most information of the original data. Therefore
extracting four common factors is appropriate, and it can also represent a comprehensive condition.
Step three: According to the common factor component scores, finding the main influencing factors of tight
sand gas deliverability
Now we build equations for four general factors according to calculated scores coefficient of general factor.
Then we select the previous two of the absolute values of the coefficient as the main factors of the impact of
tight sandstone gas reservoir fracturing capacity. Coefficient matrix of component score is shown in Table 5:
F2= 0.026SD 0.011SR 0.005SC+0.029VOE 0.079FV+0.053RT+0.484GR
F4= 0.378SD+0.242SR+0.227SC 0.009VOE 0.166FV0.716RT+0.24GR
+0.115AC 0.311CNL 0.159DEN
In Table 5, each of the largest two of absolute value of the coefficient expressions of various common factors
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Table 4. The total explained variance.
Initialeigenvalue Squareextracted and loading
percentage Total Variance’s
2 2.402 24.017 64.811 2.402 24.017 64.811
3 1.625 16.254 81.065 1.625 16.254 81.065
4 0.63 6.303 87.368 0.63 6.303 87.368
5 0.446 4.458 91.826
6 0.268 2.678 94.504
7 0.255 2.548 97.052
8 0.194 1.939 98.991
9 0.092 0.924 99.915
10 0.008 0.085 100
Table 5. Component score coefficient matrix.
1 2 3 4
SD 0.198 −0.026 0.335 −0.378
SR 0.233 −0.011 −0.182 0.242
SC 0.232 −0.005 −0.161 0.227
VOE 0.229 0.029 0.035 −0.009
FV 0.229 −0.079 −0.028 −0.166
RT 0.009 0.053 0.216 −0.716
GR −0.039 0.484 0.171 0.24
AC 0.031 −0.289 0.263 0.115
CNL −0.029 0.134 0.836 −0.311
DEN −0.009 0.503 0.067 −0.159
is: the first common factor (F1) is the sand ratio(SR), sand concentration (SC); the second common factor (F2) is
the natural gamma ray (GR), density (DEN); the third common factor (F3) is the neutron (CNL), the amount of
sand per meter(SD); the fourth common factors (F4) resistivity (RT), the amount of sand per meter(SD). In the
first common factor (F1) (Table 4 that, F1 information reflects 40.794%) expression, the five parameter coeffi-
cients represent fracturing construction accounted for a large proportion than the five logging parameters, so we
can see that fracturing construction parameter have a great impact on tight sand gas fracturing capacity.
4. Conclusions and Understanding
For tight sand reservoirs, the relationship between individual factors and gas reservoir fracturing production is
complicated, so we cannot determine the impact factors of tight sandstone gas fracturing capacity by a simple
linear correlation analysis.
In factor analysis, correlation of each factor which has an impact on tight sand gas fracturing capacity is
greater than 0.3. There must be a certain relationship among the various factors.
From factor analysis we can see that fracturing parameters is important in tight gas reservoir post-fract pro-
ductivity prediction, therefore we must consider fracturing parameter into tight sand gas fracturing capacity
The main factors determined by factor analysis are sand ratio (SR), sand concentration (SC), natural gamma
ray (GR), density (DEN), neutron (CNL), the amount of sand per meter (SD), resistivity (RT).
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