A regression model for estimation of dew point pressure from downhole fluid analyzer data
 1.6k Downloads
 2 Citations
Abstract
Accurate knowledge of dew point pressure is important in understanding and managing gas condensate reservoirs. Without a correct assessment of dew point pressure, an accurate description of phase changes and phase behavior cannot be achieved. Numerous models for predicting gas condensate dew point pressure from surface fluid data have been proposed in the literature. Some of these require knowledge of the full composition of the reservoir fluid (based on laboratory experiments), while others only need field parameters that are relatively easy to obtain. This paper presents a new model for predicting the dew point pressure from downhole fluid analyzer data. Such data are now measured (usually in real time) while obtaining downhole fluid samples. The new model predictions give a quick estimation of dew point pressure for wet gas and gas condensate reservoirs. Since it relies only on downhole measured data, the model provides an estimate of dew point pressure without the need for laboratory analyses. During downhole fluid sampling, the model can be used to ensure whether the sample is still in single phase, or whether the dew point was crossed during the sampling operation. An early estimate of dew point pressure is also valuable in designing further tests for gas condensate wells. The new model, constructed using a fluid database of nearly 700 gas condensate samples, was devised using sophisticated statistical/machine learning methods, and attained a mean absolute relative error value of 2% for predicting the logarithm of pressure. In comparison with other dew point estimation models (that use surface fluid data), the chosen model was found to attain a similar level of accuracy when tested on samples not used in the model building phase.
Keywords
Regression model Dew point pressure Downhole fluid analyzer data Gas condensate reservoirsAbbreviations
 API
API gravity of stock–tank condensate
 CFA
Compositional Fluid Analyzer
 DFA
Downhole fluid analyzer
 GCR
Gas condensate ratio, SCF/STB
 IFA
In situ Fluid Analyzer
 LFA
Live Fluid Analyzer
 Mwt_{C7+}
Molecular weight of heptane plus
 OFA
Optical fluid analyzer
 Pd
Dew point pressure, psia
 Ppr
Pseduoreduced pressure
 Psp
Primary separator pressure, psia
 Rsp
Primary separator gas–oil ratio, SCF/STB
 T
Reservoir temperature, F
 Tpr
Pseduoreduced temperature
 Tsp
Primary separator temperature, F
 Y_{i}
Component mole fraction
 Y_{C7+}
Mole Percentage of heptane plus
 ρ_{C7+}
C7 plus density, g/cc
 γ_{gsp}
Separator gas specific gravity
 γ_{g}
Gas specific gravity (air = 1)
 γ_{gR}
Reservoir gas specific gravity
 γ_{C7+}
Specific gravity of heptane plus
 γ_{cond}
Condensate gas specific gravity
 MARE
Mean absolute relative error
 AIC
Akaike information criterion
 BIC
Bayesian information criterion
 MSE
Mean squared error
 R^{2}
A criterion for correlation coefficient of a linear regression
 Beta
Model coefficients
 n
No of samples
 ϵ
Residual error term
Introduction
Dew point pressure is needed to characterize wet gas and gas condensate reservoir fluids. Industry practitioners often rely on measuring the dew point (among other phase behavior properties) using laboratory experiments. In the absence of laboratory data, dew point estimation models (correlations) are usually available to estimate the dew point with varying accuracy (discussed below). These models are based on either knowledge of fluid composition or knowledge of some surface fluid properties data (e.g., GCR, API of stock tank oil, and reservoir temperature). For many years, the oil and gas industry has been actively developing several tools to measure realtime in situ fluid composition and properties. To the best of our knowledge, we are unaware of any simple dew point estimation model based on the downhole fluid composition measurements except the one we present here. Such model, when available, will allow rapid evaluation of dew point pressure before measuring it in the laboratory with common techniques and will have several applications.
Numerous models for predicting gas condensate dew point pressure have been derived from large databases in the literature. There are essentially two types of published models for estimating dew point pressure in gas condensate reservoirs. One type of models uses detailed compositional analysis that requires laboratory PVT experiments, while another type uses easily measured parameters from production tests and downhole temperature as inputs. Marruffo et al. (2002), Nemeth and Kennedy (1966), Elsharkawy (2001, 2011), Shokir (2008), Olds et al. (1944), and Godwin (2012) require detailed compositional analysis. Marruffo et al. (2002) used nonlinear regression to fit appropriate models and build their model, applying statistical tools such as residual analyses and crossplots. The developed model required information from production tests, but did not require the knowledge of gas condensate composition. The original total PVT data sample size they used was 148. After the process of selection and validation, the database was reduced to 114 data points. Nemeth and Kennedy (1966) used 579 data points from 480 different hydrocarbon systems to develop a model that predicts dew point pressure with an average deviation of 7.4%. The model input parameters are variables measured in the laboratory with composition in mole fraction for CH4 through C_{7}H_{16}, N_{2}, CO_{2}, H_{2}S, and molecular weight and specific gravity of heptane plus fraction. Their work is regularly quoted in many of the more recent models. Elsharkawy (2001) developed a physically sound empirical method for predicting dew point pressure based on routinely measured gas analysis and reservoir temperature. In total, 340 measurements of dew point pressure were used, resulting in a model with an absolute average of 7.68%. The model included the effect of all variables such as temperature, gas condensate composition, and properties of the plus fraction on dew point pressure. Elsharkawy (2001, 2011) discussed the two types of dew points applicable to any hydrocarbon mixtures. The first dew point occurs when dry gas is compressed to the point that liquid starts to form. The second called retrograde or condensate dew point and occurs when a gas mixture containing heavy hydrocarbons in its solution is depressurized until liquid forms. He presented models for dew point prediction based on gas composition and reservoir temperature. His database included 340 data points. Shokir (2008) used genetic programming to develop a model for dew point pressure prediction from 245 gas condensate systems. The developed model uses the full composition of the gas (CH_{4} through C_{7}H_{16}+, N_{2}, CO_{2}, and H_{2}S mole fractions) in addition to the molecular weight of the heptanes plus fraction, and reservoir temperature. He also tested his model against other published models. Olds et al. (1944) studied the behavior of six symmetrically chosen mixtures from Paloma field for a range of parameters (temperatures ranged from 100 to 250 °F and pressures up to 5000 psia). They studied the influence of pressure and temperature on the composition and the retrograde gas dew point, and implemented a graphical examination in order to obtain a chart correlating volumetric and phase behavior with the composition of the system and temperature. Godwin (2012) used data from the literature and developed a dew point estimation model based on gas composition, reservoir temperature, and properties of the heptanes plus fraction. A total of 259 out of 273 data points were selected to build the new model, and 14 data points were used for testing.
On the other hand, a literature review for the models that take as input field data that are easily measured finds the following: Humoud and AlMarhoun (2001), Ovalle et al. (2005) and AlDhamen and AlMarhoun (2011). Humoud and AlMarhoun (2001) developed another model based on available field data from 74 PVT reports. They correlated the dew point pressure of a gas condensate fluid directly with its reservoir temperature, pseudoreduced pressure and temperature, primary separator gas–oil ratio, the primary separator pressure and temperature, and relative densities of separator gas and heptanes plus specific gravity. The average error for this model was 4.33%. Ovalle et al. (2005) used readily available field data to calculate the dew point pressure. Their database contained 615 points. Their model is based on initial producing gas condensate ratio from the firststage separator, initial API of the stock tank liquid, specific gravity of the initial reservoir gas, and reservoir temperature. Nonparametric approaches for estimating optimal transformations of data were used to obtain the maximum correlation between observed variables. AlDhamen and AlMarhoun (2011) developed a new model to predict dew point pressure for gas condensate reservoirs, using nonparametric approaches and artificial neural networks. Their results were based on a total number of 113 data samples obtained from constant mass expansion experiments from fields in the Middle East.
Downhole fluid analysis
The process of obtaining realtime analysis of downhole characteristics passed through many stages of development, starting with IFA and ending with DFA. Fingerprinting in fluid characterization became an important topic receiving wide attention with direct application on improving the quality of fluid samples. Many tools (e.g., OFA, LFA, CFA, and IFA) capable of detecting in situ variation of different fluids were developed over the years (1991/2001/2003/2007), (Mullins et al. 2009; Elshahawi et al. 2007; Xian et al. 2006). The development of these tools was to address several production problems (e.g., sizing of facilities, well placement, completions equipment, and production prediction). According to Betancourt et al. (2004, 2007), the Composition Fluid Analyzer (CFA) is a tool which has a sensor for performing fluorescence spectroscopy by measuring light emission in the green and red ranges of the spectrum after excitation with blue light. It was originally introduced in order to track phase transitions in gas condensate sampling. In situ Fluid Analyzer (IFA), based on optical absorption methods, can provide the mass fractions of three hydrocarbon molecular groups: CH_{4}, C_{2}H_{6}–C_{5}H_{12} and C_{6}H_{14}+, as well as CO_{2}, in real time at downhole conditions. It can also track the gas condensate (by simply dropping temporarily the sampling pressure below the saturation pressure of the fluid so as to observe the change in the fluorescence signal that will occur with dew formation at the dew point pressure).
With the development of downhole optical fluid analyzer (DFA), more capabilities were added to downhole fluid analysis. DFA has become an increasingly utilized technology in wireline logging as it enables fluid characterization by creating a downhole fluid log (versus depth along the hydrocarbon column). In multiwell applications, DFA can help in addressing fluid distribution and variation inside the reservoir, and in identification of reservoir compartments. The basic outputs from DFA measurements are weight percentages of CO_{2}, CH_{4}, C_{2}H_{6}, C_{3}H_{8}, C_{5}H_{12}, and C_{6}H_{14}+, in addition to live fluid density.
In the form of an optimized wireline logging tool, DFA is used in the Gulf of Mexico and different areas of the world for detecting hydrocarbon variations and reducing uncertainty in varied compositions cases. Compartmentalization can also be detected by these tools (Betancourt et al. 2007).
With the increased application of these downhole fluid analysis tools, valuable compositional information (for hydrocarbon groups in weight percent) becomes available to reservoir and production engineers. In this paper, we present a new dew point estimation model that is different from the other models available in the literature, as it is based on downhole fluid analyzer data. The correlation is thus capable of predicting the dew point pressure for a wide range of wet gases and gas condensate fluids without the need for full laboratory compositional analysis, production data, or production test information.
Methodology
Fluids database
McCain (1994) characterized different fluid properties and introduced widely acceptable criteria to differentiate among the five reservoir fluid types. According to McCain’s criteria, we collected fluid data (covering wide range of gas properties) from different reservoirs located in different regions of the world (with around 17% of the data from the Middle East). Part of the database came from the literature, especially the data presented by Nemeth (1966), which was extensively used in developing most available dew point pressure prediction models from surface data.
Data ranges for the complete PVT experiments gas samples (99 samples)
Laboratory measured parameter  Minimum  25th percentile  50th percentile (Median)  75th percentile  Maximum 

Reservoir gas gravity  0.558  0.765  0.89  1.08  1.86 
Primary separator gas gravity  0.56  0.67  0.72  0.77  1.42 
Field stock tank liquid gravity (°API)  37.00  43.49  48.55  54.50  67.70 
GCR, STB/MMscf  0.63  42  120  207  232 
Field gas–oil ratio, scf/STB  1147  4778  9207  19,944  159,8940 
C7+ density g/cc  0.69  0.80  0.81  0.82  0.85 
C7+ Mwt  101  144  158  180  353 
Reservoir temperature, T (°F)  143.8  223  260  296  347 
T _{sep}, °F  19.9  81  99  119  176 
P _{sep}, psia  33  255  439  624  2581 
Composition (mole%)  
Methane  9.19  66.24  73.60  82.81  99.84 
Ethane  0.05  6.34  7.96  9.28  15.04 
Propane  0.04  2.54  3.81  4.96  8.60 
Butane  0.02  0.60  1.18  1.80  6.04 
Pentane  0  0.65  1.14  2.94  3.92 
Hexane  0  0.48  0.86  1.31  5.54 
Heptane plus  0  2  5  8  24.23 
Hydrogen sulfide  0  0  0  0  18.00 
Carbon dioxide  0  0.64  2.6  5.32  67.08 
Nitrogen  0  0.2  0.49  0.75  9.86 
Data ranges for the composition available PVT gas samples (568 samples)
Laboratory measurement Parameters  Minimum  25th percentile  50th percentile (Median)  75th percentile  Maximum 

Reservoir gas gravity  0.733  0.77  0.79  0.80  0.87 
C7+ Mwt  106  128  147  160  235 
Reservoir temperature, T (°F)  40  168  212  246  320 
Composition (mole%)  
Methane  3.49  74.59  82.55  88.91  96.68 
Ethane  0.37  3.73  5.04  6.94  15.13 
Propane  0.11  1.47  2.43  4.08  10.90 
Butane  0.17  0.97  1.59  2.77  37.50 
Pentane  0  0.45  0.86  1.52  07.10 
Hexane  0  0.36  0.64  1.16  08.71 
Heptane plus  0  1.53  2.76  5.23  13.56 
Hydrogen sulfide  0  0.00  0.00  0.00  29.86 
Carbon dioxide  0  0.28  0.62  1.37  91.92 
Nitrogen  0  0.00  0.28  0.66  43.22 
Development of a new empirical model
 1.
building a database for gas samples;
 2.
making quality checks on the data samples;
 3.
filtering the samples;
 4.
converting mole% to weight% for all samples based on molecular weight of each component to match the output of the downhole fluid analyzer data;
 5.
PVT data compositions were lumped back to emulate the downhole fluid analyzer output compositions; and
 6.
checking interrelationships among the variables and removing poor predictor variables (e.g., C_{2}H_{6}).
The units of CO_{2}, CH_{4}, C_{2}H_{6}, C_{3}H_{8}, C_{5}H_{12}, and C_{6}H_{14}+ are in weight percent, temperature is in degrees Fahrenheit, and pressure is in psia. C_{3}H_{8}–C_{5}H_{12} denotes the weight percent of the group C _{3} H _{8} through C _{5} H _{12}. All logarithm (log) values denote natural log (base e).
Coefficients of the chosen model
Coefficient  Estimate  SE  P value 

β _{0}  19.1109840  1.9899250  0.000 
β _{1}  −0.0679165  0.0104606  0.000 
β _{2}  −0.0162705  0.1414375  0.908 
β _{3}  −6.6190184  1.3607809  0.000 
β _{4}  0.5104139  0.4082668  0.212 
β _{5}  1.1398989  0.2306464  0.000 
β _{6}  0.6263451  0.0487792  0.000 
β _{13}  0.0371260  0.0055541  0.000 
β _{14}  −0.0048367  0.0007388  0.000 
β _{23}  0.0573708  0.0263501  0.030 
β _{26}  −0.0565329  0.0160504  0.000 
β _{34}  0.0794272  0.0471590  0.093 
β _{35}  −0.1985207  0.0501634  0.000 
β _{56}  −0.1334765  0.0241433  0.000 
Note that n is the sample size and in our case n = 667. It is well known that R ^{2} (proportional of variability in y explained by the model) will increase and both MSE and MARE will decrease, as more variables are included in the model, despite the importance of these predictor variables. Thus, an overparameterized model (too many predictors) will have very high/low values of these measures, accordingly, and will seemingly do very well in sample, but will do poorly out of sample. The use of model selection tools based on information criteria such as AIC, AICc, and BIC tends to avoid the overfitting problem (Burnham and Anderson 2002).
Performance of the chosen model
Validation of the chosen model
The kind of modeling problem at hand is termed supervised learning in machine learning terminology, which has seen an explosion in activity in the last two decades. The most successful and theoretically sound approaches to solve this problem have recently been compiled by Hastie et al. (2009). They span the gamut of statistical methods from the high bias/low variance, e.g., linear regression, principal components (PCA), partial least squares (PLS), and least absolute shrinkage and selection operator (LASSO), to the low bias/high variance, e.g., splines, local smoothing, and neural networks. Roughly in the middle of this bias/variance tradeoff dilemma, one finds regression treebased models and extensions (bagging, boosting, random forests) to be some of the best predictive methods on a variety of different problems.
For the data set at hand, sparsity seeking and shrinkage inducing methods such as PCA, PLS, and LASSO are not really appropriate given the small number of predictors involved (only 6). Rather, more important is the capturing of complex nonlinear relationships with the output variable (dew point pressure) and interactions among the predictors. Thus, and in order to ensure we were considering all the best possible models, we decided to compare a variety of methods, restricting our attention to the following 4 classes: (1) linear regression with up to twoway interactions and all subsets search using a consistent information criterion such as BIC; (2) regression trees and the computationally intensive resamplingbased extensions such as bagging, boosting, and random forests; (3) generalized additive models with individual predictor functions estimated via splines and local smoothers; (4) feedforward neural networks with a single hidden layer. Details of these methods can be found in Hastie et al. (2009). (Note that method 1 was the strategy used to arrive at the chosen model in Table 3).
We see that all methods perform similarly, with the random forest model (a type of regression tree) having a slight edge, and linear regression a close second. However, whereas it is straightforward to write down an equation for the linear regression model, this is infeasible for the regression treebased random forest model, since it is a combination of thousands of trees, each tree being a sequence of yes/no questions about the predictors that must be answered sequentially in order to arrive at the appropriate predicted value. For this reason, and due to the fact that the difference in predictive ability between the two models is small, we have chosen to report only the linear regression model in this paper. However, our recommendation is that any future work should carefully consider regression trees.
Results and discussion
Published dew point pressure correlations
Published correlations and their required input parameters
Correlation  Number of points in data set  Input data 

Olds et al. (1944)  N/A  T, P 
Nemeth and Kennedy (1966)  579  Y mol%, C_{1}−C_{7+}, M_{C7+}, T, ρ _{7+} 
Elsharkawy (2001)  340  Y mol% C_{1}−C_{7+}, M_{C7+},T, ρ _{7+} 
Humoud and AlMarhoun (2001)  74  Rsp, T, Tsp, Psp, γ_{sp}, γ_{C7+} 
Marruffo et al. (2002)  80  YC7+, T, API, CGR 
Ovalle et al. (2005)  615  API, Rsp, \(\gamma_{gR}\) 
Shokir (2008)  245  MC7 + , T, Y mol % (C_{1}, CO_{2}, H_{2}S, N2, C_{7+}) 
AlDhamen and AlMarhoun (2011)  113  T, MC7 + , ρ _{7+}, γ_{cond}, GOR, γgs 
Godwin (2012)  259  T, Y mol % (C1, C2,…, C6, C_{7+}), MC7 + , ρ _{7+} 
The value of the new model proposed here lies in its simplicity and relative accuracy for the database used in this work. More importantly, it is based on downhole fluid data that are becoming more available in today’s applications of fluid sampling and fluid characterization. Unlike many of those available dew point models (correlations), the new model does not require information obtainable from the laboratory or production test data. Therefore, the dew point can be estimated before even taking a fluid sample from the reservoir. Also, since C_{2}H_{6} as a predictor variable is absent from the model, the output of earlier versions of downhole analyzer tools (which do not estimate the amount of C_{2}H_{6}) may be used to predict the dew point pressure.
It is envisioned that the calculated dew point from this model could be used in several applications. First, it can be employed as a form of quality control to ensure the sampling procedure takes fluid samples with downhole pressure above the dew point pressure (for more accurate sampling). This can serve as a confirmation to the current operational procedure of establishing dew point (by pumping out until liquid appears and is sensed by the tool sensors). This is particularly useful in low condensate gas ratio fluids. Secondly, it provides a quick estimate of dew point pressure that can help in any further estimation of phase behavior of gas wells for reservoir and production engineering applications. Thirdly, in cases having extensive downhole data for multiwells in the same reservoir, the calculated dew point pressure can be used to quality control the downhole data. In this application, the trend of the calculated dew point pressure will be checked to see whether it follows the expected increase with depth trend. This estimation can also be used in confirming reservoir compartmentalization.
Conclusions and recommendations

The extensive literature review to identify all dew point pressure estimation models, classifying them into two groups, comparing the performance of each, and then suggesting which one performs better based on our extensive database.

Building a model based on a small group of informationdependent variables that are measured from downhole fluid analyzer tools, after deleting noneffective variables such as C_{2}H_{6} from the pool of independent variables.

Testing and validating the model based on randomly selected data sets from our database.
A single best linear regression model that includes pairwise interactions was arrived at for the well data, by using a sophisticated statistical model selection criterion (AICc). We think the proposed model arrived at in this analysis is the best of its kind in the industry nowadays. A comparison of our proposed model versus published ones (although published models are based on surface data while our new model is based on downhole data) shows similar results in terms of accuracy in predicting dew point pressure values. As a final recommendation, more refined models could be proposed in future work taking into account the collection of more data.
Notes
Acknowledgements
The authors would like to acknowledge kind assistance through fruitful discussion with Rami Ahmed of Schlumberger, and Shabbir Hussain Shah Syed of Shell (STOS). We thank two anonymous referees for their constructive suggestions. The authors thank Hani Elshahawi, GameChanger; Formation Testing and Sampling Principal Technical Expert from Shell.
References
 AlDhamen M, AlMarhoun M (2011) New correlations for dewpoint pressure for gas condensate. Presented at the SPE Saudi Arabia section Young Professionals Technical Symposium held in Dhahran, Saudi Arabia. SPE155410Google Scholar
 Betancourt SS, Fujisawa G, Mullins OC (2004) Exploration applications of downhole measurement of crude oil composition and fluorescence. Presented at the Asia pacific Conference on integrated Modelling Asset Management held in Kuala Lumpur, Malaysia. SPE87011Google Scholar
 Betancourt SS, Dubost FX, Mullins OC, Cribbs ME, Creek JL, Mathews SG (2007) Predicting downhole fluid analysis logs to investigate reservoir connectivity. Presented the international petroleum Technology Conference held in Dubai, U.A.E. SPE11488Google Scholar
 Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical informationtheoretic approach, 2nd edn. Springer, New YorkGoogle Scholar
 Elshahawi H, Hows M, Dong C et al (2007) Integration of geochemical, mudgas, and downholefluid analysis for the assessment of compositional gradingcase studies. Presented at the 2007 SPE Annual technical Conference and Exhibition, Anaheim, California. SPE109684Google Scholar
 Elsharkawy A (2001) Characterization of the plus fraction and predicting the dewpoint pressure for gas condensate reservoirs. Presented at the 2001 SPE Western Regional Meeting held in Bakersfield, California, USA. SPE68776Google Scholar
 Elsharkawy A (2011) Predicting the dewpoint pressure for gas condensate reservoirs: empirical models and equations of state. Fluid Phase Equilibria 4900, Elsevier Science B.VGoogle Scholar
 Godwin ON (2012) A new Analytical Method for Predicting Dewpoint Pressure for Gas Condensate Reservoirs. Presented at the 2012 SPE Nigerian Annual International Conference and Exhibition, Nigeria. SPE162985Google Scholar
 Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
 Humoud AA, AlMarhoun MA (2001) A new correlation for gascondensate dewpoint pressure prediction. Presented at the 2001 SPE Middle East Oil Show held in Bahrain, SPE68230Google Scholar
 Marruffo L, Maita J, Him J, Rojas G (2002) Correlations to determine retrograde dewpoint pressure and C7+ percentage of gas condensate reservoirs on basis of production test data of eastern Venezuelan fields. Presented in Gas Technology Symposium held in Calgary, Alberta, Canada. SPE75686Google Scholar
 McCain WD (1994) Heavy components Control Reservoir Fluid Behavior. Paper SPE 28214, Technology Today series JPT 746750Google Scholar
 Mullins O, Elshahawi H, Matthew F, O’Keefe M, Vanuffellen S (2009) The impact of reservoir fluid composition variation and valid sample acquisition on flow assurance evaluation. Presented at the 2009 Offshore Technology conference held in Houston, TX. USA. OTC20204Google Scholar
 Nemeth K (1966) A correlation of dewpoint pressure with reservoir fluid composition and temperature. PhD Dissertation Texas A&M University, College Station, TX, USAGoogle Scholar
 Nemeth LK, Kennedy HT (1966) A correlation of dewpoint pressure with fluid composition and temperature. Presented at SPE Annual Fall meeting held in Dallas, TX. USA. SPE1477Google Scholar
 Olds RH, Sage BH, Lacey WN (1944) Volumetric and phase behavior of oil and gas from paloma field. Presented at Los Angles meeting, Los Angles, USA. SPE945077Google Scholar
 Ovalle A, Lenn C, McCain W Jr (2005) Tools to manage gas condensate reservoirs: novel fluid property correlations based on commonly available field data. Presented at IPTC held in Doha, Qatar. IPTC 10320PPGoogle Scholar
 R Core Team (2016) R Foundation for Statistical Computing. Vienna, Austria. http://www.Rproject.org
 Shokir E (2008) Dewpoint Pressure Model for Gas Condensate Reservoirs based on Genetic Programming. King Saud University. Presented at CIPC gas technology Symposium 2008 held in Calgary Alberta., SPE114454Google Scholar
 Xian C, Dawoud A, Carnegie A et al (2006) Identification and characterization of transition zones in tight carbonates by downhole fluid analysis. Presented at 2006 Abu Dhabi International Petroleum Exhibition and conference held in Abu Dhabi, U.A.E., SPE101257Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.