Factors That Control Condensate Production From Shales: Surrogate Reservoir Models and Uncertainty Analysis Palash Panja and Milind Deo, University of Utah Summary Rapid development of shales for the production of oils and condensates may not be permitting adequate analysis of the important factors governing recovery. Understanding the performance of shales or tight oil reservoirs producing condensates requires numerically extensive compositional simulations. The purpose of this study is to identify important factors that control production of condensates from low-permeability plays and to develop analytical “surrogate” models suitable for Monte Carlo analysis. In this study, the surrogate reservoir models were second-order response surfaces functionally dependent on the nine main factors that most affect condensate recovery in ultralow-permeability reservoirs. The models were developed by regressing the results of experimentally designed compositional simulations. The BoxBehnken (Box and Behnken 1960) technique, a partial-factorial method, was used for design of these experiments or simulations. The main factors that controlled condensate recovery from ultralow-permeability reservoirs were reservoir permeability, rock compressibility, initial condensate/gas ratio (CGR), initial reservoir pressure, and fracture spacing. Another main outcome of this paper was the generation of probability-density functions, and P10, P50, and P90 values for condensate recovery on the basis of the uncertainty in input parameters. The condensate-recovery P50 for rate-based outcome of a 5-B/D per fracture was found to be less than 10%. Introduction Current production of liquids, oils, and condensates from Eagle Ford is more than 1 million B/D. Approximately 20% of this liquid production is condensates. The increase in production is primarily because of the large number of wells being drilled. Because of the rapid pace of activity, it has not been possible to understand the important factors affecting production and to produce the most out of each well. In fact, the total production of condensates declined for the first time in the short history of Eagle Ford despite increased drilling activity (Fig. 1). The first main objective of this study is aimed at identifying important factors that affect production of condensates from ultralow-permeability reservoirs. This identification provides an early screening tool to benchmark recovery expectations of condensates being produced from shales. Prediction of condensate production from reservoirs requires compositional simulation. Simulation of hydraulically fractured wells with low-permeability matrix necessitates high-resolution simulation with a large number of gridblocks. Generation of validated response surfaces that accurately represent the results of compositional simulations would be useful in performing uncertainty and subsequently risk analysis, and would generate P10, P50, and P90 numbers for important outcomes of condensate production in shales. Early analysis will provide realistic estimates of what is feasible in these exciting, but challenging, plays. The second main objective of the study was to generate validated response-surface or surrogate models for condensate production in shales. C 2015 Society of Petroleum Engineers Copyright V Original manuscript received for review 22 November 2013. Revised manuscript received for review 28 August 2015. Paper (SPE 179720) peer approved 2 November 2015. 2015 SPE Reservoir Evaluation & Engineering Response-surface methodology has been frequently used in reservoir engineering. The quest for optimal production and the associated uncertainty started in the early 1990s with the use of response-surface methods (RSMs) (Egeland et al. 1992; Elvind et al. 1992; Aanonsen et al. 1995). Since then, the RSM has been exploited for various purposes, including uncertainty in initial hydrocarbon reserves (Peng and Gupta 2003), optimum well placements (Guyaguler and Horne 2001; Manceau et al. 2001, 2002; Landa and Güyagüler 2003; Carreras et al. 2006), and uncertainty in production performance and recovery (Dejean and Blanc 1999; Chewaroungroaj et al. 2000; Corre et al. 2000; Venkataraman 2000; Manceau et al. 2001; Mohaghegh 2006). Fielddevelopment plans for gas/condensate reservoirs were assessed by performing uncertainty analysis of reserves and production performance (Huerta Quinones et al. 2010; Descubes 2012; Huerta Quinones and Lanchimba 2012). Yeten et al. (2005) compared various design-of-experiment methods and RSMs to show the effectiveness of the technique. They determined that the RSM can be used as an efficient and fast proxy model for reservoirs to forecast the production performance and to analyze uncertainty (De Amorim and Schiozer 2012) if the appropriate design of experiment has been selected. An RSM consisting of four parameters and uncertainty analysis in oil recovery and pressure drop was studied in an Iranian fractured reservoir (Khosravi et al. 2011). Three of the most significant parameters were identified: aquifer strength, matrix-block size, and fracture permeability. An artificial-intelligence-based proxy model (Kalantari Dahaghi et al. 2012) and a pore-network model (Xie et al. 2013), by use of fundamental equations with the uncertainty in pore length, pore size, and pore number, were also generated for production performance (gas rate and cumulative gas) from shale-gas reservoirs. Simple models comprising a range of parameters to evaluate the performance and uncertainty of condensate production from ultralow-permeability (10–5,000 nd) fractured reservoirs were used. A limited number of studies on response surfaces and uncertainty evaluation for gas condensates have also been reported. Simulations were run to examine important parameters in a modified-pseudosteady-state (Diamond et al. 1996) analytical model with the gas-material-balance equation in the Britannia gas/condensate field in North Sea field (reservoir permeability of 5–100 md). Giving the uncertainty in inputs, the cumulative probabilitydistribution curve for gas rate was studied. Atbi and Aissaoui (2004) created second-order-polynomial response-surface models for cumulative gas and plateau length applied in the Tiguentourine field (conventional reservoir) in the southeast area of the Algerian desert by use of D-optimal design of experiment. P90 production profiles (gas rate and cumulative gas) were generated by use of Monte Carlo simulations. Initial reservoir condition, flowing bottomhole pressure (BHP), rock/fluid properties, and other parameters were not considered in their study. Experimental design by use of a set of comprehensive compositional simulations for ultralow-permeability condensate reservoirs (shale plays such as the Eagle Ford) has not been reported previously. The one additional difference in this study is also that the focus is primarily on parameters that affect liquid production from condensate plays in shales. Because the performance of wells producing from these plays varies considerably, identification of what affects production and 1 1,400,000 843 2,300 15,149 18,784 2008 2009 2010 200,000 200,000 150,000 100,000 129,795 352 229 400,000 731,455 163,259 600,000 250,000 400,711 800,000 300,000 Condensate Production (STB/D) Condensate (Secondary Axis) 1,000,000 1,064,624 270,884 234,669 (Primary Axis) 1,050,213 279,705 Oil 80,531 Oil Production (STB/D) 1,200,000 350,000 50,000 0 2011 2012 January through June 2013 2014 2015 0 Year Fig. 1—Texas Eagle Ford shale-oil and condensate production, 2007 through June 2015, from the Texas Railroad Commission. uncertainty in recovery given important parameter variability will be useful for screening and early-planning phases. In a play such as the Eagle Ford, fluid compositions also vary from region to region over fairly short distances. The purpose of this study was to identify parameters that affect the production of condensates in hydraulically fractured tight reservoirs and to provide uncertainty estimates over relevant parameter space, including varying fluid compositions. A sensitivity study was used to select important parameters. Second-order response-surface models for different times of production and for a minimum economic condensate rate were constructed on the basis of experimental design consisting of compositional simulations. Uncertainty in the recoveries was also studied, applying some of the probabilistic distributions in the input parameters. Methodology Reservoir Model. All simulations were conducted by use of GEM, a Computer Modelling Group (CMG 2013) compositional simulator. One vertical fracture is placed in the middle of the reservoir with one horizontal well in the x-direction. The fracture height and fracture length were the same as the reservoir height and length, respectively. The dimensions of the reservoir are shown in Fig. 2. The reservoir length is 750 ft in the y-direction, and the res- ervoir height (z-direction) is 200 ft. Dimensions in the y- and zdirection are considered constant for all simulations, but the boundary in the x-direction is altered depending on the fracture spacing used in the particular simulation. The x-dimension is the same as the fracture spacing, with the fracture in the middle of the model. The three different fracture spacings are shown in Fig. 2. The reservoir properties, namely, matrix permeability, initial reservoir pressure, and formation compressibility—are varied. Fracture width, fracture orientation, matrix porosity, and initial hydrocarbon saturation remain constant. The reservoir temperature varies depending on the reservoir fluids (defined by their initial CGRs). Reservoir simulations with conventional grid systems without refinement near the wellbore and fractures produce erroneous results (Panja et al. 2013). A minimum number of gridblocks necessary to obtain converged results is used. Additional parameters used in simulations are provided in Table 1. Input Factors. Important input factors that affect the production performance of condensate were chosen from an extensive initial mechanistic/sensitivity study (Deo and Anderson 2013). Nine factors—namely, matrix permeability, gas relative permeability exponent, critical condensate saturation, rock compressibility, initial CGR, initial pressure, flowing BHP, fracture permeability, and fracture spacing—are examined in this study. Viscosity 300 ft 180 ft 750 ft Z X 200 ft Fracture 200 ft 60 ft Z Fracture Spacing Y Fig. 2—The geometry of a simulated reservoir. 2 2015 SPE Reservoir Evaluation & Engineering y z x y x z y z Table 1—Simulation parameters used in the study. fluids are summarized in Table 3. The pressure/temperature plots of the three fluids are shown in Figs. 3a through 3c. The compositional data used to create the fluids were partly derived from the Eagle Ford reservoir in-situ fluid compositions suggested by Whitson and Sunjerga (2012). Reservoir temperatures (red arrows) for the reservoir fluids were 150 F for initial CGR of 50 STB/MMscf, 250 F for initial CGR of 125 STB/MMscf, and 350 F for initial CGR of 200 STB/MMscf. The temperatures in Eagle Ford vary considerably from region to region because of the depth and other factors, affecting fluid compositions significantly. effects are built into the compositional representation of the fluid. Porosity affects total oil production but does not influence recovery in a significant manner. Three different values of each factor are selected on the basis of available field data, as shown in Table 2. The data were gathered from a variety of publicly available documents on Eagle Ford (Chipman et al. 2011). Field-production data were obtained online from the Texas Railroad Commission (2015) website and from the production tool of Drillinginfo (2015), a dataresource company. The CGR values were chosen on the basis of compositions provided by Whitson and Sunjerga (2012). The formation compressibility of Eagle Ford shale is expected to be higher because of the presence of smectites (50%) in the clay minerals (38–88%) (Hsu and Nelson 2002). The gas relative permeability exponent is used in the Corey model to prepare gas/oil relative permeability curves. Orangi et al. (2011) used a similar approach. The water/oil relative permeability curves are kept fixed. The Corey (1954) model is given in Eqs. 1 through 6. Water/Oil System. The equations for the water/oil system are S ¼ Experimental Design. Determining the suitable experimentaldesign method is key to developing an effective response-surface model. The effectiveness of regression models is also dependent on the design of the experiment method. The Box-Behnken (Box and Behnken 1960) technique, a partial-factorial-design method, is used in this study and is also suitable for second-order responsesurface generation. The technique needs 130 runs for nine input factors. The three absolute values of each input parameter are converted to 1, 0 and þ1 by use of a linear relationship, except for matrix permeability, where logarithmic values are taken. All input parameters are summarized in Table 4. Distributions of input parameters that were used when performing uncertainty analyses are also shown in Table 4. The spread in parameter values is similar to the variation in field values shown in Table 2. ðSw  Swc Þ ; . . . . . . . . . . . . . . . . . . . . . . . ð1Þ ð1  Sorw  Swc Þ krw ¼ krw ðSorw Þ ðS Þnw ; . . . . . . . . . . . . . . . . . . . . . . . ð2Þ krow ¼ kro ðSwc Þð1  S Þno : . . . . . . . . . . . . . . . . . . . . . ð3Þ Regression Model for Building Response Surfaces. The functional relationships of output with inputs are defined by the second-order model, as shown in Eq. 7: Gas/Oil System. The equations for the gas/oil system are S ¼ ðSg  Sgc Þ ; . . . . . . . . . . . . . . . . . . . . . . . ð4Þ ð1  Sorg  Sgc Þ ln½ f ðX1 ; …; Xn Þ ¼ a0 þ krg ¼ krw ðSgc Þ ðS Þng ; . . . . . . . . . . . . . . . . . . . . . . . . ð5Þ n X k¼1 n n X X aij Xi Xj þ ; ak Xk þ i¼1 j¼1                    ð7Þ krog ¼ krg ðSorg Þð1  S Þno : . . . . . . . . . . . . . . . . . . . . . ð6Þ where Xi are the independent inputs; n are the total numbers of the independent inputs, which are nine for this study; a0 is the intercept; ak and aij are the coefficients; and ¾ is the error term (absolute value) that will be minimized (toward zero) in the multivariate method. Reservoir Fluids. Three different condensate fluids with initial CGRs of 50, 125, and 200 STB/MMscf were evaluated in this study. The compositions and the properties for the three distinct Km h Km Sw Table 2—Field data from Eagle Ford shale plays (Chipman et al 2011). 2015 SPE Reservoir Evaluation & Engineering 3 inin- Tc Pc Table 3—Composition of three distinct reservoir fluids. 5,000 4,000 CGR = 125 STB/MMscf CGR = 50 STB/MMscf 4,000 Pressure (psia) Pressure (psia) 3,000 2,000 Two-phase boundary Critical 20 vol% 30 vol% 50 vol% 1,000 0 –100 0 200 100 Temperature (°F) (a) 3,000 Two-phase boundary Critical 20 vol% 30 vol% 50 vol% 2,000 1,000 300 0 –100 400 0 100 200 300 Temperature (°F) (b) 400 500 CGR = 200 STB/MMscf 5,000 Pressure (psia) 4,000 3,000 2,000 Two-phase boundary Critical 20 vol% 1,000 0 –100 30 vol% 50 vol% 0 100 200 300 400 Temperature (°F) (c) 500 600 Fig. 3—Pressure/temperature diagram for three distinct reservoir fluids: (a) initial CGR 5 50 STB/MMscf; (b) initial CGR 5 125 STB/ MMscf; (c) initial CGR 5 200 STB/MMscf (red arrows indicate the reservoir temperatures for the reservoir fluids). 4 2015 SPE Reservoir Evaluation & Engineering Km ng Soc Rvi Pi Xf Kf Cf Pwf Table 4—List of input parameters selected for the study and their distribution for uncertainty analysis. To ensure nonnegative values of outcomes, regression was performed by use of logarithms of outcomes. Two types of models—namely, time-based and rate-based models—are used in this study. In the time-based model, coefficients for condensate recovery, gas recovery, and CGR after 90 days and 1, 5, 10, 15, and 20 years are determined. Comparatively, in the rate-based model, coefficients for condensate recovery and coefficients for gas recovery are obtained when condensate rate falls to 5 STB/D. There are 55 coefficients obtained from each model. The well was operated at constant flowing BHP, although it is variable from simulation to simulation. and NRMSE in the same plot. Values of R2 close to unity and low percentage values of NRMSE are indications of good fits of models with simulations. Simulation results and corresponding sets of results from surrogate models for condensate recoveries (Panja 2014) are shown in Figs. 5a and 5b. The time-based models for 5, 10, 15, and 20 years are shown in Fig. 5a and the rate-based model for a minimum economic rate of 5 STB/D of condensate is shown in Fig. 5b. R2 values are greater than 0.9 and NRMSE values are less than 5% for all models. Thus, the models are reasonable to accept as surrogate reservoir models to forecast production performance. Work Flow. The work flow for generating the response surfaces is shown in Fig. 4 and shows each step from creating input files to generating final response surfaces. The Box-Behnken (Box and Behnken 1960) technique for the design of an experiment with nine factors uses 130 input files for simulation. (These input files are created by use of nine input factors on three levels.) The absolute values for the three levels of all factors are shown in Table 4. A full compositional simulator, GEM from CMG, was used in all compositional simulations. All relevant results from output files were collected systematically by use of combinations of programs like windows batch files and Matlab (2013) (MathWorks). Condensate recoveries, gas recoveries, and CGRs for different times and for the minimum-economic-condensate rate are extracted from collected data to fit the second-order models, as shown in Eq. 1. Multivariate regressions were performed by use of Matlab programs (MathWorks) to obtain all the coefficients of Eq. 1. This modified multivariate-regression approach is very effective in obtaining response-surface parameters. The goodness of fit is measured by the values of R2 and normalized-root-mean-square error (NRMSE). The calculation procedures of R2 and NRMSE are found in numerous websites and published papers (Steel and Torrie 1960; Glantz and Slinker 1990; Draper and Smith 1998). Validation of the Surrogate Model. Although all models fit very well with surrogate models (on the basis of NRMSE values), validation is essential to verify the robustness of the surrogate models. Surrogate models are generated on the basis of three levels of values of input factors, as described by the Box-Behnken (Box and Behnken 1960) technique. The models should be effective with the other values of input factors within the range of study without any significant errors. Eighteen values are chosen randomly (using in-built random-value generator in Matlab) from each input distribution to validate the models. Trivalue discrete distributions were used for fracture spacing and initial CGR. Simulations were run by use of those 18 eighteen random values of each input factor, as shown in Table 5. The modeled values of condensate recovery are then compared with simulations to demonstrate the robustness of the surrogate models in Fig. 6. The response surfaces predict compositional simulation outcomes reasonably well, especially where most of the recoveries are expected to be between 5––20%. The R2 and NRMSE values also indicate the good matches of the simulation results with modeled values. The time-based models are better fitted with simulation results than the rate-based model. This validation showed that the surrogate models of condensate recoveries from ultralow-permeability reservoirs can be used with good confidence to predict condensate values. It is also important to ensure that the range of input variables used from Table 2 cover the range of outcomes observed in the field. Comparison of field production for the highest-producing (seven wells), median (five wells), and lowest-producing (five wells) condensate wells in Eagle Ford with simulated values over a range of input parameters is shown in Figs. 7a and 7b. The cumulative Results and Discussion For time-based models of condensate recoveries and gas recoveries, 5, 10, 15, and 20 years of production data are collected from simulations. The minimum economic rate of 5 STB/D of condensate is used for the rate-based model. Models are compared with the simulations by plotting them and displaying the values of R2 2015 SPE Reservoir Evaluation & Engineering 5 Input X1 Values of Inputs Input Files Input X2 Number of Inputs Design of Experiment Input Xn –1 Input Xn ...... Simulations Monte Carlo Draws Data Collection Time-Based Final Response Surface Rate-Based Outcomes Several Realizations of Outputs Multivariate Regression Yes Statistical Analysis n n n k=1 i=1j =1 f (X1,...,Xn) = a0 + ΣakXk +Σ Σ aijXi Xj +∈ Change No Random Values of Inputs Initial Response Surface Input Files Validation Tornado Plot PDF of Outputs –Range –Mean –Variance Simulations –Hierarchy –Range of Impact Fig. 4—Work flow of the methodology to generate response surfaces and to analyze uncertainty in outcomes. condensate productions were obtained from simulations with noninterfering single fractures, and net/gross ratio is considered as 0.4 for Eagle Ford. If there are five clusters per stage in a 16-stage well, approximately 80 possible fractures are expected. Analysis of the Eagle Ford cumulative production indicates that poor and median wells fall within the 50- to 100-nd permeability range. The highest-producing wells are in the reservoirs with permeability of 500–2,000 nd. It is observed from Figs. 7a and 7b that a permeability range of 10 nD to over 2000 nD is necessary to represent the performance of lean (50 stb/MMscf) and rich (200 stb/MMscf) condensates, respectively. It should be noted that higher CGR values and permeabilities go hand in hand to match the performance of better-producing wells. Forecast and Sensitivity Analysis of Production Outputs. Surrogate models can be used efficiently as forecast and sensitivity-analysis tools. Continuous-recovery curves with time are constructed by interpolating the model data of 90 days through 20 100 80 Condensate Recovery (%) Condensate Recovery (%) At 5 years; R 2 = 0.952, NRMSE = 3.6% At 10 years; R 2 = 0.940, NRMSE = 3.9% 80 60 Regression Regression 2 At 15 years; R = 0.926, NRMSE = 4.2% At 20 years; R 2 = 0.917, NRMSE = 4.5% 60 40 R 2 = 0.955, NRMSE = 4.0% 40 5 years 10 years 20 20 15 years 20 years Rate-Based 0 0 0 20 40 60 Simulation (a) Time-Based 80 100 0 20 40 Simulation 60 80 (b) Rate-Based Fig. 5—Comparison of regression model with simulation results for (a) time-based condensate recovery and (b) rate-based condensate recovery. 6 2015 SPE Reservoir Evaluation & Engineering Table 5—Random values for validation of surrogate models. years. For the input parameters shown in Table 6, the forecast and the sensitivity analysis of the condensate recovery are illustrated in Figs. 8a and 8b. The curves can be extrapolated for forecast beyond 20 years. Condensate recoveries plateau after approximately 10 years of production for 50- to 500-nd reservoirs. It is important to compare the production performances of regions with differences in properties in the same field. As an example, the effect of permeability on condensate recovery is shown in Fig. 8b. Significantly, higher condensate is recovered from the higher-permeability region. This plot shows the strong dependence of permeability on condensate recovery. Similarly, operating a well at different flowing BHP changes the recovery of condensate, as shown in Fig. 8a. Higher flowing BHP suppress the liquid dropout inside the reservoir, hence facilitating the production of liquid in vaporized form in the gas phase. The spread in condensate recovery, however, is only approximately 6–7% compared with variations of approximately 12–13% for permeability variation. These values are absolute changes in percentage recovery after 20 years of production. 45 Surrogate Model Condensate Recovery (%) At 5 years; R 2 = 0.89, NRMSE = 9.1% At 10 years; R 2 = 0.86, NRMSE = 9.6% At 15 years; R 2 = 0.85, NRMSE = 9.3% At 20 years; R 2 = 0.83, NRMSE = 9.7% At Rate; R 2 = 0.85, NRMSE = 11.4% 30 15 5 years 10 years 15 years 20 years Rate-Based 0 0 15 30 45 Simulation Fig. 6—Comparison of results from the response-surface (surrogate) models of condensate recovery with compositionalsimulation results for validation. 2015 SPE Reservoir Evaluation & Engineering Uncertainty Analysis. Given the variations in important input variables, it is important to establish the probability distributions of important outcomes, such as recoveries, and to calculate P10-, P50-, and P90-values. Uncertainties in desired outcomes after 5, 10, 15, and 20 years and when condensate reaches minimum economic rate of 5 STB/D were investigated. Probability-distribution functions (PDFs) of outcomes were generated by use of Monte Carlo simulations on response surfaces. The hierarchy of the input factors on the basis of impact on outcomes is also prepared. The work flow of the whole procedure is presented in Fig. 4. An individual PDF is assigned to each input factor. Random values are chosen from each input distribution by use of the Monte Carlo method to produce different values of outcomes from the corresponding response-surface models. The process is repeated several times to create multiple realizations of outcomes. The final PDF of the outcome is prepared by use of statistical analysis, such as dividing all realization into various bins (range of values), finding frequency of each bin, and normalizing. The PDF provides important statistical information such as mean, mode, median, and variance. The tornado plot is useful in obtaining the hierarchy of the importance of input factors. By use of statistical tools, Monte Carlo simulations construct plots of all input factors according to their influence on outcomes. The factors with the most influence appear on the top of the chart, and the factors with the least influence appear on the bottom. In addition to the hierarchy of the input factors, the plot also displays the range of the outcomes where each factor affects the outcome most. The commercial software @Risk (2015) from Palisade Corporation is used to prepare the PDF and tornado plots. Each bar in the tornado plot represents the effect of an input on output and provides the range of output where it is affected by that input. Tornado plots are prepared by use of output values obtained from all iterations of the surrogate model by use of a sequential ordering and iteration method. In the sequential ordering and iteration method, the mean of output is calculated by fixing one extreme (the lowest and the highest values, one at a time) value of input of interest and varying the rest of the inputs according to their probability distributions. These output means for the lowest and the highest values of the input are the two extreme ends of the tornado bar of that input. This process is repeated for all inputs to generate the entire tornado plot. Finally, inputs are ordered from top to bottom of the tornado plots according to their ranges. The PDF and tornado plots provide sufficient information on uncertainties in production performance from ultralow-permeability reservoirs. Although the uncertainty 7 75 450 Pi = 6,500 psi, Pwf = 500 psi Cumulative Condensate (million STB) Cumulative Condensate (million STB) Pi = 6,500 psi, Pwf = 500 psi, Initial CGR = 200 STB/MMscf Km = 2000 nd 300 Km = 1000 nd Km = 500 nd 150 Km = 100 nd 50 CGRi = 125 STB/MMscf Km = 50 nd 25 Km = 60 nd CGRi = 50 STB/MMscf Km = 20 nd 0 0 0 20 10 0 30 20 10 Time (month) Time (month) (a) (b) 30 Fig. 7—Comparison of Eagle Ford field data with compositional simulations, by varying matrix permeability and initial CGRs (CGRi). (a) Highest-producing wells; (b) median and lowest-producing wells. Km ng Soc Rvi Pi Xf Kf Cf Pwf Table 6—Values of input parameters used in sensitivity studies shown in Fig. 8. analysis is conducted for different time-based models (5, 10, 15, and 20 years), the results from the time-based model of 10 years are discussed here along with results of the rate-based model. All the model results are summarized in tables. Prior knowledge for input distribution is required to reflect the field data of reservoir parameters. One practical distribution of each input factor was assigned for the uncertainty analysis. Uniform distribution captures the total heterogeneity in the property, whereas the normal distribution has more data near the mean. The distributions of all inputs are displayed in Table 4. Results of uncertainties in the outcomes are greatly dependent on the type of distribution of input factors. Uniform distributions are selected for 36 24 Condensate Recovery (%) Condensate Recovery (%) 30 18 12 Pwf = 500 psi Pwf = 750 psi Pwf = 1,000 psi 6 27 18 Km = 50 nd Km = 100 nd 9 Km = 200 nd Pwf = 1,250 psi Km = 300 nd Pwf = 1,500 psi Km = 500 nd 0 0 0 5 10 15 20 0 5 10 Time (years) Time (years) (a) (b) 15 20 Fig. 8—Condensate recovery with time for different (a) flowing BHP and (b) reservoir permeability. 8 2015 SPE Reservoir Evaluation & Engineering 2.1 6.1 19.8 Cf 10.5 Rvi 10.2 21.7 0.015 16.3 0.010 16.1 15 10 0.020 16.6 14.8 5 0.025 0.005 20 Soc Pwf 0.030 19.0 14.9 Fit: β 0.035 19.7 14.1 ng 0.040 22.0 13.0 Kf 5.0% Condensate Recovery (%) (a) 0.000 Mode ≈ 15.6 10.7 Xf Mode ≈ 5.6 7.9 0.045 30 Pi 27.8 25 Km 35.1 90.0% 0 10 20 30 40 50 60 Condensate Recovery (%) (b) Fig. 9—Condensate recovery after 10 years of production: (a) hierarchy of input parameters; (b) probability distribution of output. all input factors except the matrix permeability. Matrix permeability has log-normal distribution with mean value at 500 nd. Trivalued distributions are selected for the initial CGR and fracture spacing. Lower CGR is observed in a field with low reservoir pressure, whereas higher CGR is observed in a high-pressure reservoir. The initial pressure has segmented uniform distributions depending on the value of initial CGR. For initial CGR of 50 STB/MMscf, range of uniform distribution of initial pressure is 5,000–5,500 psi; for initial CGR of 125 STB/MMscf, range of uniform distribution of initial pressure is 5,500–6,500 psi; and for initial CGR of 200 STB/MMscf, range of uniform distribution of initial pressure is 6,500–8,000 psi. All ranges are normalized to between –1 and 1. The tornado plot indicates that the matrix permeability, formation compressibility, initial reservoir pressure, and fracture spacing are the top four factors that have most influence on condensate production. Critical condensate saturation, flowing BHP, and initial CGR are the next-most-influential factors on condensate recovery for 10 years of production. Reservoir permeability and rock compressibility emerge as the top two factors that control recovery of condensates for more than 10 years of production or when an economic limit of 5 STB/D is considered. These findings are consistent with earlier sensitivity analyses published by Orangi et al. (2011) and Whitson and Sunjerga (2012). The significant drawdown in the vicinity of the well for the ultralowpermeability formations causes condensate dropout, and these reservoirs operate at chronically low CGRs over their lifetime. Compressibility has been established as one of the important governing parameters during primary production of condensates. Reservoir pressure, which is tied to the initial CGR, is the next ranking parameter, followed by fracture spacing. This is particularly true in the condensate sweet spots in Eagle Ford, where significant overpressure has allowed for the drilling of many prolific wells. It is somewhat surprising that even in the 60- to 180-ft range, fracture spacing emerges as an important parameter. For the permeabilities considered in this paper, that is an important finding. The range of recoveries for extreme values of these parameters is also shown on the tornado plot. The plot shows that under favorable permeability conditions, 10 times as much condensate is recovered and approximately eight times more recovery is realized when compressibility is favorable. These geologic parameters are not easily altered, but the compressibility aspect may present a tradeoff between placing the fractures in brittle zones where fracturing is expected to be more effective vs. seeking more-ductile (and hence compressible) formations to assist in the primary recovery of condensates. The initial pressure is an important reservoir attribute because higher initial pressures delay approach to dewpoint and condensate formation in the reservoir. Fracture spacing, which is one of the controllable parameters, appears to double recovery when low fracture spacing is realized. 2015 SPE Reservoir Evaluation & Engineering This will have economic implications because lower fracture spacing will increase the cost of creating hydraulic fractures. The relative permeability aspects (critical condensate saturation and gas relative permeability exponent) have surprisingly less effect, as does the BHP. Recoveries are affected when the range of BHPs is varied over a few thousand psi, but not with the range of 500–1,500 psia used in the study. In Eagle Ford, very few operators hold BHPs of more than 1,500 psia. Uncertainty in Condensate Recovery. Uncertainties in condensate recovery after 10 years of production and the hierarchy of input factors are shown in Figs. 9a and 9b. The median condensate recovery factor is only approximately 14% after 10 years of production from ultralow-permeability reservoirs. The condensate recovery spreads over a wide range in the PDF. The range of 5–95% in the PDF covers 2–39% of condensate recovery. The Weibull (1951) function closely mimics the distribution. The uncertainty in the condensate recovery after the condensate rate drops to 5 STB/D is shown in Figs. 10a and 10b. Median recovery (P50) when the condensate production reaches an economic limit of 5 STB/D was observed to be approximately 7%. The b-function best fits the PDF for this recovery function. The PDF also predicts that the most-probable (mode) condensate recovery is approximately 2%. The matrix permeability, formation compressibility, reservoir pressure, and fracture spacing are the most-influential factors. The gas relative permeability exponent, BHP, fracture permeability, and critical condensate saturation rank in the next four in the tornado plot. The results of uncertainty analysis from 5, 10, and 20 years and rate-based models are summarized in Table 7. The most influential factors in condensate recovery were matrix permeability, fracture spacing, formation compressibility, and initial reservoir pressure for all cases, although the orders of the factors change slightly with the models, as shown in Table 7. Higher matrix permeability always enhances the productivity from reservoirs. The higher formation compressibility helps to sustain the reservoir pressure, minimizing liquid dropout. Fracture permeability, critical condensate saturation, initial CGR, and gas relative permeability exponent are the next four important factors that affect recovery of condensates. Conclusions Guidelines for quick screening and uncertainty assessment of the performance of condensates in shales are needed. This is because, despite increased drilling, declining production is being observed in important resource plays such as the Eagle Ford. The purpose of this study was to provide such guidance by developing responsesurface (surrogate) models that emulated full compositional 9 0.3 2.7 24.2 Cf 6.7 Rvi 7.2 4.3 16.8 9.4 13.1 10.4 11.9 0.02 15 10 5 0 10.6 0.04 12.1 Condensate Recovery (%) Mode ≈ 11.5 Kf 0.06 13.5 Mode ≈ 0.1 9.7 ng Fit: Exponential 0.08 11.9 Soc Pwf 5.0% 0.10 25 Pi 0.12 17.5 7.7 Xf 38.5 90.0% 22.5 20 Km 0.00 0 10 20 30 40 50 60 Condensate Recovery (%) (a) (b) Fig. 10—Condensate recovery when condensate rate reaches 5 STB/D: (a) hierarchy of input parameters; (b) probability distribution of output. Table 7—Uncertainty in recoveries and rank of input parameters. reservoir simulations. The response surfaces were generated by use of the Box-Behnken (Box and Behnken 1960) experimental design and a novel multiregression strategy. The models were an excellent proxy for the computationally intensive compositional simulations, as evidenced by low RMSEs and a thorough validation exercise. Development of validated response surfaces allowed performing Monte Carlo simulations for uncertainty assessment. Uncertainty analysis revealed that reservoir permeability, compressibility, fracture spacing, and initial pressure were the mostsignificant parameters that affected condensate recovery, followed by initial CGR, fracture permeability, gas relative permeability exponent, critical condensate saturation, and the BHP. It should be noted that flowing BHP and fracture spacing could be chosen to increase recoveries. Making the flowing BHP higher increases recoveries in lower-permeability (approximately 100 nd) reservoirs. Recoveries of approximately 30% are possible with fracture spacing on the order of 50 ft. The median values of recovery (P50) for 10-year production and for an economic cutoff rate of 5 STB/D for condensate were determined to be approximately 14 and 7%, respectively. Nomenclature a0 ¼ intercept of surrogate model aij ¼ coefficient of second-order interaction of inputs 10 ak Cf kf km n ng Pi Pwf qo R2 Rvi Scc Xf Xi ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ coefficient of independent input formation compressibility, 1/psi fracture permeability, md matrix permeability, nd total numbers of independent inputs exponent of relative permeability curve for gas initial reservoir pressure, psi flowing BHP, psi condensate rate, STB/D coefficient of determination initial condensate/gas ratio, STB/MMscf critical condensate saturation fracture spacing, ft scaled independent outputs Acknowledgments The authors gratefully acknowledge the academic license to Computer Modelling Group products. Financial support to Palash Panja through the ConocoPhillips Fellowship is also acknowledged. References @Risk Software. Palisade Corporation, Ithaca, NY, USA. www.palisade. com. 2015 SPE Reservoir Evaluation & Engineering Aanonsen, S. I., Eide, A. L., Holden, L. et al. 1995 Optimizing Reservoir Performance Under Uncertainty with Application to Well Location. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 22–25 October. SPE-30710-MS. http://dx.doi.org/10.2118/ 30710-MS. Atbi, A. M. and Aissaoui, A. 2004. Quantification of Uncertainty in Production Forecast Using Experimental Design, Case Study: Tiguentourine and Taouratine Fields. Presented at the Canadian International Petroleum Conference, Calgary, 8–10 June. PETSOC-2004-097. http://dx.doi.org/10.2118/2004-097. Box, G. E. P. and Behnken, D. W. 1960. Some New Three Level Designs for the Study of Quantitative Variables. Technometrics 2 (4): 455–475. http://dx.doi.org/10.1080/00401706.1960.10489912. Carreras, P. E., Turner, S. E. and Wilkinson, G. T. 2006. Tahiti: Development Strategy Assessment Using Design of Experiments and Response Surface Methods. Presented at the SPE Western Regional/AAPG Pacific Section/GSA Cordilleran Section Joint Meeting, Anchorage, 8–10 May. SPE-100656-MS. http://dx.doi.org/10.2118/100656-MS. Chewaroungroaj, J., Varela, O. J. and Lake, L. W. 2000. An Evaluation of Procedures to Estimate Uncertainty in Hydrocarbon Recovery Predictions. Presented at the SPE Asia Pacific Conference on Integrated Modelling for Asset Management, Yokohama, Japan, 25–26 April. SPE-59449-MS. http://dx.doi.org/10.2118/59449-MS. Chipman, J., Heikkinen, D. and Lively, B. 2011. The Niobrara: A Look into the Weird Science of Tight, Light Oil Plays. DJ Basin Niobrara Primer, research report, Tudor Pickering Holt & Co., August 2011. Computer Modelling Group (CMG). 2013. GEM software, Calgary, Canada. Corey, A. T. 1954. The interrelation between gas and oil relative permeabilities. Producers Monthly 19 (November): 38–41. Corre, B., Thore, P., Feraudy, V. D. et al. 2000. Integrated Uncertainty Assessment For Project Evaluation and Risk Analysis. Presented at the SPE European Petroleum Conference, Paris, 24–25 October. SPE65205-MS. http://dx.doi.org/10.2118/65205-MS. De Amorim, T. C. A. and Schiozer, D. J. 2012. Risk Analysis Speed-Up With Surrogate Models. Presented at the SPE Latin America and Caribbean Petroleum Engineering Conference, Mexico City, 16–18 April. SPE-153477-MS. http://dx.doi.org/10.2118/153477-MS. Dejean, J. P. and Blanc, G. 1999. Managing Uncertainties on Production Predictions Using Integrated Statistical Methods. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE-56696-MS. http://dx.doi.org/10.2118/56696-MS. Deo, M. and Anderson, T. 2013. Liquids from Shale: A Mechanistic Study Phase 1. CA Report, Energy & Geoscience Institute, University of Utah, Salt Lake City, Utah. Descubes, E. 2012. Stochastic Uncertainty Analysis in Compositional Simulation for Giant Gas-Condensate Field Reservoir Performance Prediction. Presented at the SPE Russian Oil and Gas Exploration and Production Technical Conference and Exhibition, Moscow, 16–18 October. SPE-162045-MS. http://dx.doi.org/10.2118/162045-MS. Diamond, P. H., Pressney, R. A., Snyder, D. E. et al. 1996. Probabilistic Prediction of Well Performance in a Gas Condensate Reservoir. Presented at the European Petroleum Conference, Milan, Italy, 22–24 October. SPE-36894-MS. http://dx.doi.org/10.2118/36894-MS. Draper, N. R. and Smith, H. 1998. Applied Regression Analysis. WileyInterScience. Drillinginfo. 2015. Austin, Texas, United States, info.drillinginfo.com. Egeland, T., Holden, L. and Larsen, E. A. 1992. Designing Better Decisions. Presented at the European Petroleum Computer Conference, Stavanger, 24–27 May. SPE-24275-MS. http://dx.doi.org/10.2118/ 24275-MS. Elvind, D., Asmund, H. and Rolf, V. 1992. Maximum Information at Minimum Cost: A North Sea Field Development Study With an Experimental Design. J Pet Technol 44 (12): 1350–1356. SPE-23139-PA. http://dx.doi.org/10.2118/23139-PA. Glantz, Stanton A. and Slinker, B. K. 1990. Primer of Applied Regression and Analysis of Variance. McGraw-Hill. Güyagüler, B. and Horne, R. N. 2001. Uncertainty Assessment of Well Placement Optimization. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–3 October. SPE71625-MS. http://dx.doi.org/10.2118/71625-MS. 2015 SPE Reservoir Evaluation & Engineering Hsu, S.-C. and Nelson, P. P. 2002. Characterization of Eagle Ford Shale. Eng. Geol. 67 (1–2): 169–183. http://dx.doi.org/10.1016/S00137952(02)00151-5. Huerta Quinones, V. A. and Lanchimba, A. F. 2012. A Holistic Analysis Approach for Reservoir Modeling. Presented at the SPE Latin America and Caribbean Petroleum Engineering Conference, Mexico City, 16–18 April 2012. SPE-153387-MS. http://dx.doi.org/10.2118/153387-MS. Huerta Quinones, V. A., Lanchimba, A. F. and Colonomos, P. 2010. Gas/ Condensate Field Development Plan by Means of Numerical Compositional Simulation. Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Lima, Peru, 1–3 December. SPE-138886-MS. http://dx.doi.org/10.2118/138886-MS. Kalantari Dahaghi, A., Esmaili, S. and Mohaghegh, S. D. 2012. Fast Track Analysis of Shale Numerical Models. Presented at the SPE Canadian Unconventional Resources Conference, Calgary, 30 October–1 November. SPE-162699-MS. http://dx.doi.org/10.2118/162699-MS. Khosravi, M., Fatemi, S. and Rostami, B. 2011. Assessing Structured Uncertainty in a Mature Fractured Reservoir, Using Combination of Response Surface Method and Reservoir Simulation. Presented at the SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, 9–11 October. SPE-148003-MS. http://dx.doi.org/ 10.2118/148003-MS. Landa, J. L. and Güyagüler, B. 2003. A Methodology for History Matching and the Assessment of Uncertainties Associated with Flow Prediction. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 5–8 October. SPE-84465-MS. http://dx.doi.org/10.2118/84465MS. Manceau, E., Mezghani, M., Zabalza-Mezghani, I. et al. 2001. Combination of Experimental Design and Joint Modeling Methods for Quantifying the Risk Associated With Deterministic and Stochastic Uncertainties - An Integrated Test Study. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–3 October. SPE-71620-MS. http://dx.doi.org/10.2118/71620-MS. Manceau, E., Roggero, F. and Zabalza-Mezghani, I. 2002. Use Of Experimental Design Methodology To Make Decisions In An Uncertain Reservoir Environment From Reservoir Uncertainties To Economic Risk Analysis. Presented at the 17th World Petroleum Congress, Rio de Janeiro, 1–5 September. WPC-32161. Matlab. 2013. MathWorks Inc., www.mathworks.com/products/matlab/. Mohaghegh, S. D. 2006. Quantifying Uncertainties Associated With Reservoir Simulation Studies Using a Surrogate Reservoir Model. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September. SPE-102492-MS. http://dx.doi.org/ 10.2118/102492-MS. Orangi, A., Nagarajan, N. R., Honarpour, M. M. et al. 2011. Unconventional Shale Oil and Gas-Condensate Reservoir Production, Impact of Rock, Fluid, and Hydraulic Fractures. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, 24–26 January. SPE-140536-MS. http://dx.doi.org/10.2118/140536-MS. Panja, P., Conner, T. and Deo, M. 2013. Grid Sensitivity Studies in Hydraulically Fractured Low Permeability Reservoirs. J. Pet. Sci. Eng. 112 (December): 78–87. http://dx.doi.org/10.1016/j.petrol.2013.10.009. Panja, P. 2014. Understanding Liquids Production From Shales. PhD dissertation, University of Utah, Salt Lake City, Utah (December 2014). Peng, C. Y. and Gupta, R. 2003. Experimental Design in Deterministic Modelling: Assessing Significant Uncertainties. Presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, 9–11 September. SPE-80537-MS. http://dx.doi.org/10.2118/80537-MS. Steel, R. G. D. and Torrie, J. H. 1960. Principles and Procedures of Statistics with Special Reference to the Biological Sciences. McGraw Hill. Texas Railroad Commission. 2015. Texas, United States, www.rrc.state. tx.us. Venkataraman, R. 2000. Application of the Method of Experimental Design to Quantify Uncertainty in Production Profiles. Presented at the SPE Asia Pacific Conference on Integrated Modelling for Asset Management, Yokohama, Japan, 25–26 April. SPE-59422-MS. http:// dx.doi.org/10.2118/59422-MS. Weibull, W. 1951. A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME 18 (3): 293–297. Whitson, C. H. and Sunjerga, S. 2012. PVT in Liquid-Rich Shale Reservoirs. Presented at the SPE Annual Technical Conference and 11 Exhibition, San Antonio, Texas, 8–10 October. SPE-155499-MS. http://dx.doi.org/10.2118/155499-MS. Xie, J., Lee, S., Wen, X.-H. et al. 2013. Uncertainty Assessment of Production Performance for Shale Gas Reservoirs. Presented at the 6th International Petroleum Technology Conference, Beijing, 26–28 March. IPTC16866-Abstract. http://dx.doi.org/10.2523/16866-ABSTRACT. Yeten, B., Castellini, A., Guyaguler, B. et al. 2005. A Comparison Study on Experimental Design and Response Surface Methodologies. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 31 January–2 Feburary. SPE-93347-MS. http://dx.doi.org/ 10.2118/93347-MS. Palash Panja is a post-doctoral research associate at the Energy & Geoscience Institute at the University of Utah. He worked for 5 years with a variety of companies, including downstream/upstream-production companies. Panja’s current research interests include production from unconventional reservoirs such as shales, interactions between flow and thermodynamics, surrogate-model development, and artificial intelligence. He is a member of SPE, and served as treasurer in the SPE University of Utah Student Chapter. Panja holds 12 a master’s degree from the Indian Institute of Technology, Mumbai, and a PhD degree from the University of Utah, both in chemical engineering. Milind Deo is the Peter D. and Catherine R. Meldrum Professor and chair of the Chemical Engineering Department at the University of Utah. His research interests are in reservoir engineering and enhanced oil recovery with particular focus on unconventional resources, carbon dioxide management, and geothermal production. Deo’s group is currently working on understanding liquid production in shales, determining the placement and impact of hydraulic fractures in naturally fractured reservoirs, and studying the underground storage of carbon dioxide in various geological formations. The reactivetransport simulators developed in his group are applicable for the study of compositional and thermal processes in complex oil and gas and geothermal reservoirs. Deo’s research also consists of understanding and solving onshore and offshore flow-assurance problems related to waxes and asphaltenes. He is a member of SPE. Deo has supervised approximately 28 PhD degree graduates and has authored more than 100 publications in his 26-year career at the University of Utah. 2015 SPE Reservoir Evaluation & Engineering