SPE 80907 New Perspectives on Vogel Type IPR Models for ... · PDF fileSPE 80528 New perspectives on Vogel Type IPR Models for Gas Condensate and Solution-Gas Drive Systems 3 and Shaw

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This paper was prepared for presentation at the 2003 SPE Production Operations Symposium, Oklahoma City, OK, 23-25 March 2003.

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Abstract In this work we propose two new Vogel-type Inflow Perfor-mance Relations (or IPR) correlations for gas condensate reservoir systems. One correlation predicts gas production the other predicts condensate production. These correlations link reservoir rock and fluid properties (dewpoint, temperature, and endpoint relative permeabilities) to the flowrate-pressure per-formance for the system.

The proposed IPR relationships for compositional reservoir systems are based on data from over 3000 compositional re-servoir simulation runs with various fluid properties and rela-tive permeability curves. The resulting IPR curves for gas condensate systems are quadratic in nature like the Vogel IPR trends (the Vogel profile generally presumed for the case of a solution gas-drive reservoir system). However in the gas con-densate case the coefficients in the quadratic relationship vary significantly depending on the richness of the condensate and the relative permeability. A model to predict these coeffi-cients was developed using an alternating conditional expecta-tion approach (optimal non-parametric regression).

This work also includes a discussion of the Vogel IPR for solution-gas drive systems. The original work proposed by Vogel is based on an empirical correlation of numerical simu-lations for a solution-gas-drive system. Our work provides a critical validation and extension of the Vogel work by esta-blishing a rigorous, yet simple formulation for flowrate-pres-sure performance in terms of effective permeabilities and pres-sure-dependent fluid properties.

The direct application of this work is to predict the IPR for a given system directly from rock-fluid properties and fluid pro-

perties. This formulation provides a new mechanism that can be used to couple flowrate and pressure behavior for solution-gas-drive systems and it may be possible to extend the concept to gas condensate reservoir systems.

Introduction — Solution Gas-Drive Systems The first presentation of an inflow performance relationship (or IPR) concept was made by Rawlins and Schellhardt1 in 1935. In Fig. 1 we provide a reproduction of this figure — where Rawlins and Schellhardt used this plot to illustrate the effect of liquid loading on production performance.

Figure 1 — Primitive IPR plot for a gas well experiencing liquid loading (circa 1935) (after Rawlins and Schellhardt (ref. 1)).

In 1954 Gilbert2 introduced the concept of an "inflow perfor-mance relationship" (or IPR) for the purpose of optimizing producing rates and flowing bottomhole pressures. In Fig. 2 we reproduce Gilbert's IPR diagram for orientation.

In 1968 Vogel3 established an empirical relationship based on reservoir simulation results for a solution gas-drive reservoir. Vogel used twenty-one reservoir data sets to generate a broad suite of cases. In this work Vogel noted that the shape of the pressure (pwf) versus production (qo) curves were very similar at various values of cumulative oil production. As such, Vogel defined the dimensionless inflow performance curve by dividing the pressures and flowrates at each point by the

SPE 80907

New Perspectives on Vogel Type IPR Models for Gas Condensate and Solution-Gas Drive Systems R.A. Archer, University of Auckland, Y. Del Castillo, and T.A. Blasingame, Texas A&M University

2 R.A. Archer, Y. Del Castillo and T.A. Blasingame SPE 80907

intercepts on the respective x and y-axes (i.e., the average reservoir pressure on the y-axis and the maximum oil flowrate on the x-axis).

Figure 2 — Primitive IPR plot for a gas well experiencing liquid loading (circa 1935) (after Gilbert (ref. 2)).

In performing this work, Vogel elected to produce a "reference curve" that is an average of the various depletion cases for a given reservoir scenario. Vogel recognized that the liquid (oil), gas (dry gas), and solution gas drive cases have distinct behavior trends and was simply trying to produce a mechan-ism for predicting production performance with a relatively simple result. In Fig. 3a we present the Vogel plot illustrating the liquid (oil), gas (dry gas), and solution gas-drive cases.

Figure 3a — IPR schematic plot for oil, gas, and solution gas drive systems (after Vogel (ref. 3)).

The "Vogel correlation" for IPR behavior in a solution gas-drive system is given by:

2

max, 8.0 2.01

−

−=

pp

pp

qq wfwf

oo ....................... (1)

In Fig. 3b we reproduce the Vogel plot illustrating the IPR be-havior for solution-gas drive systems at various stages of de-pletion — the "reference curve" is the Vogel correlation.

Figure 3b — IPR behavior for solution-gas drive systems at various stages of depletion — the "reference curve" is the correlation presented by Vogel (after Vogel (ref. 3)).

For wells producing below the bubblepoint pressure, Fetko-vich4 derived the following generalized IPR equation using pseudosteady-state theory and a presumed linear relationship for the liquid (oil) or gas mobility functions (i.e., ko/(µoBo) or kg/(µgBg)):

nwf

oo

pp

qq

−=

2

max,1 ............................................. (2)

An illustrative schematic plot of the Fetkovich concept for a linear mobility trend is shown in Fig. 4.

Figure 4 — Mobility-pressure behavior for a solution-gas drive reservoir (after Fetkovich (ref. 4)).

Fetkovich considered the oil phase for a solution gas-drive system — but this concept has also been extended to the gas phase. The most important aspect of Fig. 4 is the presumed linearity of the mobility function for pressures below the bub-blepoint.

Richardson and Shaw5 presented a generalized inflow perfor-mance relationship for solution gas reservoirs as a function of the parameter, ν. For the Vogel case ν=0.2, and Richardson

SPE 80528 New perspectives on Vogel Type IPR Models for Gas Condensate and Solution-Gas Drive Systems 3

and Shaw propose that the ν-parameter be optimized for a given case. Richardson and Shaw provide an interesting schematic plot to illustrate the behavior of the IPR function above and below the bubblepoint pressure (see Fig. 5 for a reproduction of this schematic plot).

Figure 5 — Schematic IPR behavior for a solution-gas drive reservoir — note the "linear" and "quadratic" characteristic regions (for p>pb and p<pb, re-spectively) (after Richardson and Shaw (ref. 5)).

Particular to this work, Richardson and Shaw discuss proce-dures for testing wells where the objective is to use production data to solve for the ν-parameter directly — for example, us-ing a two or three-rate test.

The "general" IPR model presented by Richardson and Shaw is given as:

2

max, )1( 1

−−

−=

pp

vp

pv

qq wfwf

oo ...................... (3)

We will note in advance that we will use the formulation given by Eq. 3 to derive our new IPR models for gas and condensate behavior in gas condensate reservoir systems.

Another attempt to quantify the IPR behavior for solution gas-drive systems was presented by Wiggins, et. al.6 — where this result is a polynomial series given in terms of qo/qo,max and

ppwf / . The Wiggins, et. al. result is given by:

... 13

3

2

21max,

+

+

+

+=

pp

ap

pa

pp

aq

q wfwfwf

oo

....................................................................................... (4)

Where the a1, a2, a3, ... an coefficients are determined based on the mobility function and its derivatives at the average reser-voir pressure ( p ). This is a relatively impractical approach because of the derivatives involved — but, we must recog-nize that the IPR behavior can be related to fundamental flow theories.

As an aside, Wiggins, et al. (ref. 6) also present plots of oil mobility as functions of pressure (taken at various flowrates) as a means of calibrating their proposed IPR model (i.e., Eq.

6). The purpose of presenting these mobility-pressure profiles was to establish the "stability" of the mobility profile for a give depletion level — which would confirm the use of an IPR model based on a "snapshot" of reservoir performance. An example mobility-pressure profile taken from the Wiggins, et. al. reference is shown in Fig. 6.

Figure 6 — Oil mobility profiles as a function of pressure — various flowrates ("Case 2")) (after Wiggins, et al. (ref. 6)).

We will comment that the "double-linear" trend illustrated in Fig. 6 is consistent with other work produced for solution gas drive systems, and is somewhat in dispute with the model pro-posed by Fetkovich (see Fig. 4).

Introduction — Gas Condensate Systems In this section we discuss methods to represent IPR behavior for gas condensate reservoir systems. Analogs and references to the solution gas-drive system are common for the case of a gas condensate system, but our goal is to isolate the important factors/elements that must be addressed in order to correlate IPR behavior for gas condensate reservoir systems.

Inflow performance relationships have been considered for gas-condensate reservoir systems by several authors. The case of a gas condensate reservoir is more complex because of the evolution of the condensate bank as the reservoir is depleted. Fussell7 addressed this issue using a 1-D radial compositional simulator. O'Dell and Miller8 presented results which show that even a minor region of condensate blockage/banking can substantially reduce the deliverability of the well.

Fevang and Whitson9 presented a gas-rate flow equation for gas condensate systems, which employs a pseudopressure function (in terms conventional formation volume factors and gas-oil-ratios) as a mechanism to account for the effect of con-densate banking. This result is given by:

[ ] dpB

kR

Bkp

psrrkhq

ooro

sgg

gr

wfweg

3/4)/ln( 2.1411

+

+−= ∫ µµ

.............................................................................................. (5)


Fevang and Whitson suggested that the pseudopressure inte-gral could be evaluated by expanding the integral into three regions: (taken from ref. 9)

Region 1: An inner, near-wellbore region where both gas and oil flow simultaneously (at different velocities). Region 2: A region of condensate "buildup" where only gas is flowing. Region 3: A region containing single-phase (original) reservoir gas.

The producing GOR, PVT properties, and gas-oil relative permeabilities are required in order to calculate the pseudo-pressure function (Eq. 5). While Eq. 5 is straightforward — i.e., an integral in terms of pressure and saturation-dependent functions, these functions can not be known accurately in advance — which renders Eq. 5 as a possible analysis relation, but not a predictive (or modelling) relation.

It is worthy to note that Fevang and Whitson (ref. 3) comment that critical oil saturation (Soc) has no effect on gas conden-sate well deliverability. While it is not our intention to dispute this comment, we will note that our work has addressed the influence of the following parameters on gas condensate well deliverability: relative permeability, fluid composition, dew-point pressure, reservoir temperature, Soc, and Sgr.

In this work, we provide a simple methodology to estimate IPR functions for wells in gas-condensate reservoir systems — without the requirement of gas-oil ratio and saturation profiles in the reservoir as a function of pressure. The new IPR approach will be developed using a large database of composi-tional reservoir simulation cases. We use the form of the Richardson and Shaw model,5 but the parameter ν will vary depending on the various properties of a given reservoir fluid (as noted by the group of parameters we have identified as in-fluential in the case of gas condensate reservoir systems (see above)).

Method — Correlation of IPR Behavior for Gas Con-densate Reservoir Systems In this study we use compositional reservoir simulation as the mechanism to perform numerical experiments in order to characterize the IPR behavior for gas and condensate liquid performance. This section outlines the construction of the numerical model in terms of gridding and the selection of relative permeability profiles and reservoir fluid properties.

Model Construction

A 1-D radial grid is used for the simulation model since our main purpose is to evaluate the productivity of a single well in a gas condensate reservoir system. Bottomhole pressures and production rates are of critical importance for IPR correla-tions — and as such, we used fine grid cells near the wellbore to properly represent the well productivity losses due to the build up of condensate near the well, while maintaining coarser grids for the remainder of the reservoir.

Malachowski et al.10 concluded that fine grids should be used for gas condensate reservoir simulation or the predicted con-

densate saturation near the wellbore will be underestimated. As is customary, the sizing of the radial grid cell sizes follows a logarithmic distribution with the ratio between two consecu-tive cell sizes being 1.47. The maximum cell size is 500 ft.

The most convenient (and arguably the most appropriate) pro-duction constraint is that of a constant bottomhole pressure. A small initial time step is used to address the onset of conden-sate banking. A typical simulation is conducted for approxi-mately 120 years in order to assess the effect of condensate banking on ultimate recovery.

The grid cells have a uniform thickness of 30 ft and the reservoir model is considered homogeneous and isotropic — with an absolute permeability of 5 md and a porosity of 20 percent. The simulation model was initialized from an initial pressure equal to the dewpoint pressure of the selected reser-voir fluid — which means that initially, the only fluid in the reservoir is gas, as the water saturation is set to zero.

Relative Permeability Curves

Seven (7) different sets of relative permeability curves are used in this study in order to assess the influence of relative permeability on the IPR character for gas condensate systems. Corey-type relative permeability curves as well as other relative permeability curves are use to address a spectrum of relative permeability behavior. The seven sets of curves are shown in Figs. 7 and 8.

Figure 7 — Oil relative permeability data sets for the con-densate reservoir simulation study.

The relative permeability curves have different endpoint sa-turations and different shapes. A set of "straight line" relative permeability curves are included as an "extreme" case (Data Set 5). Data Set 4 is designed to represent an "abrupt" change in oil relative permeability and is taken from another study of gas condensate reservoir systems.


Figure 8 — Gas relative permeability data sets for the con-densate reservoir simulation study.

It could be argued that we could have considered more cases of relative permeability behavior — however, we believe that this set of relative permeability cases represents an appropriate suite of cases that would typically be encountered in practice.

Reservoir Fluids

In this work we considered six (6) reservoir fluid samples — four (4) of these samples were synthetic fluids and the remain-ing two samples were taken from studies for the Cusiana and Cupiagua gas condensate fields in Colombia (South America). The composition of the synthetic fluids is shown in Table 1 and we note that these four fluids have varying degrees of richness.

Table 1 — Composition of synthetic reservoir fluid samples (Fluids 1-4) (variations of fluids presented by Roussenac (ref. 11)).

Mole Fraction Fluid 1 2 3 4C1 0.8963 0.8700 0.9561 0.8700C4 0.0300 0.0300 0.0150 0.0150

C10 0.0737 0.1000 0.0289 0.1150

Initial Molecular Weight of the Fluid MixtureFluid 1 2 3 4Mmix 26.0027 29.1026 20.0832 30.2393

Tables A-1 and A-2 describe the Cusiana fluid sample and are provided in the Appendix of this paper. The sample com-position for "Fluid 5" is detailed in Table A-1 and it is clear that there are too many components for practical reservoir simulation purposes.

Data from a constant composition expansion experiment (CCE) were matched to tune a version of the Peng-Robinson equation of state (EOS) for this fluid. After tuning, the components were grouped (or lumped) using Whitson's method12. The resulting groups are shown in Table A-3. In ref. 13, Jaramillo presents further detail regarding the fluid characterization for this Cusiana sample.

The final reservoir fluid considered was based on a sample from the Cupiagua field ("Fluid 6"). This fluid composition is given in Table A-4. Similar to the fluid sample from Cusiana field, data from a constant composition expansion experiment were used to tune a Peng-Robinson EOS model. The pseudo-components used to represent this fluid in the compositional simulation cases are given in Table A-5. Additional detail and discussion of the fluid characterization for this sample is given by Guerra.14

Assumptions Used in the Simulation Model

The following assumptions are used in the development and execution of the reservoir simulation models for this case:

Interfacial tension effects and non-Darcy flow effects are not considered. Capillary pressure effects are not considered. Near wellbore effects (saturation, pressure, and mobil-ity) are accurately represented by a refined grid. Phase equilibrium is accurately calculated by the EOS. A reduced permeability zone (skin) is not considered. Gravitational segregation of the condensate is not con-sidered. No compositional gradients are considered.

Strategies for the Development of the IPR Database

We first validated the simulation model and considered the following parameters/functions (or combination of parameters/ functions) in order to generate the IPR database:

Reservoir Temperature: T = 230, 260, 300 Deg F Critical Oil Saturation: Soc = 0, 0.1, 0.3 Residual Gas Saturation: Sgr = 0, 0.15, 0.5 Relative Permeability: 7 sets of kro-krg data Fluid Samples: 4 synthetic cases, 2 field samples

We note that temperature is the primary control variable for dewpoint pressure (i.e., a change in temperature yields a change in dewpoint pressure). For each case (i.e., a particular combination of the parameter/functions considered), 30 to 45 simulation scenarios were conducted using constant (but dif-ferent) bottomhole pressures. Each simulation was begun at the dewpoint pressure of the fluid at the conditions selected — with our purpose being to evaluate only the phase behavior of the condensate fluid in the two-phase region, where gas con-densate and gas coexist together while encountering signifi-cant changes in composition.

The maximum gas (G) and condensate (N) volumes were determined for each simulated case (with respect to the separa-tor conditions) in order to evaluate the recovery of these


fluids. For all cases the pressure of the separator was set to a pressure of 14.7 psia and a temperature to 60 deg F.

Condensate (liquid) and gas production rates were recorded at eight selected "stages" of cumulative condensate (liquid) and cumulative gas production (i.e., gas or condensate "depletion ratios" — and in turn, these data were tabulated as a function of bottomhole flowing pressure. The deliverability curves for condensate (liquid) and dry gas were constructed as follows:

pwf versus qo for a given cumulative oil production (Np) pwf versus qg for a given cumulative gas production (Gp)

IPR Calibration (regression to obtain IPR trends)

Using the results from the database described above, we con-ducted a simultaneous regression of the data for all of the depletion stages for a particular case in order to estimate the average reservoir pressure and the maximum condensate or gas rate for each depletion stage. In this work we always consider 8 (eight) depletion stages per case (see Table 2).

Table 2 — Fixed values of condensate and gas cumulative production used to generate a particular IPR trend (fraction or Np/N and Gp/G will vary accord-ing to initial reservoir conditions).

Depletion Np Gp Stage (STB) (MSCF)

1 5.0x104 1.0x105 2 1.0x105 5.0x105 3 5.0x105 1.0x106 4 1.0x106 5.0x106 5 1.5x106 1.0x107 6 2.0x106 2.5x107 7 2.5x106 5.0x107 8 3.0x106 7.0x107

Our regression work also solves for the ν-parameter for a particular case (for clarity we note that νo and νg are solved independently for a given case). In our regression formulation we define the following variables:

j,

jiji q

qy

)()(

max

,,

θ

θ= (θ is the oil or gas phase) ................... (6)

j

iji p

wfpx

)(

)(, = (pwf is constant for a given simulation)... (7)

We cast the optimization problem into the following double summation form, where the SOLVER algorithm in MS Excel15 is used to minimize the "residual function," Jθ for a particular phase:

∑ ∑= =

−−−−=

82,

,,1

)(

1 )1(1

j

n

ixxyJ

wfp

jijiji θθθ νν . (8)

We note that the 8 (eight) term in Eq. 8 is the number of depletion stages considered for a given condensate or gas scenario — we have chosen to always use 8 depletion stages,

regardless of the scenario (condensate or dry gas). The (n)pwf variable is total number of simulations per case (i.e., the number of individual pwf runs per case) — generally this num-ber is between 30 and 45, depending on the reservoir pressure at a given time.

We comment that we have cast this problem into an "absolute error" form, as opposed to the typical "least squares" formula-tion. This is relevant — the SOLVER algorithm is completely general, and we believe that this form yields better results than the least squares formulation — for this problem.

Results — IPR Trends and Correlations for Gas Con-densate Systems

Base IPR Trends

We developed base IPR trends for each gas and gas conden-sate dataset (within a particular case) using the regression pro-cedure described in the previous section (there are a total of 62 cases).

After the simulation of each case, the rate and pressure results are plotted as "dimensional" IPR curves (i.e., plots of the flow-rate of condensate or gas versus the flowing bottomhole pres-sure). Once the regression procedure has been applied, we then present the "base" IPR curves in a "non-dimensional" (or dimensionless) format — in the same manner as the Vogel IPR function. Examples of "dimensional" and "non-dimen-sional" IPR trends for gas and gas condensate (Case 16) are shown in Figs. 9-12.

We consider Case 16 to be a "typical" gas condensate case (see Table A-6 for a complete inventory of all cases develop-ed in this work). In Fig. 9 (the dimensional gas IPR plot for Case 16) we note an excellent correlation of the rate and pres-sure functions (including the extrapolated trends).

Figure 9 — Example of a "dimensional" IPR trend (gas) (Case


Figure 10 — Example of a "non-dimensional" IPR trend (gas) (Case 16).

In Fig. 10 we present the "non-dimensional" (or dimension-less) gas IPR trend for Case 16 — we note good correlation of the "dimensionless" trends, and would comment there is a cluster of points in the low pressure region (probably the least accurate portion of data). We are satisfied that this case is ef-fectively represented by the "Vogel" IPR model, and would suggest that this behavior is "typical" for a gas condensate sys-tem.

Figure 11 — Example of a "dimensional" IPR trend (conden-sate) (Case 16).

The "dimensional" condensate IPR trend for Case 16 is pre-sented in Fig. 11 — we immediately note an excellent

correlation of the rate and pressure data with the proposed "Vogel" IPR model. In fact, the correlation for this case is so strong that we could consider the Vogel IPR model to be the general model for condensate (liquid) production performance. Obviously other cases must validate such a suggestion, but we do note that virtually all cases in this work exhibit a similar performance (for the condensate phase) as illustrated in Fig. 11.

In Fig. 12 we present the "non-dimensional" (or dimension-less) condensate IPR trend for Case 16, as with the dimension-al trend (Fig. 11), the correlation shown in Fig. 12 is extraor-dinary. One could argue that such correlations might be ex-pected due to the flexible nature of the general Vogel model (Eq. 3) — however, we must recognize that the data in Fig. 12 represents the simultaneous regression of 8 depletion stages (from 30-45 individual simulation cases). Such performance should be considered both relevant and unique — and should further validate the used of the general Vogel model for repre-senting the IPR behavior of gas condensate behavior (gas and liquid phases).

Figure 12 — Example of a "non-dimensional" IPR trend (con-densate) (Case 16).

As noted above, the IPR base data (i.e., the νγ and νο para-meters as well as the fluid and rock fluid properties) are sum-marized in Table A-6 for all 62 cases considered in this work.

Global Correlations — IPR Behavior for Gas Conden-sate Systems

Orientation:

In the previous section we demonstrated that gas condensate behavior can be correlated using the general Vogel model (Eq. 3). This is a significant contribution — however, it is our intention to provide a general or "global" correlation of IPR behavior for gas and condensate production performance. A quick check of Table A-6 confirms the intuitive concept that


the parameters (νγ and νο) are not the same for a particular case. The flow mechanisms and controlling factors are differ-ent for the gas and condensate phases and must be accounted for separately. In other words, we must develop separate "global" correlations for the gas and condensate cases.

Initial Efforts — Univariate Plots:

The starting point for a global correlation is to attempt to assess the influence of individual parameters — as well as the influence of groups of parameters. Our approach is systematic in that our first effort is to consider the behavior of the νγ and νο parameters with respect to the oil-in-place/gas-in-place ratio (N/G) and the initial molecular weight of the fluid mixture (Mmix,i) (Figs. 13-16).

Figure 13 — Correlation of the νg parameter as a function of the oil-in-place/gas-in-place ratio (N/G) (all data).

The correlation attempts shown in Figs. 13 and 14 (i.e., νγ and νο versus the oil-in-place/gas-in-place ratio (N/G)) clearly show a "clustered" trend of data — however, we would no consider this to be particularly useful since νγ and νο vary for each fluid sample. This indicates that more variables will be required.

The oil-in-place/gas-in-place ratio (N/G) would not be an ideal variable for correlation as we wish to present a generalized correlation — using (N/G) would be "problematic" in that we would have to have knowledge of this ratio, which in practice we typically do not. Our choice of using (N/G) is more of a validation — we wanted to establish whether or not the (N/G) parameter exerts dominance on the νγ and νο parameters. Figs. 13 and 14 suggest a strong, but not dominant influence.

Figure 14 — Correlation of the νo parameter as a function of the oil-in-place/gas-in-place ratio (N/G) (all data).

Another "logical" comparison is that of the νγ and νο para-meters with the initial molecular weight of the fluid mixture (Mmix,i) — this comparison is shown in Fig. 15 for the gas cases and in Fig. 16 for the gas condensate cases.

Figure 15 — Correlation of the νg parameter as a function of the initial molecular weight of the fluid mixture (Mmix,i) (all data).

In Figs. 15 and 16 we (again) note clustering of data — how-ever, we also note that there are multiple values of the parameters (νγ and νο) for a given value of Mmix,i. This sug-gests that the univariate correlation of the IPR parameters νγ


and νο with Mmix,i will not yield unique correlations. We recognize this issue and move towards an attempt to generate multivariate correlations of the IPR parameters. For example, we will segregate the most influential variables (T, pd, Soc, Sgr, Mmix,i, and the groups C1, C2, C7+) then correlate νγ and νο simultaneously with all variables or with optimal groups of variables. We establish the optimal grouping(s) of variables using non-parametric regression.16

Figure 16 — Correlation of the νo parameter as a function of the initial molecular weight of the fluid mixture (Mmix,i) (all data).

Before proceeding to the task of multivariate regression we compare the νγ and νο parameters in Figs. 17 and 18 to esta-blish if these parameters are strongly correlated. Intuition suggests that if the νγ and νο parameters are correlated, such a correlation may be coincidental as the νγ and νο parameters were estimated in separate regressions. Regardless, correla-tion of the νγ and νο parameters would be useful, and upon in-spection of Fig. 17 (the Cartesian format plot of νγ versus νο) we find that an apparent correlation exists (νγ ≈ 0.20 + νο). While this correlation is fairly weak — we conclude that the correlation may be of sufficient accuracy to predict one vari-able (e.g., νγ) from the other — rather than to generate two separate correlations for νγ and νο.

In Fig. 18 we present the log-log format plot of νγ versus νο. In this plot we note a similar "apparent" correlation of these parameters and we provide an approximate relation to orient the reader to this apparent correlation. We do not advocate using either the linear or power law relations presented on Figs. 17 and 18 (respectively), but we do suggest that these apparent correlations by used to orient future correlations.

Figure 17 — Correlation of the νg parameter as a function of the νo parameter (Cartesian format plot).

Figure 18 — Correlation of the νg parameter as a function of the νo parameter (log-log format plot).

Non-Parametric Multivariate Correlation of νγ and νο

Table A-6 was used as input for a non-parametric algorithm that can be applied to univariate or multivariate datasets.16 The specific version of the algorithm used in this work is called GRACE (see ref. 16) — where the GRACE algorithm is designed to perform a non-parametric regression. GRACE can also be instructed to provide a "parametic" regression by fitting generalized functions (in this case quadratic polyno-mials) to the non-parametric transform functions generated in-ternally in the GRACE algorithm.


From ref. 16 we have the following description of the func-tionality of the GRACE algorithm.

"The GRACE algorithm is based on the concept of developing non-parametric transformations of the dependent and independent variables. Moreover, the transformations are constructed pointwise based only on the data. The final result is a maximum correla-tion between the dependent and multiple independent variables with a minimum error."

In cases where the only difference between runs was a differ-ing set of relative permeability curves, a single representative simulation run was retained. This selection procedure reduced the total number of cases for analysis to 54.

Several combinations of independent variables (e.g., T, pd, Soc, Sgr, Mmix,i, and the groups C1, C2, C7+.) were used in the GRACE regression of the IPR parameter data. After considerable testing of variables (and combinations of variables) we developed what we consider to be the most re-presentative model for νo. This model includes C1, Mmix,i, pd, Sgr, Soc, and T as independent variables. Using the GRACE algorithm, the average error associated with the prediction of νo from this model is 9.23 percent (this is a non-parametric correlation — it is the minimum error possible).

Figure 19 — Correlation of the νo parameter using a para-meterized correlation of the results of the non-parametric regression.

In order to generate a correlation that can be of practical use, we must use the point-wise transform functions constructed by the GRACE algorithm and fit these transform (data) functions with functional forms (such as polynomials). Using quadratic polynomials to represent the individual transform functions, the average error increased (as would be expected) to 12.40 percent. The results from this "parametric" correlation is

shown in Fig. 19. We note that the performance of this form of the correlation degrades at the upper end of the νo scale.

The equations defining this model are:

0384.0 0206.0 0486.0

:using estimated is finally, and

1 431.0 000781.0 069.8

161.0 82.2 03.7

0238.0 246.0 158.0

117.2 0000879.0 0881.7

833.7 221.0 000402.0

318.71 312.25 1 982.19 1

2

,,,

2

2,

2,

2,

2

2

++−=

+++++=++−−=

+−=

−+−=

+−−−=

−+=

+−=

TrTro

o

TrTrocTrgrTrdewTrTrTr

Tr

ococTroc

grgrTrgr

dewdewTrdew

Tr

Tr

SumSum

TSSpMCSumTTET

SSS

SSS

ppEp

MMM

CCC

ν

ν

.............................................................................................. (6)

Figure 20 — Correlation of the νg parameter using a para-meterized correlation of the results of the non-parametric regression.

The same set of independent variables were also used in the model of the IPR parameter for gas. The GRACE model achieved an average error of 3.87 percent. When quadratic functions were used to fit the transform functions the average error increased to 4.51 percent. Unlike the model for the liquid case the "parametric" model from GRACE matches the data for all ranges of the νg parameter. A comparison of the predicted and actual νg data is given in Fig. 20.

As an overall comment we will note that the shape of the computed IPR trends is actually quite insensitive to the actual values of νo and νg. For example, 25 percent variations in these values causes a relatively small change to the shape of the corresponding IPR trends. We view the models proposed


as having definite qualitative value — but we would caution against the use of these models in cases where the values of the independent variables are beyond the ranges of the vari-ables used to develop the proposed models.

554.0 168.0 0214.0

:using estimated is finally, and

1 86.1 0065.0 0676.1

152.0 72.2 92.6

0709.0 622.0 229.0

31.1 000231.0 0806.1

10.7 190.0 000656.0

07.21 736.01 3.4 1

2

,,,

2

2,

2,

2,

2

2

++−=

+++++=++−−=

+−=

−−=

+−−−=

−+=

−−=

TrTrg

g

TrTrocTrgrTrdewTrTrTr

Tr

ococTroc

grgrTrgr

dewdewTrdew

Tr

Tr

SumSum

TSSpMCSumTTeT

SSS

SSS

ppep

MMM

CCC

ν

ν

.............................................................................................. (7)

Validation

In order to test the performance of our proposed IPR model we compared the performance of the proposed model to two validation cases. The first case is a synthetic case based on rock, rock-fluid, and fluid properties similar to those cases we constructed to generate the correlations. This approach was used because we were unable to find a suitable field data case in the published literature for which to compare our proposed IPR model. Both gas and condensate performance was compared for this synthetic case.

We did find a single literature case with which we could compare our proposed IPR model — unfortunately, only the gas performance data were available for this case (Xiong, et al.17).

For the synthetic case, sets of gas and condensate IPR curves were developed and correlated to obtain the appropriate νo and νg values (along with the qg,max, qo,max, and pavg variables). For the synthetic oil case the νo was determined to be 0.22, while the GRACE model (using quadratic transform functions) predicted 0.28. For the synthetic gas the νg estimate was 0.54 while the GRACE model predicted 0.49. These values are arguably a subset of the database used to generate the correla-tions — we should therefore accept the model estimates as reasonable.

In order to estimate νg for the Xiong, et al.17 data it was neces-sary to fit Eq. 3 to this dataset. Upon regression we obtained an estimate of 0.11 for νg. In comparison, the GRACE model predicted a νg estimate of 0.13. We conclude that these (ad-mittedly limited) cases validate the concept and encourage utilization of the proposed IPR model for gas condensate systems.

Summary and Conclusions

1. Vogel IPR Correlation Model: The generalized form of the Vogel IPR model (Eq. 3) can be used for the per-

formance prediction of oil, gas, and condensate sys-tems. The validity of this model is well-established empirically, and there are also semi-analytical valida-tions of this model for solution gas-drive systems.

2. IPR Behavior for Gas Condensate Systems: This work has validated the concept of correlating the IPR behavior for gas condensate systems — for both the gas and condensate phases. This "correlation" of behavior was based on the use of Eq. 3 as the base model. We were able to generate representative "dimensional" and "non-dimensional" IPR trends for every case considered in this work (62 cases total).

3. IPR Correlations for Gas Condensate Systems: In this work we used Eq. 3 as the IPR model and correlated the resulting νγ and νο parameters using non-parametric re-gression to identify the most influential parameters — in particular: T, pd, Soc, Sgr, Mmix,i, and the groups C1, C2, C7+.

Using the results of the non-parametric correlations, we were able to generate correlations (based on fitting functional approximations to the transform functions generated by the non-parametric regression algorithm) for both the gas and condensate phases. These correla-tion, while somewhat cumbersome, are considered to be both representative and accurate.

Nomenclature

Bg = Gas formation volume factor, scf/rcf Bo = Condensate formation volume factor, RB/STB h = Formation thickness, ft k = Formation permeability, md krg = Relative permeability to gas, fraction kro = Relative permeability to condensate, fraction Jθ = Residual function for optimization, fraction qg = Gas flowrate, MSCF/D qg,max = Maximum gas flowrate, MSCF/D qo = Condensate (oil) flowrate, STB/D qo,max = Maximum condensate (oil) flowrate, STB/D G = Original gas-in-place, MSCF N = Original condensate (oil)-in-place, STB pbar = Average reservoir pressure, psia (text and figures) p = Average reservoir pressure, psia (text and figures) pd = Dewpoint pressure, psia pwf = Flowing bottomhole pressure, psia re = Reservoir drainage radius, ft rw = Wellbore radius, ft Rs = Solution gas-oil ratio, scf/STB So = Condensate saturation, fraction Soc = Critical condensate saturation, fraction Sgr = Residual gas saturation, fraction T = Reservoir temperature, Deg F s = Radial flow skin factor, dimensionless µg = Gas viscosity, cp µo = Condensate viscosity, cp νg = Gas IPR parameter (for Eq. 3)


νo = Condensate IPR parameter (for Eq. 3)

References

1. Rawlins, E.L. and Schellhardt, M.A.: Backpressure Data on Natural Gas Wells and Their Application to Production Practices, Monograph Series, USBM (1935) 7.

2. Gilbert, W.E.: "Flowing and Gas-Lift Well Performance," Drill. and Prod. Prac., API (1954) 126.

3. Vogel, J.V.: "Inflow Performance Relationship for Solution-Gas Drive Wells," paper SPE 1476 presented at the 1968 SPE Annual Fall Meeting, Dallas, October 2-5.

4. Fetkovich, M.J.: "The Isochronal Testing of Oil Wells," paper SPE 4529 presented at the 1973 SPE Annual Fall Meeting, Las Vegas, Nevada, 30 September-3 October.

5. Richardson, J.M. and Shaw A.H: "Two-Rate IPR Testing-a Practical Production Tool," JCPT, (March-April 1982) 57-61.

6. Wiggins, M.L., Russell, J.E., Jennings, J.W.: "Analytical Development of Vogel-Type Inflow Performance Rela-tionships," SPE Journal (December 1996) 355-362.

7. Fussell, D.D.: "Single-Well Performance Predictions for Gas Condensate Reservoirs," JPT (July 1973) 860-870.

8. O'Dell, H.G. and Miller, R.N.: "Successfully Cycling a Low Permeability, High-Yield Gas Condensate Reservoirs," JPT (January 1967) 41-44.

9. Fevang, O and Whitson, C.H.: "Modelling Gas-Conden-sate Well Deliverability," paper SPE 30714 presented at the 1995 SPE Annual Technical Conference and Exhibi-tion, Dallas, 22-25 October.

10. Malachowski, M.A., Yanosik, M.A., and Saldana, M.A.: "Simulation of Well Productivity Losses Due to Near Well Condensate Accumulation in Field Scale Simu-lations," paper SPE 30715 presented at the 1995 SPE Annual Technical Conference and Exhibition, Dallas, Texas, 22-25 October.

11. Roussennac, B.: Gas Condensate Well Analysis, M.S. Thesis, Stanford University, June 2001.

12. Whitson, C.H., and Brule, M.R.: Phase Behavior, Mono-graph Series, SPE, Richardson, Texas (2000) 20, 47-65.

13. Jaramillo, J.M.: Vertical Composition Gradient Effects on Original Hydrocarbon in Place Volumes and Liquid Recovery for Volatile Oil and Gas Condensate Reservoirs, M.S. Thesis Texas A&M University. December 2000, College Station.

14. Guerra, A.: Analysis of the Dynamics of Saturation and Pressure Close to the Wellbore for Condensate Reservoirs as a Tool to Optimize Liquid Production, M.S. Thesis Texas A&M University. May 2001, College Station.

15. MS EXCEL (Office 10), Microsoft Corporation (2002).

16. Xue, G., Datta-Gupta, A., Valko, P., and Blasingame, T.A.: "Optimal Transformations for Multiple Regression: Application to Permeability Estimation from Well Logs," SPEFE (June 1997), 85-93.

17. Xiong, Y., Sun, Le., Sun Li., and Li S.: "A New Method for Predicting the Law of Unsteady Flow Through Porous Medium on Gas Condensate Well," paper SPE 35649 presented at the 1996 SPE Program Conference, Calgary, Canada, 28 April- 1 May.

Acknowledgements

The first author would like to acknowledge that this work was performed at Texas A&M University.


Appendix

Table A-1 — Molar compositions for the Cusiana reservoir fluid sample (Fluid 5) (from ref. 13).

Mole

fraction Molecular

weight Components ži Mi Mi ži

N2 0.0052 28.0130 0.1457C1 0.6897 16.0430 11.0649CO2 0.0457 44.0100 2.0113C2 0.0889 30.0700 2.6732C3 0.0418 44.0970 1.8433IC4 0.0099 58.1240 0.5754NC4 0.0140 58.1240 0.8137IC5 0.0071 72.1510 0.5123NC5 0.0060 72.1510 0.4329Benzene 0.0000 78.1140 0.0000C6 0.0099 86.1780 0.8532Toluene 0.0000 92.1410 0.0000C7 0.0102 96.0000 0.9792C8 0.0128 107.0000 1.3696C9 0.0097 121.0000 1.1737C10 0.0073 134.0000 0.9782C11 0.0053 147.0000 0.7791C12 0.0044 161.0000 0.7084C13 0.0048 175.0000 0.8400C14 0.0041 190.0000 0.7790C15 0.0036 206.0000 0.7416C16 0.0028 222.0000 0.6216C17 0.0026 237.0000 0.6162C18 0.0024 251.0000 0.6024C19 0.0019 263.0000 0.4997C20 0.0016 275.0000 0.4400C21 0.0013 291.0000 0.3783C22 0.0011 300.0000 0.3300C23 0.0010 312.0000 0.3120C24 0.0008 324.0000 0.2592C25 0.0007 337.0000 0.2359C26 0.0006 349.0000 0.2094C27 0.0006 360.0000 0.2160C28 0.0005 372.0000 0.1860C29 0.0004 382.0000 0.1528C30+ 0.0013 394.0000 0.5122

1.0000 Mmix 34.8463

Table A-2 — Separator test data (254 deg F) for the Cusiana reservoir fluid sample (Fluid 5) (from ref. 13).

Gas Specific Gravity

Pressure Temperature GOR (air = 1.0) (psig) (oF) (scf/STB) γg500 180 6696.5 0.7728 30 150 208.2 1.205 15 80 68.07 2.078

Table A-3 — Pseudocomponents for the Cusiana reservoir fluid sample (Fluid 5) (from ref. 13).

Critical Pseudo- Mole Molecular Pressure Com- Fraction Weight pc ponent Components ži Mi (psig)

CO2 0.0457 44.0100 1056.60 GRP1 N2-C1 0.6949 16.1330 651.77 GRP2 C2-C3 0.1307 34.5560 664.04 GRP3 IC4 to C6 0.0469 67.9640 490.47 GRP4 Toluene to C10 0.0400 112.5200 384.19 GRP5 C11 to C16 0.0250 178.7900 269.52 GRP6 C17 to C30+ 0.0168 303.6400 180.20

Critical Critical Tem- Critical Com-

Pseudo- perature Volume pressibilityCom- Tc vc Factor ponent Components (deg F) (ft3/lb-mole) zi

CO2 88.79 1.51 0.27 GRP1 N2-C1 -117.46 1.57 0.28 GRP2 C2-C3 127.16 2.64 0.28 GRP3 IC4 to C6 350.28 4.68 0.27 GRP4 Toluene to C10 591.91 7.26 0.26 GRP5 C11 to C16 781.91 11.10 0.24 GRP6 C17 to C30+ 1001.10 17.67 0.22


Table A-4 — Molar compositions for the Cupiagua reservoir fluid sample (Fluid 6) (from ref. 14).

Mole

fraction Molecular

weight Components ži Mi Mi ži

N2 0.0025 28.0130 0.0692 C1 0.6171 16.0430 9.8998 CO2 0.0461 44.0100 2.0288 C2 0.0944 30.0700 2.8382 C3 0.0514 44.0970 2.2678 IC4 0.0136 58.1240 0.7934 NC4 0.0180 58.1240 1.0456 IC5 0.0098 72.1510 0.7085 NC5 0.0074 72.1510 0.5361 Benzene 0.0014 78.1140 0.1063 C6 0.0127 86.1780 1.0987 Toluene 0.0042 92.1410 0.3874 C7 0.0150 96.0000 1.4414 C8 0.0160 107.0000 1.7147 C9 0.0135 121.0000 1.6371 C10 0.0100 134.0000 1.3400 C11 0.0071 147.0000 1.0393 C12 0.0058 161.0000 0.9322 C13 0.0066 175.0000 1.1515 C14 0.0057 190.0000 1.0754 C15 0.0049 206.0000 1.0011 C16 0.0038 222.0000 0.8547 C17 0.0035 237.0000 0.8247 C18 0.0035 251.0000 0.8709 C19 0.0029 263.0000 0.7600 C20 0.0025 275.0000 0.6875 C21 0.0021 291.0000 0.6198 C22 0.0020 300.0000 0.5910 C23 0.0018 312.0000 0.5522 C24 0.0016 324.0000 0.5184 C25 0.0015 337.0000 0.4954 C26 0.0013 349.0000 0.4676 C27 0.0012 360.0000 0.4464 C28 0.0011 372.0000 0.4055 C29 0.0010 382.0000 0.3782 C30+ 0.0070 394.0000 2.7658

1.0000 Mmix 44.3503

Table A-5 — Pseudocomponents for the Cupiagua reservoir fluid sample (Fluid 6) (from ref. 14).

Critical Pseudo- Mole Molecular Pressure Com- Fraction Weight pc ponent Components ži Mi (psia) GRP1 N2 - C1 0.6195 16.0880 725.83 GRP2 CO2 - C2 0.1405 34.6440 865.67 GRP3 C3 to NC4 0.0831 49.4400 615.11 GRP4 IC5 to Toluene 0.0356 84.4250 557.89 GRP5 C7 to C10 0.0546 125.3100 464.37 GRP6 C11 to C17 0.0373 212.3600 300.86 GRP7 C18 to C30+ 0.0295 394.4800 196.00

Critical Critical Tem- Critical Com-

Pseudo- perature Volume pressibilityCom- Tc vc Factor ponent Components (deg F) (ft3/lb-mole) zi GRP1 N2 - C1 -87.18 1.59 0.29 GRP2 CO2 - C2 34.65 2.09 0.29 GRP3 C3 to NC4 169.27 3.60 0.28 GRP4 IC5 to Toluene 399.51 5.62 0.27 GRP5 C7 to C10 574.61 7.81 0.26 GRP6 C11 to C17 771.16 12.80 0.23 GRP7 C18 to C30+ 995.39 21.14 0.21

Table A-6 — IPR Correlation Results from Compositional Reservoir Simulation — Gas Condensate Reservoir Systems.

N/G Mole Fraction Mmix kr Fluid Soc Sgr pdew T (STB/ C1 C1-C3 C4-C6 C7+ ρinit (lbm/ vo vg Case set set (frac) (frac) (psi) (deg F) MSCF) (frac) (frac) (frac) (frac) (lbm/ft3) lb-mole) (dim-less) (dim-less)

1 1 1 0.10 0.00 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.18 0.422 2 1 0.10 0.00 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.19 0.423 3 1 0.10 0.00 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.15 0.434 4 1 0.10 0.50 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.19 0.255 5 1 0.00 0.00 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.27 0.456 1 2 0.10 0.00 457 260 0.1541 0.870 0.000 0.030 0.100 18.705 29.10 0.19 0.497 1 3 0.10 0.00 284 260 0.0388 0.956 0.000 0.015 0.029 12.551 20.08 0.20 0.288 1 4 0.10 0.00 481 260 0.1800 0.870 0.000 0.015 0.115 19.833 30.23 0.21 0.519 1 5 0.10 0.00 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.25 0.50

10 4 5 0.10 0.50 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.29 0.4811 5 5 0.00 0.00 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.34 0.5612 4 5 0.10 0.50 504 230 0.1578 0.690 0.131 0.047 0.082 25.791 34.85 0.31 0.4913 4 5 0.10 0.50 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.26 0.4514 4 6 0.10 0.50 511 260 0.2655 0.617 0.146 0.067 0.121 30.635 44.35 0.64 0.7515 4 6 0.10 0.50 508 230 0.2655 0.617 0.146 0.067 0.121 33.289 44.35 0.65 0.7316 4 6 0.10 0.50 511 300 0.2655 0.617 0.146 0.067 0.121 36.078 44.35 0.61 0.7217 1 5 0.10 0.00 504 230 0.1578 0.690 0.131 0.047 0.082 25.791 34.85 0.26 0.5218 2 5 0.10 0.00 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.25 0.4919 3 5 0.10 0.00 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.26 0.5120 2 5 0.10 0.00 504 230 0.1578 0.690 0.131 0.047 0.082 25.791 34.85 0.26 0.5121 3 5 0.10 0.00 504 230 0.1578 0.690 0.131 0.047 0.082 25.791 34.85 0.25 0.5222 1 5 0.10 0.00 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.24 0.4823 2 5 0.10 0.00 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.24 0.4724 3 5 0.10 0.00 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.24 0.4725 5 5 0.00 0.00 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.34 0.5326 1 6 0.10 0.00 511 260 0.2655 0.617 0.146 0.067 0.121 30.635 44.35 0.55 0.7727 5 6 0.00 0.00 511 260 0.2655 0.617 0.146 0.067 0.121 30.635 44.35 0.66 0.8028 1 6 0.10 0.00 508 230 0.2655 0.617 0.146 0.067 0.121 33.289 44.35 0.58 0.8129 5 6 0.00 0.00 508 230 0.2655 0.617 0.146 0.067 0.121 33.289 44.35 0.68 0.8330 1 6 0.10 0.00 511 300 0.2655 0.617 0.146 0.067 0.121 36.078 44.35 0.52 0.7331 5 6 0.00 0.00 511 300 0.2655 0.617 0.146 0.067 0.121 36.078 44.35 0.62 0.7432 4 2 0.10 0.50 457 260 0.1541 0.870 0.000 0.030 0.100 18.705 29.10 0.23 0.4533 5 2 0.00 0.00 457 260 0.1541 0.870 0.000 0.030 0.100 18.705 29.10 0.33 0.5134 5 3 0.00 0.00 284 260 0.0388 0.956 0.000 0.015 0.029 12.551 20.08 0.16 0.3935 4 4 0.10 0.50 481 260 0.1800 0.870 0.000 0.015 0.115 19.833 30.23 0.27 0.4836 5 4 0.00 0.00 481 260 0.1800 0.870 0.000 0.015 0.115 19.833 30.23 0.35 0.5337 1 1 0.10 0.00 451 230 0.1094 0.896 0.000 0.030 0.074 17.613 26.00 0.14 0.4438 4 1 0.10 0.50 451 230 0.1094 0.896 0.000 0.030 0.074 17.613 26.00 0.18 0.4339 5 1 0.00 0.00 451 230 0.1094 0.896 0.000 0.030 0.074 17.613 26.00 0.28 0.4940 1 1 0.10 0.00 386 300 0.1094 0.896 0.000 0.030 0.074 15.469 26.00 0.22 0.4041 4 1 0.10 0.50 386 300 0.1094 0.896 0.000 0.030 0.074 15.469 26.00 0.22 0.2942 5 1 0.00 0.00 386 300 0.1094 0.896 0.000 0.030 0.074 15.469 26.00 0.26 0.3943 1 2 0.10 0.00 475 230 0.1541 0.870 0.000 0.030 0.100 19.778 29.10 0.17 0.5244 4 2 0.10 0.50 475 230 0.1541 0.870 0.000 0.030 0.100 19.778 29.10 0.25 0.4745 5 2 0.00 0.00 475 230 0.1541 0.870 0.000 0.030 0.100 19.778 29.10 0.34 0.5546 1 2 0.10 0.00 424 300 0.1541 0.870 0.000 0.030 0.100 17.428 29.10 0.26 0.4547 4 2 0.10 0.50 424 300 0.1541 0.870 0.000 0.030 0.100 17.428 29.10 0.24 0.4348 5 2 0.00 0.00 424 300 0.1541 0.870 0.000 0.030 0.100 17.428 29.10 0.31 0.4549 6 1 0.30 0.00 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.19 0.4150 6 2 0.30 0.00 457 260 0.1541 0.870 0.000 0.030 0.100 18.705 29.10 0.18 0.4951 6 5 0.30 0.00 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.26 0.5252 6 6 0.30 0.00 511 260 0.2655 0.617 0.146 0.067 0.121 30.635 44.35 0.52 0.7653 6 6 0.30 0.00 508 230 0.2655 0.617 0.146 0.067 0.121 33.289 44.35 0.57 0.8254 6 6 0.30 0.00 511 300 0.2655 0.617 0.146 0.067 0.121 36.078 44.35 0.50 0.7255 6 1 0.30 0.00 386 300 0.1094 0.896 0.000 0.030 0.074 15.469 26.00 0.24 0.4156 6 5 0.30 0.00 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.26 0.4557 7 1 0.30 0.15 427 260 0.1094 0.896 0.000 0.030 0.074 15.431 26.00 0.26 0.3958 7 1 0.30 0.15 386 300 0.1094 0.896 0.000 0.030 0.074 15.469 26.00 0.26 0.4259 7 5 0.30 0.15 501 260 0.1578 0.690 0.131 0.047 0.082 24.352 34.85 0.25 0.4660 7 5 0.30 0.15 492 300 0.1578 0.690 0.131 0.047 0.082 22.570 34.85 0.28 0.4161 7 6 0.30 0.15 510 260 0.2655 0.617 0.146 0.067 0.121 30.635 44.35 0.57 0.7962 7 6 0.30 0.15 511 300 0.2655 0.617 0.146 0.067 0.121 36.078 44.35 0.52 0.74

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