Parameter Space Reduction and Sensitivity Analysis …repository.icse.utah.edu/dspace/bitstream/123456789/...1 Parameter Space Reduction and Sensitivity Analysis in Complex Thermal

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Parameter Space Reduction and Sensitivity Analysis in

Complex Thermal Subsurface Production Processes

Jacob H. Bauman* and Milind D. Deo

Chemical Engineering Department, University of Utah, 50 S. Central Campus Drive Room 3290,

Salt Lake City, Utah 84112

[email protected], [email protected]

Abstract

As conventional resources for liquid fuels in the world become scarcer and less secure, there is a

need to develop other feasible resources. Oil shale is a massive resource local to the United States for

potential liquid fuel production. In situ oil shale processing strategies are attractive for reduced

environmental impact (in comparison to surface production operations) and provide access to resources

inaccessible to mining. The efficiency of feasible and economical development is greatly enhanced

with predictive power that is both efficient and accurate. However, modeling thermal subsurface

processes is a complex problem involving many simultaneously occurring physical phenomena. In this

study an oil reservoir simulator capable of representing thermal processes was used to explore the

impact and interplay of various pertinent parameters to an in situ oil shale processing strategy. A

statistical methodology was developed using designed factorial experiments (simulations) to expose

probable dominating parameters, including synergistic or diminutive interactions between parameters.

An empirical regression model, or response surface, was built from the simulated data. Monte Carlo

simulations were used to characterize the response surface and to estimate the uncertainty in predicted

oil recovery results due to the explored parameters.

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KEYWORDS: oil shale, thermal reservoir simulation, uncertainty analysis, experimental design

Introduction

The world is facing several interesting energy challenges. Conventional liquid fuel resources are

becoming scarcer. Carbon dioxide emissions associated with global warming demand attention and

technological solutions. Secure energy sources to supply increasing global demand will also be

necessary to address challenges moving forward. Understanding complex thermal and reactive

subsurface processes will facilitate technological development including production of oil from oil shale

and oil sands, thermal treatment of underground coal, carbon dioxide sequestration, geothermal energy

production, and so on.

Oil shale processing technology development is attractive because of the massive resources within the

United States. Resource estimates in the Green River formation located in the United States range from

1.5 trillion to 1.8 trillion barrels original oil in place from relatively rich shales exceeding 15 gallons per

ton1, 2

. Two major processing strategies exist for converting oil shale to oil: ex situ and in situ. Ex situ

strategies include mining organic rich shale followed by crushing and pyrolysis heating. Various ex situ

pyrolysis heating strategies exist. In situ processing strategies attempt to convert the organic matter to

oil underground by some form of heating, and then producing that oil in production wells. Since heat

input is required in both types of processes, heating efficiency is crucial for any successful strategy.

In situ thermal processing is a complex process that requires understanding of multiple phenomena at

multiple scales. The thermal transformation of organic matter (kerogen in oil shale) to useful fuels

(liquids and gases) requires an understanding of the parent composition, the transformation pathways

and detailed understanding of the products. The organic matter coexists with inorganic and mineral

matter, and the heat and mass transfer at the grain scale affect process effectiveness.

3

Description of the important physical phenomena and related properties

Heat transfer through reservoir scale systems is not trivial. A wide array of heating strategies

including resistive heating wells3, fracture injection with conductive material

4, underground rubblization

followed by well heating5, or radio frequency heating

6 have been proposed and developed. Effective

heating of the reservoir is crucial to the efficiency of any in situ thermal processing strategy. Modeling

of various strategies requires fundamental understanding of the physics including: thermal conductivities

and heat capacities of inhomogeneous reservoir materials, convection, phase changes, heats of reactions,

and heat losses due to inefficiencies or losses to reservoir boundaries. Estimating the significance of

these various modes of heat transfer could simplify such models since physical field data are sparse and

expensive.

As complex organic material like kerogen in oil shale is heated it is converted into lighter oil and gas

products. A variety of kinetic transformation mechanisms have been reported7-9

. Time and temperature

histories of these complex organic materials can have significant implications on product distributions

of literally thousands of components with their associated properties. Typically these components are

represented with relatively few pseudo components. The complexity of the reaction network to

represent these components is a major consideration10

. Kinetic parameters such as activation energy,

frequency factor, stoichiometry, etc. depend greatly on the complexity of the component representation.

For example, in one model from Braun and Burnham the activation energy for fractions of various

representations of type II kerogen vary from 47 kcal/mol to 54 kcal/mol11

. The stoichiometry of

reactants and products depends on the molecular weights and elemental representations of the lumped

species in order to conserve mass and elemental balances. For further cracking reactions of lumped

components, the kinetic parameters are dependent on molecular weights, aromaticity, thermodynamics,

etc. of all species represented by the representative component. Significant variation in organic

4

(kerogen) and inorganic material within and between resources has implications on the appropriate

kinetic representation of thermal processes as well.

Permeability dynamics (initial permeability and its evolution as the process unfolds) are crucial to a

successful in situ oil shale strategy. Oil shale resources are typically characterized with very low initial

permeability. As solid kerogen is heated and converted to liquid and gaseous products pore space is

created. Permeability increase is possible. Experimental studies have shown expansion followed by

subsidence of oil shale rock as it is heated12

. Decomposition of inorganic rock at high heats would have

permeability implications, including possible microfracturing of the rock, for some heating strategies.

Another possible major contributor to permeability dynamics is coke plugging of permeability pathways.

Relative permeability correlations are used in reservoir simulation to account for multiphase Darcy

flow in permeable rock. The relative permeability models are based on experimental data or are

empirically constructed, but the accuracy in relative permeability representation in complex reservoirs

may be crucial. Thermal effects on phase viscosities and dynamic capillary effects with changing rock

mechanics add complexity to relative permeability representation.

Significant interplay of parameters within and between these physical phenomena can exist. For

example, high temperatures required for oil shale pyrolysis have significant impact on organic material

composition, phase and flow behavior, and possibly geomechanics. Although the parameters are

supplied to governing equations and theoretical models in a simulator, the impact each parameter has on

the final recovery of oil predicted is not easily determined or available. This information potentially

would supply researchers and modelers the parameters that are of the greatest importance, and therefore

need the greatest attention for accurate prediction of such processes.

Simulator Description

5

The principle balance equations needed to solve thermal reservoir problems are species and energy

balance equations.

The flow term is typically calculated with Darcy’s law.

STARS from Computer Modeling Group is capable of performing four phase multi-component

thermal reservoir simulations13

. Equilibrium calculations are K-value based. The simulations in this

study were run with STARS. In these simulations, vertical heating wells surround a producer in a seven

point pattern. The heating wells supply only heat without injecting any fluids. Only a triangular wedge

Figure 1: Visualization of simulated section with dimensions.

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with fractions of two heaters and a fraction of one producer is discretized and calculated as shown in

Figure 114

. The initial dimensions of the wedge were 53 feet between heaters and 50 feet thickness of

the reservoir. The temperature at the heating wells was raised quickly to approximately 800oC and then

controlled at about 650oC in order to supply sufficient heat for adequate heat transfer throughout the

reservoir, but also maintaining reasonable temperatures near the heating well.

Geological data from the mahogany zone in the Uinta Basin well U059 was used to estimate the

richness of the layers in the reservoir. The richness of the layers varies from 12.5 – 25 wt% of

hydrocarbon material in the oil shale15

. All of the hydrocarbons were assumed to be kerogen, and this

kerogen was assumed to occupy 90-95% of the pore space, the rest of the pore space being occupied

with 99% gas saturation and 1% water saturation. The initial kerogen, water, and gas volumes in the

pore space will vary between resources or sections of a resource. This could have important

implications on the heat transfer dynamics dependent on the initial water mass and volume. Kerogen

was specified with a constant solid density, so rich layers were assigned higher porosities and lean layers

were assigned lower porosities. Porosity is defined here as total pore space occupied by kerogen, water,

and gas. Fluid porosity refers to the pore space occupied by liquids and gases. As solid kerogen is

converted to liquids and gases, fluid porosity increases while total pore space (as defined in this study)

remains unchanged. Green River oil shale has been characterized with low initial fluid porosity16

,

though this can vary between resources. The simulations studied in this paper have relatively low initial

fluid porosities, and are quite dry. Very little initial water is present in these simulations. Horizontal

permeability varied from 0.1 md at the bottom of the reservoir to 1 md at the top and vertical

permeability varied from 0.05 md at the bottom of the reservoir to 0.5 md at the top. Initial permeability

is typically low for oil shale, but permeability models where permeability increases as kerogen is

converted to fluids would make permeability dependent on initial kerogen richness as the process

unfolds. It is likely that a permeability creation/destruction model will be necessary to model this

process due to solid kerogen conversion to fluids, volume expansion of the rock, and coke plugging of

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pores. Increased permeability would allow fluids to flow more efficiently through the reservoir. If

significant permeable pathways develop, residence time of products is reduced which has compositional

implications as liquid oils could further transform to gases and coke. Also, with increased permeability

there is greater opportunity for convective heat transfer for improving heating efficiency. Typical

permeability creation/destruction models relate permeability to fluid porosity. In this particular study,

these dynamic effects were not considered.

A multiple reaction scheme was used to estimate kerogen decomposition to products. All

hydrocarbons were lumped into seven representative components: kerogen, heavy oil (HO), light oil

(LO), gas, methane (CH4), char, and coke. The reaction scheme was adapted from a previous study17

and is similar to other kerogen decomposition models18

, though the reaction scheme in this study is

relatively simple. These representative components are lumped together based on molecular weight.

Many more representative components lumped according to other physical characteristics such as

density, viscosity, aromaticity, solubility, and so on could also be represented depending on the desired

complexity in the reaction scheme. The ability to develop a more complex set of lumped components

also depends on the available data from experiments where these physical properties of interest are

analyzed. However, increased complexity can greatly increase computational cost. A simplified

reaction scheme assumes the most important physical properties for predicting reservoir behavior

depend on the molecular weight of all the components in a real system.

Reaction 1 Kerogen -> HO + LO + gas + CH4 + char

Reaction 2 HO -> LO + gas + CH4 + char

Reaction 3 LO -> gas + CH4 + char

Reaction 4 gas -> CH4 + char

8

Reaction 5 char -> CH4 + gas + coke

It should also be noted that this reaction scheme does not include mineral reactions. Carbonate

minerals present in oil shale resources in the Green River formation can also decompose at the high

temperatures encountered. These mineral transformations would have implications for CO2 emissions,

and also would have a relationship with porosity and permeability dynamics. Studies for carbonate

mineral decomposition have been done to determine the mineral reactions that could be involved19

.

Experimental Design

Factorial experimental designs give experimenters and analysts efficient tools to understand the

impact parameters have on a response in a process. Unlike “one at a time” experiments, factorial

designs allow the researcher to estimate interactions between parameters with fewer experiments. These

factorial designs allow researchers to evaluate many factors together. Experimental design methods

primarily were developed for quality assurance purposes, but have been used in a wide variety of

applications20, 21

. These experimental design tools have also been applied to various oil reservoir

studies22

. A common experimental design is the 2k full factorial design. These designs test k factors at

two levels for each factor, high levels and low levels. Each combination of high and low values of each

factor is called a run. Full factorial designs require 2k runs to test every possible combination of high

levels and low levels for k factors. When the number of factors is excessive or runs are expensive,

fractional factorial designs are used for efficiency. In fractional factorial designs runs are selectively

eliminated with the assumption that higher order interactions are much less significant than individual

factors without interactions. These designs are represented as 2k-p

fractional factorial designs. Fewer

runs are required, but information about the significance of higher order interactions is confounded with

information about individual parameters.

9

Experimental design and analysis methods are useful for comparing the sensitivity of a response due

to variable input parameters, including their possibly significant interactions. The parameters of

particular interest in this study are: molecular weight of kerogen, activation energy for kerogen cracking

reaction 1, activation energy for heavy oil cracking reaction 2, activation energy for light oil cracking

reaction 3, activation energy for gas cracking reaction 4, distributed representation for activation energy

for kerogen cracking reaction 1, relative permeability representation, and reaction enthalpy. Each of

these parameters is required for calculating the mass, energy, and momentum balances solved by the

simulator. Activation energies are required for calculating the reaction rate term in the mass balance

equation. Relative permeability is used to calculate the flow term with Darcy’s law. Reaction enthalpy

is incorporated in the energy balance equation. Ranges for each of these parameters were estimated

from various literature data, inherent uncertainty, or are estimated to explore sensitivities.

The molecular structure of kerogen is largely unknown. The molecular weight of kerogen has been

reported in ranges from about 3,00023

to 27,00024

. The stoichiometry in the chemical reactions and the

initial concentration of kerogen are dependent on the choice for molecular weight of kerogen to

conserve volume and mass for all simulation runs. Consequently, when the molecular weight of

kerogen is changed between simulation runs, the stoichiometry of the reactions and the initial molar

concentration of kerogen in the pore space must also be adjusted for mass and volume consistency. The

range of molecular weight, and associated stoichiometry for reactions 1 and 2 are shown in Table I. The

values in Table I demonstrate that stoichiometry for such a kinetic mechanism depends on the properties

(molecular weight and H/C ratio) of the pseudo components and is therefore “non-unique.” Mass and

elemental balances are important in these representations.

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Table I: High and low molecular weights and associated stoichiometry for reactions 1 and 2.

Ranges for appropriate activation energies have been reported18

, and can vary significantly depending

on experimental methods, and analysis of results. These ranges for activation energy are shown in Table

II. Studies have reported that activation energy for kerogen pyrolysis is most appropriately modeled

with some distribution18, 25

, but it is uncertain how much impact different representations of activation

energy have on the simulation results at large scales. A normal distribution with 5 kJ/mol standard

deviation is shown in Figure 2. Distribution of activation energies for kerogen pyrolysis is a complex

function, but is sometimes represented by the normal distribution26

. A perfect activation energy

distribution cannot be represented exactly in STARS, so discrete quantities, determined by integrating

under the distribution curve, represent kerogen reacting with a specified activation energy according to

the distribution.

Table II: Range of activation energies.

Reaction Low Activation

Energy (kJ/mol)

High Activation

Energy (kJ/mol)

1. Kerogen Cracking 195 225

2. Heavy Oil Cracking 208 260

3. Light Oil Cracking 208 260/233

4. Gas Cracking 235 270

Kerogen Heavy Oil Light Oil Gas Methane char coke

MW (+) 20000.55 424.49 152.03 52.01 16.04 12.60 14.55

MW (-) 2974.84 424.61 151.99 51.95 16.04 12.55 14.55

Formula (+) C1479H2220 C31.75H42.82 C11.19H17.51 C3.35H11.63 CH4 CH0.55 C1.19H0.32

Formula (-) C220H330 C31.76H42.81 C11.19H17.50 C3.35H11.62 CH4 CH0.53 C1.19H0.32

Stoic rxn 1 (+) -1 37.29 13.86 25.03 17.06 38.71 0

Stoic rxn 1 (-) -1 5.55 2.06 3.72 2.54 5.8 0

Stoic rxn 2 (+) -1 2.18 0.06 0.03 7.13 0

Stoic rxn 2 (-) -1 2.18 0.06 0.03 7.13 0

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Figure 2: Normal distribution of activation energies for reaction 1.

Relative permeability representations are often approximated in simulation, but such approximations

may have significant implications. The range of relative permeability curves are shown in Figure 3, the

low level being more linear and the high level being curved. The shape of the relative permeability

curves depends on the resource, the wetting characteristics of the rock, and the constituents present in

the pore space. Finally, heat of reaction could play an important role in the heat transfer efficiency

depending on the characteristics of the associated reactions. Efficient heat transfer through an oil shale

reservoir is crucial to any successful operation. Heat of reaction for oil shale pyrolysis has been

reported27

, but it is not certain how much heat is “lost” to reaction compared to heat required to raise the

rock temperature.

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Figure 3: Oil/water and liquid/gas relative permeability curves.

Results and Discussion

The initial experimental design was a 27-4

fractional factorial design. The eight run design for the

initial 7 factors (excluding (8) heat of reaction) is shown in Figure 4. Each row represents a simulation

Run X1 X2 X3 X4 X5 X6 X7

1 - - - + + + -

2 + - - - - + +

3 - + - - + - +

4 + + - + - - -

5 - - + + - - +

6 + - + - + - -

7 - + + - - + -

8 + + + + + + +

Figure 4: Eight run fractional factorial screening experimental design.

13

run at the parameter levels specified in the run. The un-coded levels for these parameters are shown in

Table III. Details about each of these parameters have been described. The numerical performance for

each of these runs was not equal. Some of the runs had excessive time step cuts due to rapid changes in

gas saturation. The response chosen for these runs was simulation time in order to pinpoint the possible

causes of these time step reductions. Figure 5 is a Pareto chart displaying the impact each of these

parameters have on the simulation time. Activation energy for reaction 3, or factor X4, had the greatest

impact on the simulation time. After investigation, it appeared that simulation time increased

significantly when the activation energy for reaction 3 was greater than the activation energy for reaction

4. This could be due to the combination of rapid gas creation coupled with high gas mobility causing

rapid gas saturation changes. The high value for factor X4 was lowered to 233 kJ/mol as shown in

Table II, and no major differences in simulation time were observed in subsequent runs.

Table III: Un-coded parameters for screening design.

Factor Physical Parameter Low Level (-) High Level (+)

X1 MW/Stoic/Concentration 3000 20000

X2 Eact Reaction 1 195 225

X3 Eact Reaction 2 208 260

X4 Eact Reaction 3 208 260

X5 Eact Reaction 4 235 270

X6 Eact distribution Rxn 1 Without With

X7 Relative permeability Linear Curved

Figure 5: Pareto chart for parameter effects on simulation time.

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Using the lowered value for factor X4, runs in the fractional factorial design were completed with

ultimate recovery of oil as the output response. None of the simulations produced acceptable amounts

of oil. Upon inspection it was found that oil generated from kerogen had inadequate mobility in lower

temperature zones far from the heaters to flow to the producer. As a result, oil components had large

residence times in the reservoir, and eventually converted further to gas and residual components. This

result gives insight into the design of such a process, specifically the spacing needed between wells for

successful operation. If heating wells are drilled too far from producing wells the residence time of the

oil in hot zones of the reservoir will be excessive, and these oils will convert to gasses or residual solids

significantly reducing or even prohibiting production of oil. However, capital and operating costs

increase with the number of wells drilled. Well spacing is a crucial design consideration for this process

since excessive residence time of products in the reservoir and the cost of drilling wells are competing

considerations for optimal process design.

The initial dimensions of the simulated domain were changed to resolve this issue of excessive

residence time of the oil. Reducing the spacing between these wells assures the whole reservoir was at a

high enough temperature for adequate oil mobility. Figure 6 shows the modified dimension of the

simulated wedge, changing the distance between heaters from 53 ft to 26.5 ft. The same fractional

factorial design was used with ultimate recovery of oil as the response. The normal probability plot in

Figure 7 illustrates the results of the runs. Normal probability plots, like Pareto charts, are useful

visualizing the significance of the effects for each factor. Dominating effects will appear as outlier

points on a normal probability plot. The points of the effects on this plot in Figure 7 are linear without

outliers indicating that there is no evidence from these runs that any factors are dominant or

insignificant. With the 27-4

fractional factorial design used, single factor effects are confounded with

pair interaction effects and higher order interactions. Additional runs are necessary to isolate the effects

of individual parameters from confounding with the effects of higher order interactions.

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Figure 6: Aerial view of simulated wedge. Distance between heating wells was reduced to 26.5 ft.

Figure 7: Normal probability plot of the effects on ultimate recovery of oil from 27-4

fractional factorial design.

Further runs were done with a sixteen run fractional factorial design for 6 to 8 factors. All 8 factors,

including heat of reaction were tested with this design. The design used is shown in Figure 8 where

factors E1 – E7 represent possible interactions between parameters, but individual factors are isolated

from possible confounding with interactions.

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Run Mean X1 X2 X3 X4 X5 X6 X7 X8 E1 E2 E3 E4 E5 E6 E7

1 + - - - - - - - - + + + + + + +

2 + + - - - + - + + - - - + - + +

3 + - + - - + + - + - + + - - + -

4 + + + - - - + + - + - - - + + -

5 + - - + - + + + - + - + - - - +

6 + + - + - - + - + - + - - + - +

7 + - + + - - - + + - - + + + - -

8 + + + + - + - - - + + - + - - -

9 + - - - + - + + + + + - + - - -

10 + + - - + + + - - - - + + + - -

11 + - + - + + - + - - + - - + - +

12 + + + - + - - - + + - + - - - +

13 + - - + + + - - + + - - - + + -

14 + + - + + - - + - - + + - - + -

15 + - + + + - + - - - - - + - + +

16 + + + + + + + + + + + + + + + +

Figure 8: Experimental design for 6-8 factors without confounding of individual parameters.

The results from these runs are displayed in a Pareto chart in Figure 9. It appears that the most

significant factors are X2, X4, X6, and X7 along with higher order interactions between parameters,

likely between these most significant factors. These factors are activation energy for reaction 1,

activation energy for reaction 3, activation energy distribution representation for kerogen conversion,

and relative permeability representation. It appears that activation energy for reaction 4 and heat of

reaction have the least impact on ultimate recovery of oil.

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Figure 9: Pareto chart from 16 run fractional factorial design for 8 factors.

The results from these runs can be used in a 24 full factorial design without any additional runs. The

data were regressed with the polynomial model shown in Equation 1, where β0 = the intercept (global

mean), β = single and higher order interaction linear coefficients, and x = input variables. This

polynomial model forms a multivariate surface called a response surface. The effects are calculated by

taking the difference of the averages of the responses at high and at low levels of each factor, and for

interactions between factors, and the coefficients β are half of those effects. The coefficients are

summarized in Table IV.

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Table IV: Summary of calculated effects.

Factors β

Intercept 294.6071

X1 -25.9846

X2 48.71381

X3 -8.88369

X4 -36.7407

X1X2 17.66644

X1X3 -19.9203

X1X4 7.082688

X2X3 14.89081

X2X4 -2.82519

X3X4 1.098062

X1X2X3 -5.35956

X1X2X4 0.575937

X1X3X4 -3.37056

X2X3X4 -0.70869

X1X2X3X4 2.191438

This model fit the experimental output data exactly. Although this is not a theoretical model and may

have little physical significance, insight about the significance of each parameter in the explored ranges

can be garnered. Typically higher order linear interaction effects are assumed to be negligible and can

be used to estimate error22

. Expert opinion and knowledge is advantageous for estimating error, and

elimination of terms in this model perhaps are not justified since this knowledge is unknown22

.

Three random validation simulations within the experimental space were run to estimate the quality of

the response surface, the empirical regression model, compared to a STARS simulation. The difference

between the response surface approximations for ultimate oil recovery and STARS simulation results

ranged from 3% to 15%. The quality of the response surface could be improved at the cost of more

experimental runs, either by reducing the experimental space or by adding additional runs to estimate

curvature due to nonlinearities when parameters are continuous. Alternative experimental designs could

possibly provide more accurate response surfaces with comparable or fewer total runs, however many of

these alternative designs require additional expert knowledge about the problem or unjustified

assumptions.

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Monte Carlo simulations were performed to characterize the response surface. Random values for

each parameter with uniform distributions were chosen for each run. A histogram of 80,000 Monte

Carlo runs is shown in Figure 10. The average value in these runs was 294.7 bbls oil with a standard

deviation of 40.1 bbls oil. A normal distribution with these values is also shown in the figure for

comparison. It appears the Monte Carlo results are slightly skewed to the right of a normal distribution.

This exercise helps to quantify the effects of variations in input parameters on the desired output. The

shape of this distribution could be affected by the response surface itself, the sampling locations for

Monte Carlo simulation, or by the distributions assigned to each of the factors.

Figure 10: Histogram of Monte Carlo calculations of response surface.

Conclusions

Although results for oil shale simulations in this study are calculated with theoretical governing

equations, the interplay within various parameters is not trivial due to competing physical phenomena.

Combinations of parameters that expose possible competing phenomena can have significant numerical

implications. Molecular representations for kerogen with associated stoichiometry, heat of reaction for

20

kerogen decomposition, intermediate oil cracking reaction (reaction 2) activation energy, and continuing

gas cracking (reaction 4) reaction activation energy are insignificant in determining the ultimate

recovery of oil at the scale simulated in this paper. Kerogen cracking (reaction 1) activation energy,

relative permeability representation, oil cracking to gas (reaction 3) activation energy, and activation

energy distribution representation have significant impacts on the ultimate recovery of oil in these

simulations. Expert knowledge or similar studies including large scale physical experiments are

important for estimating statistical error for developing validated surrogate models. Otherwise, more

runs are necessary for improving these models quality for approximating simulator results.

The interplay between various flow and kinetic parameters has been explored. Geomechanical, heat

transfer, and equilibrium parameters for example may also play significant roles at certain scales in

production results for such complex reactive transport systems. Parameters from acceptable theoretical

models can also be included in experimental designs to evaluate their impact on results and to include

these parameters in constructing response surface approximations as illustrated in this paper. Response

surfaces can be characterized to quantify risk and uncertainty of simulations according to variation in

input data.

Acknowledgements

The authors would like to acknowledge financial support from the U.S. Department of Energy, National

Energy Technology Laboratory – Grant Number: DE-FE0001243. We would also like to thank

Computer Modeling Group Limited (CMGL), Calgary Canada for providing academic licenses to their

reservoir simulators.

21

Nomenclature

Eact – Activation energy

– Phase specific gravity

- Phase enthalpy

- Heat of reaction

- Permeability tensor

– Phase relative permeability

- Phase viscosity

– Number of fluid phases

– Number of phases

- Number of reactions

- Phase pressure

– Phase index

- Porosity

- Source term for energy

- Source term for mass of component i

- Residual mass for component i

- Residual energy

- Reaction rate

- Reaction index

- Phase molar density

- Phase saturation

– Stoichiometric factor of component i in reaction r

– Temperature

– Time

- Phase internal energy

22

- Rock internal energy

- Phase velocity

– Mole fraction of component i in phase p

- Height or depth

References

1. Dyni, J. R.; Geology and Resources of some World Oil-Shale Deposits. Oil Shale. 2003, 20(3),

193-252.

2. Bartis, J. T.; LaTourrette, T.; Dixon, L.; Peterson, D. J.; Cecchine, G. Oil Shale Development in

the United States: Prospects and Policy Issues; RAND Corporation: Santa Monica, CA, 2005;

pp 5-9, (http://www.rand.org/pubs/monographs/2005/RAND_MG414.pdf).

3. Wellington, S. L.; Berchenko, I. E.; Rouffingnac E. P.; Fowler, T. D.; Ryan, R. C.; Shalin, G. T.;

Stegemeier, G. L.; Vinegar, H. J. U.S. Patent 6,880,633, 2005.

4. Symington, W. A.; Olgaard, D. L.; Otten, G. A.; Phillips, T. C.; Thomas, M. M.; Yeakel, J. D.

ExxonMobil’s ElectrofracTM

Process for InSitu Oil Shale Conversion. Proceedings of the 26th

Oil Shale Symposium, Golden, CO, October 17, 2006 http://www.ceri-

mines.org/documents/R05b-BillSymington-rev_presentation.pdf (accessed July 21, 2009).

5. Oil Shale Research, Development & Demonstration Project Plan of Operation. Chevron USA

Inc. 2006.

http://www.blm.gov/pgdata/etc/medialib/blm/co/field_offices/white_river_field/oil_shale.Par.37

256.File.dat/OILSHALEPLANOFOPERATIONS.pdf (accessed June 23, 2010).

6. Kasevich, R. S.; Kolker, M.; Dwyer, A. S. U.S. Patent 4,140,179, 1979.

7. Allred, V. D. Chem. Eng. Prog. 1966, 62, 55.

23

8. Rajeshwar, K.; Nottenburg, N.; Dubow, J. J. Mater. Sci. 1979, 14, 2025.

9. Strizhakova, Y.A.; Usova, T. V. Current trends in the pyrolysis of oil shale: A review. Solid Fuel

Chem. 2008. 42. 197.

10. Pepper, A.S.; Dodd, T.A. Simple kinetic models of petroleum formation. Part II: oil-gas

cracking. Mar. Pet. Geol. 1995. 12. 321.

11. Braun, R. L.; Burnham, A. K. Chemical reaction model for oil and gas generation from type I

and type II kerogen. LLNL Report UCRL-ID-114143. 1993.

12. Mattson, E.D.; Palmer, C.D.; Johnson, E.; Huang, H.; Wood, T. Permeability Changes of

Fractured Oil Shale Cores During Retorting. Proceedings of the 29th

Oil Shale Symposium,

Golden, CO, October 20, 2009.

13. Computer Modeling Group. STARS User Manual. 2007.

14. Bauman, J. H.; Huang, C. K.; Gani, M. R.; Deo, M. D. Modeling of the In-Situ Production of Oil

from Oil Shale. Oil Shale: A Solution to the Liquid Fuel Dilemma. 2010. 135-146.

15. Vanden Berg, M. D.; Dyni, J. R.; Tabet, D. E. Utah oil shale database. 2006 [CD-ROM]; Utah

Geological Survey OFR 469.

16. Tisot, P. R. Properties of Green River oil shale determined from nitrogen adsorption and

desorption isotherms. J. Chem. Eng. Data. 1962. 7. 405-410.

17. Braun, R. L.; Burnham, A. K. PMOD: a flexible model of oil and gas generation, cracking, and

expulsion. Org. Geochem. 1992, 19, 161-172.

18. Stainforth, J.G. Practical kinetic modeling of petroleum generation and expulsion. Mar. Pet.

Geol. 2009. 26. 552-572.

24

19. Campbell, J. H. Kinetics of decomposition of Colorado oil shale. II. Carbonate minerals. LLNL

Report UCRL-52089 Part 2. 1978.

20. Box, G.E.P.; Hunter, W.G.; Hunter, J.S. Statistics for experimenters: an introduction to design,

data analysis, and model building. John Wiley & Sons, Inc., New York, NY, 1978.

21. Lawson, J.; Erjavec, J. Modern statistics for engineering and quality improvement. Duxbury,

Pacific Grove, CA, 2001; pp 465-513.

22. Peng, C.Y.; Gupta, R. Experimental Design and Analysis Methods in Multiple Deterministic

Modelling for Quantifying Hydrocarbon In-Place Probability Distribution Curve. SPE Asia Pac.

Conf., Kuala Lumpur, Malaysia, 2004, March 29-30; SPE Paper 87002.

23. Yen, T. F.; Chilingar, G. V. Introduction to Oil Shales. In Oil Shale; Yen, T. F.; Chilingar, G. V.,

Eds; Elsevier Science Publishing Company: Amsterdam, 1976, pp 181-198.

24. Behar, F.; Vandenbroucke, M. Chemical modelling of kerogens. Org. Geochem. 1987. 11. 15.

25. Sundararaman, P.; Merz, P. H.; Mann, R. G. Determination of kerogen activation energy

distribution. Energy Fuels. 1992. 6 (6). 793-803.

26. Burnham, A. K. and Braun R. L.: Global kinetic analysis of complex materials, Energy Fuels.

1999. 13(1). 1-22.

27. Camp, D. W. Oil Shale Heat Capacity Relations and Heats of Pyrolysis and Dehydration.

Proceedings of the 20th

Oil Shale Symposium, Golden, CO, 1987.