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  | image  = Hedberg 4 cover final.jpg

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  | series  = Hedberg

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==Introduction==

==Introduction==

Basin modeling is an increasingly important element of exploration, development, and production workflows. Problems addressed with basin models typically include questions regarding burial history, source maturation, hydrocarbon yields (timing and volume), hydrocarbon migration, hydrocarbon type and quality, reservoir quality, and reservoir pressure and temperature prediction for pre–drill analysis. As computing power and software capabilities increase, the size and complexity of basin models also increase. These larger, more complex models address multiple scales (well to basin) and problems of variable intricacy, making it more important than ever to understand how the uncertainties in input parameters affect model results.

Basin modeling is an increasingly important element of exploration, development, and production workflows. Problems addressed with basin models typically include questions regarding burial history, source [[maturation]], hydrocarbon yields (timing and volume), [[hydrocarbon migration]], hydrocarbon type and quality, reservoir quality, and reservoir pressure and temperature prediction for pre–drill analysis. As computing power and software capabilities increase, the size and complexity of basin models also increase. These larger, more complex models address multiple scales (well to basin) and problems of variable intricacy, making it more important than ever to understand how the uncertainties in input parameters affect model results.

Increasingly complex basin models require an ever-increasing number of input parameters with values that are likely to vary both spatially and temporally. Some of the input parameters that are commonly used in basin models and their potential effect on model results are listed in Table 1. For a basin model to be successful, the modeler must not only determine the most appropriate estimate for the value for each input parameter, but must also understand the range of uncertainty associated with these estimates and the uncertainties related to the assumptions, approximations, and mathematical limitations of the software. This second type of uncertainty may involve fundamental physics that are not adequately modeled by the software and/or the numerical schemes used to solve the underlying partial differential equations. Although these issues are not addressed in this article or by the proposed workflow, basin modelers should be aware of these issues and consider them in any final recommendations or conclusions.

Increasingly complex basin models require an ever-increasing number of input parameters with values that are likely to vary both spatially and temporally. Some of the input parameters that are commonly used in basin models and their potential effect on model results are listed in Table 1. For a basin model to be successful, the modeler must not only determine the most appropriate estimate for the value for each input parameter, but must also understand the range of uncertainty associated with these estimates and the uncertainties related to the assumptions, approximations, and mathematical limitations of the software. This second type of uncertainty may involve fundamental physics that are not adequately modeled by the software and/or the numerical schemes used to solve the underlying partial differential equations. Although these issues are not addressed in this article or by the proposed workflow, basin modelers should be aware of these issues and consider them in any final recommendations or conclusions.

|-

|-

| Bulk rock properties

| Bulk rock properties

* Stratigraphy/lithology  

* [[Stratigraphy]]/[[lithology]]

** Compaction curves  

** Compaction curves  

** Thermal conductivity  

** Thermal conductivity  

|-

|-

| Source properties

| Source properties

* Thickness, original [[total organic carbon (TOC)|total organic carbon]] and [[hydrogen]] index

* Thickness, original [[total organic carbon (TOC)|total organic carbon]] and [[hydrogen index]]

* Kinetics, retention/expulsion model

* [[Kinetics]], retention/expulsion model

|| Source properties control the timing, rate, and fluid type for hydrocarbon generation and expulsion from the [[source rock]]s.

|| Source properties control the timing, rate, and fluid type for hydrocarbon generation and expulsion from the [[source rock]]s.

|-

|-

==Considering uncertainty==

==Considering uncertainty==

Uncertainty is present in most, if not all, model inputs and calibration data. These uncertainties generate uncertainties in the model outputs. Sometimes, the resultant uncertainties are not significant enough to impact decisions based on the model results. Other times, these uncertainties can make the model results virtually useless in the decision-making process. Of course, a wide range of cases exist between these extremes, and this is where basin modelers commonly work. In these cases, the model results can be useful, but the uncertainties surrounding the model predictions can be difficult to fully grasp and communicate. Successful decisions based on models in which significant uncertainties exist require that the modeler (1) identify and quantify uncertainties in key input parameters, (2) adequately propagate these uncertainties from input through to output, particularly for three-dimensional models, and (3) clearly communicate this information to decision makers.

Uncertainty is present in most, if not all, model inputs and calibration data. These uncertainties generate uncertainties in the model outputs. Sometimes, the resultant uncertainties are not significant enough to impact decisions based on the model results. Other times, these uncertainties can make the model results virtually useless in the decision-making process. Of course, a wide range of cases exist between these extremes, and this is where basin modelers commonly work. In these cases, the model results can be useful, but the uncertainties surrounding the model predictions can be difficult to fully grasp and communicate. Successful decisions based on models in which significant uncertainties exist require that the modeler (1) identify and quantify uncertainties in key input parameters, (2) adequately propagate these uncertainties from input through to output, particularly for three-dimensional models, and (3) clearly communicate this information to decision makers.

* not recognizing feasible alternative scenarios

* not recognizing feasible alternative scenarios

Why consider uncertainty? Is not a single deterministic case sufficient for analysis? Consider the simple case of estimating [[charge volume]] to a trap. The necessary minimum charge volume required for success (i.e., low charge risk) and a range associated with this minimum charge have been defined and are illustrated by the vertical black solid and dashed lines, respectively, in [[:file:H4CH12FG1.JPG|Figure 1]]. If a model predicts a charge volume greater than the minimum, then it might be said that little or no charge risk exists. Similarly, if a model predicts a charge volume less than the minimum, then we might say that a significant charge risk exists. These cases are illustrated in Figure 1 and are labeled “low risk” and “high risk,” respectively. However, the perception of what is low risk and what is high risk can change greatly when the probability of an outcome is considered. In this example, the difference between low risk and high risk becomes less definitive, as indicated in [[:file:H4CH12FG1.JPG|Figure 1]]. Although this is a simplistic illustration, all of the key input parameters in a basin model have the potential to cause this degree of ambiguity in the final results. For that reason, estimates of the range of possible outcomes are as important to the final analysis as estimates of the most likely outcome.

 

Why consider uncertainty? Is not a single deterministic case sufficient for analysis? Consider the simple case of estimating charge volume to a trap. The necessary minimum charge volume required for success (i.e., low charge risk) and a range associated with this minimum charge have been defined and are illustrated by the vertical black solid and dashed lines, respectively, in [[:file:H4CH12FG1.JPG|Figure 1]]. If a model predicts a charge volume greater than the minimum, then it might be said that little or no charge risk exists. Similarly, if a model predicts a charge volume less than the minimum, then we might say that a significant charge risk exists. These cases are illustrated in Figure 1 and are labeled “low risk” and “high risk,” respectively. However, the perception of what is low risk and what is high risk can change greatly when the probability of an outcome is considered. In this example, the difference between low risk and high risk becomes less definitive, as indicated in [[:file:H4CH12FG1.JPG|Figure 1]]. Although this is a simplistic illustration, all of the key input parameters in a basin model have the potential to cause this degree of ambiguity in the final results. For that reason, estimates of the range of possible outcomes are as important to the final analysis as estimates of the most likely outcome.

==Handling uncertainty==

==Handling uncertainty==

* Once the key parameters have been identified, uncertainties in these parameters are quantified and assigned. The quantification in this step is generally more rigorous than in step 3 (preliminary screening). Quantification typically involves selecting and populating a probability distribution (e.g., uniform, triangular, normal) for each of the key input parameters identified.

* Once the key parameters have been identified, uncertainties in these parameters are quantified and assigned. The quantification in this step is generally more rigorous than in step 3 (preliminary screening). Quantification typically involves selecting and populating a probability distribution (e.g., uniform, triangular, normal) for each of the key input parameters identified.

Step 6: Propagate the uncertainty in key input parameters through to the output properties of interest via Monte Carlo or similar analysis.

Step 6: Propagate the uncertainty in key input parameters through to the output properties of interest via [[Monte Carlo]] or similar analysis.

* The final step is a Monte Carlo simulation where values for the input parameters identified in step 4 are randomly selected from the distributions assigned in step 5. The key results from each realization are saved for subsequent evaluation.

* The final step is a Monte Carlo simulation where values for the input parameters identified in step 4 are randomly selected from the distributions assigned in step 5. The key results from each realization are saved for subsequent evaluation.

* Although several approaches could be used to quantify uncertainty in models, the approach presented uses Monte Carlo simulation. Monte Carlo simulation has the advantage of being (1) able to handle any probability distribution function, (2) able to account for dependencies between variables, and (3) straightforward to implement. It is also typically straightforward to analyze the results of the Monte Carlo simulation. The disadvantages include that it may require a large number of realizations to adequately sample the possible solution space, and it may be difficult to adequately develop probability distribution functions or the required realizations, particularly for maps and volumes.

* Although several approaches could be used to quantify uncertainty in models, the approach presented uses Monte Carlo simulation. Monte Carlo simulation has the advantage of being (1) able to handle any probability distribution function, (2) able to account for dependencies between variables, and (3) straightforward to implement. It is also typically straightforward to analyze the results of the Monte Carlo simulation. The disadvantages include that it may require a large number of realizations to adequately sample the possible solution space, and it may be difficult to adequately develop probability distribution functions or the required realizations, particularly for maps and volumes.

[[File:H4CH12FG2.JPG|thumb|300px|{{figure number|2}}Present-day depth structure map (meters) of the key migration surface. The outlines of the drainage polygons are shown in black, the closures are outlined in red, and the escape paths are shown in green. The scale bar in the legend represents 12,500 m (41,010 ft).]]

H4CH12FG2.JPG|{{figure number|2}}Present-day depth structure map (meters) of the key migration surface. The outlines of the drainage polygons are shown in black, the closures are outlined in red, and the escape paths are shown in green. The scale bar in the legend represents 12,500 m (41,010 ft).

H4CH12FG3.JPG|{{figure number|3}}Cross section through the model along the line AA' shown in [[:file:H4CH12FG2.JPG|Figure 2]].

A hypothetical example is presented to illustrate the approach described. Although the geology is synthetic, it was constructed with realistic basin modeling issues in mind. In this example, the traps of interest formed about 15 Ma. The primary question addressed by the model is, “What is the volume of oil charge to each of the traps during the last 15 m.y.?”

A hypothetical example is presented to illustrate the approach described. Although the geology is synthetic, it was constructed with realistic basin modeling issues in mind. In this example, the traps of interest formed about 15 Ma. The primary question addressed by the model is, “What is the volume of oil charge to each of the traps during the last 15 m.y.?”

For the purposes of this illustration, the migration analysis has been simplified, and it has been assumed that a present-day map-based drainage analysis is sufficient. A map view of the key surface for the map-based drainage analysis is shown in [[:file:H4CH12FG2.JPG|Figure 2]], and a [[cross section]] through the model is shown in [[:file:H4CH12FG3.JPG|Figure 3]]. A burial history curve at location X in [[:file:H4CH12FG2.JPG|Figure 2]] is shown in [[:file:H4CH12FG4.JPG|Figure 4]]. Also shown in [[:file:H4CH12FG4.JPG|Figure 4]] are three potential hydrocarbon source rocks, Upper [[Jurassic]], Lower [[Cretaceous]], and lower [[Miocene]]. The sources are modeled as uniformly distributed [[marine]] [[source rock]]s with some terrigenous input.

 

For the purposes of this illustration, the migration analysis has been simplified, and it has been assumed that a present-day map-based drainage analysis is sufficient. A map view of the key surface for the map-based drainage analysis is shown in [[:file:H4CH12FG2.JPG|Figure 2]], and a cross section through the model is shown in [[:file:H4CH12FG3.JPG|Figure 3]]. A burial history curve at location X in [[:file:H4CH12FG2.JPG|Figure 2]] is shown in [[:file:H4CH12FG4.JPG|Figure 4]]. Also shown in [[:file:H4CH12FG4.JPG|Figure 4]] are three potential hydrocarbon source rocks, Upper [[Jurassic]], Lower [[Cretaceous]], and lower [[Miocene]]. The sources are modeled as uniformly distributed [[marine]] [[source rock]]s with some terrigenous input.

 

===Step 1: identify the purpose of the model===

===Step 1: identify the purpose of the model===

As previously stated, the purpose of this model is to estimate the volume of oil charge to individual traps during the last 15 m.y.

As previously stated, the purpose of this model is to estimate the volume of oil charge to individual traps during the last 15 m.y.

 

===Step 2: develop a base-case scenario===

===Step 2: develop a base-case scenario===

The next step is to develop and calibrate a base-case scenario. Values for the selected parameters used in this example are listed in the "Most Likely" column of Table 2. In this hypothetical model, only one calibration point is present, so a match to the data is relatively straightforward, but is also nonunique ([[:file:H4CH12FG5.JPG|Figure 5]]). The uncertainty around the single temperature measurement (±15°C) is indicated by the error bars.

The next step is to develop and calibrate a base-case scenario. Values for the selected parameters used in this example are listed in the "Most Likely" column of Table 2. In this hypothetical model, only one calibration point is present, so a match to the data is relatively straightforward, but is also nonunique ([[:file:H4CH12FG5.JPG|Figure 5]]). The uncertainty around the single temperature measurement (±15°C) is indicated by the error bars.

| Magnitude of extension (''γ'', 0-1) || 0.1 || 0.64 || 0.9

| Magnitude of extension (''γ'', 0-1) || 0.1 || 0.64 || 0.9

|-

|-

| Shale conductivity (W/m.K) || 1.87 || 2.34 || 2.81

| [[Shale]] conductivity (W/m.K) || 1.87 || 2.34 || 2.81

|-

|-

| Shale heat generation (mW/m³) || 1.0 || 2.1 || 4.1

| Shale heat generation (mW/m³) || 1.0 || 2.1 || 4.1

===Step 4: perform screening simulations to identify key input parameters===

===Step 4: perform screening simulations to identify key input parameters===

Evaluating the sensitivity of results to individual parameters involves exploring the solution space by running a series of basin model simulations in which each parameter is set equal to the maximum value and then to the minimum value while all of the other parameters are held at their base-case value. This process results in 2N + 1 realizations, where N is the number of parameters for which ranges have been defined. In this example, uncertainties were defined for the surface temperature, the magnitude, age, and duration of the rifting event, the background heat flow, the shale conductivity and radiogenic heat generation, the lithology of the upper Miocene and Pliocene isopachs, the depths, the missing section, and the generative characteristics of all three source rocks. These uncertainties are summarized in the "Minimum" and "Maximum" columns of Table 2.

H4CH12FG6.JPG|{{figure number|6}}Tornado chart for total net oil yields in million stock tank barrels (MSTB) in a selected drainage polygon during the last 15 m.y. The parameters are sorted by the range of net yields (on a linear scale) for each parameter. Uncertainties in net yields caused by uncertainty in the parameters shown below the horizontal dashed line are too small to be important. Uncertainties in net yields caused by the uncertainty in the parameters for some of the parameters shown above the horizontal line may also be unimportant, particularly for ranges with high low sides. oTOC = original total organic carbon; oHI = original hydrogen index.

H4CH12FG7.JPG|{{figure number|7}}Tornado chart for total yield (million stock tank barrels [MSTB]). In this example, uncertainties in the properties of the Upper Jurassic and Lower Cretaceous source rocks have the most effect on the total oil yield. oTOC and oHI are the original source rock total organic carbon and hydrogen index, respectively. oTOC = original total organic carbon; oHI = original hydrogen index.

[[File:H4CH12FG6.JPG|thumb|300px|{{figure number|6}}Tornado chart for total net oil yields in million stock tank barrels (MSTB) in a selected drainage polygon during the last 15 m.y. The parameters are sorted by the range of net yields (on a linear scale) for each parameter. Uncertainties in net yields caused by uncertainty in the parameters shown below the horizontal dashed line are too small to be important. Uncertainties in net yields caused by the uncertainty in the parameters for some of the parameters shown above the horizontal line may also be unimportant, particularly for ranges with high low sides. oTOC = original total organic carbon; oHI = original hydrogen index.]]

Evaluating the sensitivity of results to individual parameters involves exploring the solution space by running a series of basin model simulations in which each parameter is set equal to the maximum value and then to the minimum value while all of the other parameters are held at their base-case value. This process results in 2N + 1 realizations, where N is the number of parameters for which ranges have been defined. In this example, uncertainties were defined for the surface temperature, the magnitude, age, and duration of the rifting event, the background heat flow, the shale conductivity and radiogenic heat generation, the lithology of the upper Miocene and Pliocene [[isopach]]s, the depths, the missing section, and the generative characteristics of all three source rocks. These uncertainties are summarized in the "Minimum" and "Maximum" columns of Table 2.

The simulation results are summarized in a tornado chart ([[:file:H4CH12FG6.JPG|Figure 6]]). The yields are plotted on a log scale to more clearly examine the low-yield (high-risk) cases. Analysis of this plot provides a good opportunity to think about the problem. What properties are important? How important are they? Are there any surprises? The basin modeler should spend some time evaluating the behavior of each parameter to make sure it is understood and makes geologic sense. A limitation of this process is that it does not account for dependencies between input parameters. Thus, the modeler should also give potential dependencies some thought. Examples include a positive correlation between the source rock total organic carbon and hydrogen index, between the mudline temperature and paleo–water depth, between the ages and thickness of isopachs and the timing and magnitude of extension, and between the stratigraphy and paleo–water depths.

The simulation results are summarized in a tornado chart ([[:file:H4CH12FG6.JPG|Figure 6]]). The yields are plotted on a log scale to more clearly examine the low-yield (high-risk) cases. Analysis of this plot provides a good opportunity to think about the problem. What properties are important? How important are they? Are there any surprises? The basin modeler should spend some time evaluating the behavior of each parameter to make sure it is understood and makes geologic sense. A limitation of this process is that it does not account for dependencies between input parameters. Thus, the modeler should also give potential dependencies some thought. Examples include a positive correlation between the source rock total organic carbon and [[hydrogen index]], between the mudline temperature and paleo–water depth, between the ages and thickness of isopachs and the timing and magnitude of extension, and between the stratigraphy and paleo–water depths.

Modelers should realize that although it is possible in this sort of analysis for some of these scenarios to be inconsistent with the calibration data, a mismatch on its own is not sufficient reason to narrow the range of values for one of these variables. A particular value of one parameter can cause a mismatch with the data because the value of another parameter is incorrect. If both values were set appropriately, then the model results might be consistent with the calibration data. These interdependency issues will be discussed in more detail later.

Modelers should realize that although it is possible in this sort of analysis for some of these scenarios to be inconsistent with the calibration data, a mismatch on its own is not sufficient reason to narrow the range of values for one of these variables. A particular value of one parameter can cause a mismatch with the data because the value of another parameter is incorrect. If both values were set appropriately, then the model results might be consistent with the calibration data. These interdependency issues will be discussed in more detail later.

The parameters in a tornado plot are sorted by decreasing the range of the net yield resulting from the range given to each input parameter. By constructing the plot in this way, the input parameter uncertainties producing the greatest range in model results are at the top. Twenty-six different parameters were varied in this run; only the 16 parameters with the widest range are shown in [[:file:H4CH12FG6.JPG|Figure 6]]. The uncertainties associated with the bottom three parameters, and the 10 not shown, are not significant enough to justify the additional effort. Even the uncertainty in some of those “above the line” might not warrant further work. This is because sorting by the widest range does not necessarily equate to sorting by the most important impact on the decisions made based on the results. In this example, the concern is oil yield, so a better sorting might be by the minimum oil yield. In this case, the depth of the Miocene source rock, radiogenic component of the shale, the original total organic carbon in the Miocene source, and the lithology of the Miocene–Pliocene section could be considered the most important, especially if the minimum value of oil yield required for success was on the order of 100 million stock tank barrels (MSTB). The other parameters may not warrant further work or resources.

The parameters in a tornado plot are sorted by decreasing the range of the net yield resulting from the range given to each input parameter. By constructing the plot in this way, the input parameter uncertainties producing the greatest range in model results are at the top. Twenty-six different parameters were varied in this run; only the 16 parameters with the widest range are shown in [[:file:H4CH12FG6.JPG|Figure 6]]. The uncertainties associated with the bottom three parameters, and the 10 not shown, are not significant enough to justify the additional effort. Even the uncertainty in some of those “above the line” might not warrant further work. This is because sorting by the widest range does not necessarily equate to sorting by the most important impact on the decisions made based on the results. In this example, the concern is oil yield, so a better sorting might be by the minimum oil yield. In this case, the depth of the Miocene source rock, radiogenic component of the shale, the original total organic carbon in the Miocene source, and the lithology of the Miocene–Pliocene section could be considered the most important, especially if the minimum value of oil yield required for success was on the order of 100 million stock tank barrels (MSTB). The other parameters may not warrant further work or resources.

As mentioned, it is important to remember the question(s) that are being addressed when building a basin model and deciding what input parameters need the most attention. [[:file:H4CH12FG7.JPG|Figure 7]] shows the tornado plot for the total expelled hydrocarbon yield as opposed to the net hydrocarbon yield expelled during the last 15 m.y. ([[:file:H4CH12FG6.JPG|Figure 6]]). Little similarity exists between the parameters that are the most important in these two cases. For the net yields, understanding the timing is critical. For the case in which the total yield is the output property of interest, the generative potential of the Cretaceous and Jurassic sources is more critical than the generative potential of the Miocene source rock.

As mentioned, it is important to remember the question(s) that are being addressed when building a basin model and deciding what input parameters need the most attention. [[:file:H4CH12FG7.JPG|Figure 7]] shows the tornado plot for the total expelled hydrocarbon yield as opposed to the net hydrocarbon yield expelled during the last 15 m.y. ([[:file:H4CH12FG6.JPG|Figure 6]]). Little similarity exists between the parameters that are the most important in these two cases. For the net yields, understanding the timing is critical. For the case in which the total yield is the output property of interest, the generative potential of the Cretaceous and Jurassic sources is more critical than the generative potential of the Miocene source rock.

Although we commonly build our models to address a particular question, in a world of limited time and resources, models can be used for multiple purposes, including purposes that were not originally envisioned at the time the models were constructed. In cases where a model is used for a purpose for which it was not originally built, the modeler should always reexamine the uncertainty in the inputs in light of the new questions being asked.

Although we commonly build our models to address a particular question, in a world of limited time and resources, models can be used for multiple purposes, including purposes that were not originally envisioned at the time the models were constructed. In cases where a model is used for a purpose for which it was not originally built, the modeler should always reexamine the uncertainty in the inputs in light of the new questions being asked.

[[file:H4CH12FG8.JPG|thumb|300px|{{figure number|8}}Schematic diagram showing calculated hydrocarbon yields after trap formation as a function of heat flow. At a low heat flow, the source is immature present day and a limited amount of hydrocarbon is generated, and at a high heat flow, the source rock is depleted before the trap forms.]]

H4CH12FG8.JPG|{{figure number|8}}Schematic diagram showing calculated hydrocarbon yields after trap formation as a function of heat flow. At a low heat flow, the source is immature present day and a limited amount of hydrocarbon is generated, and at a high heat flow, the source rock is depleted before the trap forms.

Commonly, when looking at yields or charge, the behavior is nonlinear and at first glance may not be intuitive. In this example, the magnitude of the extension and the amount of lower Miocene missing section do not, as might be expected, bracket the base case. That is, the post-15 Ma yields are higher than the base case for both the minimum and maximum input values. Consider the straightforward nonlinear relationship between hydrocarbon yield after trap formation and the basal heat flow illustrated in [[:file:H4CH12FG8.JPG|Figure 8]]. At a low heat flow, the source rock is immature and too little hydrocarbons are generated, and at a high heat flow, the source rock is depleted before the trap forms. This behavior is clearly nonlinear because both high– and low–heat flow scenarios can generate less yield than the base case. However, in the example case presented, the relationship between yield and basal heat flow is the opposite, both high– and low–heat flow cases generate more yield than the base case. This seemingly nonintuitive behavior is a consequence of the inclusion of multiple source rocks in the model and becomes clear when we examine the yield for the three extension cases in detail ([[:file:H4CH12FG9.JPG|Figure 9]]).

Commonly, when looking at yields or charge, the behavior is nonlinear and at first glance may not be intuitive. In this example, the magnitude of the extension and the amount of lower Miocene missing section do not, as might be expected, bracket the base case. That is, the post-15 Ma yields are higher than the base case for both the minimum and maximum input values. Consider the straightforward nonlinear relationship between hydrocarbon yield after trap formation and the basal heat flow illustrated in [[:file:H4CH12FG8.JPG|Figure 8]]. At a low heat flow, the source rock is immature and too little hydrocarbons are generated, and at a high heat flow, the source rock is depleted before the trap forms. This behavior is clearly nonlinear because both high– and low–heat flow scenarios can generate less yield than the base case. However, in the example case presented, the relationship between yield and basal heat flow is the opposite, both high– and low–heat flow cases generate more yield than the base case. This seemingly nonintuitive behavior is a consequence of the inclusion of multiple source rocks in the model and becomes clear when we examine the yield for the three extension cases in detail ([[:file:H4CH12FG9.JPG|Figure 9]]).

In the base case, the Cretaceous and Jurassic source rocks are depleted by about 25 Ma, and the Miocene source rock barely starts generating during the last 2 m.y. In the minimal extension case, the yield from the Cretaceous and Jurassic source rocks is delayed (relative to the base case) so a significant amount of generation from the Cretaceous and Jurassic sources occurs during the last 15 m.y. In the large extension case, the Cretaceous and Jurassic source rocks are depleted by about 35 Ma, before trap formation, and Miocene source rocks begin generating at 12 Ma instead of at 2 Ma. The net result is that in the base case, little post–trap formation net yield occurs. Volumes of post–trap formation yield are greater than the base case yield in both the minimal and large extension cases. Calculating post–15 Ma hydrocarbon yield as a function of extension allows this effect to be illustrated clearly ([[:file:H4CH12FG10.JPG|Figure 10]]).

In the base case, the Cretaceous and Jurassic source rocks are depleted by about 25 Ma, and the Miocene source rock barely starts generating during the last 2 m.y. In the minimal extension case, the yield from the Cretaceous and Jurassic source rocks is delayed (relative to the base case) so a significant amount of generation from the Cretaceous and Jurassic sources occurs during the last 15 m.y. In the large extension case, the Cretaceous and Jurassic source rocks are depleted by about 35 Ma, before trap formation, and Miocene source rocks begin generating at 12 Ma instead of at 2 Ma. The net result is that in the base case, little post–trap formation net yield occurs. Volumes of post–trap formation yield are greater than the base case yield in both the minimal and large extension cases. Calculating post–15 Ma hydrocarbon yield as a function of extension allows this effect to be illustrated clearly ([[:file:H4CH12FG10.JPG|Figure 10]]).

===Step 6: propagate uncertainty to output properties of interest===

===Step 6: propagate uncertainty to output properties of interest===

The goal of this step is to translate the uncertainties in the key input parameters, as described by the probability distribution functions, to uncertainties in the output properties. In the Monte Carlo approach, this translation is accomplished in a brute force manner by calculating a large number of possibilities based on the possible distributions of input parameters. In the absence of calibration data, the results are saved and used to build distributions for the output properties; however, calibration data can be used to show that some realizations are more probable than others.

The goal of this step is to translate the uncertainties in the key input parameters, as described by the probability distribution functions, to uncertainties in the output properties. In the Monte Carlo approach, this translation is accomplished in a brute force manner by calculating a large number of possibilities based on the possible distributions of input parameters. In the absence of calibration data, the results are saved and used to build distributions for the output properties; however, calibration data can be used to show that some realizations are more probable than others.

The primary advantage of the alternate least squares approach is that it gives more weight to realizations that are better fits to the calibration data. This approach (1) allows explicit weighting of different calibration data, (2) produces no sharp divide between accepted and rejected values, and (3) weights realizations that are better fits to the calibration data more than those that are not. The primary disadvantages of this approach are that (1) it is difficult to build a rigorous objective function (a measure of the fit of the model results to the calibration data) and (2) realizations that are clearly inconsistent with the calibration data will be accepted. The sum of the squares of the residuals (or whatever difference measurement is used) may not be a good measure of the probability that a given model output matches a calibration point because some uncertainty ranges may not be symmetric and, because all realizations are accepted, many unlikely realizations may be accepted. In the additional temperature point example, this alternative approach provides results, but the modeler might not ever recognize that none of the realizations are consistent with both data points. If the same weights were used for each temperature, a most likely result would probably split the difference and not match either point. If the modeler did recognize the issue, it could be addressed by giving the points appropriate weights and/or reevaluating the quality of the calibration data.

The primary advantage of the alternate least squares approach is that it gives more weight to realizations that are better fits to the calibration data. This approach (1) allows explicit weighting of different calibration data, (2) produces no sharp divide between accepted and rejected values, and (3) weights realizations that are better fits to the calibration data more than those that are not. The primary disadvantages of this approach are that (1) it is difficult to build a rigorous objective function (a measure of the fit of the model results to the calibration data) and (2) realizations that are clearly inconsistent with the calibration data will be accepted. The sum of the squares of the residuals (or whatever difference measurement is used) may not be a good measure of the probability that a given model output matches a calibration point because some uncertainty ranges may not be symmetric and, because all realizations are accepted, many unlikely realizations may be accepted. In the additional temperature point example, this alternative approach provides results, but the modeler might not ever recognize that none of the realizations are consistent with both data points. If the same weights were used for each temperature, a most likely result would probably split the difference and not match either point. If the modeler did recognize the issue, it could be addressed by giving the points appropriate weights and/or reevaluating the quality of the calibration data.

The purpose of this article is not to recommend one of these approaches over the other, but to remind the modeler to think about the quality of the calibration data and to understand that multiple approaches are present to incorporate the data. The best option will commonly be problem dependent. For example, a least squares–type approach might be better for weighting a vitrinite reflectance data point from a cuttings sample, where uncertainty exists regarding the measurement, the sample depth, or whether the sample contains reworked material. A reject-accept approach might be better for considering known hydrocarbon accumulations. A spectrum of intermediate cases exists so a hybrid method might prove to be better in some cases than either of the above approaches. For example, there could be some range around each data point that is considered an exact match, a range around that to which some weighting function is applied and then an outer range that is not acceptable.

The purpose of this article is not to recommend one of these approaches over the other, but to remind the modeler to think about the quality of the calibration data and to understand that multiple approaches are present to incorporate the data. The best option will commonly be problem dependent. For example, a least squares–type approach might be better for weighting a [[vitrinite]] reflectance data point from a cuttings sample, where uncertainty exists regarding the measurement, the sample depth, or whether the sample contains reworked material. A reject-accept approach might be better for considering known hydrocarbon accumulations. A spectrum of intermediate cases exists so a hybrid method might prove to be better in some cases than either of the above approaches. For example, there could be some range around each data point that is considered an exact match, a range around that to which some weighting function is applied and then an outer range that is not acceptable.

 

 

 

[[:file:H4CH12FG11.JPG|Figure 11]] shows the resulting thermal profiles for 100 realizations of the hypothetical model described. In panel A of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations are accepted. In panel B of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations within the temperature error bars are accepted. In this filtered case example, it is assumed that a reasonable estimate of the accuracy of the single temperature point exists. Given that assumption, realizations outside the error bars are rejected and those inside the error bars are accepted. If the estimate of the accuracy of the temperature data was less precise, the least squares approach might be a good, or even a better, approach. In either case, if the calibration data are to be given any weight, taking all the realizations and weighting them equally would be a poor choice.

[[:file:H4CH12FG11.JPG|Figure 11]] shows the resulting thermal profiles for 100 realizations of the hypothetical model described. In panel A of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations are accepted. In panel B of [[:file:H4CH12FG11.JPG|Figure 11]], the first 100 realizations within the temperature error bars are accepted. In this filtered case example, it is assumed that a reasonable estimate of the accuracy of the single temperature point exists. Given that assumption, realizations outside the error bars are rejected and those inside the error bars are accepted. If the estimate of the accuracy of the temperature data was less precise, the least squares approach might be a good, or even a better, approach. In either case, if the calibration data are to be given any weight, taking all the realizations and weighting them equally would be a poor choice.

The results from a Monte Carlo simulation can be displayed and analyzed in several ways. For example, [[:file:H4CH12FG12.JPG|Figure 12]] shows the exceedance probability curves for the yield during the last 15 m.y. for one of the drainage polygons. Curves are shown for both the filtered and unfiltered cases ([[:file:H4CH12FG11.JPG|Figure 11]]) to illustrate how rejecting realizations that do not honor the observed temperature data affect the exceedance probability. In this example, filtering the simulation results significantly limits the probability of larger oil yields. [[:file:H4CH12FG13.JPG|Figure 13]] shows a map of the probability of the oil yield (summed for all three source rocks) during the last 15 m.y. being greater than 1 MSTB/km². The map shows regions that have a high probability of having generated a specified yield (1 MSTB/km² in this case), regions that have a low probability, and regions where significant uncertainty exists whether or not a specified yield was generated.

The results from a Monte Carlo simulation can be displayed and analyzed in several ways. For example, [[:file:H4CH12FG12.JPG|Figure 12]] shows the exceedance probability curves for the yield during the last 15 m.y. for one of the drainage polygons. Curves are shown for both the filtered and unfiltered cases ([[:file:H4CH12FG11.JPG|Figure 11]]) to illustrate how rejecting realizations that do not honor the observed temperature data affect the exceedance probability. In this example, filtering the simulation results significantly limits the probability of larger oil yields. [[:file:H4CH12FG13.JPG|Figure 13]] shows a map of the probability of the oil yield (summed for all three source rocks) during the last 15 m.y. being greater than 1 MSTB/km². The map shows regions that have a high probability of having generated a specified yield (1 MSTB/km² in this case), regions that have a low probability, and regions where significant uncertainty exists whether or not a specified yield was generated.

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