Changes

''¹The base case used the "Most Likely" values. The "Minimum" and "Maximum" values were used in the screening step and as bounds on the Monte Carlo distributions.''

''¹The base case used the "Most Likely" values. The "Minimum" and "Maximum" values were used in the screening step and as bounds on the Monte Carlo distributions.''

''²oHI = original [[hydrogen]] index of the [[source rock]]; oTOC = original [[total organic carbon (TOC)|total organic carbon]] content of the source rock; OMT = organic matter type of the source rock.

''²oHI = original [[hydrogen]] index of the [[source rock]]; oTOC = original [[total organic carbon (TOC)|total organic carbon]] content of the source rock; OMT = organic matter type of the source rock.

===Step 3: identify and estimate uncertainty in input parameters===

===Step 3: identify and estimate uncertainty in input parameters===

In addition to the uncertainties in source type, kinetics, and thickness, it is hypothesized that uncertainties in the depths, amount of missing (eroded) section, lithology (rock properties), shale grain conductivity, radiogenic heat contribution, surface temperature, and basal heat flow (magnitude and timing of extension) could significantly affect the outcome of the model. The estimations of uncertainty in these input parameters are listed in the “Minimum” and “Maximum” columns in Table 2.

In addition to the uncertainties in source type, kinetics, and thickness, it is hypothesized that uncertainties in the depths, amount of missing (eroded) section, lithology (rock properties), shale grain conductivity, radiogenic heat contribution, surface temperature, and basal heat flow (magnitude and timing of extension) could significantly affect the outcome of the model. The estimations of uncertainty in these input parameters are listed in the “Minimum” and “Maximum” columns in Table 2.

===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.

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.

[[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.]]

[[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.]]

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.

====Nonlinear behavior====

====Nonlinear behavior====

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.

How should realizations that fall outside the range of the calibration data be handled? One approach would be to reject those realizations as not appropriate. An alternative approach is to accept all realizations, but weight the results based on the fit to the calibration data using a weighting parameter related to the fit to each calibration point. “Fit” in this case is based on a least squares analysis. Both approaches have advantages and drawbacks.

How should realizations that fall outside the range of the calibration data be handled? One approach would be to reject those realizations as not appropriate. An alternative approach is to accept all realizations, but weight the results based on the fit to the calibration data using a weighting parameter related to the fit to each calibration point. “Fit” in this case is based on a least squares analysis. Both approaches have advantages and drawbacks.

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.