1 Jun, 2019

Geostatistical Approaches to Prospect Risk

A risk assessment is an estimate of the prospect chance of adequacy (probability) for sufficient hydrocarbon levels to meet or exceed the amount required for minimum economic accumulation. In this article, we will discuss geostatistical approaches for determining the probability of oil and gas in a prospect.

In risk assessment, there are two key questions that must be answered for any exploratory assessment.

1. How much oil and gas may be present – The Volumetric Analysis

2. What is the chance of commercial oil and gas being present – The Risk Assessment

Last month’s Tip of the Month discussed volumetric analysis and how it is used to assess prospects and plays in our industry. This technical series is designed to equip explorationists with the most well-considered approaches to solving the business problems of finding new exploratory resources and a thorough understanding of the fundamentals of assessing oil and gas resources. 

The most crucial step in a risk assessment is to understand the geologic factors controlling oil and gas occurrences. These control factors, if inadequate or missing at the prospect or play being assessed, become the geologic risks that deny success.


Risking Terms – Definitions

Uncertainty: Uncertainty and risk are often used interchangeably in casual conversation. In this course, these terms are distinctly different. Uncertainty relates to measures, or most frequently estimates, of the size of a prospect or play volume factor. For example, in modelling the prospect, we can estimate the thickness of reservoir expected. The geological research might show that the prospective reservoir thickness might range from 20 meters to 35 meters in thickness; this is an expression of uncertainty.

Probability: Probability is the chance that an event will occur. It is expressed as a predicted percentage occurrence of an event. It is important to understand that the events are mutually exclusive, only one will occur.  As an example, we will either find more than 20 meters of reservoir or we will not. If the predicted probability of finding 20 meters of reservoir is 20% it means that as we have modelled the situation we will find in excess of 20 meters of reservoir 20 out of 100 times that we test these conditions.

Risk: The probability of an event normally stated as a negative.  Risk assessment must always relate to a standard and expressed as a measure of risk of a specific event (i.e. reservoir thickness)

Chance of success: Explorationists focus on finding new reserves for the organization and, therefore, use a measure that predicts the positive side of the risk process. Chance of success expresses the probability of finding the critical play or prospect elements or the actual presence of the play or prospect itself. Chance of success is equal to 1 minus Risk. Chance of success may also be called probability of success or abbreviated as COS, COA or POS.

Describing Prospect Risks

Risk must be identified against its alternative circumstance. In exploration, this most often refers to a probability of failure to achieve a predicted condition. If the condition is not defined properly, then risking is useless. Therefore, the first step in risking is to ask the question “risk of what”. This might, for example, be the risk of finding any reservoir rock or it might relate to some required minimum thickness of reservoir rock.

It is very important to align the work and activities of the explorationists with the business of the organization. Based on this, it is best to align the risk with the same critical business measures. Using the example of reservoir thickness from above, the best question might be “what is the risk of not having sufficient reservoir thickness for the prospect to be economic?”



Prediction of probability of meeting minimum economic limit based upon the chance of success of the basic geologic controls:

• Sealed Trap

• Reservoir

• Source

• Recoverability



Chance of success of a prospect or play is the product of the probabilities of the individual prospect elements. Each of these elements is judged against the amount of this factor required to reach the minimum economic reserves.

► Chance of success of minimum economic accumulation not presence or absence

► Used for individual factors and combined for entire accumulation

► 1 minus Risk

► Chance of success of prospect or play equals the product of individual geologic control factors

• Sealed Trap

• Reservoir

• Source

• Recoverability



It is extremely important to establish a standard throughout the organization so that there is a consistent assessment standard by which to compare business options. This allows for a common platform for consideration of prospects generated on far-flung continents to be compared on a fairly even basis.

An important aspect of risk assessment is to convert the assessment that is most often expressed in qualitative terms into a quantitative measure. It is recommended that measures as shown above be applied across the organization to normalize these judgments. Application of new geostatistical techniques and data acquisition methods will help improve quantitative estimates of risk, but the results will still be highly qualitative due to the fact that the real answer will never be known till after drilling occurs.



► Establish a standard throughout the organization

► Implement training that includes practice in making consistent assessments

► Prospect post-mortems to define risking success and refine the process



There are numerous “guides” for estimating the chance of success assessment values. Basically, all of the guides are qualitative.  Though many guides today are automated and self-calculating, overall the input/rationalization is still qualitative.  In short, there is no magic tool to automatically estimate/determine prospect risk. Chance of success assessment is still a humanistic endeavor.

Immediately below are the chance of success guidelines taught in our Prospect and Play Assessment (PPA) course. These values are used for individual risk factors or combined for a prospect or play likelihood.  

Geostatistical Approaches

Care should be taken when assigning values to each of the risk assessment factors. Assistance from other disciplines can provide better answers to provide an informed estimated value. Due to significant advances in geostatistical approaches, we have additional tools available. Quality of output from these approaches is directly proportionate to the quality of the geoscience input; it is important to remember the old computer mantra “garbage in, garbage out.”

Modeling allows the geoscientist to predict reservoir occurrence in much more powerful ways than previously possible. The capability to offer multiple realizations of the reservoir with many options built into three-dimensional presentations bring capabilities that did not exist previously. Geostatistics lends itself to these multiple realizations allowing effective economic analysis. Geostatistics also serves as an excellent mechanism for the integration of geological and geophysical data to generate a three dimensional model of a reservoir that incorporates all available data. Using the modeling process brings the disciplines together to consider a broader range of possibilities that may exist within the data sets and ways to integrate the divergent data.

The traditional approach to geologic modeling was to define the reservoir through the use of horizon maps, facies distribution maps, and top and bottom structural maps. These were used to define reservoir thickness and geometry; then sand/shale ratios, porosity, permeability and other properties that are typically interpolated from well to well and displayed in probability distributions. This approach works reasonably well with fairly isotropic reservoir but is lacking in sufficient detail and variability for reservoirs that are more complex. Geostatistics provides a way for reservoir scientists to more closely approximate the heterogeneous nature of the earth. It will model both structural information and reservoir property data into a three-dimensional model which may be used as a basis for a reservoir simulation study.



There is always a sampling bias in our subsurface data. Conventional petroleum data is extremely biased toward the current structural high points, which may have no relevance to past geologic structures. The well control is neither perfectly random nor perfectly geometrically ordered; thus having a spatial bias. Not all wells are sampled in exactly the same manner so there can be a bias in the sampling of well information. Seismic data is a well ordered dataset however it has it own set of biases. There are imaging limitations, both vertically and horizontally, that can change over the area of the survey due to changes in the acquisition parameters, changes in the processing or merging of surveys and more importantly changes in sub-surface conditions.

Geostatistical analysis is a tool to attempt to remove much of the fundamental biases as well as fill in areas of limited data with distributions of statistically valid populations of potential data. Modern workstations have many built-in algorithms that allow the creation of maps based on either limited or almost unlimited data. The algorithms used have no fundamental concepts of geologic principles so it is the responsibility of the interpreter to understand the use and limitations of each algorithm and when each can and should be applied. In the section below one of the most popular algorithms, cokriging, will be examined.


Geostatistical Overview

There are two categories of geostatistical approaches:

► Estimation methods - best linear estimate

• Kriging, cokriging

• Lacks influence of extremely high or low values

► Multiple simulation methods

• Reproduces variability

• Many equi-probable answers

• How to rank multiple answers


Wolf et al. (1994) describes one application of geostatistical processes:

The geostatistical method is a four-step procedure that calls on several statistical tools. The first step is to quantify the spatial continuity of the well data using Variogram analysis. The second step is to find and quantify a relationship between the well and seismic data. The third step is to use what has been learned to grid the well data using the seismic as a guide via kriging with external drift. The last step is to assess the accuracy of the map just made. Traditionally, a geoscientist creates a map that is assumed correct until additional information becomes available. Only rarely is an estimate made of the map's accuracy. A geostatistician creates an expected value or average map and has a quantitative estimate of its accuracy. Conditional simulation is a geostatistical tool that yields a quantitative measure of the error in a map.

Fig. 2-27


Kriging with External Drift (KED)             

Cokriging is mathematically intensive and but is one of the most popular algorithms in modern workstations. Geostatisticians have also developed an external drift model (KED) to handle an ordered movement (drift) or orientation (skewness) in the data. In this approach, the guide data are directly applied in calculating the weighted averages of the grid points. Practical applications have shown little difference between cokriging and KED. This process is illustrated by Wolf et al. (Figure 2-27).


Conditional Simulation               

Rather than developing a single "best fit" answer as in the kriging or cokriging process, conditional simulation offers a number of plausible solutions – each of which fits the conditions described; each of these equi-probable solutions is a potential answer to the conditions. Typically, a great number of solutions are derived, and statistical analyses are performed. From these analyses, the probability of any occurrence can be determined.

Fig. 2-28  Wolfe et al. (1994) demonstrates a geostatistical approach to assessment.


Fig. 2-29  Base map with hand contoured thickness estimates.


Fig. 2-30  These same data can be computer contoured.


Fig. 2-31  The seismic horizon equivalent to the sandstone – note amplitude changes along the interval.


Fig. 2-32  Relationship between Seismic amplitude and sand thickness


Fig. 2-33  Distribution of seismic amplitudes


Fig. 2-34  One of the realizations from the geostatistical analysis.


Fig. 2-35

Thicknesses were then arranged in ascending order and plotted on a graph, Figure 2-36. This is a compilation for sand thickness estimates at the location. In the prospect risk assessment, there were many trials run to predict the thickness of the reservoir at the prospect drill site. These predictions are shown here in a histogram. Previously it was determined that 40 feet of sandstone is required to satisfy economic minimum. In this case, thirty-five percent of the outcomes were less than 40 feet. Risk for reservoir thickness in this prospect is therefore 0.35; which means that if you drill a prospect like this there is a 35% probability of failure based only on sand thickness. Adequacy for reservoir at this prospect location is 0.65 (1 – risk or 1.0 – 0.35). Keep in mind that when this prospect is drilled, only one thickness of sandstone will actually be found!

Fig. 2-36  Sand Distribution


The following map displays the data generated in the last few slides at all points on the map and computes the possibility of having less than 40 feet of sand. A preferred format would be to display the probability of having more than the economic minimum, a more positive view.

Figure 2-37  

Wolfe et al. (1994) demonstrates a geostatistical approach to assessment. In their method, 200 realizations are generated for thickness of sand at a prospect location, and then ranked from low to high. Thicknesses were then arranged in ascending order and plotted on a graph (see illustration below). This is an assessment curve for sand thickness at the location being considered.

Figure 2-38  

In this example, the median sand thickness expected is 46.5 feet and there is, for example, an 80% probability of having 32 feet or more of sand at the modeled location. This type of analysis can be conducted for any location on the map or for any number of parameters. Another possibility with the data set is to plot the economic threshold for a specific location and then directly read the probability of exceeding that value. The next illustration demonstrates that approach.

Figure 2-39  


Risk Assessment Curve

The final step in this evaluation process would be to combine the chance of adequacy predictions with the unrisk assessment curve (Figure 2-41). The combination results in a second curve, the risk assessment curve. This display will represent our full assessment of the potential sizes of the successful evaluated accumulation and its chance of adequacy.  

Figure 2-41  Risk assessment curve.


The risk assessment curve demonstrates the probability of finding each reserve amount. The difference with the unrisk curve is that the risk curve considers those cases that are dry holes or less than economic minimum. In this example, the average result of all cases, successes, and failures, has a risk mean reserves of 35 million barrels. This value is derived by multiplying the unrisk mean reserve (140 million barrels) by the prospect adequacy (0.25).

Risk reserve calculations can be very misleading. The curve does not represent reality; it represents the statistically adjusted results if a significant number of tests just like this one were drilled. It combines the volumes for successes and failures, artificially reducing the mean size of successful prospects. To use this curve for decision-making for a single test gives simulated results that do not reflect realism.

A question then follows; if a risk-adjusted assessment does not represent reality, why make the calculation? The easy answer is that when a drilling program is considered, the sum of the risk means should equal the total reserves found in a successful program. It does not identify which prospects will contribute reserves and which will be failures. Used carefully, the risk mean may be employed as a tool to compare prospects or plays. In summary, risk mean reserves are important estimations if a population is considered, but dangerous when applied to a single prospect.

It is extremely important to establish a standard throughout the organization so that there is a consistent assessment by which to compare business options. This allows for a common platform for consideration of prospects generated worldwide to be compared on a fairly even basis.
An important aspect of risk assessment is to convert the assessment that is most often expressed in qualitative terms into a quantitative measure. It is recommended that measures as shown above be applied across the organization to normalize these judgments.

Some practical steps your company can take:

► Establish a single standard throughout the organization in order that

• Assessments can be compared on the same basis

• Assessments are consistent through time

► Make sure that the assessments are compatible with the corporate:

• Business processes

• Language

• Comfort for risk

• Culture 

► Implement training that includes practice in making consistent assessments

► Conduct Prospect after drill reviews to define risking success

Risk assessment is an important tool in aligning the work and activities of explorationists with the business of the organization. To learn more about risk assessment in prospects or plays, we recommend enrolling in the upcoming session of Prospect and Play Assessment (PPA).

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