SIMULATION DEMONSTRATES ECONOMICS OF MINNELUSA POLYMER FLOODS

John R. Schuyler
Consultant
Aurora, Colo.

Steven M. Hochanadel
Tiorco Inc.
Englewood, Colo.

Defining some variables with a probability distribution can establish more precisely the economic value of such projects as polymer flooding in the Minnelusa formation.

An enhanced-oil-recovery (EOR) project often presents a difficult investment decision. The substantial risks and performance uncertainties must be carefully weighted against the investment costs.

A Monte Carlo simulation model was used to characterize the incremental economics of a Minnelusa polymer flood. The principal questions addressed were:

What is the likelihood of the EOR project being an economic success?
What is the expected economic benefit of the polymer flood?

With representative field parameters and price projections, the typical Minnelusa polymer flood was found to have a 93% chance of economic success. The expected monetary value (EMV) for the project is $1.6 million.

This expected net gain results from the incremental cost of about $50,000 for additional surface equipment and about $480,000 for chemicals.

Although each project must be evaluated on its own merits, these results present a strong case for considering polymer-augmented floods in the Minnelusa.

MINNELUSA FORMATION

The Minnelusa formation of Wyoming's Powder River basin is a clean, fine-grained sandstone of Pennsylvanian and lower Permian age. There are three principal zones, with most production from the upper A and B zones. The Minnelusa is known for its high permeability variations and adverse mobility conditions. 1

Waterflooding is a common practice, and these floods are often augmented with polymer. The Minnelusa is an excellent waterflood candidate because only 5-15% of the original oil in place (OOIP) is recovered from primary production.

Hochanadel, et al., 2 provide data showing typical waterflood recoveries of about 50% of OOIP. The polymer treatment reduces both the mobility ratio and the permeability variation.

The incremental EOR investment consists of about $50,000 for polymer feed equipment and about $480,000 for chemical costs. The chemical costs are based 2 on a 1% pore-volume slug of cationic polyacrylamide, a 15% pore-volume slug of anionic polyacrylamide and aluminum citrate, followed by a 10% pore-volume slug of anionic polyacrylamide. The chemical costs are expended, at a decreasing rate, over 4 years.

SIMULATION

The authors analyzed the EOR project economics from the context of reservoir, flood performance, and economic uncertainties. What is especially frustrating about this type of evaluation is that one cannot tell, in hindsight, how successful the polymer flood was (or would have been).

The analysis necessarily relies heavily upon the professional judgments, especially the assessment of the polymer improvement.

The decision analysis discipline provides the only logical and consistent way to incorporate judgments about risk and uncertainty into an analysis. Monte Carlo simulation and decision-tree analysis are the two principal evaluation techniques. Both provide solutions based on the expected value concept, and each method has its advantages.

Monte Carlo simulation has more flexibility in allowing the evaluation model to fully represent judgments about uncertain parameters and chance events.

Simulation is needed because closed-form solutions to most real-world problems of interest are not possible. A simple sampling technique provides integration of the expected value equation:

[SEE EQUATION]

where:

EMV is the expected monetary value, the decision parameter to optimize
x is the output value function, usually present value (PV) discounting at the cost of capital rate
p(x) is probability (density) function for x.

When the objective is to maximize a company's value, the optimal decision rule is to choose the alternative having the highest EMV. This rule is sometimes modified for capital-constrained situations and for organizations which have a policy of being conservative.

A simulation model, illustrated in Fig. 1, is a very straightforward extension to a conventional, single-point model. The conventional model is called a "deterministic model" because all values are singly determined.

A simulation cash flow model (Fig. 1) is the same as a deterministic cash flow model except that certain key parameters are represented by distributions instead of by single-point estimates. The simulation process is diagrammed in Fig. 2.

Every trial pass through the model generates a plausible scenario. This can be thought of as automatically generating very many sensitivity runs.

Monte Carlo simulation is appealing because the method is comprehensible and straightforward.

MODEL DESCRIPTION

The detailed economic model generates net cash-flow projections of both a waterflood and a polymer flood. The difference in the net cash-flow streams is the incremental cash-flow projection of the polymer-flood project over a conventional waterflood.

The base data were drawn from Hochanadel, et al. 2 The model recognizes income tax effects, including the enhanced oil recovery credit and the Wyoming state excise tax reduction on new tertiary production. The key model parameters for the base case are:

25% water saturation
1.05 formation volume factor
5.819 million bbl pore volume
1,200 b/d waterflood injection rate, reduced, on average, 1.7% when injecting polymer
8% of OOIP primary production
16% improvement in cumulative oil production of a polymer flood over a waterflood after injecting 100% pore volume.
10%/year PV discount rate
12.5% royalty
34% income tax rate
12% production, severance, and ad valorem taxes; 2% relief on polymer-flood project during the first 5 years
500,000 investment in injection surface equipment for a waterflood; another $50,000 added for a polymer flood
$480,000 chemical cost (in project-start dollars), expended over 4 years
$25,000/month lease operating expense (in project-start dollars), increasing 5%/year plus inflation
$20/bbl starting oil price, corresponding to West Texas intermediate (WTI); adjusted downward 25% or $5/bbl for sulfur content and gravity
5.84%/year average inflation escalation (geometric mean)
1.88%/year average real oil price escalation (geometric mean).

The most critical judgmental input is how much improvement can be expected from a polymer flood. The analysis presented here assumes a normal (bell-shaped) distribution, with a mean of 16% and a standard deviation of 8%. The authors believe this assessment is representative and possibly conservative.

The 16% average improvement is intermediate between:

A set of historical data 2 which averaged 12.7% recovery improvement. The sample included some poorly managed floods and older technology.
Reservoir simulators which predicted higher recoveries. For example, a 43.9% improvement was obtained in a simulation by Mack and Duvall. 1

Fig. 3 shows how base-case recoveries for the two flood types are modeled.

The price and inflation models simulate the trend and dynamics of these economic parameters. Unfortunately, space here does not allow a discussion of the price and inflation models.

However, Fig. 4a illustrates several example simulation trials and the mean annual oil price projection.

Fig. 4b shows confidence bands for oil prices. These figures show the rich representation of oil price behavior that is possible with Monte Carlo simulation.

The initial evaluation model was developed in a Lotus 12-3 spreadsheet.

An add-in simulation program, @RISK, (Palisade Corp.), provided the probability distributions and simulation functions.

The model was subsequently converted to Microsoft QuickBASIC in order to facilitate enhancements and to provide a cleaner representation.

Variables with critical impact on the outcome value were identified with sensitivity analysis. Table 1 shows the mean and 90% confidence interval bounds for the seven variables modeled as chance events.

Fig. 5a summarizes the deterministic sensitivity of the model to the seven chance (stochastic) variables. This type of graph is often rotated clockwise 90 and called a "tornado diagram" because of the profile shape.

This method improves over a conventional sensitivity analysis in that these variables are additionally characterized by their 80% confidence ranges.

Only a decision tree or simulation analysis can determine the effect, within the model, of these variables interacting.

ANALYSIS RESULTS

It is important to note that the simulation result is often substantially different than the answer from a deterministic model. The more accurate simulation value is a product of properly handling the probabilities throughout the calculations. In this example:

Deterministic model: PV = $1.867 million
Simulation model (1,000 trials): EMV = $1.621 0.040 million

An evaluation using the conventional model would have been 15% too high.

A distinguishing feature of a decision analysis is that certain input assessments are represented in the form of probability distributions. Although decision trees can be rolled-forward to calculate a cumulative probability distribution, it requires additional effort.

However, a distribution output is easily obtained from Monte Carlo simulation. The curves for the waterflood, polymer flood, and net models are shown in Fig. 5b.

The leftmost curve is the profile of the cash-flow PV difference between polymer floods and waterfloods. As read from the graph, there is about a 93% chance that the value added by the polymer injection will have a positive PV (thus, economic). The $1.62 million EMV provides the most objective prediction of how much the polymer project adds to the company's value in terms of present value.

Some decision makers prefer a frequency form of presentation, A histogram of simulation outcomes, as shown in Fig. 5C, approximates the probability distribution.

For planning, it is often desired to have confidence curves for production, net cash flow, and other time-spread variables. The mean (i.e., average or EV) annual net cash flow projection for the polymer flood is shown in Fig. 5d.

ADVANTAGES

The EOR model demonstrates how one can explicitly represent risks and uncertainties in an analysis. Even when the data are highly judgmental, most situations are much too complex to evaluate with intuition.

Deterministic models fall short because they do not represent uncertainty. The Monte Carlo simulation model provides the following benefits to an evaluation analysis:

A framework is developed for all aspects of the decision problem. All important details are captured using a flexible, systematic process which can be used at any level of knowledge. The decision model clarifies the problem and facilitates a team analysis.
Judgments are expressed in the form of probability distributions. Instead of a single-point estimate, the full range of possible outcomes and relative likelihoods are represented. With a little practice, most people become comfortable with using probability distributions to represent judgments about uncertainty.
Significantly greater accuracy is achieved when probability distributions are carried through the evaluation model calculations. This is especially important when valuing marginal projects, buy/sell transactions, and risk/benefit trade-offs.
Formerly soft aspects of a decision can be represented explicitly in the decision model. This helps achieve clarity, objectivity, and consistency.

The decision maker's attitudes about different objectives, time value of money, and risk can be expressed quantitatively and, thus, represented consistently in the analysis.

REFERENCES

Mack, J.C., and Duvall, M.L., "Performance and Economics of Minnelusa Polymer Floods." paper SPE 12929, 1984 Rocky Mountain Regional Meeting, Casper, Wyo., May 21-23, 1984.
Hochanadel, S.M., Lunceford, M.L., and Farmer, C.W., "A Comparison of 31 Minnelusa Polymer Floods with 24 Minnelusa Waterfloods," paper SPE/DOE 20234, Seventh Symposium on Enhanced Oil Recovery, Tulsa, Apr. 22-25, 1990.