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A production engineer is responsible for generating the production forecast for a well or for a field. Where does the engineer start? Darcy’s law gives an estimate of the initial production. The following factors influence how long, or if, the well or field will maintain a plateau production rate:
- drive mechanism
- physical constraint
- well geometry
Once production drops from the peak or plateau rate, the engineer needs an estimate of decline rate. One can quickly realize that, with all these uncertainties, production forecasts are another candidate on which to use risk analysis techniques to help quantify the uncertainty. Ironically, even producing wells with historical data have uncertainty about their decline rates because of errors or omissions in production monitoring and because of noise or erratic production profiles that allow for various interpretations.
Single well production forecast
Table 1 illustrates a simple spreadsheet model for a single-well production forecast. The model has one main assumption, which is that the production is represented using exponential decline for the oil [q = qie–at, and q(n +1) = qne–a], where qi is the annual production of the first year, and a is the annual percentage decline rate. While this model used exponential decline, similar models can be built for linear, harmonic, or hyperbolic declines.
Choice of input distributions
In this simple single-well production forecast, there are only two input distributions required:
- production start rate
- decline rate
The production in time period one (year one) is estimated from Darcy’s Law, a “product model” with factors of permeability, pay (1/viscosity), and so on. Because this is a product, one would expect that the distribution is approximately log-normal. In fact, experience has shown that there is a great deal of uncertainty and variability in production start rates. Thus, not only initial production rate, but also the production in each subsequent time period, is right-skewed.
Decline rate, on the other hand, does not typically have a wide variability in a given reservoir environment. If the production is to be maintained for 10 years, it will be impossible to have a very high decline rate. If the decline rate is too low, we will be simulating an unrealistic recovery of reserves over the forecast period. These constraints, whether practical or logical, lead us to conclude that decline rate is best suited to be represented with a normal distribution.
Simulated production forecast
Fig. 1 shows the production forecast for the well for the first 10 years. The summary graph shows the mean of the profile as well as the interquartile (P25 and P75) and the 90% confidence interval (P5 and P95). Beware, the figure represents the production for individual years, and connecting the points with their envelope forming the P5 line is extremely unlikely to give something that can be called the P5 production forecast.
Producing a forecast with multiple wells
Many times the requirement for a production forecast is not for a single well but for some group of wells. What if our forecast were for a field coming online with 10 wells drilled and ready to produce in Year 1? The model becomes something like shown in Table 2, with further questioning needed for correct modeling. Will the wells be independent of one another, or will the production rates and decline rates be correlated from well to well? The resulting production forecast from the uncorrelated wells case is illustrated in Fig. 2. Notice that this is an aggregation model in which the year-to-year production distributions are nearly normal and the ranges are narrower than we might have intuited. Now look at Fig. 3, the resulting production forecast for the 10 wells, but now with moderated correlation both between the initial production rates and the decline rates among the wells. The effect of this positive correlation is to increase the standard deviation (but not the means) of the forecast year to year.
Finally, consider the opportunity to participate in a sequence of wells similar to the previous example but where we will have one well come online per year. What will our production forecast look like then? It becomes a sequencing-and-aggregation problem, and one can imagine the spreadsheet shown in Table 2 altered so that Well 2 begins in Year 2, Well 3 coming online in Year 3, and so on. Our production forecast is shown in Fig. 4 and looks significantly different from the previous examples. Production increases as each new well is brought on in years 1 through 10, although the earlier wells are each individually declining (as in Fig. 2). Peak production is achieved in Year 10, and the field is on constant decline thereafter.
How these forecasts may be used:
- To help with well timing requirements and facility design.
- To schedule workover frequencies.
- To suggest to the drilling engineers the completion geometry that will optimize production (in concert of course with the reserve estimates and spatial considerations of the productive intervals).
- As input to the economics model(s).
Production forecast with workovers or disruptions
There are many refinements we can make to the model, and one that might come quickly to mind is that there are no interruptions or disruptions to the production. We can implement sporadic or random interruptions by using a binomial variable, where in each time step there is some probability that the production will be stopped or curtailed.
The cash-flow calculation is the one upon which most decisions are based. It is the culmination of the engineering effort. There are three ways that cash flows are currently being calculated under the guise of producing stochastic cash flows. In the first method, deterministic number (usually either most likely or average) estimates are collected from all the engineers (i.e., a single capital expenditure estimate, a single reserve estimate, a production profile, etc.) and then the financial modeler applies some ranges to these estimates (sometimes with input from the engineers) and produces a probabilistic cash flow. This method is clearly inadequate because the probabilistic components must be built from the ground up and not tacked on as an afterthought.
In the second method, P10, P50, and P90 scenarios for each of the inputs to the cash flow model are requested. In this case the financial modeler uses a hybrid-scenario approach:
- all the P10 estimates are combined to get P10 economics
- all the P50 estimates are combined to get P50 economics
- all the P90 estimates are combined to get P90 economics
Even if the percentiles are correct for the cash-flow inputs, why would those percentiles carry through to the same percentiles for net pressure value (NPV) or internal rate of return (IRR)? In fact, they do not.
In the third method, the correct one, the following are retained as probabilistic estimates:
- capital expenditures
- production profiles
The economic model is run as a Monte Carlo simulation, and full probabilistic cash flow (NPV, IRR) estimates result. That is, we build a cash-flow model containing the reserves component as well as appropriate development plans. On each iteration, the field size and perhaps the sampled area might determine a suitable development plan, which would generate capital (facilities and drilling schedule), operating expense, and production schedule—the ingredients, along with prices, for cash flow. Full-scale probabilistic economics requires that the various components of the model be connected properly (and correlated) to avoid creating inappropriate realizations. The outputs include distributions for NPV and IRR.
We extend our example for the single well production profile to predict cash flow, NPV, and IRR for the investment. Table 3 shows the new spreadsheet model, which now has columns for price, capital expenditures, operating expenses and revenue.
- Capital expenditure is an equal investment, occurs once in Year 0, and is a distribution, such as one that would have been obtained from a probabilistic authorization for expenditure (AFE) model
- Production decline
- Price escalates linearly at a fixed annual percentage [p(n +1) = pn × (1 + s)], where s could be 5%, for example.
- Operating expense has a fixed component and a variable component.
- Year-end discounting (Excel standard).
The output from this model now gives us not only the probabilistic production profile but also probabilistic estimates of NPV and IRR, as illustrated in Figs. 5 and 6, respectively. What are the drivers in this model for NPV? Fig. 7 shows the sensitivity graph, in which production dominates the other variables.
Using the third (correct) method, we can answer questions like:
- What is the chance of making money?
- What is the probability of NPV > 0?
- What is the chance of exceeding our hurdle rate for IRR?
These questions are equally applicable whether the economic model is for evaluating a workover or stimulation treatment, a single infill well, an exploration program, or development of a prospect. For prospect or development planning and ranking, the answers to these questions, together with the comparison of the reserves distributions, give us much more information for decision making or ranking the prospects. Moreover, the process indicates the drivers of NPV and of reserves, leading to questions of how best to manage the risks.
No one will argue that it is simple to build probabilistic cash-flow models correctly. The benefits of probabilistic cash-flow models, however, are significant, allowing us to make informed decisions about the likelihood of attaining specific goals and finally giving us the means to do portfolio optimization.
|P||=||probability of an event, dimensionless|
|q||=||annual production, vol/yr|
|qi||=||annual production of the first year, vol/yr|
|qn||=||annual production of the nth year, vol/yr|
|S||=||success event, as in P(S), the probability of success|
Noteworthy papers in OnePetro
Dejean, J.-P. and Blanc, G. 1999. Managing Uncertainties on Production Predictions Using Integrated Statistical Methods. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3–6 October. SPE-56696-MS. http://dx.doi.org/10.2118/56696-MS
Hegdal, T., Dixon, R.T., and Martinsen, R. 2000. Production Forecasting of an Unstable Compacting Chalk Field Using Uncertainty Analysis. SPE Res Eval & Eng 3 (3): 189-196. SPE-64296-PA. http://dx.doi.org/10.2118/64296-PA
Jensen, T.B. 1998. Estimation of Production Forecast Uncertainty for a Mature Production License. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 27–30 September. SPE-49091-MS. http://dx.doi.org/10.2118/49091-MS
Spencer, J.A. and Morgan, D.T.K. 1998. Application of Forecasting and Uncertainty Methods to Production. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 27-30 September 1998. SPE-49092-MS. http://dx.doi.org/10.2118/49092-MS
Lia, O., Omre, H., Tjelmel, H. et al. 1997. Uncertainties in Reservoir Production Forecasts. AAPG Bull. 81 (5): 775-802. http://archives.datapages.com/data/bulletns/1997/05may/0775/0775.htm
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