A Statistical Model To Evaluate Infill Drilling Prospects In An Upper Devonian Field In Central Alberta
Authors: Papst W. , Asgarpour Soheil 
Published: March 2010

Abstract
This paper presents a mathematical model based on Monte Carlo simulation to predict the profitability indicators of future in/ill wells in an Upper Devonian field in central Alberta. A wide range of geophysical and engineering data was obtained from 26 infill wells drilled during 1981–1985. This data provided the distribution of input variables required for Monte Carlo simulation. For other variables such as price forecasts a triangular distribution was assigned. All input variables were tested for dependency.
The proposed model predicts the profitability indicators of infill wells accounting for the technical risk associated with infill drilling and the risk related to future oil and gas prices.

Introduction
The economic success of infill drilling is greatly dependent on uncertain variables such as future oil and gas prices and all variables required to determine incremental reserves and generate production forecasts. Sometimes infill wells accelerate the existing production without contributing to the incremental reserves. Profitability indicators for rate acceleration will be different from those calculated for incremental reserves. Conventional economic evaluation does not consider risk and uncertainty of input variables. Although sensitivities to investment, production costs and forecast take some degree of risk into account, the probability of occurrence of all possible levels of profitability cannot be displayed. In order to evaluate all possible levels of profitability a method is required which includes risk and uncertainty. The Monte Carlo method is the most widely accepted approach to include the inherent risk in investment decisions(1–3).

The Monte Carlo Model
The model developed for infill drilling analysis follows the principles of Monte Carlo simulation outlined in the literature(4–5). The Monte Carlo technique is used to calculate the incremental reserves, annual production rates and the profitability indicators. Incremental reserves are calculated using the volumetricformula,
Np = (A)(l-C)(h)(φ)(l-Sw)(RF)/Bo
where C is a measure of the reservoir continuity, which is defined as the portion of net pay that can be correlated and connected between two or more wells at a particular well spacing. Figure 1 illustrates the distributions and cumulative frequency plots of the input variables for the volumetric formula. If all production from an infill well can be attributed to incremental reserves, the production forecast is described with decline equations in terms of an initial production rate, a decline rate and incremental reserves. For the specific field study the exponential decline equations are used:a = (qi-qa)/Npqt = (qi)e−at
where t is the time in months. Figure 2 shows the distributions and cumulative frequency plots of variables qi and Np. In the event of rate acceleration, normalized production schedules are used as summarized in Table 1.
The economic analysis in the Monte Carlo model is a conventional discounted cash flow calculation including Federal and Alberta Provincial tax:
St = (qt)(Pt) + (GOR)(qt)(Gt)-OC-R-FT-PT
and to discount the annual net cash flows:
Equation Available In Full Paper.
where t is the time in years. Figure 3 illustrates the distributions and the cumulative frequency plots of the input variables Gt, Pt, OC and Ci.