Fractured Reservoir Evaluation Using Monte Carlo Techniques (includes associated paper 16991 )

Abstract

Summary. Pro forma cash-flow analysis of petroleum ventures usually isconsidered as a dterministic model. In the last 10 years, Monte Carlo analysishas allowed the introduction of probability distributions of input variables inplace of single-valued functions. Reserve determination and rate scheduling inthese current Monte Carlo techniques have relied on the volumetric formula, which works well in nonfractured reservoirs. Recent massive drilling in fractured reservoirs has rendered this approachunusable. This paper develops a variation of the Arps rate-cumulative equationas a basic model for the determination of the distribution of original reservesand the decline rates. Continuation of the Monte Carlo technique into netpresent value analysis and internal rate of return (IRR) is also developed. Introduction Estimating the profitability of petroleum ventures is a risky business atbest. The prices of oil and gas are not the least of many uncertain variablesin any standard cash-flow model. Friedman used the idea of Monte Carlosimulation in competitive bidding strategy. Hertz popularized teh idea of MonteCarlo modeling to treat uncertainty in a business situation. Several authorshave applied this concept to petroleum ventures, particularly in the earlystages of development of a reservoir or even during exploration. The basicmodel used in these calculations has always been the volumetric model outlinedbelow. That approach works well in conventional reservoirs where porosity, netthickness, and recovery factor can be measured or estimated. In tight ornaturally fractured reservoirs, however, the volumetric approach fails becausethe hydrocarbons are not in an isotropic, homogeneous matrix as in conventionalreservoirs but instead are confined largely to the fracture system. A MonteCarlo model for fractured reservoirs using the general approach is outlinedbelow, but it is based on the Arps rate-cumulative and rate/time empiricalequations. The model is used to determine both the distribution of reserves andthe extraction schedule that woudl result. These lead to computation of the netpresent value of the reserves. The volumetric formula is based on the equation (Equation 1) P. 71^