Application of Quantitative Risk Analysis to Pore Pressure and Fracture Gradient Prediction

Abstract

Abstract The present deterministic pore pressure and fracture gradient prediction techniques simplify the input variables from a statistical range of data to a deterministic value, thereby producing over-simplified deterministic pore pressure and fracture gradient results. As a consequence, we lose the ability to quantitatively analyze risks, and we cannot quantify the uncertainties of our pore pressure and fracture gradient prediction. This paper describes a methodology for quantitative risk analysis (QRA) of pore pressure and fracture gradient prediction and shows that applications of QRA in this area will improve the techniques of pore pressure and fracture gradient calculations. In addition, QRA will open a full range of new applications in risk prediction, risks evaluation, risk management, decision making, real-time kick and loss-return risk monitoring, risk control, and casing design. Introduction The present methods of pore pressure and fracture gradient prediction are deterministic approaches that use seismic, logging and drilling data to calculate pore pressure and fracture gradient. The result of the prediction is a single-line curve for pressure and for fracture gradient as shown in Fig. 1. The sources of input variables, such as density log for formation bulk density, sand strength analysis log for Poisson's ratio, resistivity log, seismic or sonic log, and mud log etc, determine that the input data for pore pressure and fracture gradient prediction have randomness in their statistical ranges at any given depth. Therefore, the output results we get from the input data will be statistically distributed. A Gaussian distribution can approximate the probabilistic distribution of pore pressure.1 It is safe to assume that the fracture gradient is a Gaussian distribution as well. To drill safely, we must design the mud weight to balance formation pressure and at the same time not to exceed the formation fracture gradient. The current deterministic techniques design the mud weight by adding a positive safety margin to the estimated pore pressure and a negative margin to the fracture gradient. The bottomhole equivalent hydrostatic pressure or equivalent mud weight (EMW) is a function of mud weight, annular resistance, mud rheological properties, hole cleaning, and pipe moving speed. It is easy to understand that the actual bottomhole EMW has a range of randomness. Study shows that the bottomhole EMW is a Gaussian distribution.2 The deterministic methods simplify the input variables; thereby produce simplified pore pressure and fracture gradient results. This eliminates the ability to quantitatively analyze the risks involved in pore pressure and fracture gradient prediction. Fig. 2 shows the typical distribution of pore pressure, fracture gradient, and bottomhole EMW. It also shows that the three principle output results are combinations of randomly distributed individual input variables. There will be risks of EMW being lower than pore pressure and greater than fracture gradient, and it is important to know the risks involved. The deterministic method could not provide the quantitative risk information on the probabilities of bottomhole EMW to fall below formation pressure or to exceed fracture gradient. The objectives of this paper are to describe a methodology using the QRA method to predict pore pressure and fracture gradient, and to explain the applications of the QRA results. QRA Methodology QRA has been used widely in the construction industries, and also has been used in casing design and well planning by the oil and gas industries.1–3 The QRA approach considers the uncertainty of each input variable and provides comprehensive statistical properties of pore pressure, fracture gradient, and EMW, such as means, deviations, and probabilities. The information will be critical for high-pressure, high-temperature (HPHT) wells when pore pressure and fracture gradient margin is low.