Ozyurtkan, Mustafa Hakan (Istanbul Technical University) | Altun, Gursat (Istanbul Technical University) | Ettehadi Osgouei, Ali (Istanbul Technical University) | Aydilsiz, Eda (Istanbul Technical University)
Static filtration of drilling fluids has long been recognized as an important parameter for drilling operations. Since the standard laboratory testing procedures only consider static conditions, the filtration and cake properties under continuous circulation and dynamic borehole conditions are not usually well determined. Therefore, the measurement of dynamic filtration is particularly important in order to mimic actual downhole conditions.
An experimental study has been carried out by the ITU/PNGE research group to characterize the dynamic filtration properties of clay based drilling fluids. This study is an impressive attempt to figure out the dynamic filtration phenomena of clay based muds. The experimental results obtained from a dynamic filtration apparatus (Fann Model 90) are reported in this study.
Bentonite and sepiolite clays based muds formulated with commercial additives have been investigated throughout the study. Numerous dynamic filtration histories with test duration of 45 to 60 minutes at temperature conditions ranging from 150 to 400 oF, and a differential pressure of 100 psi have been applied to muds. Three key parameters namely spurt loss volume, dynamic filtration rate (DFR), and cake deposition index (CDI) have been determined to characterize the dynamic filtration properties of mud samples.
Results have revealed that bentonite based muds have better dynamic filtration properties than those of sepiolite muds at temperatures up to 250 oF. However, they have lost their stability over 250 oF. Furthermore, formulated sepiolite based muds have remarkable dynamic filtration rates and cake depositions above 300 oF. To sum up, the experimental results of this study point out that sepiolite based muds might be a good alternative to drill wells experiencing high temperatures, particularly in deep oil, gas and geothermal wells.
In oil and natural gas production projects, many investment and development plans are based on oil and gas reserve estimates. There is a large uncertainty in the calculation of hydrocarbon reserves because the input variables always contain uncertainties to some degree that propagate into reserve estimates. From the view point of a field investment, an accurate assessment of uncertainty in reserves is crucial for making decisions that will create value and/or mitigate loss in value. Therefore, to make good decisions, one must be able to accurately assess and manage the uncertainties and risks. In this study, we present an analytical uncertainty propagation method (AUPM) for modeling of uncertainties on volumetric reserve estimations. Analytical uncertainty propagation equations (AUPEs) are derived based on a Taylor-series expansion around the mean values of the input variables. The AUPEs are general in that correlation among the input variables, if it exists, can also be accounted for on the resulting uncertainty. Comparative studies that we have conducted show that the AUPM is as accurate as the Monte Carlo method (MCM). The AUPM provides a fast alternative to Monte Carlo simulation for accurately characterizing uncertainty markers such as variance, P90, P50, and P10. In addition, we present uncertainty percentage coefficient for simulating uncertainty contribution of each parameter and correlated parameter pairs to the total uncertainty in volumetric calculations.
We also discuss the problem of probabilistic aggregation of reserves for projects involving more than one reservoir or field. We provide a general analytical formulation for estimating the values of mean, variance, P10, P50 and P90 for aggregated estimates. Probabilistic aggregation requires the knowledge of pair-wise correlation of the fields. In this study, we propose uncertainty sorting method (USM) to determine pair-wise correlation coefficients for multiple resources. The method provides a simple and fast analytical approach based on uncertainty percentage coefficient of individual field parameters. Proposed analytical models can be used as a fast tool eliminating the need for MCM.
Uncertainty is inherent in estimation of any type of resources from underground energy systems. Unfortunately, this is also true regardless of any method used for estimation, e.g., volumetric, decline curve, or reservoir simulation methods because the input variables required for the estimation problem always contain uncertainties to some degree that propagate into estimates. Therefore, to make good decisions, one must be able to accurately assess and manage the uncertainties and risks.
In this work, we limit our study to the assessment of uncertainty in oil and gas reserves estimated and probabilistic resource aggregation by the volumetric methods. Volumetric methods are usually used in the early life of oil and gas reservoirs. Estimation of the resources/reserves requires geological, geophysical, and petro-physical data including reservoir area, thickness, porosity, saturations, etc. The values of these input variables have usually large uncertainties associated with them; hence it is very important to propagate these uncertainties on to the estimation of hydrocarbon reserves or resources. Although we use the terms reserve and resources interchangeably here and throughout this paper, their definitions differ indeed; normally reserve is defined as the economically recoverable part of a resource. From the view point of a field investment, an accurate assessment of uncertainty in recoverable and in place reserves is a crucial task from which to make decisions that will create value and/or mitigate loss in value (risk).
Boussinesq equations with improved dispersion characteristics are used to simulate the generation and propagation of waves due to moving pressure fields. With surface pressure terms in the momentum equations the numerical scheme is first run for a moving 3-D hemispherical pressure field for a range of Froude numbers. The wedge angles obtained from simulations are compared with the values calculated from the analytical formulas of Havelock. Furthermore, two ship-like slender pressure fields, representing a moving catamaran, are employed to visualize the interaction of the waves generated. INTRODUCTION The first depth-integrated nonlinear wave model that included the weakly dispersive effects as a non-hydrostatic pressure was derived by Boussinesq (1871) for constant water depth. Much later, Mei and LeMeháute (1966), and afterwards Peregrine (1967) derived Boussinesq equations for variable depth. While Mei and LeMeháute used the velocity at the bottom as the dependent variable, Peregrine used the depth-averaged velocity. Due to wide popularity of the equations derived by Peregrine, these equations are often referred to as the standard Boussinesq equations for variable depth in the coastal engineering community. To obtain a set of equations with better dispersion characteristics Madsen et. al (1991) and Madsen and Sørensen (1992) added higher-order terms with adjustable coefficients into the standard Boussinesq equations for constant and variable water depth, respectively. Beji and Nadaoka (1996) gave an alternative derivation of Madsen et. al’s (1991) improved Boussinesq equations. Liu & Wu (2004) presented a model with specific applications to ship waves generated by a moving pressure distribution in a rectangular and trapezoidal channel by using boundary integral method. Torsvik (2009) made a numerical investigation on waves generated by a pressure disturbance moving at constant speed in a channel with a variable cross-channel depth profile by using Lynett et. al (2002) and Liu & Wu (2004)’s COULWAVE long wave model.
Bilgin, N. (Istanbul Technical University) | Balci, C. (Istanbul Technical University) | Copur, H. (Istanbul Technical University) | Tumac, D. (Istanbul Technical University) | Avunduk, E. (Istanbul Technical University)
Copur, H. (Istanbul Technical University) | Balci, C. (Istanbul Technical University) | Bilgin, N. (Istanbul Technical University) | Tumac, D. (Istanbul Technical University) | Avunduk, E. (Istanbul Technical University)