Wall Pressures In a Channel Flow Obstructed By a Line of Inclined Rods: Invariant Groups and Semi-Empirical Correlations

An experiment is conducted in a rectangular channel obstructed by a transverse line of four inclined cylindrical rods. The wall pressure around the perimeter of a central rod and the pressure drop through the channel are measured varying the inclination angle of the rods. Three assemblies of rods with different diameters are tested. The measurements were analyzed applying momentum conservation principles and semi-empirical considerations. Several invariant dimensionless groups of parameters relating the pressure at key locations of the system with characteristic dimensions of the rods are produced. It was found that the independence principle holds for most of the Euler numbers characterizing the pressure at different locations, that is, the group is independent of the inclination angle provided that the inlet velocity projection normal to the rods is used to non-dimensionalize the pressure. The resulting semi-empirical correlations can be useful for designing similar hydraulic units.

Novel Analytical Solution and Type-Curves for Lost-Circulation Diagnostics of Drilling Mud in Fractured Formation

Loss of circulation is a major problem that often causes interruption to drilling operations, and reduction in efficiency. This problem often occurs when the drilled wellbore encounters a high permeable formation such as faults or fractures, leading to total or partial leakage of the drilling fluids. In this work, we present a novel semi-analytical solution and type-curves that offer a quick and accurate diagnostic tool to assess the lost-circulation of Herschel-Bulkley fluids in fractured media. Based on the pressure and mud loss trends, the tool can estimate the effective fracture conductivity, the cumulative mud-loss volume, and the leakage period. The behavior of lost-circulation into fractured formation can be assessed using analytical methods that can be deployed to perform flow diagnostics, such as the rate of fluid leakage and the associated fracture hydraulic properties. In this study, we develop a new semi-analytical method to quantify the leakage of drilling fluid flow into fractures. The developed model is applicable for non-Newtonian fluids with exhibiting yield-power-law, including shear thickening and thinning, and Bingham plastic fluids. We propose new dimensionless groups and generate novel dual type-curves, which circumvent the non-uniqueness issues in trend matching of type-curves. We use numerical simulations based on finite-elements to verify the accuracy of the proposed solution, and compare it with existing analytical solutions from the literature. Based on the proposed semi-analytical solution, we propose new dimensionless groups and generate type-curves to describe the dimensionless mud-loss volume versus the dimensionless time. To address the non-uniqueness matching issue, we propose, for the first time, complimentary derivative-based type-curves. Both type-curve sets are used in a dual trend matching, which significantly reduced the non-uniqueness issue that is typically encountered in type-curves. We use data for lost circulation from a field case to show the applicability of the proposed method. We apply the semi-analytical solver, combined with Monte-Carlo simulations, to perform a sensitivity study to assess the uncertainty of various fluid and subsurface parameters, including the hydraulic property of the fracture and the probabilistic prediction of the rate of mud leakage into the formation. The proposed approach is based on a novel semi-analytical solution and type-curves to model the flow behavior of Herschel-Bulkley fluids into fractured reservoirs, which can be used as a quick diagnostic tool to evaluate lost-circulation in drilling operations.

Formation of spiral waves in cylindrical containers under orbital excitation

The lowest swirling wave mode arising in upright circular cylinders as a response to circular orbital excitation has been widely studied in the last decade, largely due to its high practical relevance for orbitally shaken bioreactors. Our recent theoretical study (Horstmann et al., J. Fluid Mech., vol. 891, 2020, A22) revealed a damping-induced symmetry breaking mechanism that can cause spiral wave structures manifested in the so far widely disregarded higher rotating wave modes. Building on this work, we develop a linear criterion describing the degree of spiralisation and classify different spiral regimes as a function of the most relevant dimensionless groups. The analysis suggests that high Bond numbers and shallow liquid layers favour the formation of coherent spiral waves. This result paved the way to find the predicted wave structures in our interfacial sloshing experiment. We present two sets of experiments, with different characteristic damping rates, verifying the formation of both coherent and overdamped spiral waves in conformity with the theoretical predictions.

Dimensional characterization of heat flux in aquifers with horizontal water flow. Velocity estimation from temperature-depth profiles

From the dimensionless governing equations obtained through an adequate selection of dependent and independent dimensionless variables, and the use of spatial discrimination, the dimensionless groups that govern the solution patterns of the heat transfer problem in aquifers with horizontal flow velocity are determined. As a boundary condition on the surface, the cases of constant and harmonic temperature are studied. The emergence of a characteristic length that, in its dimensionless form, depends on the deduced groups, allows the direct determination of the water flow from experimental measurements of the temperature profiles in the classical form of the inverse problem.

Estimation of Cuttings Concentration and Frictional Pressure Losses During Drilling Using Data-Driven Models

Drilling practice has been evolving parallel to the developments in the oil and gas industry. Current supply and demand for oil and gas dictate search for hydrocarbons either at much deeper and hard-to-reach fields, or at unconventional fields, both requiring extended reach wells, long horizontal sections, and 3D complex trajectories. Cuttings transport is one of the most challenging problems while drilling such wells, especially at mid-range inclinations. For many years, numerous studies have been conducted to address modeling of cuttings transport, estimation of the concentration of cuttings as well as pressure losses inside the wellbores, considering various drilling variables having influence on the process. However, such attempts, either mechanistic or empirical, have many limitations due to various simplifications and assumptions made during the development stage. Fluid thixotropy, temperature variations in the wellbore, uncertainty in pipe eccentricity as well as chaotic motion of cuttings due to pipe rotation, imperfections in the wellbore walls, variations in the size and shape of the cuttings, presence of tool joints on the drillstring, etc. causes the modeling of the problem extremely difficult. Due to the complexity of the process, the estimations are usually not very accurate, or not reliable. In this study, data-driven models are used to address the estimation of cuttings concentration and frictional loss estimation in a well during drilling operations, instead of using mechanistic or empirical methods. The selected models include Artificial Neural Networks, Random Forest, and AdaBoost. The training of the models is determined using the experimental data regarding cuttings transport tests collected in the last 40 years at The University of Tulsa – Drilling Research Projects, which includes a wide range of wellbore and pipe sizes, inclinations, ROPs, pipe rotation speeds, flow rates, fluid and cuttings properties. The evaluation of the models is conducted using Root Mean Square Error, R-Squared Values, and P-Value. As the inputs of the data-driven models, independent drilling variables are directly used. Also, as a second approach, dimensionless groups are developed based on these independent drilling variables, and these dimensionless groups are used as the inputs of the models. Moreover, performance of the data-driven model results are compared with the results of a conventional mechanistic model. It is observed that in many cases, data-driven models perform significantly better than the mechanistic model, which provides a very promising direction to consider for real time drilling optimization and automation. It is also concluded that using the independent drilling variables directly as the model inputs provided more accurate results when compared with dimensional groups are used as the model inputs.

Non-Stationary Contaminant Plumes in the Advective-Diffusive Regime

Porous media with low/moderate regional velocities can exhibit a complex dynamic of contamination plumes, in which advection and molecular diffusion are comparable. In this work, we present a two-dimensional scenario with a constant concentration source and impermeable upper and lower boundaries. In order to characterise the plume patterns, a detailed discriminated dimensionless technique is used to obtain the dimensionless groups that govern the problem: an aspect ratio of the domain including characteristic lengths, and two others relating time and the horizontal length of the spread of contamination. The monomials are related to each other to enable their dependences to be translated into a set of new universal abacuses. Extensive numerical simulations were carried out to check the monomials and to plot these type curves. The abacuses provide a tool to directly manage the contamination process, covering a wide spectrum of possible real cases. Among other applications of interest, they predict the maximum horizontal and transversal plume extensions and the time-spatial dependences of iso-concentration patterns according to the physical parameters of the problem.

Semi-analytical model to predict the performance of cyclic steam stimulation oil wells

Prediction of the performance of oil wells under Cyclic Steam Stimulation (CSS) is challenging in complex and heterogeneous reservoirs, especially with limited data. Analytical and numerical simulation models do not usually give accurate predictions in such conditions. In this work, a semi-analytical model was developed to determine consistent mathematical relationships between the injected steam and some of the effective oil production parameters for more accurate prediction of oil production rates. Field investigation indicates that the change of the Cumulative Oil to Steam Ratio (COSR) to production days is related to a group of effective oil production parameters. This group of parameters includes the cumulative injected steam relative to the drainage volume, the oil net pay thickness relative to the gross pay thickness, and the vertical permeability relative to the thermal diffusivity. These parameters were arranged in two dimensionless groups. It was found that plotting these two dimensionless groups on Log–Log scale for any reservoir yields a straight line (correlation). For any reservoir under CSS, measurements of two steam cycles are sufficient to identify the constants of the proposed correlation. This method has been applied and validated on six reservoirs with different reservoir characterizations. Six different wells with a total of 43 steam cycles from these reservoirs were analyzed with the same approach. The mathematical relationships of the dimensionless groups were calculated, and the Log–Log plot was constructed for each well using the data of the first two cycles. Then, the proposed correlation was developed for each well and used to predict the well performance starting from the third steam cycle. At the end, the predicted performance of each well was compared with the corresponding actual measurements. The results showed that the average absolute percentage deviation between the actual and the predicted cumulative oil production through the well lifetime is less than 5% for the six wells. In addition, the absolute instantaneous deviation between the actual and the predicted cumulative oil production for each individual cycle in all cases is (1) less than 15% for about 42% of the tested CSS cycles, (2) between 15 to 25% for about 39% of the tested CSS cycles, and (3) higher than 25% for about 19% of the tested CSS cycles. This work is considered an original contribution to develop dimensionless relationships that can be used to predict the oil production of the CSS operations for reservoirs with limited data. The required data are the historical production rate, steam injection rate, and basic petrophysical parameters.

Hydrology without Dimensions

<div> </div><div> <div> <div>Dimensional analysis offers an ideal playground to tackle complex hydrological problems. The powerful dimension reduction, in terms of governing dimensionless groups, afforded by the PI-theorem and the related self-similarity arguments is especially fruitful in case of nonlinear models and complex datasets. After briefly reviewing these main concepts, in this lecture I will present several applications ranging from hydrologic partitioning (Budyko's curve) and stochastic ecohydrology, to global weathering rates and soil formation, as well as landscape evolution and channelization. Since Copernicus-dot-org asks me to add at least 25 words to the abstract, I would like to thank the colleagues who supported my nomination for the Dalton medal and my many collaborators.</div> </div> </div>