J. Energy Resour. Technol. 1989;111(4):205-213. doi:10.1115/1.3231425.

This paper presents Chevron Oil Field Research Company’s operating experience using the sonic nozzle as a proving device for measuring natural gas flows in field tests. The nozzle reference flow rate was used for calibrating orifice, turbine, and vortex meters in three tests with a pipeline quality gas and an unprocessed natural gas as the working fluid. For pipeline gas, the field calibration results show good agreement between the sonic nozzle reference and a turbine meter while the accuracy of orifice metering is size dependent. The 4-in. (102-mm) orifice meter flow rates agree well with the nozzle reference, but the 16-in. (406-mm) orifice flow measurements are up to 2 percent lower. Deviations between the test meters and the sonic nozzles are generally larger for the unprocessed gas. These field projects demonstrate that sonic nozzles can be operated successfully as a prover for processed natural gas, while more work is needed to study the critical flow in nozzles for unprocessed natural gas.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):214-220. doi:10.1115/1.3231427.

Free convection in rectangular porous media has been numerically investigated incorporating the dependence of fluid density on temperature in all the conservation equations. The fluid density dependence on temperature is described through a parametric equation which can be used for different fluids. The method of successive accelerated replacement scheme has been employed to obtain numerical results for a wide range of Rayleigh numbers, 50 to 1000, aspect ratio, 0.1 to 10 and density difference ratio of 0 to 0.75. The increase in the average Nusselt number at a Rayleigh number of 100 and an aspect ratio of unity is 9.57 percent when density difference ratio is 0.25, whereas it is as high as 19.88 percent when the density difference ratio is 0.5.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):221-230. doi:10.1115/1.3231428.

The linear analysis in the frequency domain is presented for the surge motion of a tension leg platform (TLP) in the case of random waves only and random waves with constant current. A single-degree-of-freedom model of a TLP is employed for response. The superposition method, one of the simulation techniques, is applied to random sea wave, and the response analysis of TLP in time is developed with wave velocity and wave acceleration simulations. Wave-induced forces are calculated using the modified Morison equation, which takes into account relative motion. Computational methods for both analyses are developed, and the results of stochastic, dynamic response of the TLP, with and without the presence of current, are presented and compared.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):231-238. doi:10.1115/1.3231429.

A general analytical approach which directly determines the optimum thermodynamic and economic behavior of thermal systems and which is described in detail in von Spakovsky and Evans (1987) and von Spakovsky (1986) is briefly discussed here in the context of establishing a “stable economic environment” around each cycle component. Such environments allow for isolated, individual component optimizations which need not to be performed at the time the system is optimized, but which nonetheless correspond to some overall system optimum. In these environments, very “detailed” thermoeconomic component models can be optimized without the added complications resulting from a consideration of all the other system variables. The development and optimization of these “detailed” models is illustrated using the example of a feedwater heater. Utilizing the Second Law and typical Second Law costing techniques, the method presented here provides for the creation of mathematical models which balance operating costs and capital expenditures. Such models can be solved numerically for the optimum design point or the optimum operating point of a thermal system and each of its components.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):239-245. doi:10.1115/1.3231430.

We are currently investigating the engineering feasibility of drilling into an active magma body at a depth of roughly 5 km from the earth’s surface, establishing a downhole heat exchange region, and extracting thermal energy from the magma body by circulating fluid through this heat exchange region. In the present paper, we evaluate the overall thermodynamic performance of a conceptual magma energy system in which energy is added as heat to the fluid within the magma region and is converted to useful work in a power conversion cycle at the surface. Unusually high return temperatures and pressures may be available at the wellhead of such a circulating well. Investigated here is an open Rankine power system in which heated water from the magma well is circulated directly through a power conversion cycle. The downhole heat exchange region is established during the drilling process. As drilling proceeds into the magma, a solidified layer forms about the drilling tube due to heat exchange to the fluid. This solidified layer thermally fractures because of large temperature gradients between the cooled inner region and the heater outer region, thereby opening secondary flow paths. Two models of the downhole behavior have been used. In the simplest approach, denoted as the “infinite area model,” the water entering the pipe to return to the surface is assumed to be always at the temperature of the magma, independent of mass flow rate and other parameters. The other model is more detailed and the fractured heat exchange region is modeled as a cylindrical porous layer through which fluid flows vertically. The net power and other performance aspects for the systems are investigated in terms of various parameters, including the characteristics of the downhole heat transfer. It is concluded that the open Rankine cycle probably will not be appropriate for this application; however, the analysis provides the first insights into possible characteristics of this energy resource.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):246-249. doi:10.1115/1.3231431.

General nondimensional iso-deflection and iso-bending moment curves for the elastic response of orthotropic rectangular plates under lateral pressure pulse are presented. Similarities of loads and plate properties are employed to develop the curves, which represent the peak response for various combinations of orthotropy, density, geometry and loading. The presented curves are valid within the elastic small deflection theory of plates, and their usefulness and limitations are discussed in the paper.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):250-253. doi:10.1115/1.3231432.

We consider the test-problem of simple shearing of a thermoviscoplastic solid subject to steady or time-dependent boundary velocities or shear forces. Previously derived stability and nonlocalization criteria are presented. The influence of boundary conditions on the time-asymptotic “solution,” the role of nonuniformities and the localization of plastic deformation are discussed. Finally, a perturbation analysis of homogeneous solution under steady boundary velocities or stresses of a material with a gradient-dependent flow stress is presented and “shear-banding” criteria are derived.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):254-257. doi:10.1115/1.3231433.

A new one-dimensional theory for estimating the dynamic yield strength of materials, based on post-test measurements of Taylor impact specimens, has been developed by the authors. This theory offers the advantage of mathematical simplicity, while requiring only measurements of final specimen length, final undeformed length, and impact velocity as experimental data inputs. It is observed that the theory can accommodate a variety of material constitutive relations while preserving its basic simplicity. In particular, the dynamic material strength on impact, Y , can be directly correlated with impact velocity V through the relation Y = − Y 0 − BV 2 . Here Y 0 is the static yield strength and B is a material constant. This relation provides a rate-dependent constitutive law that is potentially useful in situations such as rod penetration, for example.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):258-263. doi:10.1115/1.3231434.

Friction pile settlement in frozen ground is tyically predicted on the basis of a creep equation relating shear stresses at the soil/pile interface to pile displacement rates. Creep parameters are used to characterize soil type, soil/ice structure, temperature, and loading conditions. Experimental tests involving model steel piles embedded in frozen sand provided data showing that change in a given test variable can alter the numerical value for some of the creep parameters. The test variables included static, incremental, and dynamic loading; pile surface roughness; soil ice content; and sand particle size. Changes observed included the apparent effect on creep rate when a small dynamic load was superimposed on the static load. A tabulation of observed creep parameter changes is included.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):264-269. doi:10.1115/1.3231435.

Schemes for the disposal of medium to high level atomic waste involve placing the spent material in repositories deep within stable rock formations. The waste will continue to generate heat after storage underground, and it is of interest to be able to predict the effects of this heating on the surrounding rock, as this may lead to cracking of the rock and the potential contamination of ground water. A solution method is presented for problems involving decaying heat sources of rectangular shape which lie within horizontally layered materials. The method requires very little computer storage (unlike finite element and finite difference techniques) and may easily be implemented on microcomputers. Solution of the time-dependent problem is achieved by applying Laplace transforms to the field variables, solving the resulting equations, and then using numerical inversion to obtain the solution in real time.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):270-278. doi:10.1115/1.3231436.

Stress distribution in a rock material containing cracks, without thickness, and joints, with thickness, is controlled by two basic principles, namely equilibrium and compatibility. Two deformation models representing these two basic requirements are used to construct the rock mass’ local composite moduli that are then combined to obtain the rock mass’ global moduli. Deformational modes in the form of compliances give upper and lower value moduli representing the constraints of compatibility and equilibrium, respectively. In a loaded rock mass there is no stress redistribution involved in the application of the equilibrium model, while for the compatibility model there are stress redistributions. For cracks, with no thickness, only the equilibrium model defines the deformation moduli, whereas for joints both the equilibrium and compatibility models are required because of the joint’s volume effects. Using both the joint’s shear strength and the Griffith’s crack initiation criteria, the Griffith’s strength loci for firm-hard and soft rock masses are produced. The strength loci representing normal and shear failure modes for the firm-hard rock mass are significantly different, whereas for the soft rock mass they are similar.

Commentary by Dr. Valentin Fuster
J. Energy Resour. Technol. 1989;111(4):279-283. doi:10.1115/1.3231437.

The problem of estimating the nonlinear parameters associated with the hyperbolic decline curve equation is considered in this paper. Estimation equations are developed to estimate these nonlinear parameters. The condition under which the results can be used to predict future oil productions is examined using actual field data. An approximate linear term is obtained from the nonlinear hyperbolic equation through Taylor’s series expansion, and the optimum parameter values are determined by employing the method of least squares through an iterative process. The estimated parameters are incorporated into the original hyperbolic decline equation to provide realistic forecast function. This method does not require any straight line extrapolation, shifting, correcting and/or adjusting scales in order to estimate future oil and gas predictions. The method has been successfully applied to actual oil production data from a West Cameron Block 33 Field in South Louisiana. The results obtained are provided in Fig. 1.

Commentary by Dr. Valentin Fuster


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