Inline Setup Provides Automatic Measurement of PVT Behavior of Drilling Fluids

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 204084, “Automatic Measurement of the Dependence on Pressure and Temperature of the Mass Density of Drilling Fluids,” by Eric Cayeux, SPE, NORCE, prepared for the 2021 SPE/IADC International Drilling Conference and Exhibition, originally scheduled to be held in Stavanger, 9–11 March. The paper has not been peer reviewed. The mass density of drilling fluids usually is measured manually with a mud balance. The pressure and temperature dependence of the mass density of the fluid [i.e. its pressure/volume/temperature (PVT) behavior] then is estimated. Variations in the composition of the fluid mix and uncertainties regarding the PVT behavior of each component, however, may lead to inaccuracies. An apparatus that measures the PVT behavior of the drilling fluid contained in a pit directly and automatically has been designed. Inline PVT Measurement The pressure and temperature dependence of drilling fluids can be described by a biquadratic function. However, API Recommended Practice 13D recommends using a linear function of temperature combined with a quadratic form of pressure. Because this process involves six parameters, at least six measurements must be made under different conditions of pressure and temperature. A starting point is to measure the mass density of the fluid under six different pairs of pressures and temperatures. To keep the design of the apparatus as simple as possible, it ideally would not operate under high-pressure and -temperature conditions. Therefore, knowing the range of pressures and temperatures sufficient for taking sample measurements is useful in order to be able to extrapolate the model at higher pressure and temperature conditions with acceptable accuracy. The densitometer’s measurement precision of 0.05 kg/m3 and repeatability of 0.01 kg/m3 is known, so stochastic simulations of the possible measurement error for various spans of investigated pressures and temperatures can be performed. In this study, the authors con-sider that the calibrated PVT model shall be used for a range of pressure of 1000 bar and a range of temperature of 200°C. It is possible to calculate the root mean square of the proportion error between the predicted density value and the “true” value when varying stochastically the systematic bias on the density measurement when the calibration samples are spanning small ranges of pressure and temperature. A possible design for an inline apparatus could be to pump the drilling fluid past a controllable heating element and having a controllable choke downstream of the densitometer apply a pressure while measuring the mass density. The setpoints for the heating element and the choke would be changed six times in order to collect the necessary mass densities to calibrate the PVT model. Changing the temperature of the heating element, however, can require several minutes, and gathering a complete set of calibration measurements may easily take 15 to 30 minutes. An alternative could be to perform six measurements simultaneously. The densitometers can be mounted in series. The configuration could be with six parallel branches or any combinations between series and parallel branches. With two parallel branches, in one branch the temperature of the fluid is not modified, while it is modified in the second branch. For each of the two branches, back pressure is applied at two intermediate positions. This configuration has the advantage of using fewer chokes and pressure sensors (four instead of five).

A Novel Mathematical Model Considering Real Gas PVT Behavior to Estimate Inflow Performance Relationship of Gas Well Production

Inflow performance relationship (IPR) is one of the most important methods for the analysis of the dynamic characteristics of gas reservoir production. The objective of this study was to develop a model to improve the accuracy of the IPR for evaluating and predicting the production of gas reservoirs. In this paper, a novel mathematical model, taking into account the real gas PVT behavior, is developed to accurately estimate the inflow performance relationship. By introducing a pseudo-pressure function and a real gas properties database, this model eliminates the error caused by the linearization method and improves the calculation accuracy. The results show that more than 90% of the energy in the flow field is consumed by inertial forces, which leads to significant high-velocity non-Darcy effects in the gas reservoir. The reservoir permeability, original reservoir pressure, stress sensitivity coefficient, and skin factor have a great impact on the inflow performance relationship of gas reservoir production. This model predicts gas IPR curves with excellent accuracy and high efficiency. The high-precision gas well inflow performance relationship lays a solid foundation for dynamic production analysis, rational proration, and intelligent development of the gas field.

Automatic Measurement of the Dependence on Pressure and Temperature of the Mass Density of Drilling Fluids

Drilling fluids are subjected to large variations of pressure and temperature while they are circulated in a well. This span of pressures and temperatures is so large that the mass density of the drilling mud differs from one depth to another. For a precise estimation of the hydrostatic and hydrodynamic pressures, it is therefore important to have a good estimation of the pressure and temperature dependence of the mass density of drilling fluids. Usually, the mass density of drilling fluids is manually measured with a mud balance. The pressure and temperature dependence of the mass density of the fluid, i.e. its PVT behavior, is then estimated based on the PVT behavior of its components and their relative proportions. However, variations in the composition of the fluid mix and uncertainties on the PVT behavior of each components, may lead to inaccuracies. To circumvent these limitations, an apparatus that measures directly and automatically the PVT behavior of the drilling fluid contained in a pit has been designed. The setup measures both the mass density and the speed of sound in the fluid at specific conditions of pressure and temperature. From the speed of sound in the liquid mix, it is possible to estimate the adiabatic compressibility. The device also utilizes a heat exchanger from which the thermal conductivity and specific heat capacity of the drilling fluid can be estimated. Combining the specific heat capacity, thermal conductivity and the adiabatic compressibility, the isothermal compressibility can be calculated. By combining measurements made at different conditions of pressure and temperature, a PVT model of the drilling fluid is estimated. By providing automatically, and on a continuous basis, the actual PVT behavior of drilling fluids, drilling automation systems can gain in precision and at the same time, their configuration can be simplified, therefore making them more accessible to any drilling operation.

Continuous Two-Domain Equations of State for the Description of the Pressure-Specific Volume-Temperature Behavior of Polymers

The two-domain Schmidt equation of state (EoS), which describes the pressure-specific volume–temperature (pvT) behavior of polymers in both the equilibrium molten/liquid state and non-equilibrium solid/glassy state, is often used in the simulation of polymer processing. However, this empirical model has a discontinuity problem and low fitting accuracy. This work derived a continuous two-domain pvT model with higher fitting accuracy compared with the Schmidt model. The cooling rate as an obvious influencing factor on the pvT behavior of polymers was also considered in the model. The interaction parameters of the equations were fitted with the experimental pvT data of an amorphous polymer, acrylonitrile-butadiene-styrene (ABS), and a semi-crystalline polymer, polypropylene (PP). The fitted results by the continuous two-domain EoS were in good agreement with the experimental data. The average absolute percentage deviations were 0.1% and 0.16% for the amorphous and semi-crystalline polymers, respectively. As a result, the present work provided a simple and useful model for the prediction of the specific volume of polymers as a function of temperature, pressure, and cooling rate.