Pressure Buildup Analysis Research Articles

Well - test analysis for wells with gas rich CO2 in carbonate reservoir Song Hong Basin

The evaluations of properties of carbonate reservoirs containing gas with very high carbon dioxide (CO2) content often face many difficulties. In fact, there is a significal difference in interpretation results compared to conventional gas well testing due to: there is a gas to liquid phase transition; noise, abnormal increase or decrease in pressure and temperature during flow period, etc. These abnormal behaviors are all directly related to the specificity of CO2 properties with high compressible than that of natural gas, which can vary greatly density and can reach supercritical liquid state, transitioning solid to liquid or liqid to gaseous states even when pressure and temperature changes within a small range. During the testing of gas wells with high CO2 content, the phenomenon of pressure drop while pressure buid-up often occurs, leading to the analysis of reservoir parameters according to the conventional pressure build-up analysis method usually not feasible. The content of the article is aimed at researching and applying the method of interpreting well test data in the drawdown period while multi-rate flowing to more accurately estimate reservoir properties and mitigate risks in the design of the field development plan to achieve the economic efficiency.

Guest Editorial: Want To Learn Something New About DFITs? Start With an Old Book

Early in the development of unconventional reservoirs, the industry had little choice but to rely on the toolsets handed down from decades of conventional engineering practices. Later, new tools would be crafted in the hopes of better fitting the unconventional paradigm. This presents a choice to the technical community—rely on a traditional and proven method, or one designed for the unconventional system but less tested? Recently, many hydraulic fracturing engineers have been asking themselves this question when it comes to the diagnostic fracture injection test (DFIT). That includes myself, and the journey I took to find an answer culminated in a technical paper (SPE 206239) that was presented at the 2021 SPE Annual Technical Conference and Exhibition. What follows are some of that paper’s key findings which are being shared with the intent to further the discussion on best practices for those challenged with interpreting unconventional diagnostics. The paper utilizes the concept of permeability to validate traditional minimum stress interpretations across multiple reservoir conditions by comparing DFIT fracture closure time permeability estimates with core, pressure buildup, after-closure pressure, and rate transient analysis. This author was able to further support the results by the integration of a wide range of diagnostic technologies such as fiber optics, microseismic, and, among others, DFIT numerical inversions shared through eight case histories. Diagnostic Injections, a Long History Made Short One of the few ways to begin a conversation with a reservoir is by pumping treated fluid at fracturing rates and analyzing how the pressure falls off with time after the injection is stopped. The language for such dialogue and information exchange is formed by the dimensionless time function called “G-function” and was introduced by Ken Nolte in 1979. Nolte’s innovative postulations allowed our industry to determine the expected frac geometry, its conductivity, the formation flow capacity, and the optimum hydraulic fracture design as well as the means necessary to place the treatment. Recently introduced into industry literature is the proposed fracture closure pressure interpretation based on the fracture compliance method, interpreting an earlier, higher-stress estimation than estimates from well‑established methodologies. The practitioner is now faced with the dilemma of finding out which fracture closure interpretation technique is correct since this has a profound impact on how fracture geometry is modeled and optimized. To answer this question, a multibasin analysis of pre-frac tests from the Russia, North Sea, Europe, North Africa, and South America regions was undertaken.

Pressure buildup analysis of TRISO-coated fuel particles

The pressure buildup in the buffer layer of TRISO fuel particles is one of the most important factors influencing the mechanical behavior of the fuel. The pressure inside the particles is a driving force for many other phenomena (such as kernel migration, chemical attack of SiC layer, mechanical degradation, etc), therefore even small changes in pressure value could later have a critical impact on the fuel performance. Current TRISO fuel performance models are considering only Xe, Kr and CO (CO2) gases, however at high burnup values low concentration gases also could have essential impact. Therefore, in this paper we analyzed pressure buildup inside TRISO particles including also binary and ternary fission gases. The concentrations of fission gases inside the fuel kernel was calculated by Serpent code. For the calculations of molecular gases Proksch approximation was used. Pressure values inside TRISO particles were calculated using both Redlich-Kwong equation of state and ideal gas law. Finally, the maximum stress on the TRISO particles SiC layer was estimated using thin-shell approximation and the failure fraction of the SiC layer was evaluated. Calculations are done both for UCO and UO2 type fuel kernels for max 150MWd/kgU burnup level.

Pore pressure evaluation of formation testing while drilling under supercharged conditions

Formation Testing While Drilling (FTWD) to evaluate pore pressure has significantly progressed in geo-energy exploitation. However, with the increasing number of unconventional reservoirs, this technology is facing some challenges owing to the common occurrence of supercharging in the vicinity of boreholes. The pressure response of FTWD under supercharged conditions is different from that of non-supercharged; thus, conventional methods — such as Pressure DrawDown (PDD), Pressure BuildUp (PBU), and Formation Rate Analysis (FRA) — cannot be used to determine the original pore pressure. In this paper, a new mathematical model of the FTWD pressure response under supercharged conditions is proposed by considering the time-dependent filter cake, supercharging, skin, geometry, and storage effects. The calculated results indicated that when the formation permeability was lower than 5 mD, the supercharging effect on the pressure response of FTWD cannot be neglected. The pressure response curve of FTWD under supercharged conditions only includes three segments: the fast pressure drawdown stage, pressure buildup stage, and recovered pressure decreasing stage. It is also found that the pressure response in the later stage is independent of the withdraw withdrawal pumping modes and the pressure response curves are nearly the same. Based on the pressure response characteristics, a novel method to evaluate the original pore pressure was proposed. Case studies show that the proposed method can obtain the correct virgin pore pressure after a few iterations and the relative error is lower than 0.2%. Compared with conventional methods, this method is more accurate and saves time; thus, it can be used to evaluate the original pore pressure of FTWD under supercharged conditions.

Horner Analysis for Negative Inflow Tests of Well Barriers

SummaryNegative tests, or inflow tests, are conducted to verify the integrity of well barriers in the direction of potential flow, subjecting a barrier to a negative pressure differential, while monitoring for signs of a leak. A common practice is to observe the rate of flowback from the well. Flowback may be a sign of a leak due to an influx of formation fluids into the well. However, even when there is no leak, flowback is commonly observed due to thermal expansion of wellbore fluids. Heat transfer will occur between the wellbore fluids in each annulus and with the surrounding formation until temperatures reach an equilibrium. This behavior is described by the process of thermal diffusion, with the resulting temperature increase causing expansion of wellbore fluids and flowback from the well.Industry guidelines state “Horner” analysis may be used when monitoring flowback or pressure buildup during an inflow test. In doing so, engineers and wellsite supervisors may use a “Horner plot” to determine if flowback or pressure buildup is attributable to thermal effects. Those without a reservoir engineering background may not be aware the method was originally derived from a radial flow equation for the purpose of monitoring pressure buildup in a well when shut in after a period of production. The apparent similarity of the radial flow and thermal diffusion equations is what led Horner's technique to subsequently be applied to the prediction of static formation temperature from well logs. However, although thermal expansion is a function of formation temperature, Horner analysis of flowback or pressure buildup during an inflow test has remained a black box that is poorly understood.For the first time, with support from empirical data from offshore wells, we reveal that Horner analysis of thermal expansion is a practice without theoretical justification. The radial equation on which Horner analysis depends, along with the constraints implied by the boundary conditions, fails to accurately account for the conditions of an inflow test. As a result, the method should not be used for analyzing flowback or pressure buildup during an inflow test. Instead, a new method is proposed to interpret a trend of flowback when monitoring well barriers. The findings of this study can help improve understanding Horner analysis and techniques for interpreting inflow tests.

Flow Regime Analysis on Pressure Build-up Test Result of Z-01 Well Using Dual Porosity Reservoir Model

Flow regime analysis on the results of pressure build-up Z-01 well test was conducted to determine the type of flow that occurs in each time region section. In the early time stage there is a flow which is dominated by linear flow which is then followed by bilinear flow. At the middle time there is a radial flow where the pressure disturbance has spread towards the reservoir. In the late time flow stage is dominated by steadystate flow where the flow is affected because there is a support pressure caused by the constant pressure boundary. In the analysis of pressure build-up used to determine reservoir parameters can be used in the middle time region. This is used because the plot results between ΔP vs. log HTR (Horner Time Ratio) are straight lines which can be used to calculate reservoir parameter values such as permeability (k), formation damage factor (s). This test was analyzed using the Ecrin software and obtained a dual porosity model with a permeability value of 4.8 md, skin -3.57. From the analyzed model, it is obtained that the well fracture-finite conductivity model means that the Z-01 well has been stimulated to increase production.

Pressure build-up analysis in the flow regimes of the CO2 sequestration problem

In this work we analyse theoretically and numerically the pressure build-up on the cap rock of a saline aquifer during CO2 injection in all flow regimes. Flow regimes are specific regions of the parameter space representing the mathematical spread of the plume. The parameter space is defined in terms of the CO2-to-brine relative mobility λ and the buoyancy parameter Γ. In addition to the known asymptotic self-similar solutions for low buoyancy regimes, we introduce two novel ones for the high buoyancy regimes via power series solutions. Explicit results for the peak pressure value on the cap, which arises in the vicinity of the well, are derived and discussed for all flow regimes. The analytical results derived are then applied for cap integrity considerations in six test cases of CO2 geological storage from the PCOR partnership, most of which correspond to high buoyancy conditions. The validity of the self-similar solutions which are late time asymptotics, is verified with CFD numerical simulations with a commercial software. The comparison between the self-similar solutions and CFD for the pressure estimations are in excellent agreement and the self-similar solutions are valid for typical injection durations even for early times.

Lubrication Mechanisms Between Parallel Rough Surfaces

This paper presents a numerical analysis of the hydrodynamic pressure build-up between parallel surfaces. According to the Reynolds theory, it is not possible to generate a pressure between flat parallel sliding surfaces. However, experimental results demonstrate that mechanical seal surfaces can be separated by a full fluid film if the sliding speed is high enough. Several theories, including the roughness effect, have been proposed to explain this unexpected lift-off. A real demonstration of the roughness induced pressure generation has only recently been made possible with the development of deterministic mixed lubrication models. It is demonstrated that a transverse pumping mechanism that varies from place to place with the surface topography can explain the pressure build-up. A simplified model is proposed to include the transverse pumping and to simulate the roughness induced pressure generation.

Effect of Stress-Sensitive Fracture Conductivity on Transient Pressure Behavior for a Horizontal Well With Multistage Fractures

Summary In this study, theoretical models have been formulated, validated, and applied to evaluate the transient pressure behavior of a horizontal well with multiple fractures in a tight formation by taking stress-sensitive fracture conductivity into account. On the basis of the superposition principle in the Laplace domain, we propose a coupled matrix/fracture-flow model with consideration of the stress-sensitivity effect in fractures, which strengthens the nonlinearity of the governing equations. More specifically, a new slab-source function in the Laplace domain was developed to describe the transient pressure responses caused by fluid flow from the matrix to the fracture, and a new solution was derived to describe the fluid flow in the fracture under the stress-sensitivity effect. Subsequently, a semianalytical method was applied by discretizing each hydraulic fracture into small segments, and a linearization scheme and an iteration method are adopted to deal with the nonlinear problem in the Laplace domain. Meanwhile, a modified superposition principle was proposed and applied to generate the pressure distributions for buildup tests with consideration of stress-sensitive fracture conductivity. Furthermore, pressure responses and their corresponding derivative type curves were generated to examine the effect of stress-sensitive conductivity. For pressure-drawdown tests, it is found that gradual increases in both pressure drop and pressure derivative occur over time because of the partial closure of the fractures. The stress-sensitivity effect in fractures becomes more evident with a smaller fracture conductivity and a larger fracture-permeability modulus. From the pressure-buildup curves, a one-fourth-slope line characteristic of the bilinear-flow period and constant derivatives of 0.5 representing a pseudoradial-flow regime can be clearly observed. Only fracture conductivity near the wellbore at the shut-in time can be estimated from the buildup pressures obtained in this work, whereas pressure-buildup analysis derived from the traditional superposition principle will result in an erroneous evaluation of the stress-sensitive fracture conductivity. It is also found that the effect of permeability hysteresis in the fractures has a negligible impact on the pressure-buildup responses.

Effect of Pretreatment Process on Scale Formation in the Re-Boiler Section of Monoethylene Glycol Regeneration Plant

Monoethylene glycol (MEG) regeneration plants often use pretreatment vessels to precipitate divalent cations, such as Fe2+, Ca2+, and Mg2+, in order to avoid or reduce fouling in downstream reboilers and heat exchangers. This pretreatment process operates under alkaline conditions and moderate temperatures (~ 80 °C) to accelerate the formation of low-solubility divalent salts. The objective of the present research was to determine whether the pretreatment process could be minimized, without negatively impacts on the MEG regeneration process from to the formation of scale on the heater bundle in the presence of low concentrations of divalent cations in the rich MEG stream. Scale formation was analyzed under MEG regeneration process conditions using a dynamic scale loop (DSL) test and verification experiments were performed in a MEG regeneration and reclamation pilot plant, both with and without pretreatment conditions. The scaling tendencies of several rich MEG–brine mixtures were evaluated at different pH pretreatment levels and dissolved CO2 concentrations. An evaluation temperature of 180 °C was chosen to match the skin temperature of the reboiler heater bundle during the MEG regeneration process. The experiments of pH 7.24 showed high amounts of precipitation scale within the reboiler due to high remaining concentrations of mineral ions. In addition, small concentrations of calcium and magnesium ions led to the precipitation of calcite, dolomite, and magnesium hydroxide on the reboiler bundle and within associated filtered outputs even when a pretreatment vessel was present. These results were confirmed by the differential pressure build-up and Scanning Electron Microscopy analyses for each experimental condition. Another interesting finding is that pH increased within the reboiler due to CO2 gas boiling off at high operating temperatures, thus contributing to increased alkalinity levels, which in turn promoted scale formation. These results indicate that pretreatment should not be reduced, even with divalent ion concentrations as low as ~ 5 ppm TDS, due to the harsh conditions within the reboiler heater bundle.

Well Test and Short Term Multiple Rate Flow Tests Analyses to Successfully Hydraulic Fracturing Program of Block X

Well test analysis was conducted to determine the characteristics of reservoir rocks. From the well test analysis it is obtained information such as permeability and skin factor. The skin factor is a quantity indicating the presence of disturbance in the formation as a result of drilling operations, production operations, perforating casing, gravel pack installation, remedial well work, acidizing operation, and hydraulic fracture operation. The objective of this research is to determine the relationship of multi rate test method of Jones, Blount, and Glaze and the comparison result among pressure buildup test and pressure drawdown test analyses, using Kappa software or manually calculation. Therefore, in this paper will study the method of Jones, Blount, and Glaze and the well test analyses to determine further work of the wells on block X. The data used in this paper is secondary data, namely the results of well test from three wells.Applying drawdown test analysis of A, Y, and Z wells yield skin factor values of 3.37; 27.10; and -1.39. Where in buildup pressure Horner method analysis of A, Y, and Z wells yield skin factor values of 16.10; 11.18; and -2.07. In the method of type curve derivatives the drawdown analysis of A, Y, and Z wells yield skin factor values of 7.04; 11.18; and 4.20. The analysis of pressure buildup, of A, Y, and Z wells yield skin factor value of 25.11; 14.47; and 1.93. In the analysis using Kappa software of A, Y, and Z wells yield skin factor values of 5.56; 10.2; and 2.00. The skin results of these wells indicate the formation damages. The Short Term Multiple Rate Flow Tests analysis using Jones, Blount, and Glaze method from the plots of Δp/q versus oil flow rate (q) are b’ high and b’/b low. These indicate that the three wells are encountering formation damages. The Jones, Blount, and Glaze method as well as the pressure buildup and pressure drawdown test analyses in block X indicate that these wells require to be stimulated.

Experimental and numerical study of the behavior of LPG tanks exposed to wildland fires

Abstract The safety of small and medium LPG (liquefied petroleum gas) storage tanks in civil and industrial facilities when affected by forest fires in the framework of Wildland–Urban Interface (WUI) was investigated. Large scale experimental tests were carried to characterize the behavior of LPG tanks in case of distant source radiation caused by forest fires. A data set was obtained and used for the validation of a dedicated two-dimensional computational fluid dynamic (2D CFD) model for the analysis of pressure build-up in vessels exposed to different types of transient heat radiation, featuring different geometry types and operating conditions. The combined experimental and numerical analysis allowed determining the critical exposure conditions for LPG vessels. Specific key performance indicators were defined and calculated on the basis of 2D CFD simulation results in order to derive conservative indications on failure conditions of LPG storage vessels induced by forest fires.

Designing an atmosphere controlling hollow fiber membrane system for mango preservation

We devised an atmosphere controlling facility to gain a longer life span for mango. A membrane module made of polyethersulfone/polydimethylsiloxane (PES/PDMS) composite membrane was applied to selectively permeate CO2 from the gas mixture of the fruit container. To design the membrane separation system, two models were introduced into our mathematical simulations: (1) an equilibrium model giving the optimal membrane area, the compositions of CO2 and O2 in the fruit container, feed flow rate and pressures on both the feed and permeate sides of the module, and (2) a dynamic model simulating the change in the gas composition of the fruit container with time. The pressure build-up in the bore side of the hollow fiber was also discussed using the Hagen-Poiseuille equation. The best membrane module configuration was obtained based on the pressure build-up analysis. That was (1) the vacuum pressure should be set at 0.1 bar, (2) the hollow fiber inner diameter should be 0.45 mm, and (3) the vacuum should be applied at both ends of the hollow fiber bore sides.

Pressure buildup test analysis in wells with sustained casing pressure

When the well's casing head pressure cannot be permanently bled off with a needle valve, the casing is said to exhibit Sustained Casing Pressure (SCP). Rebuilding of surface pressure (pressure buildup – after closing the valve) results from migration of gas in the leaking cement sheath of the well's annulus. Problem of sustained casing pressure (SCP) has been widespread in the Gulf of Mexico and also reported in Canada, Norway, and other places. Regulations require 24-hr testing of SCP wells comprising pressure bleed-down followed with pressure buildup. In these tests, the rate of pressure buildup is indicative of the size of cement leak – prompt buildup implies larger leak on a relative scale with no quantification. Presented here is the first mathematical model for quantitative analysis of pressure buildup in SCP wells. The model simplifies transient gas flow in cement and ignores migration time of gas in the annular fluid column above the cement top. The simplification allows finding the size of cement leak and the depth and value of gas pressure source formation.Also presented is validation of the model with actual field data from testing SCP wells. Matching the model to field data gives acceptable estimates of the gas-source formation depth and pressure, cement leak size, and expected maximum casing pressure value. The results also reveal a correlation between the pressure buildup-stabilization pattern and well parameters - cement leak size controls the pressure buildup rate, while the gas-source formation pressure controls the stabilized pressure value. Quantitative analysis of SCP buildup with the new model could be extremely useful as it provides values of three parameters (cement leak size, gas source formation depth and pressure) that are critically important for designing remedial treatment.

Pressure-buildup analysis method for a post-treatment evaluation of hydraulically fractured tight gas wells

Tight gas reservoirs have a very low permeability, usually approximately <0.1 md. Consequently, a fractured horizontal well drawn from these reservoirs will encounter difficulty reaching a radial flow regime after completion. The effective reservoir permeability and the effective fracture half-length cannot be determined using short-term well test data. In addition, the wellbore storage effect tends to obscure early flow regimes in hydraulic fractures, thereby hampering the calculation of fracture conductivity. Fitting well test curves in the absence of early flow regimes in the fracture and middle radial flow regime is not sufficient. In this paper, a deconvolution-based pressure buildup analysis method amended with a modified Schroeter deconvolution model is proposed. The proposed method utilizes short-term pressure buildup and long-term flow rate data to recover the true reservoir pressure response. A synthetic case is presented to demonstrate that the proposed deconvolution model and algorithm can eliminate the wellbore storage effect and recover the fracture linear flow and formation radial flow regimes. A field case in the East China Sea is further presented to demonstrate the feasibility of the proposed method. This study demonstrates that a short-term pressure buildup test data can still be used to calculate the fracture and reservoir dynamic parameters of tight gas wells. Thus, the hydraulic fracturing treatment can be quantitatively evaluated.

Bilinear Flow in Horizontal Wells in a Homogeneous Reservoir

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 174325, “Bilinear Flow in Horizontal Wells in a Homogeneous Reservoir: Huntington Case Study,” by Wei Cher Feng, E.ON E&amp;P; Peyman Nurafza, BG Group; Basil Al-Shamma, E.ON E&amp;P; and Alain Gringarten, Imperial College London, prepared for EUROPEC 2015, Madrid, Spain, 1–4 June. The paper has not been peer reviewed. In the Huntington field in the North Sea, bilinear flow with a clear one-quarter slope in the pressure derivative has been observed during intermediate times in horizontal-well tests, instead of the usual linear flow with a one-half slope expected in a homogeneous reservoir. This paper offers insight into an integrated effort at combining analytical information, numerical well-test models, and geological evidence to explain the reservoir behavior observed in the Huntington field. Reservoir Description The Huntington field is a sandstone reservoir with a maximum oil-column thickness of 120 ft, located within a sand-rich turbidite system in the central North Sea. Vertical appraisal wells show a largely homogeneous reservoir with average porosities of 20%, net/gross ratio of 80–90%, and average permeabilities of 30–60 md. Core samples do not indicate any inherent natural fractures. The reservoir contains undersaturated light oil with gravity of 43 °API, viscosity of 0.3 cp, and bubblepoint pressure of 2,200 psig at reservoir pressure of 4,000 psig and temperature of 250°F. Well tests of two vertical wells match a homogeneous-reservoir model, but four horizontal producers drilled in this reservoir exhibited a one-quarter-slope straight line in the pressure derivative, stretching up to two log cycles during intermediate time. Reservoir Connectivity and Areal Anisotropy. Reservoir-connectivity investigations indicate no obvious barriers between the wells and good reservoir connectivity between all the wells. However, the modified pulse tests indicate possible reservoir heterogeneity between the wells. The minimum-permeability direction was determined from data sets of three well tests, two horizontal and one vertical. It was found that areal permeability anisotropy could exist within the reservoir, with the minimum- permeability direction in the northeast/southwest direction of the Huntington field. Rate History and Production-Time Effects on Well Data An incomplete rate history can mask pressure-derivative response because of the use of superposition time in pressure-buildup analysis. Production-time effects can also affect the shape of the pressure derivative of a pressure-buildup well test. During a buildup, as the pressure stabilizes when reservoir pressure approaches equilibrium, pressure variations become smaller and signal/noise ratio decreases. The transition effect of characteristic flow regimes is discussed in detail in the complete paper. Ultimately, a one-quarter- slope straight line in the pressure derivative is not unique to bilinear flow but could be caused by a combination of transition effects of the characteristic flow regimes in a horizontal well.

Diagnosis of nonlinear reservoir behaviour for correctly applying the superposition principle and deconvolution

The superposition principle is the fundamental theory of pressure-transient analysis. Many pressure analysis methods, such as pressure build-up analysis and deconvolution, are based on the superposition principle. Deconvolution, which can provide the equivalent constant-rate pressure response from variable-rate pressure data, has become more popular in recent years. Mathematically, the superposition principle is only valid in a linear system. However, many reservoir behaviours can make the system nonlinear and the superposition principle invalid, such as the time-dependent skin factor and permeability, multiphase flow and non-Darcy flow. Erroneously applying the superposition principle and related methods will lead to incorrect analysis results and inappropriate production decisions. To reduce the analysis uncertainties and obtain the correct reservoir information, diagnosing the nonlinear reservoir behaviour and selecting the appropriate pressure analysis method are important. In this paper, nonlinear reservoir behaviours are diagnosed from transient pressure data with the wavelet transform. A defined diagnosis function can effectively diagnose the nonlinear reservoir behaviours. As studies have proved, the diagnosis function is constant in the linear system and time varying in the nonlinear system. Based on the diagnosis result, the nonlinear system can be linearized in a short time period using the sliding window technique, and the superposition principle and related methods can be correctly applied.

Pressure buildup behavior of vertically fractured wells with stress-sensitive conductivity

Abstract This paper presents the results of a study on pressure buildup analysis of a vertically fractured well with the consideration of stress-sensitive permeability and hysteresis effect in fracture. A new function was established to better characterize the variation of fracture permeability on pore pressure, and a mathematical model was derived for the buildup test of fractured wells with stress-sensitive conductivity. Several simulation cases involve various conductive fractures were run to plot pressure buildup type curves under stress damage condition. The influence of stress effect on buildup behavior and the variation of the fracture conductivity are discussed extensively. Results of this investigation demonstrate that for stress-sensitive conductivity fractured wells, a straight line with slope value of 0.25 which defines the bilinear flow regime is still clearly observed on pressure buildup type curves after pressure drops. The stress sensitivity behavior of a producing fractured well could not be determined from a single buildup test. The effect of permeability hysteresis in the fracture has a negligible influence on the pressure buildup curves. From the test data of the bilinear flow, only the conductivity value near the wellbore at shut-in time can be estimated using conventional methods.

Numerical analysis of heat-mass transport and pressure buildup of unsaturated porous medium in a rectangular waveguide subjected to a combined microwave and vacuum system

This paper presents two-dimensional numerical analysis of heat-mass transport and pressure buildup inside an unsaturated porous packed bed which is filled in a rectangular waveguide and subjected to a combined microwave and vacuum system. A microwave system supplies a monochromatic wave in a fundamental TE10 mode. The unsaturated porous media is composed of glass beads, water and air. The finite difference time domain method is used to determine the electromagnetic field distribution in the rectangular waveguide by solving the transient Maxwell’s equations. The finite difference method together with Newton–Rephson technique is employed to predict the heat, multiphase flow and pressure buildup. The influences of vacuum pressure and operating microwave frequency on temperature, microwave power absorbed, saturation and pressure buildup distribution, and movement of fluid inside the unsaturated porous media are investigated during microwave vacuum drying process.

Numerical Analysis of Heat–Mass Transport and Pressure Build-Up in 1D Unsaturated Porous Medium Subjected to a Combined Microwave and Vacuum System

This article presents one-dimensional numerical analysis of heat-mass transport and pressure build-up inside an unsaturated porous media under microwave energy at a vacuum pressure condition. The unsaturated porous media is composed of glass beads, water, and air. The absorbed microwave power term is computed based on Lambert's law. The finite difference method together with Newton-Raphson technique is employed to predict the heat, multiphase flow, and pressure build-up. Based on the numerical analysis of the effects of vacuum pressure and types of dielectric materials, it was found that the vacuum pressure had a strong effect on temperature, absorbed microwave power, saturation and pressure build-up distribution, and movement of fluid inside the unsaturated porous media during the microwave drying process.