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Rate transient analysis (RTA) is a practical and cost‐effective method for CO2 injection data analysis and storage capacity evaluation of saline aquifers. However, the nonlinear behavior introduced by two‐phase CO2–brine flow, coupled with pressure‐dependent fluid and rock properties, significantly limits the applicability of conventional production‐based RTA models, which typically assume single‐phase flow and rely solely on pressure propagation. To overcome these limitations, this study presents a novel two‐phase RTA method that, for the first time, explicitly incorporates both pressure evolution and CO2 front migration, while accounting for the nonlinearities associated with brine displacement and pressure‐sensitive reservoir behavior. First, a two‐phase flow model is developed for CO2 injection in saline aquifers, and an analytical solution is derived by introducing new definitions of pseudo‐pressure and pseudo‐time that capture the effects of both multiphase flow and pressure‐dependent properties. By introducing distinct definitions of the radius of investigation (ROI) for the pressure front and the CO2 front, average pressure and saturation are evaluated based on their respective controlling regions and incorporated into the estimation of pseudotime. Second, a two‐step RTA approach is proposed to analyze CO2 injection data, including flow regime identification using a two‐phase diagnostic plot and subsurface properties estimation using a specialty plot. Finally, we provide a workflow that integrates formation properties evaluation with storage capacity prediction under the more realistic conditions of variable injection. The proposed method is validated using synthetic data from numerical simulations and a field example from the Illinois Basin Decatur Project (IBDP). The close estimation of CO2 storage capacity, reservoir pore‐volume, and permeability confirm the accuracy of the proposed model and demonstrate the method's reliability compared with numerical simulations for rapid assessment of storage potential and analytical RTA methods for considering the specific nonlinearities. With the proposed approach, the scattered CO2 injection pressure and rate data are, for the first time, transformed into clear straight‐line behaviors with unique slope, revealing the underlying two‐phase flow characteristics during CO2 injection up to the injection limit.

We present a generalized shear deformation theory in combination with isogeometric (IGA) approach for nonlinear transient analysis of smart piezoelectric functionally graded material (FGM) plates. The nonlinear transient formulation for plates is formed in the total Lagrange approach based on the von Kármán strains, which includes thermo-piezoelectric effects, and solved by Newmark time integration scheme. The electric potential through the thickness of each piezoelectric layer is assumed to be linear. The material properties vary through the thickness of FGM according to the rule of mixture and the Mori–Tanaka schemes. Various numerical examples are presented to demonstrate the effectiveness of the proposed method.

The hydraulic fracturing technique (also termed mini-frac test) is commonly used to estimate the in situ stress field. We recently conducted a mini-frac stress measurement campaign in the newly-established Bedretto Underground Laboratory (BedrettoLab) in the Swiss Alps. Four vertical boreholes, dedicated for stress characterization of the granitic rock mass, hosted a total of 19 mini-frac test intervals. Systematic pressure transient analysis was performed to carefully estimate the magnitude of the least principal stress (S3). We compared five different methods (inflection point, bilinear pressure decay rate, tangent, fracture compliance, and jacking pressure) to identify an adequate approach best suited for our test scale and the host rock mass. We found that the methods used to determine the fracture closure pressure underestimate the magnitude of S3, presumably due to the rapid closure of the hydraulic fracture after shut-in. The most consistent results were found using the inflection point and bilinear pressure decay rate method, which both determine the (instantaneous) shut-in pressure as the proxy for the S3 magnitude. The determined shut-in pressure, or S3 magnitude, is 14.6±1.4 MPa from the inflection point method. This allowed us to further estimate the stress environment around the BedrettoLab, which is transitional between normal and strike-slip faulting. The measured local pore pressures from extended shut-in periods are between 2.0 and 5.6 MPa, significantly below hydrostatic. A combination of drainage, cooling, and the excavation damage zone of the tunnel may have significantly perturbed the in situ stress field in the vicinity of the BedrettoLab.

Strategic pipeline asset management requires accurate and up-to-date information on pipeline condition. As a tool for pipeline condition assessment, inverse transient analysis (ITA - a pipeline model calibration approach) is typically formulated as a deterministic problem, and optimization methods are used for searching a single best solution. The uncertainty associated with the single best solution is rarely assessed. In this paper, the pipeline model calibration problem is formulated as a Bayesian inverse problem, and a Markov Chain Monte Carlo (MCMC) based method is used to construct the estimated posterior probability density function (PDF) of the calibration parameters. The MCMC based method is able to achieve parameter estimation and uncertainty assessment in a single run, which is confirmed by numerical experiments. The proposed technique is also validated using measured hydraulic transient response data from an experimental laboratory pipeline system. Two thinner-walled pipe sections (simulating extended deterioration) are successfully identified with an assessment of the parameter uncertainty. The results also suggest that proper sensor placement can reduce parameter uncertainty and significantly enhance system identifiability.

Current analytical approaches for temperature transient analysis heavily rely on the assumption of the constant rate production, which is often invalid for the extended period of oil production. This work addresses this issue by introducing novel analytical approaches to model the temperature signal under dynamic rate and pressure conditions. The introduced methods share underlying theories of superposition principle and production rate normalization from pressure transient analysis and include a newly derived analytical solution when these theories are not applicable. With adapting these methods, cases with complex production history are modeled using analog cases producing with a constant rate. The dynamic temperature analysis developed herein is validated using synthetic temperature data both graphically and by quantitative estimation of reservoir properties. The estimation outputs of these methods include permeability, drainage area, and damaged zone properties. Other features of existing temperature transient analysis, such as fluid property correction and monitoring well surveillance, are also extended to variable rate and pressure conditions in this paper. Two cases documented in the literature are addressed by dynamic temperature analysis for which decent reservoir characterization results are obtained. The dynamic temperature analysis proposed in this paper extends the scope of temperature transient analysis to complex production constraints and demonstrates convincing results for practical purposes.

In this work, a novel refined higher-order shear deformation plate theory is integrated with nonlocal elasticity theory for analyzing the free vibration, bending, and transient behaviors of fluid-infiltrated porous metal foam piezoelectric nanoplates resting on Pasternak elastic foundation with flexoelectric effects. Isogeometric analysis (IGA) and the Navier solution are applied to the problem. The innovation in the present study is that the influence of the in-plane variation of the nonlocal parameter on the free and forced vibration of the piezoelectric nanoplates is investigated for the first time. The nonlocal parameter and material characteristics are assumed to be material-dependent and vary gradually over the thickness of structures. Based on Hamilton's principle, equations of motion are built, then the IGA approach combined with the Navier solution is used to analyze the static and dynamic response of the nanoplate. Lastly, we investigate the effects of the porosity coefficients, flexoelectric parameters, elastic stiffness, thickness, and variation of the nonlocal parameters on the mechanical behaviors of the rectangular and elliptical piezoelectric nanoplates.

UT-Austin’s Devine Fracture Pilot Site, 50 miles southwest of San Antonio, Texas, has been targeted for a comprehensive, multidisciplinary development of fracture diagnostic techniques that are cross-validated by ground-truth data acquisition near a recently created, 175-ft-deep, horizontal hydraulic fracture (Ahmadian et al. 2018 Demonstration of proof of concept of electromagnetic geophysical methods for high resolution illumination of induced fracture networks. In Proceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 23–25 January 2018. SPE-189858-MS.). To evaluate the fracture diagnostic methods at this site, we conducted injection tests with a predefined volumetric flow-rate profile, resembling a diagnostic fracture injection test on September 2020. Subsequently, we developed hydrogeological and geomechanical models based on flow-rate and bottomhole-pressure measurements. History-matching efforts using a simplified layer-cake hydrogeological model resulted in the field-scale formation permeability of 9.87 × 10–15 m2 (10 mD) and Darcy-scale fracture permeability. The analysis of the bottomhole pressure and injection-rate history showed that (1) the newly created horizontal fracture was closed adjacent to the injection well pre-injection and (2) the initial pump-pressure increase at a nominal volumetric injection rate led to near-well fracture reopening, fluid conductivity increase, and abrupt injection-rate increase. To overcome hydrogeological-model limitations of predicting fracture reopening throughout injection, we extended the modeling to a finite-element, poroelastic analysis of horizontal-fracture growth using a cohesive-zone model. Using this fracture-reopening model, we improved the history match of the transient-pressure response during the experiment by adjusting the hydromechanical properties. Post-injection pressure transient analyses helped reduce uncertainty in the overburden-stress gradient, and the initial hydraulic-fracturing simulation verified the plausibility of achieving the surveyed propped fracture area.HighlightsWe proposed a procedure for developing a hydrogeological model to improve the history matching of the bottomhole pressure during a hydraulic-fracture reopening.We compared the outcomes of this hydrogeological model with a calibrated poroelastic model, showing the advantage of the later model for fracture reopening and re-closure.We suggest using a spatiotemporally variable fracture permeability obtained from a poroelastic model in a hydrogeological model to simulate fracture reopening.We estimated an almost similar overburden-stress gradient using G-function pressure transient analysis of post-shut-in bottomhole pressure data from two short and long injection tests.

Two phase flow and horizontal well completion pose additional challenges for rate-transient analysis (RTA) techniques in under-saturated coal seam gas (CSG) reservoirs. To better obtain reservoir parameters, a practical workflow for the two phase RTA technique is presented to extract reservoir information by the analysis of production data of a horizontal well in an under-saturated CSG reservoir. This workflow includes a flowing material balance (FMB) technique and an improved form of two phase (water + gas) RTA. At production stage of a horizontal well in under-saturated CSG reservoirs, a FMB technique was developed to extract original water in-place (OWIP) and horizontal permeability. This FMB technique involves the application of an appropriate productivity equation representing the relative position of the horizontal well in the drainage area. Then, two phase (water + gas) RTA of a horizontal well was also investigated by introducing the concept of the area of influence (AI), which enables the calculation of the water saturation during the transient formation linear flow. Finally, simulation and field examples are presented to validate and demonstrate the application of the proposed techniques. Simulation results indicate that the proposed FMB technique accurately predicts OWIP and coal permeability when an appropriate productivity equation is selected. The field application of the proposed methods is demonstrated by analysis of production data of a horizontal CSG well in the Qinshui Basin, China.

Transient behavior analysis, including rate transient analysis (RTA) and pressure transient analysis (PTA), is a powerful tool to investigate the production performance of the vertical commingled well from long-term production data and capture the formation parameters of the multilayer reservoir from transient well testing data. Current transient behavior analysis models hardly consider the effect of vertical non-uniform boundary radii (VNBR) on transient performances (rate decline and pressure response). The VNBR may cause an obvious novel radial flow regime and rate decline type, which can easily be mistaken as a radial composite reservoir. In this paper, we present a VNBR transient behavior analysis model, the extended vertical uniform boundary radii (VUBR), to investigate the rate decline behavior and pressure response characteristics through diagnostic type curves. Results indicate that the dimensionless production integral derivative curve or pressure derivative curve can magnify the differences so that we can diagnose the outer-convex shape and size of the VNBR. Therefore, it is significant to incorporate the effects of VNBR into the transient behavior analysis models of the vertical commingled well, and the model proposed in this paper enables us to better evaluate well performance, capture formation characteristics and diagnose flow regimes based on rate/pressure transient data.

Microseismic monitoring in the field has widely shown nonuniformity and asymmetry of hydraulic fractures resulted from multi-stage hydraulic fracturing operations. Considering these influential features of the hydraulic fractures, this paper presents semi-analytical solutions for the wellbore pressure (oil well) and pseudo-pressure (gas well) during production from multi-fractured horizontal wells (MFHW). The solutions further account for bounded and naturally fractured rock formations, recovering existing dual-porosity dual-permeability solutions for a vertical wellbore with one single hydraulic fracture and single-porosity solutions for MFHW. Instead of using the common and simple Warren and Root model, which neglects fluid flow in rock matrix, we adopt the Barenblatt model, which considers fluid flow in both rock matrix and natural fractures. We introduce a permeability ratio, kD, and show that Warren and Root model becomes problematic when kD is larger than 0.05. Comparison analysis shows that the nonuniformity of the hydraulic fracture length distributed along the horizontal wellbore, the nonuniformity of the fracture height, and their asymmetry could have a bigger role than the spacing in the rate transient analysis. For the cases with symmetric and uniform hydraulic fractures, analytical expressions are derived for the classical + 1/2, 0, and + 1 slopes with six characteristic times related to the flow regimes. The application of the semi-analytical solutions to rate transient analysis is demonstrated through five field case studies, consisting of two horizontal and three vertical wells.