Transient Pressure Characteristics Research Articles

Leakage detection method based on transient pressure behaviors during pigging process in pipelines

Pipelines are the most common way to transport oil and gas due to its convenience. They are facing many threatens such as leakage, which may cause serious pipeline accidents. This paper proposes a leakage detection method coupled with the transient pressure characteristics to recognize leaks in pipeline. A coupled dynamic mesh method was used to achieve the movement of pigging device. The explicit and implicit coupling method has been developed to simulate transient pressures and leak behaviors. Cases has been conducted through the established experimental pipeline system to validate the proposed leakage detection method. The reasonable agreement between the results from these two methods verify that the proposed leakage detection method is accurate enough to simulate transient pressure behaviors in pipelines during the pigging process. Leak volume and location identification methods have been presented and the calculation accuracy is verified in a reasonable range. The proposed leakage detection method in this paper is a supplement to the field of subsea pipeline detection.

Applications of Asymptotic Solutions of the Diffusivity Equation to Infinite Acting Pressure Transient Analysis

Summary Understanding how pressure propagates in a reservoir is fundamental to the interpretation of pressure and rate transient measurements at a well. Unconventional reservoirs provide unique technical challenges as the simple geometries and flow regimes [wellbore storage (WBS) and radial, linear, spherical, and boundary-dominated flow] applied in well test analysis are now replaced by nonideal flow patterns due to complex multistage fracture completions, nonplanar fractures, and the interaction of flow with the reservoir heterogeneity. In this paper, we introduce an asymptotic solution technique for the diffusivity equation applied to pressure transient analysis (PTA), in which the 3D depletion geometry is mapped to an equivalent 1D streamtube. This allows the potentially complex pressure depletion geometry within the reservoir to be treated as the primary unknown in an interpretation, compared with the usual method of interpretation in which the depletion geometry is assumed and parameters of the formation and well are the unknown properties. The construction is based upon the solution to the Eikonal equation, derived from the diffusivity equation in heterogeneous reservoirs. We develop a Green’s function that provides analytic solutions to the pressure transient equations for which the geometry of the flow pattern is abstracted from the transient solution. The analytic formulation provides an explicit solution for many well test pressure transient characteristics such as the well test semi-log pressure derivative (WTD), the depth of investigation (DOI), and the stabilized zone (SZ) (or dynamic drainage area), with new definitions for the limit of detectability (LOD), the transient drainage volume, and the pseudosteady-state (PSS) limit. Generalizations of the Green’s function approach to bounded reservoirs are possible (Wang et al. 2017) but are beyond the scope of the current study. We validate our approach against well-known PTA solutions solved using the Laplace transform, including pressure transients with WBS and skin. Our study concludes with a discussion of applications to unconventional reservoir performance analysis for which reference solutions do not otherwise exist.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil–water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery. In contrast to water, polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening, polymer convection, diffusion, adsorption retention, inaccessible pore volume and reduced effective permeability. Meanwhile, the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution, formation damage, and proppant breakage. In this paper, we present an oil–water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior, and non-uniform fracture characteristics in fractured polymer flooding. The hydraulic fracture is firstly divided into two parts: high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section. A hybrid grid system, including perpendicular bisection (PEBI) and Cartesian grid, is applied to discrete the partial differential flow equations, and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution. The combination of polymer behavior characterizations and numerical flow simulations are applied, resulting in the calculation for the distribution of water saturation, polymer concentration and reservoir pressure. Compared with the polymer flooding well with uniform fracture conductivity, this non-uniform fracture conductivity model exhibits the larger pressure difference, and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section. The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately, and yields fracture half-lengths that better match engineering reality, enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity. The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology, as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Pressure Transient Analysis for a Well Drilling into a Large-Size Cave in Fracture-Caved Carbonate Gas Reservoirs

This paper studies the influence of large-size cave on pressure transient characteristics in fracture-caved carbonate gas reservoirs (FCCGR). With the rapid increase of energy demand, the exploration and development of unconventional oil and gas becomes more and more important. In recent years, many FCCGR have been discovered in western China and contribute significantly to Chinese gas reserves. However, with the presence of large-size cave, FCCGR have complex pore structures and strong heterogeneity. Traditional pressure transient analysis models cannot describe the gas flow accurately. This paper develops a novel pressure transient analysis model for FCCGR by coupling the fluctuating pressure and minor energy loss. Based on the solutions, the typical curves are plotted to analyze the pressure transient characteristics. It is found that the flow process can be subdivided into six stages, including the following: (I) wellbore storage, (II) first transition stage, (III) cave storage, (IV) second transition stage, (V) interporosity flow, and (VI) radial flow. The findings indicate that a concave is added, and the wellbore storage occurs earlier due to the existence of cave. Then, the influences of key parameters are studied. The pressure propagation coefficient and cave volume factor influence the stages I, II, III, and IV. When pressure propagation coefficient increases, the wellbore storage becomes larger and cave storage becomes smaller. The first concave moves to upper right. When cave volume factor increases, the wellbore storage occurs earlier and the curves move left in stage I. Interporosity flow factor and storage ratio influence the location and depth of the second concave. Finally, a field gas well is interpreted by using the proposed model, which verifies the reliability and correctness of the model. The findings of this study can help to better understand the influence of large-size cave on pressure transient characteristics. In addition, it can help engineers invert the cave volume, which is of great significance for the development in FCCGR.

The Effect of Nozzle Body Volume on Pressure Dynamics in a PWM Sprayer System

Highlights The variability in damping ratio between different sized nozzle tips was reduced with an increase in nozzle body volume, indicating that the previous works using pressure-sensing manifolds in PWM systems may have underestimated the nozzle pressure fluctuations. Pressure sensors installed at the nozzle body and the manifolds tested exhibited a different damping ratio, suggesting a slight change in sensor location might yield different measurements of transient pressure characteristics. A minimally invasive instrumented pressure sensor at the nozzle body is needed to accurately measure nozzle pressure dynamics. Abstract. Nozzle pressure measurements in agricultural sprayers are commonly conducted by adding a manifold between the nozzle body and nozzle tip. The additional component substantially increases the internal volume of the nozzle body, which affects nozzle pressure dynamics. This research focused on the effect of nozzle body volume on pressure dynamics when operating a spray nozzle under pulse-width-modulation control. A nozzle body and two manifolds of different volumes were instrumented with embedded pressure sensors. In a static test environment, pressure data were collected at 345 kPa nominal pressure at 50% duty cycle with a variety of nozzle orifice sizes. A second-order transfer function was used to model a portion of the dynamic pressure data. The damping ratio generally decreased as the volume of the nozzle body increased due to the addition of a manifold. The variability in damping ratio with respect to nozzle orifice size was reduced when adding a manifold. The lower damping ratios when a manifold was present generally resulted in more overshoot and slower settling time. Results also showed a slightly higher damping ratio at the nozzle body than at the manifold when either manifold was added. The differences in nozzle pressure dynamics with and without the addition of a pressure sensing manifold suggest that previous studies using instrumented nozzle bodies under PWM control may have underestimated the amplitude of pressure oscillations and the time to reach equilibrium. Keywords: Agricultural Sprayers, Measurement Accuracy, Nozzle Body Volume, Pressure Dynamics, Pulse Width Modulation (PWM).

A semi-analytical mathematical model for the pressure transient analysis of multiple fractured horizontal well with secondary fractures

Over the recent years, several researchers have performed pressure transient analysis (PTA) of multi-fractured horizontal wells (MFHWs). However, most of these studies only considered hydraulic fractures (HFs), and the effect of secondary fractures (SFs) was ignored. To this end, in this study, a semi-analytical model is established based on the discrete coordinate method to examine the influence of SFs on the transient pressure characteristics of MFHWs. The mathematical model is solved using Laplace transform theory, source function theory, and superposition principle, and the actual pressure of the reservoir is obtained using the Stehfest numerical inversion algorithm. The efficacy of the model is verified through an industrial simulator (Ecrin-KAPPA). Further, sensitivity analysis is conducted to examine the impact of fracture parameters on the MFHW with and without SFs. The results indicate that the reservoir with SFs undergoes eight flow regimes in which the SF radial flow is a new flow process. The number of SFs mainly affects the SF radial flow regime and the bilinear flow regime, while the SF half-length also affects the first linear flow regime in addition to the above two regimes. The fracture conductivity mainly affects the SF radial flow regime, the bilinear flow regime, and the first linear flow regime. Overall, the proposed model facilitates accurate and effective analysis of the dynamics of unconventional multi-fractured reservoirs, and it can be potentially used to interpret the characteristics of actual reservoir pressures on site.

Investigation of Flow Separation Characteristics in a Pump as Turbines Impeller Under the Best Efficiency Point Condition

Abstract The impeller, which is the main energy conversion component of a pump as turbine (PAT), is designed for pumping mode, and its internal flow characteristics are quite complicated even at the best efficiency point (BEP) of the turbine mode. This study aims to investigate the flow separation characteristics in a PAT impeller under the BEP condition by numerical method. The hydraulic performance and transient pressure characteristics of PAT predicted numerically were verified through experimentation. The surface friction lines and flow topological structure were applied to diagnose the flow separation at the surface of the blade. The relationship between flow topological structure and vortex in the impeller and static pressure at the blade were analyzed. Analysis results show that the backflow and open flow separation are observed significantly in the leading region and near the shroud of the trailing region of suction side. The passage vortex always appears near the spiral node. The saddle point and spiral node correspond to the peak position of adverse pressure and the lowest position between two peak values of the static pressure of the blade, respectively. The inflow conditions of blade and shape of the trailing edge significantly influence the flow separations in the impeller.

A Novel PPA Method for Fluid Pipeline Leak Detection Based on OPELM and Bidirectional LSTM

Pipeline leak detection has attracted great research interests for years in the energy industry. Continuous pressure monitoring is one of the most straightforward approaches in leak detection which utilizes pressure point analysis (PPA) algorithms to exploit the transient pressure characteristics and identify leak events. However, a critical issue that jeopardizes the deployment of PPA based methods is the high false alarm rate. In this paper, a novel PPA based leak detection method is proposed which can accurately detect the leak events and dramatically decrease the number of false alarms compared to existing methods. Firstly, the proposed method takes advantage of the good approximation ability and fast learning speed of optimally-pruned extreme learning machine (OPELM) to produce a preliminary leak detection result. Then, the strong memorizing ability of bidirectional long-short term memory (BiLSTM) network is exploited to identify the true positive from the preliminary detection result, hence significantly decrease the number of false alarms. Furthermore, a feature extraction mechanism is also proposed to obtain both the dynamic and static characteristics from raw pressure wave. Experiments and verifications are performed on different real world data sets obtained from pipeline leak tests. It shows that the proposed method can achieve higher detection accuracy with significantly less false alarms. It enhances the practicality of pressure monitoring based leak detection schemes.

Experimental Investigation on Transient Pressure Characteristics in a Helico-Axial Multiphase Pump

In oil and gas exploitation, the multiphase pump is a vital piece of equipment to guarantee production with high efficiency and stable operation. The complicated pattern of multiphase flow in the multiphase pump affects the pump performance; for this reason, the multiphase performance and the inner flow should be sufficiently investigated. In the present work, a liquid-gas multiphase pump is designed and manufactured, and then tested in a specialized test rig to reveal the transient pressure characteristics of the multiphase pump. Results show that the dominant frequency under water and water-air conditions is the blade passing frequency, which is induced by the rotor stator interaction. In the downstream of the impeller, the pressure fluctuation is obviously weakened, because the splitter-blade design could improve the control ability of flow pattern in the downstream region. In comparison with water condition, the pressure fluctuation of water-air condition greatly increases, and the multiples of impeller rotating frequency are stimulated due to the movement and merging of air bubbles. Finally, the correlation of transient pressure and phase distribution in impeller is revealed by using a high-speed camera. With the gradual pressure rise from impeller inlet to outlet, the relative movement and separation of two phases induce violent pressure fluctuations.

An innovative model to evaluate fracture closure of multi-fractured horizontal well in tight gas reservoir based on bottom-hole pressure

Due to formation damage and fracture closure, the effective fracture half-length is usually much shorter than the designed half-length. However, available pressure transient analysis (PTA) models of multi-fractured horizontal wells (MFHWs) hardly consider the effect of non-uniform fracture closure of double-segment fractures (DSF) on transient pressure characteristics, which could bring about incorrect results since conductivity and flux density of fracture segment near wellbore are much larger than those of fracture segment far from wellbore. To fill this gap, this paper aims at presenting a novel approach to evaluate effective fracture properties through PTA more accurately. This new model allows each hydraulic fracture of MFHW consists of two individual segments with their own properties (e.g. length, conductivity and flux density, etc). Pressure and its derivative curves are developed for flow-regime analysis. The solution is validated with numerical results in Saphir. Sensitivity analysis further seek the feasible application on interpretation of effective fracture properties. The field application demonstrates the practical use of the proposed model in estimating fracture half-length with different conductivity during production stage to identify the extent of fracture closure using pressure data.

A Novel Approach To Detect Interacting Behavior Between Hydraulic Fracture and Natural Fracture by Use of Semianalytical Pressure-Transient Model

Summary The detection of interacting behavior between the hydraulic fracture (HF) and the natural fracture (NF) is of significance to accurately and efficiently characterize an underground complex-fracture system induced by hydraulic-fracturing technology. This work develops a semianalytical pressure-transient model in the Laplace domain to detect interacting behavior between HF and NF depending on pressure-transient characteristics. Our results have shown that no matter what the flow state (compressible or incompressible flow) within a hydraulically induced fracture system, we can easily detect interacting behavior between HF and NF depending on whether the “dip” shape occurs at the formation radial-flow regime. Referring to sensitivity analysis, distance between NF and well, horizontal distance between NF and HF, and NF length are the three most sensitive factors to detect fracture-interacting behavior. Depending on interference analysis, although the pressure-transient characteristics of a pseudosteady-state dual-porosity model can interfere with our proposed methodology, the difference between our model and a pseudosteady-state dual-porosity system lies in whether the value of the horizontal line of dimensionless pressure derivative is equal to 0.5 at the formation radial-flow regime. Our work obtains some innovative insights into detecting fracture-interacting behavior, and the valuable results can provide significant guidance for refracturing operations and fracture detection in an underground fracture system.

Pressure-Transient Characteristics of Fractured Horizontal Wells in Unconventional Shale Reservoirs With Construction of Data-Constrained Discrete-Fracture Network

Summary Unconventional shale reservoirs require massive and multistage hydraulically fractured horizontal wells to produce economically. Induced hydraulic fractures interacting with in-situ natural fractures result in complex or discrete fracture networks (DFNs). Even though well-testing characteristics in fractured reservoirs with vertical wells have been investigated extensively, there is a lack of good understanding of well-testing response for hydraulically fractured horizontal wells in complex fracture networks. First, three practical approaches are presented regarding how to generate complex fracture networks in the context of developing unconventional shale reservoirs with hydraulically fractured horizontal wells. Complex fracture networks can be generated (1) from stochastic algorithms that enter fracture density, length, and strike distributions, or (2) from the flowing-producing DFN (FP-DFN) area that is constrained by microseismic information, or (3) from digitization of realistic outcrop maps. Then, new unstructured fracture gridding and discretization techniques specially tailored for complex fracture networks are developed to handle nonuniform fracture aperture, extensive fracture clustering, and nonorthogonal fracture intersections. Finally, the numerical simulation of pressure buildup is performed in complex fracture networks that are generated from three proposed approaches with both synthetic and field examples. Flow regimes are identified and are discussed on the basis of pressure-derivative plots. Complex fracture networks show that the most representative characteristics are formation/fracture bilinear flow and formation linear-flow regimes. The appearance of the bilinear-flow regime during early period might not be clear because of the impact of the wellbore-storage effect as both the wellbore volume and the volume of the larger natural fractures in communication with the wellbore. In addition, the microseismic-based approach reduces the uncertainties of fracture characterization with percentiles of FP-DFN areas. The pressure-buildup response observed clearly indicates that the higher the percentiles of FP-DFN areas (or intense naturally fractured portion of the completion), the lower the pressure difference and derivative curves. Fracture mineralization affects pressure-buildup responses significantly. The decrease in nonuniform fracture apertures causes pressure-diagnostic plots to shift upward. The effect of boundary in the outcrop-based complex fracture network shows an early deviation from the formation linear-flow regime. No classic dual-porosity behavior is observed in all cases to quantify related parameters. Three practical techniques are proposed to generate complex fracture networks. Pressure-transient characteristics are identified and summarized. Further research areas are discussed and highlighted. The combination of techniques such as microseismic, horizontal core, production logging or some method to characterize the fracture network can be used to close the loop between the inferred network and the response that it should exhibit during pressure-transient analysis.

Integrated reservoir flow and geomechanical model to generate type curves for pressure transient responses of a hydraulically-fractured well in shale gas reservoirs

Shale gas reservoirs have ultra-low matrix permeability and consist of matrix and natural fracture systems. Horizontal wells with hydraulic fractures are necessary to economically exploit shale gas reservoirs. Due to these complex features of shale gas reservoirs, understanding pressure transient characteristics is of importance. Through coupling of flow and geomechanical models for well/reservoir/hydraulic fracture systems, a new approach has been established to predict the pressure transient behavior and to generate type curves. To account for geomechanical effects with stress dependent permeability, linear elastic geomechanical models and two stress dependent permeability correlations, exponential and power law correlations, from previous experimental researches were implemented in the reservoir model. A number of cases considering a geomechanical model, exponential correlation, and power law correlation were compared. These processes showed roughly a 1–5% variation of productivity in shale gas reservoirs. Based on the extensive numerical simulations with the updated model, a series of type curves were developed in terms of dimensionless pseudopressure and derivative of dimensionless pseudopressure versus dimensionless time considering various reservoir and fracture properties. Using the type curves as a guide, we then presented flow regimes that are expected for different values of geomechanical properties, number of fractures, length of the fractures, spacing between fractures, and properties of stimulated reservoir volume (SRV). Using the characteristics of new dimensionless parameters and the developed type-curve set, a simple and practical procedure was presented to estimate reservoir properties in multi-fractured horizontal wells. Application of type curve matching to synthetic data was shown to be useful in estimating effective fracture and matrix permeability and porosity. A history match of a field example in Barnett Shale data indicates that the model with stress-dependent properties matches the actual production data better than the model with constant properties. This study provides insight into the characteristics of a hydraulically-fractured horizontal well, and the newly developed type curves yield more unique and accurate results.

Pressure-Transient Characteristics of Hydraulically Fractured Horizontal Wells in Shale-Gas Reservoirs With Natural- and Rejuvenated-Fracture Networks

Summary During the past few years, several studies have analyzed the pressure-transient responses of hydraulically fractured horizontal wells in shale-gas reservoirs. However, that research included simplified models that reflected natural and hydraulic fractures -only, unlike real shale reservoirs. To develop an accurate shale-gas model, this study considers the effects of rejuvenated fractures as well as natural and hydraulic fractures. Rejuvenated fractures, regarded as an important specificity in this paper, are revitalized natural fractures created by hydraulic fracturing. To analyze the pressure-transient characteristics and productivity of fractured horizontal wells in shale reservoirs, extensive numerical simulations have been conducted. This model considers the effects of natural- and rejuvenated-fracture permeability, matrix permeability, parameters of hydraulic fractures (e.g., width, height, and half-length), and the range of stimulated reservoir volume. Results show a clear distinction between existing models and the proposed model. In the proposed model, the boundary induced by the rejuvenated fractures generates pseudoboundary-dominated flow. This work expands our insight into the pressure-transient characteristics of a hydraulically fractured horizontal well in a shale-gas system.

Study on the steady and transient pressure characteristics of shale gas reservoirs

The flow law was obtained by combining the mechanics of continuous media and molecular kinematics method for shale gas reservoirs with nano/micropores. The new non-linear seepage model considering the diffusion, slippage and desorption effects was established and simplified. The steady and transient governing equations were constructed on the basis of the non-linear model. The pressure characteristic analytical solution was then obtained. The permeability adjustment factor changes largely when the pore throat radius is less than 100 nm. Therefore, the flow law in nano/micropore departs significantly from Darcy's law. Numerical simulation results show that the flux of gas changes significantly with the permeability of the pore throat radius, and the flow in nano/micropore reservoir shows the microscale effect. Compared with the pressure distribution calculated by Darcy's law, the pressure distribution calculated by the new model decreases slowly because of the diffusion and desorption effect. The results provide a theoretical foundation for developing shale gas reservoirs.

Effect of hydraulic brake pipe inner diameter on vehicle dynamics

During the operation of the brakes the behavior of the brake fluid in the brake piping is one element that has a large effect on feel and on transient pressure characteristics. In the present study investigates the effect of fitting a brake pipe with different inner diameters to each wheel at the rear axle on the brake performance and vehicle dynamics. Theoretical analysis and road tests were conducted and applied on a Fiat 128 vehicle to investigate the changes in brake efficiency and brake force balance. The theoretical and experimental results showed the improvement of the car brake efficiency and brake balance when fitting a brake pipe with the same inner diameter (without orifice) for each wheel.

Pressure Transient Analysis of Multi-stage Hydraulically Fractured Horizontal Wells

The horizontal well with multiple transverse fractures has proven to be an effective way to exploit tight reservoirs economically. Due to the nature of ultralow permeability, it would take a significant long period of time for a well producing in transient flow regimes. Therefore, pressure transient analysis for such a well is important in both evaluation of fracturing treatment by estimating fracture and reservoir parameters and prediction of the long-term production behavior of wells in oil recovery. This paper discusses the analysis of pressure-transient responses of horizontal wells intercepting multiple infinite-conductivity transverse fractures. Then a numerical model is utilized to simulate the whole well flow regimes and pressure transient characteristics of multiple fractured horizontal wells. Accordingly, appropriate analytical pressure-transient models and analysis procedures are provided to determine fracture properties, i.e. average fracture half-length and spacing and estimate the oil in place in the stimulated reservoir volume.

The Transient Flow Analysis of Fluid in a Fractal, Double-Porosity Reservoir

The mathematical model for transient fluid flow in porous media is based in general on mass conservation principle. Because of the small compressibility of formation fluid, the quadratic term of pressure gradient is always ignored to linearize the non-linear diffusion equation. This may result in significant errors in model prediction, especially at large time scale. In order to solve this problem, it may be necessary to keep the quadratic term in the non-linear equations. In our study, the quadratic term is reserved to fully describe the transient fluid flow. Based on this rigorous treatment, the mathematical models are established to analyze the transient flow behavior in a double porosity, fractal reservoir with spherical and cylindrical matrix. In addition, Laplace transformation method is employed to solve these mathematical models and the type curves are provided to analyze the pressure transient characteristics. This study indicates that the relative errors in calculated pressure caused by ignoring the quadratic term may amount to 10 % in a fractal reservoir with double porosity, which can’t be neglected in general for fractal reservoirs with double porosity at large time scale.

Automotive brake pipes characteristics and their effects on brake performance

During the operation of the brakes the behavior of the brake fluid in the brake piping is one element that has a large effect on feel and on transient pressure characteristics. This paper investigates the effect of fitting a brake pipe with different inner diameters to each wheel at the rear axle on the brake performance.Theoretical analysis and road tests were conducted and applied on a Fiat 128 vehicle to investigate the changes in brake efficiency and brake force balance.The theoretical and experimental results showed the improvement of the car brake efficiency and the brake balance when fitting a brake pipe with the same inner diameter for each rear wheel.

Pressure Buildup During Supercritical Carbon Dioxide Injection From a Partially Penetrating Borehole into Gas Reservoirs

Injecting CO2 into a subsurface formation causes a buildup of pressure in the vicinity of the injection well. While a large injection rate can reduce the cost associated with injection, an indefinitely large injection rate can result in excessive formation damage. To obtain an optimal injection rate without exceeding the safe pressure limits, one will like to have some knowledge of the transient pressure buildup characteristics resulting from a particular injection rate. While elaborate numerical simulations can provide reliable pressure buildup predictions, they require extensive knowledge about the formation, which is normally not available at the start of an injection process. To alleviate this problem, using some simplifying assumptions, we have developed a solution to predict the transient buildup of pressure resulting from injection of supercritical carbon dioxide from a partially penetrating well into a gas reservoir. The solution in space and time is first obtained in the Fourier–Laplace transform space, and then inverted back into real space (in cylindrical coordinates) and time. We use the solution to study pressure transient characteristics for different formation permeabilities and anisotropy ratios. Results obtained using the solution compared well with those from numerical simulations.