A Single Equation to Depict Bottomhole Pressure Behavior for a Uniform Flux Hydraulic Fractured Well

Pressure transient analysis for a vertically hydraulically fractured well is evaluated using two different equations, which cater for linear flow at the early stage and radial flow in the later stage. However, there are three different stages that take place for an analysis of pressure transient, namely linear, transition and pseudo-radial flow. The transition flow regime is usually studied by numerical, inclusive methods or approximated analytically, for which no specific equation has been built, using the linear and radial equations. Neither of the approaches are fully analytical. The numerical, inclusive approach results in separate calculations for the different flow regimes because the equation cannot cater for all of the regimes, while the analytical approach results in a difficult inversion process to compute well test-derived properties such as permeability. There are two types of flow patterns in the fracture, which are uniform and non-uniform, called infinite conductivity in a high conductivity fracture. The study was conducted by utilizing an analogous study of linear flow equations. Instead of using the conventional error function, the exponential integral with an infinite number of wells was used. The results obtained from the developed analytical solution matched the numerical results, which proved that the equation was representative of the case. In conclusion, the generated analytical equation can be directly used as a substitute for current methods of analyzing uniform flow in a hydraulically fractured well.

Revision of Pressure Transient Analysis in Mature Condensate-Rich Tight Gas Fields in Sultanate of Oman

Pressure transient analysis (PTA) has been used as one of the important reservoir surveillance tools for tight condensate-rich gas fields in Sultanate of Oman. The main objectives of PTA in those fields were to define the dynamic permeability of such tight formations, to define actual total Skin factors for such heavily fractured wells, and to assess impairment due to condensate banking around wellbores. After long production, more objectives became also necessary like assessing impairment due to poor clean-up of fractures placed in depleted layers, assessing newly proposed Massive fracturing strategy, assessing well-design and fracture strategies of newly drilled Horizontal wells, targeting the un-depleted tight layers, and impairment due to halite scaling. Therefore, the main objective of this paper is to address all the above complications to improve well and reservoir modeling for better development planning. In order to realize most of the above objectives, about 21 PTA acquisitions have been done in one of the mature gas fields in Oman, developed by more than 200 fractured wells, and on production for 25 years. In this study, an extensive PTA revision was done to address main issues of this field. Most of the actual fracture dynamic parameters (i.e. frac half-length, frac width, frac conductivity, etc.) have been estimated and compared with designed parameters. In addition, overall wells fracturing responses have been defined, categorized into strong and weak frac performances, proposing suitable interpretation and modeling workflow for each case. In this study, more reasonable permeability values have been estimated for individual layers, improving the dynamic modeling significantly. In addition, it is found that late hook-up of fractured wells leads to very poor fractures clean out in pressure-depleted layers, causing the weak frac performance. In addition, the actual frac parameters (i.e. frac-half-length) found to be much lower than designed/expected before implementation. This helped to improve well and fracturing design and implementation for next vertical and horizontal wells, improving their performances. All the observed PTA responses (fracturing, condensate-banking, Halite-scaling, wells interference) have been matched and proved using sophisticated single and sector numerical simulation models, which have been incorporated into full-field models, causing significant improvements in field production forecasts and field development planning (FDP).

Fracture Geometry Calibration Using Multiple Surveillance Techniques

An accurate Mechanical Earth Model (MEM) is of vital importance in tight gas reservoirs where hydraulic fracturing is the only way to produce hydrocarbons economically. The Barik tight gas reservoir is the main target in Khazzan and Ghazeer Fields at the Sultanate of Oman (Rylance et al., 2011). This reservoir consists of multiple low-permeability sandstone layers interbedded with marine shales. A good understanding of the fracture propagation in such a reservoir has a major effect on completion and fracturing design. The MEM derived from sonic logs and calibrated with core data needs to be further validated by independent measurements of the fracturing geometry. Multiple surveillance techniques have been implemented in the Barik reservoir to validate the MEM and to match observations from hydraulic fracturing operations. These techniques include closure interpretation using a wireline deployed formation testing assembly, the use of mini-frac injection tests with deployed bottomhole pressure gauges, execution of post injection time-lapse temperature logging, the injection of radioactive tracers, associated production logging, subsequent pressure transient analysis and other techniques. A cross-disciplinary team worked with multiple sources of data to calibrate the MEM with the purpose of delivering a high-confidence prediction of the created fracture geometry, which honors all available surveillance data. In turn, this validation approach provided a solid basis for optimization of the completion and fracturing design, in order to optimally exploit this challenging reservoir and maximize the economic returns being delivered. For example, combination of stress testing with radioactive tracers provided confidence in stress barriers in this multilayered reservoir. Pressure transient analysis allowed to calibrate mechanical model to match fracturing half-length that is contributing to production. This paper provides extensive surveillance examples and workflows for data analysis. Surveillance of this degree in the same well is uncommon because of the associated time and cost. However, it provides unique value for understanding the target reservoir. This paper demonstrates the Value Of Information (VOI) that can be associated with such surveillance and provides a concrete and practical example that can be used for the justification of future surveillance programs associated with the hydraulic fracturing operations.

Delivering Pressure Transient Analysis During Drawdown on ESP Wells: Case Studies and Lessons Learned

While pressure transient analysis (PTA) is a proven interpretation technique, it is mostly used on buildups because drawdowns are difficult to interpret. However, the deferred production associated with buildups discourages regular application of PTA to determine skin and identify boundary conditions. Several case studies are presented covering a range of well configurations to illustrate how downhole transient liquid rate measurements with electrical submersible pump (ESP) gauges enable PTA during drawdown and therefore real-time optimization. The calculation of high-frequency transient flow rates using ESP gauge real-time data is based on the principle that the power absorbed by the pump is equal to that generated by the motor. This technique is independent of fluid specific gravity and therefore is self-calibrating with changes in water cut and phase segregation. Analytical equations ensure that the physics is always respected, thereby providing the necessary repeatability. The combination of downhole transient high-frequency flow rate and permanent pressure gauge data enables PTA using commonly available analytical techniques and software, especially because superposition time is calculated accurately. The availability of continuous production history brings significant value for PTA. It makes it possible to perform history matching and to deploy semilog analysis using an accurate set of superposition time functions. However, the application of log-log analysis techniques is usually more challenging because of imperfections in input data such as noise, oversimplified production history, time-synchronization issues, or wellbore effects. These limitations are solved by utilizing high-frequency downhole data from ESP. This is possible first as superposition time is effectively an integral function, which dampens any noise in the flow rate signal. Another important finding is that wellbore effects in subhydrostatic wells are less impactful in drawdowns than in buildups where compressibility and redistribution can mask reservoir response. Key reservoir properties, in particular mobility, can nearly always be estimated, leading to better skin factor determination even without downhole shut-in. Finally, with the constraint of production deferment eliminated, drawdowns can be monitored for extended durations to identify boundaries and to perform time-lapse interpretation more efficiently. Confirming a constant pressure boundary or a change in skin enables more effective and proactive production management. In all cases considered, a complete analysis was possible, including buildup and drawdown data comparison. With the development of downhole flow rate calculation technology, it is now possible to provide full inflow characterization in a matter of days following an ESP workover, without any additional hardware or staff mobilization to the wellsite and no deferred production. More importantly, the technique provides the necessary information to diagnose the cause of underproduction, identify stimulation candidates, and manage drawdown.

A Comprehensive Model Integrating the Stress Sensitivity for Pressure Transient Behavior Study on the Two-Zone System for Offshore Loose Sandstone Reservoirs

Permeability changes in the weakly consolidated sandstone formation, caused by sand migration, has a serious impact on the interpretation of well testing and production prediction. In this article, a two-zone comprehensive model is presented to describe the changes in permeability by integrating the produced sand, stress sensitivity characteristics. In this model, inner zone is modeled as a higher permeability radial reservoir because of the sand migration, while the outer zone is considered as a lower permeability reservoir. Besides, non-Newtonian fluid flow characteristics are considered as threshold pressure gradient in this paper. As a result, this bi-zone comprehensive model is built. The analytical solution to this composite model can be obtained using Laplace transformation, orthogonal transformation, and then the bottomhole pressure in real space can be solved by Stehfest and perturbation inversion techniques. Based on the oilfield cases validated in the oilfield data from the produced sand horizontal well, the flow regimes analysis shows seven flow regimes can be divided in this bi-zone model considering stress sensitive. In addition, the proposed new model is validated by the compassion results of traditional method without the complex factors. Besides, the effect related parameters of stress sensitivity coefficient, skin factor, permeability ratio and sanding radius on the typical curves of well-testing are analyzed. This work introduces two-zone composite model to reflect the variations of permeability caused by the produced sand in the unconsolidated sandstone formation, which can produce great influence on pressure transient behavior. Besides, this paper can also provide a more accurate reference for reservoir engineers in well test interpretation of loose sandstone reservoirs.

Evaluating Phase Blockages and Mobility Changes During Pressure Transient Analysis

Pressure transient analysis (PTA) is a cogent methodology to evaluate dynamics of hydrocarbon reservoirs. Numerous analytical and numerical models have been developed to model various types of wellbore, reservoir, and boundary responses. However, the near-wellbore region remains to be perplexing in pressure transient analysis. In this paper we investigate the pressure transient behavior of phase blocking and mobility variations caused by fluid phase interactions or properties, such as viscous drag forces and surface tension at the near-wellbore region and their impact on pressure transient evaluation. We have used real field examples to scrutinize relative effects of mobility variations in pressure transients. The impact of capillary number (Nc) acting on the near-wellbore region and its influence on pressure transient behavior and skin alteration were examined in detail. Several real field examples honoring actual reservoir rock special core analysis (SCAL) and fluid pressure/volume/temperature (PVT) properties have been studied. Actual field data discussed in this paper for PTA were captured during drill stem testing (DST) operations from various hydrocarbon reservoirs in the Berkine Basin of Algeria. PVT laboratory-measurement-based fluid properties were used in conjunction with tuned equation of state (EOS) models to ensure consistency between wells and reservoirs. Pressure transient analysis of a gas condensate reservoir system can depict various mobility regions, especially while flowing below dew point pressure. In some cases, three-distinct-mobility regions can be identified as: a far-field zone with initial gas and condensate saturation; a mid-field zone with increased condensate saturation and lower gas relative permeability; and a near-wellbore zone with high Nc which increases gas relative permeability and mobility. These three-distinct-mobility regions form due to condensate dropping out and fluid interactions in the near wellbore. We demonstrate, with real-life field examples of the near-wellbore region, how the relative effects of viscous drag forces and surface tension forces acting across the liquid and gas interface can enable the reference fluid phase to regain its mobility. We further investigate the evaluation of skin factor in such circumstances and show how the existence of phase blocking and velocity stripping can cause over-estimation or under-estimation of skin factor. We present a novel set of real field examples and relations between various zones in hydrocarbon reservoirs to avoid snags of misleading pressure transient interpretations and how composite models can be accurately used to represent complex cases. Field examples from Algerian hydrocarbon reservoirs are depicted. The findings could be easily applied for similar reservoirs in other parts of the globe to identify and model such intricate systems.

A New Method to Identify and Quantify Hydraulic Communication between Isolated Reservoir Systems Using Pressure-Transient Data

A new analytical workflow that uses pressure-transient data to characterize connectivity between two originally non-communicating reservoir zones is presented. With this technique, hydraulic communication is clearly identified and corresponding fluid crossflow rates accurately quantified. It is applicable to a wide range of communication mechanisms, including inactive commingled-completion wells, conductive fractures and faults, in addition to behind-casing completion problems. The impact of interference is also captured by handling an unlimited number of wells and communicating media. The solution uses pressure-transient data effectively to diagnose communication and estimate the amount of transported fluids. The new formulation is a general formulation for handling an unlimited number of producing wells and communicating media, which helps analyze pressure responses under the influence of interference. The reservoir system under consideration is assumed to be two-dimensional with two initially-isolated reservoir zones, intersected by an arbitrary number of wells, part of which are active producers while others can be penetrating wells with commingled completion, in addition to other communicating media. The well test duration is assumed long enough for the pressure-transient data to be affected by fluid communication. To demonstrate the applicability of the new model, a synthetic case study is presented to diagnose a fluid-communication mechanism. The system under consideration consists of two isolated reservoirs and two wells: a single producer completed in the top reservoir in which pressure responses are measured, and an offset well connecting both reservoirs through a fluid communication mechanism. Using the model, type-curves have been utilized to diagnose the hydraulic communication in the offset well. The connectivity of the communication channel in the offset well is also estimated by matching the pressure-transient responses of the model with the measured data. The rate of crossflow between the two reservoirs is also quantified as a function of time. It is observed from the log-log plot that higher connectivity values of the cement sheath causes a steeper merging ramp in the transition region, following a period dominated by the producing reservoir. Although the rate of crossflow depends on the magnitude of the connectivity, it is observed that there is an upper limit controlled by the rock and fluid properties of the individual reservoirs. In addition, the pressure regime at the location of the offset well plays an important role in the rate of crossflow. This study presents a novel analytical approach to detect communication from pressure-transient data, and to quantify the magnitude of crossflow rates between reservoir zones. The formulation captures the influence of interference between wells caused by production. While complementing diagnostic information from other sources to confirm fluid movement from isolated zones, the method also quantifies the connectivity of the communicating media, and the amount of crossflow rates as a continuous function of time.

Diffusive Mass Transfer and Gaussian Pressure Transient Solutions for Porous Media

This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.