productivity index

The main objective of this paper is understanding the phenomenal anomalous diffusion flow mechanisms in unconventional fractured porous media. This understanding is crucial for estimating the impact of these flow mechanisms on pressure behavior, flow regimes, and transient and pseudo-steady state productivity index of the two cases of inner wellbore conditions: constant sandface flow rate and constant wellbore pressure. The targets are hydraulically fractured unconventional reservoirs characterized by porous media with complex structures. These media are consisted of a matrix and naturally induces fractures embedded in the matrix as well as hydraulic fractures.

Several analytical models for pressure drop and decline rate as wells productivity index in ultralow permeability reservoirs are presented in this study for the two inner wellbore conditions. A numerical solution is also presented in this study for pressure behavior using a linearized implicit finite difference method. The analytical models are developed from trilinear flow models presented in the literature with a consideration given to the temporal and spatial fractional pressure derivative for the ano malous diffusion flow that could be the dominant flow mechanism in the stimulated reservoir volume between hydraulic fractures. Mittag-Leffler functions are used for solving fractional derivatives of pressure and flow rate considering that temporal and spatial fractional exponents are less than one. Two solutions are developed in this study for the two inner wellbore conditions. The first represents the transient state condition that controls fluid flow in unconventional reservoirs for very long produc tion time. The second is the solution of pseudo-steady state condition that might be observed after transient state flow. The second solution is used for estimating stabilized pseudo-steady state productivity index considering different reservoir conditions. In the numerical solution, the temporal and spatial domains are discretized into several time steps and block-centered grids respectively. The results of the analytical models are compared with numerical solutions.

The outcomes of this study are: 1) Understanding the impact of temporal and spatial diffusion flow mechanisms on pressure behavior, flow rate declining pattern, and productivity index scheme during early and late production time. 2) Developing analytical and numerical models for fractional derivatives of pressure and flow rate considering diffusion flow mechanisms 3) Developing analytical models for different flow regimes that could be developed during the entire production life of reservoirs. 4) Studying the impact of reservoir configuration and wellbore type as well as different temporal and spatial diffusion flow conditions on stabilized pseudo-steady state productivity index. The study has pointed out: 1) Temporal and spatial diffusion flow have a significant impact on pressure drop, flow rate, and productivity index. 2) Wellbore pressure drop for constant Sandface flow rate declines rapidly as the temporal diffusion flow mechanism is the dominant flow pattern in the porous media. 3) Wellbore pressure drop for constant Sandface flow rate slightly increases during transient state flow as the spatial diffusion flow mechanisms increase and rapidly increases during pseudo-steady state flow. 4) Productivity index of diffusion flow is higher than the index of normal diffusion flow during transient and pseudo-steady state conditions. 5) The linear flow regime is most affected by anomalous diffusing flow and can be used to characterize the type of diffusion flow.

This paper introduces an analytical approach for generating the inflow performance relationships (IPR) of different reservoirs depleted by different wellbore types at different conditions. The main focus of this paper is given to multiphase flow (oil, gas, water) and two-phase flow (oil, gas) during transient and pseudo-steady state flow conditions. The proposed approach presents new integrated models for the IPR that correlates the wellbore pressure with the multiphase total flow rate or the normalized pressure and rate by the bubble point pressure and single-phase flow rate at this pressure. These models consider the changes in reservoir fluid physical properties and reservoir relative permeabilities by coupling PVT data and relative permeability curves. The motivation of this study is reducing the uncertainty in the IPR of reservoirs undergoing the multiphase flow.

Predicting multiphase IPRs may go throughout three tasks. The first is developing the pressure functions of reservoir mobility and total compressibility by developing several correlations for reservoir fluid properties such as oil, gas, and water formation volume factor as well as gas solubility in oil and water. Several correlations are needed also for relative permeability behavior of the three fluids with the pressure. These correlations can be generated by the multi-regression analysis of PVT data and relative permeability curves. The second represents developing the analytical models for the flow regimes that could be developed during the entire production life of the reservoirs. The single and multiphase flow IPRs for different flow regimes are predicted in the third task. The proposed IPR in this study is plotted between the wellbore pressure and the total flow rate at reservoir condition or the normalized reservoir pressure and flow rate.

The observations obtained from this study are: 1) The proposed approach for the multiphase flow IPRs is not only time-variant but also depends on the flow condition whether transient or pseudo-steady state flow. 2) The IPR of the multiphase flow gives lower performance than the single-phase flow. 3) The IPR of the early time transient production is better than the late time pseudo-steady state production. 4) It is highly recommended to develop the models of fluid properties for each reservoir instead of using the models presented in the literature.

The novel points presented in this paper are: 1) Introducing a new approach for the inflow performance relationships in the reservoirs experiencing multiphase flow and depleted by horizontal wells or multiple hydraulic fractures. 2) Introducing the pressure functions of the multiphase flow reservoir mobility and multiphase flow total reservoir compressibility that consider the changes in reservoir fluid properties and relative permeabilities with production time and pressure in constructing the IPRs.

History matching is a crucial step in process of gaining reliable model, which further will be used for production profile forecasting, well planning, choosing proper development plan of a field. Target reservoir for which it needed to construct and history match a model included several features that made this process quite challenging: - high lithological heterogeneity due to alluvial genesis of rocks, - large influence of diagenetic alteration of sediments on reservoir quality, - impossibility of direct using of 3D seismic data because of low thickness of reservoir formation. This work was successfully performed through complex application of following methods: - building detailed facial maps based on conceptual depositional model, core and wireline log data from enormous number of wells, - using both well test and production data during adjustment of model for matching. Concerning a key peculiarity of the reservoir - salt cementing - unique method of its modeling in both static and dynamic models was applied. This model also has the feature of changing salinization coefficient of reservoir during waterflooding. The basis for applying of salt cementing of reservoir is relationship found between wireline log and salinization coefficient from core data.

Descriptive Analytics is the first step of a three-step data-driven analytics workflow used for managing and optimizing completion, production and recovery of shale wells. The comprehensive data-driven analytics workflow for the unconventional resources is called Shale Analytics (Mohaghegh 2017). The key behind Shale Analytics is the incorporation of all field measurements that contribute to the productivity of shale wells. There are workflows in the market that claim to be data analytics related but do not make use of all the available field measurements when performing their analyses. These workflows are mainly based on traditional statistical algorithms rather than Artificial Intelligence and Machine Learning. Such approaches represent different versions of Decline Curve Analysis.

Shale Descriptive Analytics takes into account seven categories of field measurements; (i) well construction and trajectory, (ii) well spacing and stacking, (iii) reservoir characteristics, (iv) completion design, (v) hydraulic fracturing implementation, (vi) operational constraints, and (vii) well productivity. Each of the above categories of field measurements include several parameters. Shale Descriptive Analytics provides two types of insight on the contribution of all the field measurements to well productivity. The first type of insight compares and quantifies the contribution of the different categories of field measurements to well productivity. The second, more detail type of insight compares and quantifies the contribution of each of the parameters of the first six categories to the final category that is well productivity and then compares all the parameters to one another. The Shale Descriptive Analytics presented in this article demonstrate the results of more than 800 shale wells in one of the most productive shale plays in Texas.

Two conclusions have been achieved as the result of this study. (a) In the early life of a shale asset, when the wells are NOT too close to one another (when Frac-Hit is not an issue), using well productivity indices (such as initial production, initial decline rate, first 30, 60, 90, 120, 180 and 365 days of cumulative production, etc.) can provide realistic insight for completion optimization, well productivity and recovery. (b) Once the number of wells in a given asset increases, resulting in the reduction of the distances between parent and child wells (Frac-Hit impacts production and recovery), well productivity indices will no longer be able to provide the required insight for modeling and analysis of field measurements. This is because as the number of wells increases in a given shale asset, the fracture-driven interaction between wells (also known as Frac-Hit) takes over the overall productivity of all the wells in the field. Frac-Hit not only negatively influences parent and child wells productivity and recovery, it completely undermines all the existing techniques (traditional techniques such as RTA and numerical simulation as well as all the existing techniques based on Data Analytics) for completion and production optimization of shale wells. At the conclusion of this article, a new approach to overcome this specific problem is introduced.

Reservoir depletion can induce substantial changes in the stress state of the rock. The coupled interaction between the pore fluid pressure and rock stress will then alter the reservoir permeability, which in turn reversely affects the productivity index of the production well. A new nonlinear analytical solution is developed for the drawdown-dependent productivity index of reservoirs under steady-state flow. Biot's theory of poroelasticity is used to derive the depletion-induced changes in the reservoir rock porosity and permeability. The well-known Mindlin's solution for a Nucleus of Strain in a semi-infinite elastic medium is applied as Green's function and integrated over the depleted volume of reservoir rock to obtain the 3D distribution of stress and volumetric strain distributions. The fluid transport equation is nonlinearly coupled to the solid mechanics solution via the stress-dependent permeability coefficients. A perturbation technique is applied to mathematically treat the described nonlinearity to solve for the coupled equations of pore fluid flow and rock stress under steady-state flow. The good match between the obtained analytical approximations for productivity index and the numerical solutions verifies the correctness and robustness of the proposed model.

Results indicate and confirm the expected strong dependency of the well productivity index to the drawdown magnitude as well as the poroelastic constitutive parameters of the reservoir rock, with the highest sensitivity to drained bulk modulus, followed by the reservoir depth and solid-grain modulus. The lowest PI sensitivity is to the pore fluid modulus and Poisson's ratio. The resulting productivity index is found out to be drawdown-dependent, which can render values substantially different than the productivity index estimate from the conventional flow-only analysis. The presented estimates for the related nonlinear productivity index can be readily used by the practicing engineers.

The Gulf of Mexico, and more precisely the Wilcox trend, has long been considered as challenging area for developing profitable hydrocarbon fields. In fact, the safe drilling of deep offshore wells needs to take into account the geological and geomechanical complexities, generated by the different sedimentological and tectonic events that accompanied the development of the Wilcox trend. In the case of Buckskin field, located in Keathley Canyon protraction (Figure 1), and in order to overcome those challenges, we developed a workflow that ranks all the parameters related to the geometry, the geology, the rock quality and the geomechanics characteristics of the reservoir. The core of the workflow is articulated around a probabilistic method that will assess the uncertainty of the productivity index, based on experimental design and Monte Carlo simulation. The proposed workflow allowed the optimization of the PI of the well thanks to a highly deviated reservoir section at a depth below 24,000', combined with an optimal fracking job.

Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. The productivity index or PI is a measure of the well potential or ability to produce and is a commonly measured well property. The symbol J is commonly used to express the productivity index; as well as, being the preferred symbol by the Society of Petroleum Engineers. See also: "Productivity index" Search

When considering the performance of oil wells, it is often assumed that a well's performance can be estimated by the productivity index. However, Evinger and Muskat[1] pointed out that, for multiphase flow, a curved relationship existed between flow rate and pressure and that the straight-line productivity index did not apply to multiphase flow. The constant productivity index concept is only appropriate for oil wells producing under single-phase flow conditions, pressures above the reservoir fluid's bubblepoint pressure. For reservoir pressures less than the bubblepoint pressure, the reservoir fluid exists as two phases, vapor and liquid, and techniques other than the productivity index must be applied to predict oilwell performance. There have been numerous empirical relationships proposed to predict oilwell performance under two-phase flow conditions.

There are two fundamental problems that make accurately estimating the productivity of a horizontal well more difficult than estimating the productivity of a vertical well. The theoretical models available have a number of simplifying assumptions and the data required for even these simplified models are not likely to be available. Still, we must make estimates and decisions based on those estimates. In this page, two productivity models that have proved useful in practice are discussed. The first, published by Babu and Odeh[1] in 1989, is limited to single-horizontal wells.

Introduction The first hydraulic fracturing treatment was pumped in 1947 on a gas well operated by Pan American Petroleum Corp. in the Hugoton field.[1] Kelpper Well No. 1, located in Grant County, Kansas, was a low-productivity well, even though it had been acidized. The well was chosen for the first hydraulic fracture stimulation treatment so that hydraulic fracturing could be compared directly with acidizing. Since that first treatment in 1947, hydraulic fracturing has become a common treatment for stimulating the productivity of oil and gas wells. Hydraulic fracturing is the process of pumping a fluid into a wellbore at an injection rate that is too great for the formation to accept in a radial flow pattern. As the resistance to flow in the formation increases, the pressure in the wellbore increases to a value that exceeds the breakdown pressure of the formation open to the wellbore. Once the formation "breaks down," a fracture is formed, and the injected fluid begins moving down the fracture. In most formations, a single, vertical fracture is created that propagates in two directions from the wellbore. These fracture "wings" are 180 apart and normally are assumed to be identical in shape and size at any point in time; however, in actual cases, the fracture wing dimensions may not be identical. In naturally fractured or cleated formations, it is possible that multiple fractures can be created and propagated during a hydraulic fracture treatment. Fluid that does not contain any propping agent (called the "pad") is injected to create a fracture that grows up, out, and down, and creates a fracture that is wide enough to accept a propping agent.