Pseudo-steady State Flow Condition Research Articles

Analytical Model for Predicting Productivity of Radial-Lateral Wells

An analytical model for predicting the productivity of Radial-lateral wells (RLW) drilled using radial jet drilling technology was developed in this work. The model assumes uniformly distributed equal-geometry laterals draining oil or gas under pseudo-steady state flow conditions within the lateral-reached drainage area. A numerical simulation and production data from three field cases of RLW were used to compare and validate the model. The result indicates that the model overestimates the well production rates for wells by 7.7%, 3.25%, and 8.8%, respectively. The error is attributed to several sources including, lack of data for well skin factor, uncertainty of horizontal permeability (kH) in the well area, uncertainty of permeability anisotropy (Iani), and uncertainty in bottom hole pressure (pw). Error analysis of uncertainties in kH, Iani, and pw showed that the model could predict productivity well with an acceptable error (10%) over practical ranges of these parameter values. Parameter sensitivity analyses showed that an increasing number of laterals, lateral length, and horizontal permeability would almost proportionally increase productivity. Well productivity is sensitive to well skin factor and oil viscosity, but not sensitive to the radius of the lateral.

Prediction of productivity of high energy gas-fractured oil wells

The use of fresh water as a fracturing fluid has limitations such as limited water availability in arid areas and negative impacts of water on oil and gas production in formations with high clay content. Alternatives to water for well fracturing include tailored energetic materials such as novel explosives. High energy gas fracturing (HEGF) creates radial fractures with fracture-orientations independent of formation stress anisotropy and heterogeneity. This eliminates the requirement of in-situ stress orientation for designing multi-hydraulic water-fracturing horizontal wells. Assuming uniformly distributed radial fractures around wellbore, an analytical well productivity model was derived in this study to predict productivity of HEGF-completed oil wells under pseudo steady state flow condition. Field case studies and sensitivity analyses were performed with the analytical model. Result of field case studies indicates that the analytical model over-predicts productivity of HEGF-completed wells by about 10%. Sensitivity analysis with the analytical model shows that the productivity of HEGF-completed wells reaches a maximum value at an optimal number of radial fractures around the wellbore. The productivity of the HEGF-completed wells increases non-linearly with fracture conductivity. But the benefit of increasing fracture conductivity levels out beyond fracture conductivity 2000 md-inch for the typical case investigated in this study.

Modeling well performance for fractured horizontal gas wells

In tight gas reservoirs, horizontal wells have been used to increase reservoir recovery and hydraulic fracturing has been applied to further extend the contact with the reservoir. In the past, many models, analytical or numerical, were developed to describe the flow behavior in horizontal wells with fractures. Source solution is one of analytical/semi-analytical approaches. The source method was advanced from point sources to volumetric source, and pressure change inside fractures was considered in the volumetric source method. We have developed a method that can predict horizontal well performance, and the model can also be applied to fractured horizontal wells. The method solves the problem by superposing a series of slab sources under transient or pseudo-steady state flow conditions. The principle of the method comprises the calculation of semi-analytical response of a rectilinear reservoir with closed outer boundaries. The slab source approach assigns sources a geometry dimension, similar to the volumetric source method; but has the solution similar to the point source method by neglecting the effect of the flow inside the source. When solving the source problem the pressure/flow effect inside source is considered sequentially by superposition principle over multiple sources.The pressure response is integrated over time to provide continuous pressure behavior. Flow effect inside fractures can be studied by dividing the fracture into several segments, and each can be treated as a slab source. The method is validated by comparison with the results of analytical solutions and other commercial software of horizontal wells with uniform flux and infinite conductivity, and fractured wells with uniform flux, finite or infinite conductivity. For multiple fractures in a horizontal well, the method was also compared with some published field data. The method provides an effective tool for horizontal well design and well stimulation design for gas reservoirs.In this paper, we present the details of model development. We use a case study to illustrate how the model can help to optimize wellbore and fracture design by comparing production performances of vertical well, slanted well, horizontal well, and fractured vertical and horizontal wells. The method in this paper is more accurate compared with conventional point-source solution, and can handle the transaction from transient flow to pseudo-steady state flow smoothly.

Analytical Production Modeling for Hydraulically Fractured Gas Reservoirs

: This article presents a complete analytical method to efficiently generate gas production profiles from hydraulically fractured reservoirs. Equations for production rates are first developed incorporating fracture parameters in the diffusivity-based drawdown solutions for transient as well as pseudo steady-state flow conditions. Some important considerations for modeling the key propped-fracture parameter—dimensionless fracture conductivity—are detailed for realistic production prediction. A time-step algorithm is then discussed to apply the rate equations to generate production profiles over a period of time. Analytical equations are presented to update declining reservoir pressure and resulting rock and gas properties in every time-step as functions of cumulative gas productions. Finally, a simple new equation is developed through a series of parametric applications of the two rate equations, to determine the time to switch from the transient rate equation to the pseudo steady-state equation, particularly in low-permeability reservoirs. To establish confidence in the predictability of the model, results are verified by a numerical reservoir simulator. Thus, the model is a high potential for efficient repetitive computation in early-stage design optimization of hydraulic fracture treatments for gas reservoirs.

Improved Estimation of Gas Well Deliverability From Single-Point Tests

Abstract Chase and Alkandari developed dimensionless inflow performance (IPR) curves for predicting the stabilized deliverability of hydraulically fractured gas wells using just a single-point test, namely a pressure build-up or draw-down test. Unfractured wells can also be analysed by converting the apparent skin factor to an equivalent ratio of Xe/Xf. Results obtained from the dimensionless IPR curve model can be used to generate values of n and C for the equation of stabilized deliverability. This research describes the process used to evaluate the effectiveness of the single-point model using data from 25 Canadian well tests and nine simulated well tests. The tests were analysed using fourpoint test methods, the dimensionless IPR curve method, and by assuming that the exponent of the stabilized deliverability equation was equal to one. The mean absolute value of error between the AOF predicted using multi-point deliverability test analysis methods and the dimensionless IPR curve method for the 25 Canadian wells was 9.2%, with a standard deviation of 8.7%. The mean absolute value of error between the AOF predicted using multi-point deliverability test analysis methods and the dimensionless IPR curve method for the nine simulated wells was 5.6% with a standard deviation of 4.3%. The mean absolute value of error between the AOF predicted using multi-point test methods and by assuming that the exponent of the stabilized deliverability equation was equal to one for the 25 Canadian wells was 30.5% with a standard deviation of 25.2%. The dimensionless IPR curve model appears to offer a conservative, easonably accurate, and economical method for predicting current and future gas well inflow performance from a single-point transient pressure test. Introduction The deliverability or inflow performance of a gas well is usually predicted by utilizing one of three well testing methods: the conventional backpressure test(1); the isochronal test(2); or the modified isochronal test(3). All three methods normally require that four flow tests be performed on a well, including one to stabilization, to accurately predict stabilized deliverability. Industry practice sometimes shortcuts these methods utilizing just three, two and sometimes just one flow test. In the latter case, the exponent, n, of the stabilized deliverability equation, given by Equation (1) is frequently assumed to be equal to one in order to estimate deliverability. Equation (1) Available In Full Paper. Chase and Alkandari(4) developed a single-point test method that uses dimensionless IPR curves for predicting the inflow performance of fractured gas wells producing under stabilized or pseudosteady state flow conditions. The model was developed in an attempt to better estimate gas well deliverability when just a one-point test, namely a drawdown or build-up test, is conducted. The model was based on concepts proposed by Vogel(5) and Standing(6) for oil wells, and Mishra and Caudle(7) for unfractured gas wells. The following equation serves as the basis for the single-point dimensionless IPR curve method. Equation (2) Available In Full Paper. The SPE paper by Chase and Alkandari describes how a Monte Carlo simulation was used to develop the model and generate values for the coefficient M and exponent N as a function of Xe/Xf.

Comprehensive Reservoir/Wellbore Model for Horizontal Wells

Summary Comprehensive, three-dimensional, anisotropic and transient, reservoir/wellbore coupling models are developed for infinite-conductivity and finite-conductivity wellbores to calculate the productivity of a horizontal well placed in a box-shaped drainage volume under single phase flow conditions. The finite-conductivity well model considers frictional and accelerational pressure drops in the wellbore. It also takes into account the effects of fluid inflow into the well. These models are semianalytical in nature and can be used under transient or pseudosteady state flow conditions. The infinite-conductivity well model is compared with the uniform flux model to show the differences in well productivity calculations. The effects of wellbore pressure drop on well productivity are shown using the finite-conductivity well model. These models can provide reference solutions to calculate well indices or to check the accuracy of a numerical simulator. Because of their analytical nature they are easier and faster to use than numerical simulators. Using superposition in space and time, these models can be run under a variety of constraints. We believe that our finite-conductivity well model is more general than any published previously.

Effects of Some Simplifying Assumptions On Interpretation of Transient Data

Abstract Fluid flow in porous media is described by the diffusional type of partial differential equation. In deriving the flow equation for the constant compressibility fluids, an important assumption is made regarding the magnitude of the pressure gradient: it is assumed that this gradient is small enough that the square of this term becomes negligible. In this study, an attempt is made to quantify the effect of this simplification. Data generated by numerical simulator and analytical solutions are compared in order to determine the conditions under which this simplification is justified. Except for extreme conditions (non-linear coefficient greater than 0.01), it is justifiable to ignore the square of the pressure gradient term in oil diffusional equation. The drawdown solution on gas wells contains gas properties, which are pressure dependent. As the system is being depleted, the average reservoir pressure declines. Although it seems logical to consider the gas properties at the prevailing reservoir pressure, the gas viscosity and compressibility are usually evaluated at the initial pressure level. Comparison of the analytical solutions with numerical solutions obtained for a variety of typical well test conditions indicates the magnitude of inaccuracy incurred by using standard approach to data interpretation. Based on this investigation, several pressure levels for properties calculation are considered. In applying analytical equations for pseudo-steady state flow conditions, gas properties should be evaluated at an average value of the initial and current reservoir pressures. Introduction Well test analysis is based on expressions obtained by solving the flow (diffusion) equation for a variety of boundary conditions. The flow equation which represents the core of the pressure transient method is based on the principle of mass conservation, Darcy's law and an appropriate constitutive assumption: the constant compressibility concept for liquids and the equation of state for real gases. The general form of the flow equation contains a nonlinear term, the square of the pressure gradient. Obviously, the occurrence of this non-linearity is mathematically inconvenient and thus should be eliminated if possible. The simplification is achieved by assuming small pressure gradients in the formation; consequently, a square of a small number can be ignored. To the best of our knowledge, no study has been reported which would determine whether or not such a simplification is indeed justified. In this study, the effect of a non-linear term on the interpretation of transient data was evaluated by comparing the analytical solutions with numerical solutions which are generated for the identical test conditions. For gas reservoirs, a step-wise approach and a pressure averaging method for evaluating the gas properties in analytical solutions are proposed. The one dimensional flow of a slightly compressible fluid (oil) in a porous medium can be expressed, in a dimensionless form, as follows: Equation 1–8 (available in full paper) The numerical simulator is based on Equations (1) and (4). The solutions are obtained for the condition of a constant production rate, the early transient and the pseudo-steady state time periods. The finite difference implicit method and the iterative Newton- Raphson procedure are applied.

A Simple Buildup Analysis Method To Determine Well Drainage Area and Drawdown Pressure for a Stabilized Well

Summary This paper presents a new method that applies to wells that are shut in after having reached pseudosteady-state flow conditions. Based on the complete Miller-Dyes-Hutchinson (MDH) equation, a corrected pressure is defined that allows extension of the semilog straight line by about two log cycles for symmetric systems and one-half log cycle for others. The drainage area is directly computed. If the final recorded shut-in pressures depart from the straight line, it is also possible to compute the shape factor and the average pressure independently of the initial pressure.

An Analysis of Changing Backpressure Test Curves From Some Gulf Coast Area Gas Wells

Abstract Estimates of gas well deliverability based on initial testing may be in error due to liquid saturation increases around the wellbore created by invasion of drilling and/or workover fluids. Flow coefficient C and exponent n of the backpressure test equation may change after a well has been placed on production. This change will depend on the degree and nature of saturation, and on properties of the reservoir being investigated. This article discusses examples of field test data obtained during the producing life of many Gulf Coast area gas wells. The data indicate a shifting of the backpressure curve, and show that deliverability may significantly improve after a well has been placed on production. This improvement is due mainly to an increase in the relative permeability to gas. Also discussed are time requirements for cleaning up a gas completion. Introduction Accurately predicting gas well deliverability is a common problem in the natural gas industry. These predictions are essential to any attempt at optimum operation of a gas-producing complex. The large investments required for additional deliverability demand that both current and future capabilities be known as accurately as possible for each well in a gas sales system so that a minimum of standby or backup deliverability is required. Future deliverability predictions become especially important since in many cases major additions of deliverability require at least 1 year of lead time for installing the required field equipment. A large amount of data obtained during the past 10 years indicates that deliverability characteristics of a gas well may improve from an initial value after the well is placed on production. The noted improvements have been great enough to merit a thorough analysis of these data. This article presents results of this investigation in hopes that the conclusions will help provide the industry better answers to two basic questions concerning gas well test data:How reliable is initial backpressure test data forpredicting future deliverability?Recognizing that liquid saturation increases aroundthe wellbore caused by drilling and/or workover fluidswill adversely affect backpressure test data, how long musta well be cleaned before this area of increased saturationis removed or reduced to a point where reasonablyaccurate test data can be obtained? Theory The most common equation for steady-state flow of gas from porous media is the backpressure test equation Q = C (Pf - Pa )n. The performance coefficient C varies with the relative permeability to gas, with the Z factor and viscosity of the gas involved, and with the drainage radius of the reservoir. The exponent n is a turbulence term included to account for the effects of nondarcy flow occurring in the vicinity of the wellbore. As the flow regime progresses from laminar or Darcy flow to complete turbulence, the exponent n is usually considered to vary between 1.0 and 0.5. During a conventional gas well backpressure test, stabilized or pseudosteady-state flow usually does not exist because pressure change effects occurring at the wellbore have not had time to reach the drainage radius of the completion. Due to this instantaneously changing drainage radius with time, the values of C and n measured on a conventional test will differ from the values that will exist when the well reaches a pseudosteady-state flow condition. The correct value of n for a completion must be obtained either by an isochronal testing procedure or by adjusting conventional backpressure test data to an isochronal basis. Various methods proposed for predicting the stabilized performance coefficient C require use of additional test data (usually a pressure buildup curve). Without such data an assumption is required to determine the stabilized constant C. The assumption is that the skin and turbulence factors expressed in both pseudosteady-state and unsteady- state equations for gas flow in the reservoir can be replaced by the adjusted isochronal n, and this n will account for all skin and turbulence effects. JPT P. 1541ˆ