A review of pressure transient analysis in reservoirs with natural fractures,vugs and/or caves

A review of the pressure transient analysis of flow in reservoirs having natural fractures,vugs and/or caves is presented to provide an insight into how much knowledge has been acquired about this phenomenon and to highlight the gaps still open for further research.A comparison-based approach is adopted which involved the review of works by several authors and identifying the limiting assumptions,model restrictions and applicability.Pressure transient analysis provides information to aid the identification of important features of reservoirs.It also provides an explanation to complex reservoir pressuredependent variations which have led to improved understanding and optimization of the reservoir dynamics.Pressure transient analysis techniques,however,have limitations as not all its models find application in naturally fractured and vuggy reservoirs as the flow dynamics differ considerably.Pollard’s model presented in 1953 provided the foundation for existing pressure transient analysis in these types of reservoirs,and since then,several authors have modified this basic model and come up with more accurate models to characterize the dynamic pressure behavior in reservoirs with natural fractures,vugs and/or caves,with most having inherent limitations.This paper summarizes what has been done,what knowledge is considered established and the gaps left to be researched on.

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.

Well interference evaluation considering complex fracture networks through pressure and rate transient analysis in unconventional reservoirs

Severe well interference through complex fracture networks(CFNs)can be observed among multi-well pads in low permeability reservoirs.The well interference analysis between multi-fractured horizontal wells(MFHWs)is vitally important for reservoir effective development.Well interference has been historically investigated by pressure transient analysis,while it has shown that rate transient analysis has great potential in well interference diagnosis.However,the impact of complex fracture networks(CFNs)on rate transient behavior of parent well and child well in unconventional reservoirs is still not clear.To further investigate,this paper develops an integrated approach combining pressure and rate transient analysis for well interference diagnosis considering CFNs.To perform multi-well simulation considering CFNs,non-intrusive embedded discrete fracture model approach was applied for coupling fracture with reservoir models.The impact of CFN including natural fractures and frac-hits on pressure and rate transient behavior in multi-well system was investigated.On a logelog plot,interference flow and compound linear flow are two new flow regimes caused by nearby producers.When both NFs and frac-hits are present in the reservoir,frac-hits have a greater impact on well#1 which contains frac-hits,and NFs have greater impact on well#3 which does not have frac-hits.For all well producing circumstances,it might be challenging to see divergence during pseudosteady state flow brought on by frac-hits on the logelog plot.Besides,when NFs occur,reservoir depletion becomes noticeable in comparison to frac-hits in pressure distribution.Application of this integrated approach demonstrates that it works well to characterize the well interference among different multi-fractured horizontal wells in a well pad.Better reservoir evaluation can be acquired based on the new features observed in the novel model,demonstrating the practicability of the proposed approach.The findings of this study can help for better evaluating well interference degree in multi-well systems combing PTA and RTA,which can reduce the uncertainty and improve the accuracy of the well interference analysis based on both field pressure and rate data.

A Transient-Pressure-Based Numerical Approach for Interlayer Identification in Sand Reservoirs

Almost all sandstone reservoirs contain interlayers. The identification and characterization of these interlayers iscritical for minimizing the uncertainty associated with oilfield development and improving oil and gas recovery.Identifying interlayers outside wells using identification methods based on logging data and machine learning isdifficult and seismic-based identification techniques are expensive. Herein, a numerical model based on seepageand well-testing theories is introduced to identify interlayers using transient pressure data. The proposed modelrelies on the open-source MATLAB Reservoir Simulation Toolbox. The effects of the interlayer thickness, position,and width on the pressure response are thoroughly investigated. A procedure for inverting interlayer parametersin the reservoir using the bottom-hole pressure is also proposed. This method uses only transient pressuredata during well testing and can effectively identify the interlayer distribution near the wellbore at an extremelylow cost. The reliability of the model is verified using effective oilfield examples.

PRESSURE TRANSIENT ANALYSIS OF HETEROGENOUS RESERVOIRS WITH IMPERMEABILITY BARRIER USING PERTURBATION BOUNDARY ELEMENT METHOD

The transient flow mathematical model of arbitrary shaped heterogeneous reservoirs with impermeability barrier is proposed in this paper. In order to establish this model, the perturbation method is employed and the solution of model is expanded into a series in powers of perturbation parameter. By using the Boundary Element Method (BEM) and Duhamel principle, wellbore pressure with effects of skins and wellbore storage is obtained. The type curves are plotted and analyzed considering effects of heterogeneity, arbitrary shape and impermeable barriers. Finally, the results obtained by perturbation boundary element method is compared with the analytical solution and is available for the transient pressure analysis of arbitrary shaped reservoirs.

THE LINE-SOURCE SOLUTION AND FLOW ANALYSIS OF FLUID IN FRACTAL RESERVOIR

The fluid flow at a constant rate from both an infinite reservoir and a finite reservoir into a line source well were considered. Analytical solutions of the partial differential equation that governs the transient flow of fluid through a fractal reservoir were given by using the Laplace transformation and the property of the Bessel function for an infinite reservoir and finite circular reservoir. A large-time approximation solution for an infinite reservoir was also studied. Pressure transient behavior of fluid flow in fractal reservoir was analyzed by using analytical solution. Typical pressure curves were shown. An example was analyzed by using a large-time approximation solution for an infinite reservoir, and fractal parameters were obtained by employing oil reservoir description.

Pressure-rate convolution and deconvolution response for fractured conventional and unconventional reservoirs using new decline rate model

This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs.This approach demonstrates the impact of variable Sand face flow rate on reservoir performance.A new model for P/R deconvolution is used to convert pressure pulse from variable flow rate to single and constant rate response.The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume.Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while decline flow rate behavior is described by newly proposed model in this study.This model depicts,instead of van Everdingen model,indirectly the declining rate with time by using pressure responses with production time.Decline flow rate behavior simulated by linear and bi-linear flow models are also studied and compared with the one obtained by the new model.Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable flow rate considering different reservoir configurations and operating conditions.The results are interpreted and analyzed for better understanding pressure behaviors,flow regime types,and productivity index trends for continuously changing flow rate especially at early production time.Estimating stimulated reservoir volume(Vsrv)is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state flow when late time boundary dominated flow regime is reached.The outcomes of this study can be summarized as:1)Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline flow rate model that indirectly simulates variable flow rate with time.2)Generating analytical models for dimensionless pressure and flow rate for constant and variable flow rate using the concept of P/R convolution and deconvolution.3)Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior.4)Studying the applicability of linear and bi-linear flow models in converting variable flow rate pressure response to single and constant flow rate pressure response.5)Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume.The most interesting points are:1)The main difference in wellbore pressure behavior between variable and constant flow rate can be seen at early production time,however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure.2)A unit slope line flow regime could be developed for varied flow rate pressure response at very early production time similar to the wellbore storage dominated flow regime.3)Productivity index calculated by the proposed models for variable flow rate is greater than the index for constant flow rate.4)The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant flow rate.5)The decline rate models for linear and bi-linear flow are not applicable in pressure deconvolution technique.

A STUDY ON TRANSIENT FLUID FLOW OF HORIZONTAL WELLS IN DUAL-PERMEABILITY MEDIA

To adopt horizontal wells in dual media reservoirs, a good understanding of the related fluid flows is necessary. Most of the recent studies focus on dual porosity media instead of dual permeability media. In this article, through both integral transformation and sink-source superposition, a new Laplace-domain solution is obtained for the slightly-compressible fluid flow in the 3-D dual-permeability media in which the horizontal well is operating in a constant rate of production. Major asymptotic characteristics of diagnosis curves of dimensionless downhole pressure are analyzed by the limited analysis. Effects of parameters of dual-permeability media including mobility ratio k, storativity ratio ω and inter-porosity flow parameter k on the downhote pressure are studied by using the Laplace numerical inversion. The new solution obtained in this article includes and improves the previous results and then can be used as a basis for either pressure transient analysis or formation behavior evaluation for the typical reservoir with horizontal wells.

Exact analytical solutions for moving boundary problems of one-dimensional flow in semi-infinite porous media with consideration of threshold pressure gradient

By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical solutions for both constant-rate and constant-pressure inner boundary constraint problems are obtained by applying the Green＇s function. Two transcendental equations for moving boundary problems are obtained and solved using the Newton-Raphson iteration. The exact analytical solutions are then compared with the approximate solutions. The Pascal＇s approximate formula in reference is fairly accurate for the moving boundary development under the constant-rate condition. But another Pascal＇s approximate formula given in reference is not very robust for constant-pressure condition problems during the early production period, and could lead to false results at the maximum moving boundary distance. Our results also show that, in presence of larger TPG, more pressure drop is required to maintain a constant-rate production. Under the constant-pressure producing condition, the flow rate may decline dramatically due to a large TPG. What＇s more, there exists a maximum distance for a given TPG, beyond which the porous media is not disturbed.

Analytical models & type-curve matching techniques for reservoir characterization using wellbore storage dominated flow regime

The applicability of early time data in reservoir characterization is not always considered worthy.Early time data is usually controlled by wellbore storage effect.This effect may last for pseudo-radial flow or even boundary dominated flow.Eliminating this effect is an option for restoring real data.Using the data with this effect is another option that could be used successfully for reservoir characterization.This paper introduces new techniques for restoring disrupted data by wellbore storage at early time production.The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures.Several analytical models describe early time data,controlled by wellbore storage effect,have been generated for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures.The relationships of the peak points(humps)with the pressure,pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients.For horizontal wells,a complete set of type curves has been included for different wellbore lengths,skin factors and wellbore storage coefficients.Another complete set of type curves has been established for fractured formations based on the number of hydraulic fractures,spacing between fractures,and wellbore storage coefficient.The study has shown that early radial flow for short to moderate horizontal wells is the most affected by wellbore storage while for long horizontal wells;early linear flow is the most affected flow regime by wellbore storage effect.The study has also emphasized the applicability of early time data for characterizing the formations even though they could be controlled by wellbore storage effect.As a matter of fact,this paper has found out that wellbore storage dominated flow could have remarkable relationships with the other flow regimes might be developed during the entire production times.These relationships can be used to properly describe the formations and quantify some of their characteristics.

Application of a hybrid algorithm ePSOSA in well test parameter estimation

Estimating the significance parameters,such as skin factor,permeability,wellbore storage coefficient,are the most component of transient pressure analysis.Many optimization algorithms have been applied to parametric estimation and realized the minimum error of well test curve.Although a flexible heuristic particle swarm optimization can hunt optimal solution rapidly,it is difficult to search further in the vicinity of the optimal solution.Hence,to alleviate the local optimum and premature convergence,a global hybrid algorithm referred to as particle swarm simulated annealing is proposed,and proves to have better performance of convergence and accuracy than traditional methods,which are more suitable for parameter estimation.