Summary Matrix-acidizing models have traditionally underpredicted acid-stimulation benefits because of underprediction of wormhole penetration and the corresponding magnitude of completion-skin factors in vertical wells. For long horizontal wells drilled in carbonate reservoirs, productivity enhancement is a function of acid placement and effective wormhole penetration. However, prediction of wormhole penetration requires more effective analysis than that provided by current industry models. This paper presents results of matrix-acid modeling work for horizontal wells and describes a practical engineering tool for analyzing the progress of matrix-acid stimulation in carbonate reservoirs. The wormhole-growth model is based on the Buijse and Glasbergen empirical correlation. Combining with the mechanistic model of the wormhole propagation based on acid transport and fluid loss from a single wormhole, a modified Buijse-Glasbergen wormhole-growth model is developed that relates the wormhole growth rate to the in-situ injection velocity at the tip of the dominant wormhole. The wormhole constitutive model developed in this study also accounts for core-size dependencies seen in laboratory acid-flood experiments. A semianalytical flow correlation is derived for estimating interstitial velocities at the tip of the dominant wormholes based on a number of 3D FEM simulation analyses, accounting for more realistic flow regimes (radial and spherical flow) typically observed in field application. The scaleup procedure developed in this study extends the wormhole geometry and penetration from laboratory flow tests on small cores to field-sized treatments. The scaleup procedure developed in this work can be applied to cemented and uncemented horizontal wells, including barefoot and perforation-cluster completions typically employed in carbonate reservoirs. Application of this modeling shows that acid wormholing through carbonate formations can provide significant stimulation, resulting in post-stimulation skins as low as–3.5 to–4.0 vs. previously predicted values in the –1.0 to–2.0 range.

Summary In this paper, we present a new analytical model for formation damage skin factor and the resulting reservoir inflow, including the effect of reservoir anisotropy and damage heterogeneity. The shape of the damaged region perpendicular to the well is based on the pressure equation for an anisotropic medium and, thus, is circular near the well and elliptical far from the well. The new model can be used for various distributions of damage along the well, depending on the time of exposure during drilling and completion. The inflow equation for a damaged, parallel-piped-shape reservoir illustrates the importance of the ratio of the reservoir thickness to the drainage length perpendicular to the well on the influence of formation damage for horizontal well productivity. Our model gives a simple, analytical expression for determining this effect. Introduction Horizontal well completion technology has become an important part of oil and gas recovery. Horizontal wells have proven to be excellent producers for thin reservoirs or for thicker reservoirs with good vertical permeability. A horizontal well creates a drainage pattern that is quite different from that for a vertical well. The flow geometry in a horizontal well is more likely to be radial near the well and linear far from the well while, in general, the vertical well has radial flow geometry. Another major difference between horizontal and vertical wells is the strong influence of horizontal to vertical permeability anisotropy on horizontal well productivity. Because of these factors, near-wellbore formation damage has a different effect on a horizontal well than on a vertical one and must be described with a different skin-factor model. Another critical difference between vertical and horizontal wells is that the damage distribution around a horizontal well is likely to be highly nonuniform. Reservoir anisotropy may lead to an elliptically shaped damage zone perpendicular to the well, depending on the ratio of the vertical to horizontal permeability. Because of the large formation length contacted by a horizontal well, formation damage is not likely to be uniformly distributed. Therefore, the damage zone around a horizontal wellbore cannot be assumed to be simply a cylindrical region of reduced permeability, as is the usual assumption for vertical wells. The objective of this paper is to provide a basis for estimating the overall damage-skin effect for horizontal wells and for determining the horizontal well productivity, including the productivity loss caused by formation damage near the wellbore in an anisotropic reservoir. Our model accounts for the effects of permeability anisotropy and can be used for various damage distributions along the well. Formation-Damage-Skin Model for a Horizontal Well There are two key parts to our new model of the formation damage skin factor. The first is a model of the local skin factor, s(x), describing the effect of damage in the y-z plane perpendicular to the wellbore (Fig. 1). The second element of the new model is the manner of accounting for any arbitrary distribution of damage along the horizontal well, as illustrated in Fig. 2. Local Skin-Factor Model, s(x). To derive an analytical model of the local skin factor at Position x along a horizontal well, we must make some assumptions about the distribution of damage in the y-z plane. We assume that the cross section of damage perpendicular to the well (Fig. 1) mimics the isobars given by Peaceman's solution1 for flow through an anisotropic permeability field to a cylindrical wellbore. This solution shows that isobars are a series of concentric ellipses with aspect ratios (ratio of the major to minor axis lengths) being 1 at the wellbore and increasing as the distance from the wellbore increases. Because formation damage is often directly related to flux or velocity, we assume that the damage is distributed similar to the pressure field (i.e., the outer boundary of the damaged zone will lie on an isobar). With this assumption about the distribution of the damage in the y-z plane, Hawkins' formula2 can be transformed for anisotropic space, and an analytical expression for local skin can be derived, as shown in Appendix A.

In this paper, we present a new analytical model for formation damage skin factor and the resulting reservoir inflow that includes the effect of reservoir anisotropy and damage heterogeneity. The shape of the damaged region perpendicular to the wellbore is based on the pressure equation for an anisotropic medium, and is thus circular near the well and elliptical far from the well. This assumption gives an appropriate skin factor even for a small penetration of damage. The new model can be used for any distribution of damage along the well. The new skin factor model can be easily incorporated into any existing model of reservoir inflow for a horizontal well. We also present a new reservoir inflow equation for a damaged parallelepiped-shape reservoir drained by a horizontal well. This equation shows that the ratio of the reservoir thickness to the drainage length perpendicular to the well is a very important factor for determining the influence of formation damage on horizontal well productivity because the linear flow geometry becomes dominant for a thin reservoir. The larger the ratio of thickness to drainage length perpendicular to the well axis, the larger the influence of near-well formation damage on well productivity. In examples presented in the paper, a truncated elliptical cone of damage with a larger penetration near the vertical section of the well (at the heel)is presumed to compare our model with an existing horizontal well damage skin factor model. The comparisons show that, for an anisotropic reservoir with shallow-penetrating formation damage, our model avoids the negative skin result calculated by the previous model and predicts higher skin factor than the existing model. For deep damage, the new model predicts lower skin factor than the previous model. The impact of formation damage on the overall production is also shown in examples. In general, the effect of near well formation damage for a horizontal well completion is relatively small compared with vertical wells. However, if the reservoir thickness is large, radial flow becomes dominant and the impact of formation damage on a horizontal well is more significant, more like that of a vertical well. Our model gives a simple, analytical expression for determiningthis effect. Introduction Horizontal wells have become an important completion technology for oil and gas recovery. They have proven to be excellent producers for thin reservoirs or for thicker reservoirs with good vertical permeability. A horizontal well creates a drainage pattern that is quite different from that for a vertical well. The flow geometry in a horizontal well is more likely to be radial near the well and linear far from the well while in general the vertical well has radial flow geometry. Another major difference between horizontal and vertical wells is the strong influence of horizontal to vertical permeability anisotropy on horizontal well productivity. Because of these factors, near-wellbore formation damage has a different effect on a horizontal well than on a vertical well and must be described with a different skin factor model. Another critical difference between vertical and horizontal wells is that the distribution of damage around a horizontal well is likely to be highly non-uniform. Reservoir anisotropy may lead to an elliptically shaped damage zone perpendicular to the well, depending on the ratio of the vertical to horizontal permeability. Because of the large length of formation contacted by a horizontal well, formation damage is not likely to be uniformly distributed along the well. Therefore, the damage zone around a horizontal wellbore cannot be assumed to simply be a cylindrical region of reduced permeability, as is the usual assumption for vertical wells.

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Summary Horizontal wells or laterals are completed as openhole, slotted-liner, cased and perforated, or gravel-pack completions. We have developed a comprehensive skin-factor model to predict the performance of any of these completion types and have calibrated this model with extensive finite-element simulations of flow for a horizontal-well completion. This model can be used to predict the performance of virtually any horizontal-well completion. The new completion skin-factor model accounts for the effects of formation damage, convergent flow to perforations and slots, and flow through slots, with interaction among these effects. To account for formation damage, we extended our previous rigorous model of a damaged horizontal well to include the presence of perforations within, or extending through, the damage zone. The formation damage model is also integrated with the models of slotted-liner performance to model these completions. The model of slotted- or perforated-liner performance is made on the basis of the relationship between pressure drop and flow rate for turbulent flow in these geometries. The slotted-liner model accounts for partial plugging of the slots by grains of formation minerals or precipitates (scale). Turbulence effects are a major part of the apparent skin factor for these completion types. The model shows the recommended conditions to obtain high-productivity (i.e., low skin factor) completions in horizontal wells. In particular, the interactions among damage effects and skin effects caused by perforations or slots are shown to greatly affect horizontal-well completion performance. The models developed can be applied to design optimal completions for horizontal wells or laterals. Introduction A comprehensive model for well completions is presented in this paper, which can be used to select and design optimal completion for horizontal wells. The completion-selection process starts by determining Earth stresses, rock mechanical properties, and formation stability over the producing life of the well.1 Preventing borehole collapse and production of formation sand through the wellbore are major issues in the completion choice. Following these analyses, details of the selected completion need to be determined. An optimal completion maintains formation integrity while minimizing pressure losses through the completion hardware and the near-wellbore vicinity. Our model provides inflow performance of horizontal-well completions using skin factors. Skin is a dimensionless factor calculated to evaluate the production efficiency of a well by comparing actual conditions with theoretical or ideal conditions. The skin concept was originally introduced to account for an additional pressure drop, ?ps, caused by mechanical factors using the radial-flow solution: (Eq. 1) The skin concept has been interpreted in a wide sense to mathematically account for any deviations of the flow and pressure field in the near-well vicinity from the perfect radial flow to a wellbore radius, rw. A positive skin value indicates some damage or influences that are impairing well productivity. A negative skin value indicates enhanced productivity, typically resulting from well stimulation. The development of horizontal and multilateral wells has further complicated the skin concept because the impact of skin factors on the overall well productivity greatly depends on the well configuration and the reservoir geometry. As discussed in our previous work,2 the effects of skin on vertical- and horizontal-well production could be significantly different, even with same skin values, depending on the reservoir anisotropy and the ratio of the reservoir thickness to the drainage length perpendicular to the well. Although the effects of skin factor on well productivity are influenced by the well and reservoir geometries, skin factors are independent of those factors if radial flow occurs in the near-well vicinity. This is usually a reasonable assumption because, in most cases, the outer boundary of the reservoir is sufficiently distant from the wellbore to be insignificant on the near-wellbore scale. Thus, we can use skin factor to analyze the completion performance and identify problems in the near-wellbore vicinity.