Well production indicators in a deformable reservoir interacting with rocks

Steady-state flow towards a well through a thin porous deformable two-layer reservoir with allowance for deformation of the surrounding rocks is investigated. The permeability of the reservoir is considered to be a function of the displacements of its top and bottom. The effect of deformation on the well production indicators is studied. The results obtained agree qualitatively with the data of full-scale experiments. Earlier, in [1–5], in considering the self-consistent processes of flow through porous media and their deformation attention was concentrated on the analysis of the stress-strain state of the rocks and reservoir and on unsteady problems within the framework of the nonlocally elastic flow regime.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–93, January–February, 1995.     

Flow processes with change of regime in fractured reservoirs

Experimental and industrial observations indicate a strong nonlinear dependence of the parameters of the flow processes in a fractured reservoir on its state of stress. Two problems with change of boundary condition at the well — pressure recovery and transition from constant flow to fixed bottom pressure — are analyzed for such a reservoir. The latter problem may be formulated, for example, so as not to permit closure of the fractures in the bottom zone. For comparison, the cases of linear [1] and nonlinear [2] fractured porous media and a fractured medium [3] are considered, and solutions are obtained in a unified manner using the integral method described in [1]. Nonlinear elastic flow regimes were previously considered in [3–6], where the pressure recovery process was investigated in the linearized formulation. Problems involving a change of well operating regime were examined for a porous reservoir in [7].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–73, May–June, 1991.     

Hydrodynamic features of the exploitation of highly nonuniform source-type oil formations

The flow of a weakly compressible fluid in a highly nonuniform formation with block structure, classified as source-type, is considered. An analytic solution of the problem of fluid flow into a well in a bounded circular reservoir is obtained. On the basis of this solution the effect of the fluid offtake rate on the depletion of the reservoir is investigated. It is shown that in highly nonuniform media a number of unsteady effects, which cannot be described by the classical model with steady mass transfer, occur.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 113–120, September–October, 1993.     

Analysis of the transition from constant output to fixed well-bottom pressure for elastic regime of oil extraction

The elastic flow regime of stratal fluids has been well studied in the literature [1, 2] and the results have been widely applied in practice in the development of oilfields [3, 4]. Consideration is given below to the new problem of the reduction in the output of a well at fixed well-bottom pressure after it has been operating for some time at constant output. There is a practical aspect to this sort of problem. For instance, the degassing of the reservoir in the region of the well is considered an undesirable feature in the exploitation process. If degassing begins, the resistance to flow grows sharply and the well outputs fall considerably. Once the well-bottom pressure has fallen to the saturation pressure, it must not be allowed to fall further, or gas will be given off in the well region of the reservoir. It is desirable to keep the well-bottom pressure higher than the saturation pressure.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 82–87, March–April, 1985.     

Unsteady-state flow induced by a well in a deformable stratum interacting with the adjacent rocks

Unsteady-state plane radial flow induced by a well in a thin deformable stratum is studied taking into account the stratum interaction with the adjacent rocks. The stratum permeability is assumed to depend on the lateral deformation. The behavior of the well productivity properties for harmonic reservoir pressure oscillations and after pressure drawdown in a bilayered stratum is analyzed. Steady-state well behavior under these conditions was studied in [1]. A qualitative estimate of the well productivity variation due to a stepwise pressure change in an adjacent stratum was previously derived in [2].Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 85–90, January–February, 1996.     

Contribution of capillary forces to the volume of residual oil pillars

Equations for calculating the limiting equilibrium shapes of the residual oil pillars in homogeneous and stratified inhomogeneous reservoirs of varying wettability are written within the framework of a two-phase displacement model with allowance for capillary pressure. Comparative calculations for an individual well in a circular reservoir show that, in general, the effect of capillary pressure on the shape and volume of the pillars is not negligibly small and may reach 10% of the pore volume.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 114–123, January–February, 1991.     

Simulation of the thermal recovery process in a layered reservoir

The thermohydrodynamic interaction of the layers in a layered oil reservoir in the presence on in situ combustion is considered.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 122–128, May–June, 1994.     

Exact solutions of problems of fluid inflow into a well with a vertical hydrofracture and their use in numerical models of flow through porous media

The plane steady flow of a homogeneous incompressible fluid in a reservoir containing a vertical elliptic hydrofracture is considered. The flow in the reservoir and fracture obeys Darcy's law. Exact solutions of the problem of inflow into a fracture of finite conductivity are obtained both in the case of a uniform reservoir and in the presence in the neighborhood of the fracture of a zone with permeability different from that of the rest of the reservoir. On the basis of the solutions obtained, the effect of the parameters of the polluted zone in the vicinity of the well on its production rate is estimated in the presence of a fracture of finite conductivity, the efficiency of hydraulic fracture of the producing and injection wells is analyzed for regular development systems, and a method of taking hydrofractures of arbitrary orientation and length into account is proposed for finite-difference models of flow through porous media in a system of wells.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 69–80, November–December, 1996.     

A method for calculating the two-dimensional temperature field of a reservoir with thermal injection

In [1–3] and other studies devoted to the determination of the temperature field of an oil reservoir when injecting into it a fluid with a temperature different from that of the initial reservoir temperature, the one-dimensional fluid flow (linear or radial) was considered in the case of an injection gallery or a single injection well in the reservoir. The problem was formulated in [4] with an arbitrary distribution of wells, but the solution was obtained only for the integral thermal-loss characteristic. To evaluate the coverage of the reservoir by the thermal effect, we must know the temperature distribution in the multi-well reservoir system at any instant of time. In this paper we propose a method for calculating the reservoir temperature field in the case of two-dimensional fluid flow using the simplifying assumptions which were used earlier by Lauwerier [1] and other authors to describe the thermal phenomena in a reservoir.     

Estimating the filtration characteristics of reservoirs from data of nonstationary studies of horizontal wells

Regularization methods are used to construct computational algorithms for the interpretation of results from hydrodynamic studies of horizontal wells that provide estimates of the reservoir anisotropy, reservoir pressure, and the dependence of the in-place permeability on pressure. In contrast to graphic analytic methods, the proposed approach does not require the identification of flow regimes.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 109–114, March–April, 2005.     

Depeletion of the elastic reserve of a sealed and fractured formation with anomalously high formation pressure

Analysis of the exploitation of deposits with anomalously high formation pressures has shown [1] that when the weighted-mean formation pressure drops below a certain critical value (close to the hydrostatic pressure) a rather sharp sudden fall in output, together with a change in the rate of decline of pressure, is observed. The fall in output is attributable to the closing of the joints and the resulting catastrophic deterioration in the permeability of the reservoir [2]. In this paper an attempt is made to develop a joint closing hypothesis, to calculate the motion of the joint closing front from the bottom of the well to the edge of a homogeneous circular formation, and to derive expressions for predicting the fall in the output of the wells and the pressure in the formation. In order to obtain solutions it is assumed that the reservoir depletion regime is quasisteady, so that the results should be regarded as approximate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 73–83, November–December, 1985.     

A Simple Model of a Two-Layered High-Temperature Liquid-Dominated Geothermal Reservoir as a Part of a Large-Scale Hydrothermal Convection System

The Kakkonda geothermal reservoir, Japan, is a typical high-temperature liquid-dominated geothermal reservoir, except for its distinctive two-layered temperature structure. It has a shallow permeable reservoir of 230–260°, and a deep less permeable reservoir of 350–360°. Geology and hydrology indicate that the shallow reservoir is one to two orders of magnitude more permeable than the deep reservoir, but that the two reservoirs communicate. It has been widely assumed in engineering and scientific circles that the connection between the two reservoirs is a zero or low permeability barrier to fluid flow. We show that this hypothesis is untenable, based on both physical evidence and numerical simulation. We numerically model the evolution of the geothermal system as it heats after emplacement of an intrusion. The two-layered temperature structure is found to be a consequence of the permeability difference, i.e. the two-layered permeability structure.     

Onset of liquid-phase flow as a result of the accumulation of gaseous products

The flow of a gaseous mixture of hydrocarbons and carbon dioxide through a model reservoir with a stationary hydrocarbon liquid phase has been investigated theoretically and experimentally. The possibility of the onset of liquid-phase flow as a result of the accumulation of gaseous products is demonstrated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 185–188, March–April, 1990.     

Unsteady-state filtration from screened water reservoirs and from the storage elements of industrial drainage systems

This paper considers the axisymmetric problem of unsteady-state filtration from a water reservoir or from the storage element of industrial drainage systems, which are round in a plan view.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 165–170, November–December, 1971.     

Effect of the interlayer connectivity of nonuniform reservoirs on the volume of the residual oil pillars

The limiting-equilibrium pillars of residual oil with an initial pressure gradient are calculated for reservoirs of the layer cake type whose nonuniformity conforms to a random (Pearson) distribution. It is assumed that hydrodynamically in the direction of stratification the layers are completeiy disconnected. A parametric investigation of the volume of the pillars is carried out for two problems (fivepoint area flooding scheme and a single well in a circular reservoir) and the results are compared with those for reservoirs with ideal interlayer connectivity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5. pp. 184–186, September–October, 1989.     

Mathematical model of the dissociation of gas hydrates coexisting with ice in natural reservoirs

The dissociation of gas hydrate coexisting with ice in a low-temperature natural reservoir is investigated. A mathematical model of the process consisting of a generalization of the Stefan problem and containing two unknown moving phase transition boundaries — the hydrate dissociation and ice melting fronts — is constructed. It is shown that in high-permeability reservoirs the velocity of the dissociation surface is higher than that of the ice melting surface. As the permeability decreases, the fronts change places. The problem is solved in the self-similar approximation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 84–92, March–April, 1993.     

Effect of gel plugs on water and oil flow in a nonhomogeneous porous reservoir

The factors influencing gel plug emplacement, their breakdown time, and the effect of the plugging on the flow distribution in a reservoir and the water-oil ratio in producing wells after plug emplacement are discussed.Tyumen'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 99–107, March–April, 1995.     

Pressure recovery processes in fractured reservoirs

The analysis of the pressure recovery in an oil field following the shutting in of a well is one of the basic methods of determining or refining the reservoir parameters. For fractured reservoirs the process is complicated by the strong dependence of their flow-capacity characteristics on the state of stress. It is shown that, qualitatively, the pressure recovery processes in fractured and fractured porous media can be correctly described using the integral conservation laws. Numerical solutions are derived in order to estimate the validity of the results obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 77–83, September–October, 1990.     

Gas-gas displacement in a fractured porous reservoir

The results of an experimental investigation of the process of miscible displacement of a gas from a fractured porous reservoir by another gas are presented. It is established that the displacement process is influenced by convective and molecular diffusion. The displacement coefficient depends both on the reservoir properties of the formation and on the technological displacement parameters. The experiments revealed a decrease in the displacement coefficient with increase in the permeability ratio of the joints and the blocks and with decrease in formation pressure. The dependence of the displacement coefficient on the average gas velocity in the reservoir, i.e., the ratio of the gas flow rate to the product of the flow area and the total reservoir porosity coefficient (including the blocks and the joints), is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–79, May–June, 1991.     

Transient analysis of dam–reservoir interaction including the reservoir bottom effects

In this paper, time-domain transient analysis of elastic dam–reservoir interaction including the reservoir bottom effects is presented by coupling the finite element method in the infinite fluid domain and in the solid domain. An efficient coupling procedure is formulated by a substructuring method. Sommerfeld's boundary condition for the far end of the infinite domain is implemented. To verify the proposed scheme, numerical examples are given to compare with available exact solutions for rigid and elastic dam cases. Finally, a numerical example is studied to evaluate the effects of the reservoir bottom.