A mathematical model was developed to study tbe transient behavior o/a well with a finite-conductivity vertical /racture in an iniinite slab reservoir. For values 0/ dimensionless time 0/ interest, tD 210-3, the dimensionless wellbore pressure, PwlD~can be correlated by the dimensionless group, wkl/xf k , where w, kf, and x i are tbe width, permeability, and half length o/ t e /racture, respectively, and k represents the {ormation perrneabi!ity. Results when plotted as a [unction of pwfD us 10g tD give, for !urge t~, a 1. 151+iope straight line; hence, semilogaritbmic pressure analysis methods can be app!ied. When p[ottcd in terms of log pwjD vs log tD, a family o/ Curves 0/ cbaraCter. istic shape result, A type-curve matching procedure can be used to analyze early time transient presszdre data to obtain the formation and jracture characteristics.

This paper investigates the influence of pressure-dependent fluid and rock properties on well production decline in con-stant wellbore pressure tests. The rock properties considered variable are permeability, porosity, pore compressibility and formation thickness, and thefluid properties are density, com-pressibility and viscosity. Singlephase flow through the porous medium is considered. Various geometries, ratios of in-itial to wellbore pressure, and data sets of rock and fluid pro-perties are studied. For allpractical ratios of initial to wellbore pressure and for transient flow conditions, production rate decline expressed in terms of a dimensionless rate qdis essen-tially the same as the production rate decline qo] for constant property liquid flow. The only exceptions occur for bounded reservoirs after the flow is affected by the outer boundary. These deviations are such that in pressure-sensitive systems production rate declines faster than in constant-property systems. It is shown that variable property decline solutions, when compared to constant property decline solutions, do not follow any of the three common types of production decline curves-exponential, hyperbolic or harmonic. Type curve matching of variable property production rate decline to con-stant property flow solutions gives the correct size of the reser-voir, but other reservoir parameters can be in error. When variable property type curves are used for matching, all reser-voir parameters are correctly estimated. The method of Jacob and Lohman(19) and of van Poolien(21) areproperly modified to accountfor the pressure-dependency of rock andfluid proper-ties. Introduction It is well accepted that porous media are not always rigid and non-deformable. This should influence the transient well behaviour. A frequent assumption is to use average values for both pressure-dependent rock and fluid properties. This helps to reduce the errors involved, but does not totally eliminate them. When rock and fluid property changes are important over *Now with Petroleos Mexicanos, Mexico City. pressure range of interest, then these changes cannot be neglected and a variable property solution should be obtained. A flow equation considering the pressure dependency of all rock and fluid properties has been presented in the literature(l). This equation, when expressed as a function of a pseudo-pressure m(p), resembles the diffusivity equation. Samaniego et al.(2.3) studied this variable property problem for a greater variety of flow conditions. These authors only investigated constant rate cases.There are two basic radial flow cases in the flow of fluids through porous media: (a) constant well rate; and (b) constant well pressure. It is the purpose of this study to investigate the influence of pressure-dependent rock and fluid properties on the constant pressure case. One of the objectives is to find out how production rate decline would vary in these pressure-dependent systems, and if methods of analysis for constant pressure flow testing can be properly modified...

A mathematical model was developed to study the transient flow behavior for a well near an infinite conductivity vertical, nonintersecting, natural fracture in an infinite slab reservoir. A slightly compressible fluid was considered. Results when plotted as a function of a dimensionless time follow at early times a straight line of 1.151 slope characteristic. of radial flow. After this radial flow period, the well pressure behavior starts to be affected by the natural fracture and this causes a negative pseudo-skin factor, which is a function of time, and becomes a constant for large values of time, giving a second 1.151-slope straight line. This pressure behavior is similar to the one predicted by the models of Warren and Root and de Swaan for a uniform naturally fractured reservoir. Results from interference tests, for reservoirs having a natural fracture show that it is impossible to characterize uniquely the reservoir by means of the transient pressure test data alone. An integrated approach-or transient pressure test data registered at several observation wells can be used for a unique characterization. From these tests, underestimation or overestimation of the reservoir parameters could result, depending on the location of the observation References and illustrations at end of paper.well relative to the natural fracture.