UDC 532.546 Based on the modification of the "exact-on-average" method, simple analytical formulas have been found for calculation, in the zero and first asymptotic approximations, of pressure fields in an inhomogeneous anisot- ropic bed in constant drainage for the case of one-dimensional linear flow. The results of calculations of the fields from the obtained formulas have been given. Introduction. Problems on pressure fields appearing in filtration of liquids in porous media form the basis for the theory of mass transfer in these media and are of great practical importance for oil and gas production, hydrogeol- ogy, ecology, etc. (1). The problem on filtration of a liquid occupies a special place among the indicated problems be- cause of the variety of conditions of such filtration and its practical significance. Analytical dependences for description of pressure fields appearing in the indicated bed as a result of the liquid filtration in it can be obtained by modification of asymptotic methods whose capabilities have not been completely realized. Such modification is ef- fected through selection of the formal parameter of asymptotic expansion. It becomes necessary to construct the zero and first coefficients of this expansion, boundary-layer functions, and estimating expressions for the remainder term. The resulting zero coefficient of asymptotic expansion describes the averaged value of a physical parameter. Construc- tion of the first expansion coefficient requires supplementary conditions that are based on the trivial solution of the av- eraged problem for the remainder term. From this viewpoint, expressions for the zero and first approximations are called "exact-on-average" (2). This work seeks to determine the zero and first coefficients of asymptotic expansion that describe pressure fields in an inhomogeneous anisotropic bed with constant drainage from one-dimensional linear flow. In this case the zero coefficient describes pressure values averaged over the bed's thickness, whereas the first coefficient refines de- scription of the fields in the averaging zone and determines the steady-state field at large times. 1. Formulation of the Problem for Linear Flow in Constant Drainage. Figure 1 gives the flow geometry in a plane coordinate system (x, z) whose z axis coincides with the axis of the well. The medium is represented by three regions with plane boundaries z = 1; the covering bed and the underlying bed are assumed to be low-perme- able in the horizontal direction k 1x = 0; the central region −1 < z < 1 is highly permeable in the horizontal k x and in the vertical k z directions. For the sake of simplicity it is assumed that flow is one-dimensional and linear along the x axis, the surround- ing rocks are strongly anisotropic, and the vertical permeability k 1z dominates the horizontal permeability k 1x in them. This enables us to disregard the term with the second derivative with respect to the horizontal coordinate x for the sur- rounding medium. Next, we assume that the properties of the underlying and covering beds are identical. In accordance with this, we can simplify the formulation of the problem, using the symmetry condition ∂P ⁄ ∂z = 0 and z = 0. The considered problem is substantially simplified through the use of the so-called quasistationary approxima- tion without perceptible distortions of the basic regularities under study. This approximation is widely used in electro- dynamics for studying electromagnetic fields in electric circuits; its essence is neglect of the time derivative in the